Arithmetic Reasoning ASVAB

Mr. and Mrs. Clifton bought a home for $55,000. It was assessed at 80 percent of the purchase price. If the real estate tax was $4.74 per $100, how much realty tax did the Cliftons pay? A. $2,085.60 B. $1,985.60 C. $2,607.00 D. $285.60

A. $2,085.60 1) 55,000 x .80 = 44,000. You can just do 88 x 55 can add the three zeros. 2) Since were considering for every 100 we divide it by 100. 44,000/100 = 440 3) 4.74 x 400 = $2,085.60

A baker made 20 pies. A Boy Scout troop buys one-fourth of his pies, a preschool teacher buys one-third of his pies, and a caterer buys one-sixth of his pies. How many pies does the baker have left? A. 3/4 B. 15 C. 12 D. 5

Answer: B One person buys 1/4 of pies Another buys 1/3 of pies another buys 1/6 of the pies 1) 1/4+1/3+1/6- find common denominator 12 is common denominator so lets change the fractions 3/12 + 4/12 + 2/12 = 9/12 - reduce to 3/4 or 75% 2) Now take 75% of 20. 75/100 x 20/1 -reduce 75/5 x 1/1 75/5 = 15 which is answer B.

A candy store sells 3 lbs. of candy mix for $4.80. What is the price of a 5-oz bag of this mix? A. $1.00 B. $2.40 C. $0.25 D. $0.50

D. $0.50 Concert the 3lbs into Oz. Remember 16 ounces = 1 lb. 16 x 3 = 48 ounces Now see how much 1 oz cost. 48 ounces x = $4.80 - solve for x 4.80/48 = 0.10 $0.10 = 1 oz If there is a 5oz bad simply multiply 0.10 by 5 which will be 0.50 D.

A man invests $6,000 at 5 percent annual interest. How much more must he invest at 6 percent annual interest so that his annual income from both investments is $9000? A. $3,000 B. $5,000 C. $8,000 D. $10,000

D. $10,000 6,000 x .05 = $300 She needs 900 so that means we need $600. Since it will be a 6 percent investment we simply divide 600 by 0.06 = 10,000

What is the fifth term in the series 5 , 2 , 9 , 6 A.16 B.15 C.14 D. 13

D. 13 5→2 = -3 2→9=+7 9→6=-3 Next one means were adding 7 which is 13

If a laborer works from 7:15 a.m. to 3:45 p.m. with 1 hour off for lunch, his working time equals A. 7 hours. B. 7 1/2 hours.. C. 8 hours. D. 8 1/2 hours.

D. 8 1/2 hours. 7:15am - 2:15pm = 7 hours 2:15pm-3:00pm = 45 minutes 3:00pm - 3:45pm = 45 minutes 45 minutes + 45 minutes =90 minutes or 1 hour and 30 minutes 7 + 1 (1/2) hours is 8 hours and 30 minutes or D.

As a member of FEMA, you're required to set up a contingency plan to supply meals to residents of a town devastated by a tornado. A breakfast ration weighs 12 ounces, and the lunch and dinner rations weigh 18 ounces each. Assuming a food truck can carry 3 tons and that each resident will receive 3 meals per day, how many residents can you feed from one truck during a 10-day period? (A) 150 residents (B) 200 residents (C) 250 residents (D) 300 residents

(B) 200 residents First find how many ounces of rations each truck can hold. One ton = 2,000 lbs, so one truck can carry three times that, or 6,000 pounds. There are 16 ounces in a pound, so one truck can carry 96,000 ounces: 6000 lb. x 16 oz = 96 000 oz. Then figure out how many daily rations are in a truckload. The total daily ration for each resident is 12 ounces+ 18 ounces+ 18 ounces = 48 ounces. You can express the number of daily rations supplied as 96,000 oz/48 oz= 2000 daily rations. These rations need to last 10 days. Dividing 2,000 by 10 days results in 200 residents who can be fed by one truck during this 10-day period.

A rectangle is 1(1/2) times as long as it is wide. The perimeter of the rectangle is 100 inches. What's the length of the rectangle? (A) 20 inches (B) 30 inches (C) 40 inches (D) 45 inches

(B) 30 inches The formula for the perimeter of a rectangle is P = 2l + 2w. P = 100 l = 1.5w Solve for w 100 = 2 (1.5w) + 2w 100 = 3w + 2w 100 = 5w w = 20 The width of the rectangle is 20 inches. Because the length is 1 (1/2) times the width, 1.5 x 20 = 30.

Go-Cart One and Go-Cart Two are on a 360- foot circular track. There is a camera at the center of the track for each go-cart. Camera One is following Go-Cart One, and Camera Two is following Go-Cart Two. If the angle between the two cameras is 40 degrees, how far apart are the two go-carts? (A) 30 feet (B) 40 feet (C) 50 feet (D) 60 feet

(B) 40 feet They are asking for the circumference 40 degrees locked 40/360 = 1/9 360 x 1/9 = 40 feet

A teacher deposits $3,000 in a retirement fund. If they don't add any more money to the fund, which earns an annual interest rate of 6%, how much money will they have in 1 year? (A) $180 (B) $3,006 (C) $3,180 (D) $6,000

(C) $3,180 3,000 x 0.06 = $180 Remember when you're dealing with interest the money you put in doesn't go down. She will have $3,180 to withdraw whenever she wants in the 1 year.

A half-pint of cream is what part of a gallon? (A) 1/8 (B) 1/4 (C) 1/16 (D) 1/6

(C) 1/16 There are 2 pints in a quart, and 4 quarts make up a gallon; therefore, a gallon contains 2x4 = 8 pints, or 16 half-pints. One half-pint equals 1/16 of a gallon.

Robert charges a flat fee of $15 plus $20 per half-hour to repair computers. He started one job at 8:45 a.m. and worked until he finished. The total charge for that job was $75. What time did he finish the job? (A) 12:15 p.m. (B) 11:45 a.m. (C) 10:15 a.m. (D) 9:30 a.m.

(C) 10:15 a.m. Subtract the $15 base fee from $75 to find Robert's total hourly earnings: $ $ 75 - 15 = $60. Divide $60 by $20 to find the number of half-hours that he worked: 60/20= 3 half hours. Three half-hours equal 1.5 hours, so add this amount of time to 8:45 a.m. to discover that he finished the job at 10:15 a.m.

The neighbor's dog barks at a raccoon every 15 minutes at night. If it first barks at 10 p.m., when you're trying to fall asleep, how many times will it have barked by 2 a.m., when you give up trying to sleep and decide to read a book instead? (A) 16 times (B) 132 times (C) 17 times (D) 15 times

(C) 17 times The dog is barking every 15 minutes, or 4 times per hour. The time between 10 p.m. and 2 a.m. is 4 hours. Multiply the total number of hours in the time period by 4 barks per hour. Then add 1 because the dog barked at the beginning of the period also: (4 x 4) + 1 = 16 + 1 = 17

A stack of lumber is 6 feet high. If each piece of lumber is 4 inches thick, how many pieces of lumber are in the stack? (A) 72 (B) 12 (C) 18 (D) 10

(C) 18 Multiply the height of the stack in feet by 12 to determine the height of the stack in inches: 6 x 12 = 72 inches. Divide that number by 4 inches, the thickness of each board, to determine the number of pieces of lumber in the stack: 72/4 =18

Margaret is getting married and must be ready by 11:15 a.m. If it's now 8:30 a.m., how much time does she have to get ready? (A) 1 (1/2) hours (B) 2 (1/2) hours (C) 2 (3/4) hours (D) 2 (1/3) hours

(C) 2 (3/4) hours 8:30am -10:30am = 2 hours :30 - :15 = 45 min 45/60 = 3/4 2 (3/4)

Two bicyclists head toward each other from the opposite ends of Main Street, which is 6 miles long. The first biker started at 2:05 going 12 mph. The second biker began peddling 4 minutes later at a rate of 14 mph. What time will they meet? (A) 2:13 (B) 2:24 (C) 2:21 (D) 2:34

(C) 2:21 Distance = rate x time Were looking for time. First bike got a 4 minute headstart. going 12 mph Distance = rate x time 12mph x 4 min/60min = 48/60 = 4/5mile head start When the second bike leaves the distance between them is 5.2 miles 6 miles - 4/5miles = 5.2 miles So.. Distance = rate x time Going opposite directions so we add the rates. 12+14 = 26 26t = 5.2 5.2/26 = .2 or 1/5 1/5 of an hour is 12 minutes. The second bike left at 2:09, so both bikes will meet at 2:21.

A three-digit code must be used to access a computer file. The first digit must be an A or a B. The second digit must be a number between 0 and 9. The final digit is a single letter from the alphabet from A to Z. How many possible access codes can there be? (A) 38 (B) 468 (C) 520 (D) 640

(C) 520 There are two possibilities for the first digit (A or B), 10 possibilities for the second digit (0 to 9), and 26 possibilities for the third digit. Using the multiplication principle, 2 x 10 x 26 = 520 possible access codes.

Tom is going to hang three framed pictures side by side on a wall. How many different ways can he arrange the pictures? (A) 9 (B) 5 (C) 6 (D) 27

(C) 6 For the first picture to be hung on the wall, there are three choices. After he hangs the first picture, there are two choices left for the second picture, and then one choice left for the last picture. Multiply to find the number of different ways he can arrange the three pictures: (3)(2) (1) = 6 ways.

A baker sells a dozen donuts for $3.99. The cost to make three donuts is $0.45. How much is the total profit on 5 dozen donuts? (A) $17.70 (B) $13.20 (C) $2.19 (D) $10.95

(D) $10.95 Multiply $0.45 (the cost of making three donuts) by 4 to find the cost of making a dozen donuts: $0.45x 4 = $1.80. Then subtract the cost of making one dozen donuts from the selling price of one dozen donuts to get the profit on one dozen donuts: $3.99 -$1.80 = $2.19. Because the baker sold five dozen donuts, multiply the profit on one dozen donuts times 5 to determine the profit on five dozen donuts: $2.19 x 5 = $10.95.

If you roll two six-sided dice, what's the probability of not rolling a five on either die? (A) 1/36 (B) 1/6 (C) 4/36 (D) 25/36

(D) 25/36 For each die, the probability of rolling a 5 is 1 out of 6 that is, 1/6 , So the probability of not rolling a 5 is 1-1/6, or 5/6 . With two dice, the probability of not rolling a 5 is 5/6 x 5/6 , or 25/36.

A 3-yard-long ribbon was used to trim four dresses. Each dress used the same amount of ribbon. How much ribbon was used for each dress? (A) 1 yard (B) 2/3 yard (C) 1/2 yard (D) 3/4 yard

(D) 3/4 yard Divide the amount of ribbon (in yards) used by the number of dresses to determine how much ribbon (in yards) was used in each dress: 3/4. Three-quarters of a yard of ribbon was used to make each dress.

A square has an area of 121 cm2. What is the perimeter? (A) 121 cm (B) 22 cm (C) 33 cm (D) 44 cm

(D) 44 cm To find the length of one side of the square, find the square root of the area: √121 =11 Multiply the side length by 4 to find the perimeter: 4 x 11 = 44.

The sun is 93 million miles from Earth, and light travels at a rate of 186,000 miles per second. How long does it take for light from the sun to reach Earth? (A) 5 minutes (B) 6 1/2 minutes (C) 7 minutes (D) 8 1/3 minutes

(D) 8 1/3 minutes The distance formula is distance equals rate times time, or d = rt. Substitute the known values: 93,000 000 =186,000t. Therefore, t = 500 seconds. Divide 500 by 60 to convert to minutes: 500 seconds 60 seconds/minute = 8 1/3 minutes.

If 2lbs of cottage cheese cost $3.20, what is the cost of a 3-ounce portion of cottage cheese? A. $0.30 B. $0.20 C. $0.25 D. $0.15

A. $0.30 16 ounces = 1 pound 2lbs = 32 ounces We need to know how much 1 ounce is so 32x=3.20 x = 0.1 for 1 ounce. 0.1 x 3 = 0.30.

In the town of Hampshire, houses are assessed at 75 percent of the purchase price. If Mr. Johnson buys a house in Hampshire for $80,000 and real estate taxes are $4.83 per $100 of assessed valuation, how much realty must he pay? A. $2,898 B. $3,864 C. $600 D. $604.83

A. $2,898 So the cost is only being assessed at 75% of the price $80,000 x .75 = 60,000 Every $100 dollars it will be 4.83 $60,000/$100 = 600 assessed. $600 x $4.83 = $2,898

Evelyn has made a deposit of 15,000 in a bank at an annual simply interest rate of 7%. How much will she gain in total in the nearest dollar if she does not touch it for 5 years? A. $20,250 B. $20,260 C. $21,124 D. $22,780

A. $20,250 I=Prt P= principle = $15,000 r= rate = 7% = 0.07 t= time = 5 years 1) Interest I = 15,000 x 0.07x 5=5,250 2) 15,000+5,250 = $20,250 which is A.

A partnership agreement calls for the two partners to share the profits of their business in the ratio of 4:5. If the profit for the year is $63,000, what is the share paid to the partner who gets the smaller portion. A. $28,000 B. $7,000 C. $35,000 D. $15,750

A. $28,000 The ratio 4:5 means one partner got 4 shares and the other got 5 shares. Lets find out what 1 share is worth. Let x equal 1 share. 4x+5x = $63,000 9x = $63,000 x = 7,000 is one share. The smaller portion was 4 shares so 7k x 4 = 28,000

Jonathan's monthly take-home pay is $2,556.36. If 28 percent is routinely taken out of his pay for taxes and insurance, what is his original pay before the deductions? A. $3,550.50 B. $3,665.72 C. $4,175.50 D. $4,278.50

A. $3,550.50 Create an equation. Let x equal the original pay $2,556.36 = x - 0.28x 1.00-0.28 = 0.72 $2,556.36 = 0.72x $2,556.36/0.72 = $3,550.50

The wage rate in a certain trade is $8.60 an hour for a 40-hour week and 1 (1/2) times the base pay for overtime. An employee who works 48 hours in a week earns. A. $447.20 B. $498.20 C. $582.20 D. $619.20

A. $447.20 8.60 x 40 = $344 We have 8 hours extra. Anytime extra is 1.5 more than normal. 8.60 x 1.5 = 12.9 12.9 x 8 = $103.2 $344 + $103.2 = $447.20

Mackenzie has a 20 year term life insurance policy for $100,000. The annual premium is $12.00 per thousand. What is the total premium paid for this policy every 6 months. A. $600 B. $1,200 C. $100 D. $2,400

A. $600 Were only considering per thousand of the 100k $100,000/$1,000 = 100 $100 x $12 = $1,200 annually Since they want to know every 6 months instead of annually. We cut it in half. $600

Michael bought 2 (1/4) pounds of lumber at $4.00 per pound. If a 7% sales tax was added, how much did Michael pay? A. $9.63 B. $9.98 C. $10.70 D. $11.77

A. $9.63 1 lbs = $4 We've got 2 pounds = $8 1/4 lbs = 1/4 of $4 which is just $1 8+1 = 9 We have a 7% sales tax 0.07 x 9 = .63 9+.63 = $9.63

At the rate of 40 words per minute, how long will it take a typist to type a 3,600-word article? A. 1 (1/2) hours B. 1 (3/4) hours C. 2 hours D. 2 (1/4) hours

A. 1 (1/2) hours 3600/40 = 90 minutes or 1.5 hours

When a stretch of Loop 1 was converted from non-paid to a toll road, the traffic declined from 11,200 cars per day to 10,044. What was the percent of the decline in traffic? A. 10.3% B. 11.5% C. 10.1% D. 8.9%

A. 10.3% 11,200 - 10,044 = 1,156 11,200x = 1,156 - round 1,156 up to 1,160 to make it easier 1,160/11,200 = 116/1,120 = 10.3%

A table usually sells for $240, but because it is slightly damaged, the store manager lets it go for $210. What is the percentage of reduction? A. 12 1/2% B. 14 2/7% C. 16 2/3% D. 18 3/4%

A. 12 1/2% The amount reduction is $30. 240x=30 x = 30/240 - reduce by 10 3/24 - reduce by 3 1/8. 1/8 is .125 but in percentage its 12.5% or 12 1/2% which is A.

Travis' salary was increased from $260 per week to $290 per week .what was the increase in his salary to the nearest percent? A. 12% B. 11% C. 10% D. 9%

A. 12% 1) First find the salary increase. 2) 290- 260 = $30 3) Now we need percentage that gets us that $30 so 4) 260x = 30 - solve for x 5) 30/260 = Reduce by 10 6) 3/26 = 0.115 or 11.5 and in this case 12% which is A.

A sweater originally priced at $40 is on sale for $35. What percent has the sweater been discounted? A. 12.5 percent B. 13 percent C. 14 percent D. 15 percent

A. 12.5 percent Difference is $5 5/40 = 0.125 or 12.5 percent. If the answers give you exactly what it is then choose it. DO NOT ROUND UP WHEN IT IS ALREADY GIVING TO YOU.

When a certain number is divided by 15, the quotient is 8 and the remainder is 7. What is the number ? A. 127 B. 8 (1/2) C. 3 (3/5) D. 77

A. 127 1) One way of checking a division example is to multiply the quotient (the answer) by the divisor. After multiplying, add the remainder ( if there was one in the division). 2) x/15 = 8 - multiply 15 both sides. 3) x =120, if the remainder is 7 we just add. 4) 120 +7 is 127 answer A.

Standing by a pole, a boy 3 (1/2) feet tall casts a 6-foot shadow. The pole casts a 24-foot shadow. How tall is the pole? A. 14 feet B. 18 feet C. 28 feet D. 41 feet

A. 14 feet Proportion question Let x = the pole's height. Then, cross-multiply and solve for x: 3.5 / 6 = x/24 84 = 6x 84/6 = 14

21 cups of flour are used for every 9 cups of milk in a pancake recipe. If there are 80 total cups of pancake batter, how many cups of milk were used? A. 24 B. 36 C. 40 D. 60

A. 24 21 cups of flour + 9 cups of milk = 30 total cups of pancake batter. They want to know how many cups of milk are there in 80 cups of pancake batter. 9 cups for every 30 total so set up the proportion. 9/30 = x/80 80x9 = 720 720/30 = 24

If a train can travel 500 miles in 5 hours, how far can it travel in 15 minutes? A. 25 miles B. 30 miles C. 57 miles D. 125 miles

A. 25 miles 1) Convert hours to minutes 5 x 60 = 300 minutes 2) Get 1 minute per mile 300 minutes = 500 miles 500/300 = 1.66 miles/minute 1.7min/mile x 15 minute = 25

A shopkeeper buys a box of candy with $20 and sells with $25. What is the percentage profit? A. 25% B. 20% C. 15% D. 17%

A. 25% 1) 25-20 = 5 2) So what times 20 gives us 5? 3) 20x = 5 - solve for x 4) 5/20 = 1/4 or 0.25 which is 25%

A scientist planted 120 seed, of which 90 sprouted. What percentage failed to sprout? A. 25% B. 24% C. 30% D. 75%

A. 25% 1) First lets find out how many failed to sprout 2) 120-90 = 30 - failed to sprout 3) Now lets put that over 120 and find out the percentage 4) 30/120 - reduce with 10 5) 3/12 - reduce with 3 6) 1/4 which is 25% answer A.

Christopher marks where he is currently standing with a piece of tape. Then, Christopher takes 9 steps right, 19 steps left, 18 steps left, and 2 steps right. Where is Christopher now in relation to where he started? A. 26 steps left B. 24 steps left C. 22 steps left D. 19 steps left

A. 26 steps left 9 steps to the right where he started. Then he goes 19 steps left. 19-9 = 10 steps left from the point 18 steps left 18+10 = 28 left of the point 2 steps right 28-2 = 26 steps left of the point

On her maiden voyage, the S.S. United States made the trip from New York to England in 3 days, 10 hours, and 40 minutes, beating the record set by the R.M.S. Queen Mary in 1938 by 10 hours and 2 minutes. How long did it take the Queen Mary to make the trip? A. 3 days, 20 hours, 42 minutes B. 3 days, 15 hours, 38 minutes C. 3 days, 12 hours, 2 minutes D. 3 days, 8 hours, 12 minutes

A. 3 days, 20 hours, 42 minutes 3 days 10 hrs. 40 min 10 hrs. 2 minutes + ______________________________________ 3 days 20 hrs. 42 minutes

Patrick took a trip on his motorcycle. He drove at a steady speed of 50 mph, and the trip took him 3 hours. How long would the trip have taken if his speed was 40 mph? A. 3.75 hr B. 4.00 hr C. 4.25 hr D. 4.45 hr

A. 3.75 hr When you see distance, rate, and time you need to use formula D = rt If Patrick traveled at 50 mph for 3 hours, the trip was 3(50) or 150 miles. Substitute what you know. D = 150 miles; r = 40. 150 = 40t. Solve for t. t = 3.75 hours.

An engineering drawing on a sheet of paper that measures 12 inches wide by 18 inches long is to be enlarged so that the length is 45 inches. How many inches wide will the enlarged drawing be? A. 30 inches B. 39 inches C. 66 inches D. 33 inches

A. 30 inches Think x when we need a missing number with these questions. We need the wide measurement after the length was increased to 45. Thus, 12 inches wide/18inches long = x/45 inches long, solve for x 12/18 - reduce by 6 2/3=x/45 - multiply both sides by 45 2/3 x 45/1 - 3 goes into 45 15 times. 2/1 x 15/1 = 30 inches.

Working together, Michael and Kimberly can complete a certain task in 21 minutes. If It takes 70 minutes by herself to complete the task, how long would it take Michael by himself? A. 30 minutes B. 27 minutes C. 40 minutes D. 25 minutes

A. 30 minutes Remember 1/a + 1/b = 1/c 1/70 + 1/x = 1/21 - solve for x 1)Subtract 1/70 both sides 1/21-1/70 = 10/210 - 3/210 = 7/210 7/210 = 1/x 2) We need the x as the numerator. What you do to one side you have to do to the other. x/1 = 210/7 210/7 = 30 x = 30 minutes

If a car travels 1/100 of a kilometer each second, how many kilometers does it travel in an hour ? A. 36 B. 60 C. 72 D. 100

A. 36 1 hour = 60 min x 60 sec = 3600 seconds. If it says it travels 1/100 kilometer each second we simply divide 3600 by 100 which will give us 36

Soap, ordinarily priced at 2 bars for $0.66, may be purchased in lots of one dozen for $3.48. What is the savings per bar when it is purchased in this way? A. 4 cents B. 8 cents C. 16 cents D. 19 cents

A. 4 cents Original = 2 bars = 0.66, or $0.33 for 1 bar Dozen (12) = 3.48, for 1, 3.48/12 = $0.29 for 1 bar $.33-$.29 = $ 4 cents

The perimeter of a rectangle is 40 feet. If the length is 15 feet, 6 inches, what is the width of the rectangle? A. 4 feet, 6 inches B. 9 feet, 6 inches C. 5 feet, 6 inches D. 5 feet

A. 4 feet, 6 inches 2W+2l = perimeter 15 feet , 6 inches is the same as 15 1/2 1) 15 1/2 x 2 = 31 feet (2 lengths) 31 + 2x = 40 - solve for x x = 9/2 or 4 1/2. Which is the same as saying 4 feet, and 6 inches.

The fuel tank of a gasoline generator contains sufficient capacity to operate the generator for 1 hour and 20 minutes. How many times must the fuel tank be filled to run the generator from 9:15am to 3:55pm? A. 5 B. 6 C. 4 1/2 D. 4

A. 5 First find out how long is 9:15am to 3:55pm From 9:00am to 3:00pm is 6 hours. How much does :15 need to get to :55, 40 minutes. Thus, 9:15am to 3:55pm is 6 hours and 40 minutes. How many 1 hour and 30 minutes go into 6 hours and 50 minutes? Every 3 hours is 1 hour more. So it will be 5.

A jet takes off from an airport and heads east at an average speed of 500 miles per hour. There is a plane 400 mile east of the jet traveling at an average speed of 420 miles per hour in the same direction. How long will it take for the jet to catch up to the plane? A. 5 hours B. 6.5 hours C. 8 hours D. 10 hours

A. 5 hours Distance = rate x time Same direction going at the same time means we are subtracting the rates. 400 miles = (500-420) x time 400 miles= 80 mph x time 400/80 = 5 hours

Two planes leave the same airport travelling in opposite directions. One is flying at the rate of 340 miles per hour, the other at 260 miles per hour. In how many hours will the two planes be 3,000 miles apart. A. 5 hours B. 4 hours C. 6 hours D. 10 hours

A. 5 hours Remember opposite directions means we add them both. 340+260 = 600 miles. Since we have the distance this what it looks like. 600 miles x time = 3,000, solve for the time. 3,000/600 = 30/6 = 5 hours.

What is the average of 1/4 and 1/6? A. 5/24 B. 7/24 C. 5/12 D. 1/5

A. 5/24 1) Average means divide the sum how many numbers there are in this case 2. 2) First change both fractions to a common denominator. Remember it says 1/4 "and" 1/6 means were adding. 3) 1/4 + 1/6 - common denominator is 12 4) 3/12 + 2/12 = 5/12 5) Now we divide 5/12 by 2 6) 5/12 ÷ 2 - 2 is 2/1 so lets multiply by inverse 7) 5/12 x 1/2 = 5/24 which is A.

A painter charges $12 an hour while his son charges $6 dollars an hour. If the father and son worked the same amount of time together on a job, how many hours did each of them work if their combined charge for their labor was $108. A. 6 B. 9 C. 12 D. 18

A. 6 Let x equal how much the son made. 1) Son does $6 an hour x 2) Father works $12 which is double the son. 2x 3) x +2x = $108 3x= $108, x = $36 (how much the son made) 4) If the son made $36 and he makes $6/hour 36/6 = 6 hours. The father is also 6 hours as its mentioned that they both work the same amount of time. This can be futher checked by multiplying both hourly rates by 6 and adding them together. 12 x 6 = 72 6x6 = 36 72+36 = $108

Leon wants to paint the four walls in his dining room. Each wall is 8 feet high by 30 feet wide. A quart of paint covers 40 ft². How many gallons of paint must he purchase? A. 6 B. 8 C. 12 D. 15

A. 6 Look at the word "Each" This means we need to multiply by 4 after we get the area of one. First find area of the room. 8ft x 30ft = 240 ft ² for each of four walls. For all four walls, multiply 240 by 4, giving a total square footage of 960 ft ² 4 quarts = 1 gallon. 1 quart covers 40ft² 960 ft ² / 40ft² = 24 quarts. 24 quarts/ 4 = 6 gallons.

A 25-ounce solution is 20% alcohol. If 50 ounces of water are added to it, what percent of the new solution is alcohol? A. 6 (2/3)% B. 7 (1/2)% C. 10 % D. 13 (1/3)%

A. 6 (2/3)% In the original solution, how many ounces is alcohol? 20% x 25 = 5 ounces of alcohol. Lets add the 50 water to the 25 solution and now we have 5 ounces of alcohol/75 ounce solution 1/15 = 0.66 as a percent is 6 (2/3)%

Tickets for movie admission for adults are $4.00 each, but half price is charged for children. If 265 adult tickets were sold and the box office collected $1,200, how many children's ticket were sold? A. 70 B. 35 C. 280 D. 140

A. 70 265 adult tickets were sold for 4 dollars each. $265 x $4 = $1060 from adults $1,200 were sold $1,200 - $1060 = $140 from the children Since kids pay half the adults $2. divide $140 by 2 to see how many kids attended. $140/$2 = 70

The local performing arts troupe saw, before the curtain went up ,that 76 percent of a 500 seat theater was occupied, and that three quarters of those attending were adults. How many children were seated in the theater? A. 95 B. 100 C. 76 D. 285

A. 95 500 x 0.76 = 380 were occupied 3 quarters = 3/4 or 75% are adults. 1) This means that 25% are children. 380 x 25% = 95

A ladder is placed against a building. If the ladder makes a 55° angle with the ground, what is the measure of the angle that the ladder makes with the building? A. 35° B. 40° C. 55° D. 90°

A. In this problem, you know two of the three angles, one measuring 55° and the other measuring 90°. Together those two angles measure 145°. Since a triangle has a total of 180°, the third angle must measure 180° - 145° = 35°.

A car manufacturer usually makes 15,412 SUVs, 25,815 station wagons, 50,412 sedans, 8,123 trucks, and 18,312 hybrids a month. About how many cars are manufactured each month? a. 120,000 b. 200,000 c. 300,000 d. 12,000 e. 20,000

A: Rounding can be used to find the best approximation. All of the values can be rounded to the nearest thousand. 15,412 SUVs can be rounded to 15,000. 25,815 station wagons can be rounded to 26,000. 50,412 sedans can be rounded to 50,000. 8,123 trucks can be rounded to 8,000. Finally, 18,312 hybrids can be rounded to 18,000. The sum of the rounded values is 117,000, which is closest to 120,000.

What are the two values that always describe a vector? a. Magnitude and direction b. Magnitude and length c. Length and position d. Direction and position e. Magnitude and position

A: The vector is described as having both magnitude and direction. The magnitude is the size of the vector and the direction is the path along with which the force is being applied. The second answer choice has magnitude and length, which are essentially the same. The third, fourth, and fifth answer choices include length and position, but position is also not part of the description of a vector.

Collen purchased a large bag of apples. She used 1/2 of them to make applesauce. Of those she had left, she used 3/4 to make an apple pie. When she was finished, she had only three apples left. How many apples were there to begin with? A. 21 B. 24 C. 28 D. 36

Answer B. Firstly Collen took 1/2 (i.e 50%) of the apples she bought and used it. After, she used 3/4 of the apples to make apple pie with 1/4 left over. The 1/4 left over ended up being 3 apples. So if 1/4 is 3 apples than 4/4 3x4 will be 12 apples. Now since she took 1/2, 50% before we know 12 is that half so we double that which will give us 24 the total amount of apples she bought.

You will have 29 minutes to answer the 25 questions that are on the Arithmetic Reasoning Subtest when you take the AFOQT. What is the maximum amount of time you should spend on any single question (in seconds)? Note: Assume each question will warrant the same 'maximum time' for the sake of this problem. A. 55 seconds B. 69.6 seconds C. 88.1 seconds D. 99.3 seconds E. 119 seconds

Answer B. Convert 29 minutes to seconds. 29*60 = 1740. Divide 1740 seconds by the amount of questions 1740/25 = 69.6

Alice leaves her house, driving east at 45 miles per hour (mph). Thirty minutes later her husband Dave notices she forgot her cell phone and sets off after her. How fast must Dave travel in order to catch up with Alice 3 hours after he leaves? (a) 49 mph (b) 50.5 mph (c) 52.5 mph (d) 54 mph

Answer C. 1) She drives east = 45mph Half an hour of 45 mph is 22.5 mph 2) He needs to catch up to her after it's been 3 hours after he left half an hour ago so we divide 22.5 by 3 22.5mph ÷ 3 hours - make whole 225 ÷ 3 = 75 move back 1 time which will be 7.5 mph 3) Now we add the 45 miles to the 7.5 to see how fast he must be going to reach her. 45 mph +7.5 mph = 52.5 mph which is C.

A security guard walks the equivalent of six city blocks when he makes a circuit around the building. If he walks at a pace of eight city blocks every 30 minutes, how long will it take him to complete a circuit around the building, assuming he doesn't run into any thieves? (a) 20.00 minutes (b) 3.75 minutes (c) 22.50 minutes (d) 7.5 minutes

Answer C. 1) We need to first know how long it takes him to walk one block. 30 minutes /8 blocks = 3.75 minutes/block 2) If he walks six city blocks then we multiply 3.75 by 6 3.75 x 6 - move decimal 375 x 6 = 2250- move back 2 22.50 which is C.

Joe received an hourly wage of $8.15. His boss gave him a 7% raise. How much does Joe make per hour now? (a) $0.57 (b) $8.90 (c) $8.72 (d) $13.85

Answer C. We see that Joe received a 7% raise. What this means is (1 + 0.07 ) = 1.07 Now we can multiply 1.07 x 8.15 - make whole 107 x 815 = 87205 - move decimal back 4 times 8.72 which is answer C.

If a car is towed 12 miles to the repair shop and the tow charge is $3.50 per mile, how much does the tow cost? (a) $12.00 (b) $3.50 (c) $42.00 (d) $100.00

Answer C. 1 mile = 3.50 We need to know how much 12 miles is so we multiply 3.50 x 12 = $42.00

If Lydia's height is 2/a of Francine's height and Francine is b inches tall, how tall is Lydia? A. 2/ab B. 2(ab) C. 2(a/b) D. 2b/a

Answer D. So first we need to think of it like a normal fraction. Say Lydia's height is 1/5. And Francine is 30 inches tall. Well we need to multiply 1/5 x 30 to get Lydias height. Same principle. We multiply 2/a x b 2/a x b/1 = 2b/a which is D.

The population of Grand Island, Nebraska, grew by 600,000 people between 1995 and 2005, one-fifth more than the town council predicted. The town originally predicted the city's population to grow by (a) 400,000 (b) 500,000 (c) 300,000 (d) 100,000

Answer is B. Let x = the original prediction. Now the town believed 100 percent that it would grow one way. In reality it was 1/5 more than predicted.. 1/5 = 20% 100% + 20%+ = 120% 600,000 = 120%x - change percent to decimal 600,000 = 1.20x - divide both side by 1.20 x = 500,000 which is B

A hiker walks 40 miles on the first day of a five-day trip. On each day after that. he can walk only half as far as he did the day before. On average, how far does he walk each day? A. 10 miles B. 15.5 miles C. 20 miles D. 24 miles

Answer is B. It says each day is halved by the previous day so this is the sequence to get the average. First day is 40 Second day is 20 Third day is 10 4th day is 5 5th day is 2.5 Add all 40+20+10+5+2.5 = 77.5 Now for average divide by how many numbers there are which is 5 77.5/5 = 15.5 which is B.

A bag contains 105 jelly beans: 23 white, 23 red, 14 purple, 26 yellow, and 19 green. What is the probability of selecting either a yellow or a green jellybean? A. 3/7 B. 1/6 C. 1/12 D. 2/9

Answer: A First there are 105 jelly beans total so this will be our denominator. They want to know the probaility of either yellow or green jelly beans so we add yellow (26) and green (19) giving us 45. We put this over 105 and reduce 45/105 - reduce by 5 45 can be reduced to 9 105 can be reduced 21 9/21 this can be reduced further by 3 9 reduced by 3 gives us 3 21 can reduced by 3 to 7 3/7 which is Answer A.

What are the dimensions of a rectangular room with a perimeter of 42 feet if the long side is twice as long as the short side? A. 7 feet by 14 feet B. 8 feet by 16 feet C. 12 feet by 24 feet D. 14 feet by 28 feet

Answer: A First to get the perimeter of a rectangle we add all sides. We know the long side is twice as long (2x) as the short side (x) There are 2 long sides and 2 short sides so 2x+2x+x+x = 6x Total is 42 so lets solve for x 6x=42 - divide both sides by 6 X = 7 Now we know that's x double that is 14 since the long side is doubled so the answer is A.

The cost of milk at Jonesy Smith Grocery rose from $2.50 to $2.80 over the course of several months. What was the percentage increase in the cost of milk? A. 12% B. 30% C. 10.7% D. 8.3%

Answer: A First we know the difference of $2.80 and $2.50 is .30 cents. The percentage increase can be the variable so we can set up the problem like this. .30 = 2.50x - to find the percentage increase one must multiply the percentage to the initial cost hence why 2.50 is used instead of 2.80. .30 = 2.50x - solve for x divide both sides by 2.50 .30/2.50 - remember move the left to make whole do same to the right. 30/250 = .12 now as a percent move 2 decimals to the right you get 12% which is answer A.

Over a period of four days, Roberto drove a total of 956.58 miles. What is the average number of miles Roberto drove each day? A. 239.145 B. 239.250 C. 249.045 D. 249.045

Answer: A We simply divide 956.58 by 4. Simply remember as you are doing the calculation remove the choices as you go. You don't have to do the whole calculation. Wastes too much time.

Jason is six times as old as Kate. In two years, Jason will be twice as old as Kate is then. How old is Jason now? A. 3 years old B. 6 years old C. 9 years old D. 12 years old E. 15 years old

Answer: A. "Jason is six times as old as Kate" = 6K In 2 years = Jason + 2 and K+2 Twice as old as Kate = 2 (k+2) Kate is also 2 years older So it will be j+2 = 2(k+2) Substitute 6k for J 6K+2 = 2(k+2) 6k+2=2k+4 - sub 2 to both sides 6k=2k+2 - sub 2k to both sides 4k=2 - divide 4 to both sides K= 2/4 or 1/2 Sub 1/2 into the initial 6k 6(1/2) = 6/2 or 3 which is answer A

The sum of two numbers is 70. One number is 8 more than the other. What's the smaller number? (a) 31 (b) 33 (c) 35 (d) 36

Answer: A. The sum of two numbers x + x one number is 8 more than the other x + x + 8 = 70 - Solve 2x+8 = 70 - Subtract 8 to both sides 2x = 62 - Divide 2 both sides X = 31 A.

If a pound of rice costs $4.20, how much does ¾ pound cost? A. $3.15 B. $4.00 C. $3.75 D. $3.35 E. $3.95

Answer: A. 4.2 *.75 = 3.15 Or 1/4.20 = 3/4/x - Solve for x

If the smallest angle in a right triangle is 32 degrees, what are the degree spans of the other two angles? A. 90 degrees, 58 degrees B. 90 degrees, 68 degrees C. 80 degrees, 68 degrees D. 80 degrees, 58 degrees E. 90 degrees, 48 degrees

Answer: A. We know one of the sides is 90 since its a right angle. We are giving info that the smallest angle is 32. There are only 3 sides to a triangle. Subtract 90 by 32 = Which is 58. Check: Triangle is 180 total. Add 90+32+58 = 180. Answer A is the right choice.

Celine has a fish tank in the shape of a cube. If the volume of her fish tank is 1,000 cubic inches, what is the area of one of the sides of Celine's fish tank? A. 10 square inches B. 100 square inches C. 333 square inches D. 666 square inches

Answer: B Cube means all the sides are the same. We know its 1000 so lets find what time times itself 3 times will give us 1000. We know that 10 x 10 x 10 will give us 1000 The cube is 10 x 10 x 10 One square of that will be 10 x 10 So we know that each square is 10 x 10 which is 100 answer B.

60% of which number is equal to 19? A. 33.33 B. 31.67 C. 40.4 D. 11.4 E. 72.41

Answer: B. 60%x = 19 - Solve for x Divide 60% each side 19/.60 = 31.67

A can contains 200 mixed nuts: almonds, cashews. and peanuts. If the probability of choosing an almond is 1/10 and the probability of choosing a cashew is 1/4, how many peanuts are in the can? A. 90 B. 110 C. 130 D. 186

Answer: C 1/10 = 10% 1/4 = 25% So 35% is accounted for of the 200 peanuts what is left is 65%. So what is 65% of 200. Well we know 65 of 100 is 65 so double that is 130.

The state of Connecticut will pay two-fifths of the cost of a new school building. If the city of New Haven is building a school that will cost a total of $15,500,00 what will the state pay? A. $3,100,000 B. $7,750,00 C. $6,200,000 D. $4,550,000

Answer: C 2/5 = 40% Take 40% of 155 155 x .40 = 62 Only answer with that is C.

A Triangle has an Area of 9 square inches. If its base is 3 inches, what is its height in inches? A. 3 B. 4 C. 6 D. 12

Answer: C First Area of a triangle = 1/2(b)(h) So lets plug in 1/2(3)(h)=9 3/2(h)=9 - Multiply 2 both sides 3h=18 - divide 3 by both sides H= 6 which is Answer C.

Derek earns $64.00 er day and spends $4.00 per day on transportation. What Fraction of Derek's daily earnings does he spend on transportation? A. 1/32 B. 1/18 C. 1/16 D. 1/8

Answer: C Since their asking on the fraction of Derek's daily earnings on transportation we put it as 4/64. 4/64- reduce by 4 1/16 which is C.

On a state road map, one inch represents 20 miles. Denise wants to travel from Garden City to Marshalltown, which is a distance of 4(1/4) inches on the map. How many miles will Denise travel? A. 45 B. 82 C. 85 D. 90

Answer: C Well since every inch is 20 miles we can first multiply 4 from the 4 (1/4) by 20 4 x 20 = 80 Now for the 1/4 we can do the same 1/4 x 20 = 20/4 = 5 80+ 5 = 85 which is answer C.

A bread recipe calls for 6(1/2) cups of clour, but Leonard has only 5(1/3) cups. How much more flour does Leonard need? A. 2/3 cup B. 5/6 cup C. 1(1/6) cups D. 1(1/4) cups

Answer: C We need to subtract 6(1/2) by 5(1/3) At the start we know its gonna be C or D as we know there will be a 1 on the side. common denominator of 2 and 3 is 6 so only answer with that is C.

At the Greene Country Summer Fair, Brad sold the following pieces of artwork: a sculpture for $80, an oil painting for $168, an ink drawing for $52, and a photograph for $52. What was the average (mean) price for the pieces of artwork he sold? A. $52 B. $80 C. $88 D. $92

Answer: C You are simply adding all and dividing by 4 to get the answer. A faster way to do this is making some of them simpler to speed up the calculation. Those 2 52's can be just 50 to give us 100 We can take 100 from the 168 leaving us with 68 and 80 left over 100+100+80 = 280 +68 = 348/4 = 87 which is close to 88 answer C.

Tatum used a $100.00 bill to buy a fax machine for her office. The machine cost $60 plus an additional 8% tax. How much change did she receive after purchasing the fax machine with the $100.00 bill? A. $32.00 B. $32.50 C. $35.20 D. $64.80

Answer: C. First we need to add the 8% additional tax to the $60. So first be convert 8% to decimal and multiply. 0.08 x 60 = 4.80 Now we add this to the 60 giving us $64.80 Now we subtract 64.80 from 100 Total being $35.20 answer C.

Of 7,562 college students, 3,451 have taken part in some intramural sport program. What percentage of students have played intramural sports? A. 56.7% B. 52.1% C. 45.6% D. 50.6% E. 60.4%

Answer: C. 3451/7562 = 0.456 to make percent multiply by 100 (Move decimal twice to the right. 45.6%

Carpet stain protector costs $0.65 per square yard to apply. How much will it cost to apply the protectant to a 16-foot by 18-foot carpet? A. $187.20 B. $62.40 C. $20.80 D. $96.00

Answer: C. First we need to find the area of the carpet 1) Area = Length x width 16ft x 18ft = 288ft² - its ft² this is important 2) Now we must convert the ft into yards 3 ft = 1 yard Because we are dealing with square feet the 3 ft in 1 yard will be squared as well so it will be 9 ft per yard in this scenario. 288ft ÷ 9 = 32yd² 3) Now its $0.65 per yard so now we just need to multiply 32 by 0.65 0.65 x 32 - Change .65 to whole 65 x 32 = 2080- move back 2 20.80 is your answer which is C.

What is the estimated product when 157 and 817 are rounded to the nearest hundred and multiplied? A. 16,000 B. 80,000 C. 160,000 D. 180,000 E. 1,600,000

Answer: C. Rounding to the nearest hundreds. 157 is closer to 200 than to 100. 817 is closer to 800 than to 900. 200 x 800 = 160,000 which is C. Other examples 12 → 0 50 → 100 127 → 100 149 → 100 150 →200 952 → 1000

Mr. Thaler is driving from Los Angeles to San Francisco. If he drives 3 hours in Traffic at an average speed of 32 miles an hour, and then 4.5 hours on the freeway, at an average speed of 72 miles per hours what was his overall average speed on his trip to San Francisco? A. 45 miles per hour B. 52 miles per hour C. 56 miles per hour D. 60 miles per hour

Answer: C. We need to first find the total mileage 1) 3 hours = 32 miles/hr We multiply 3 x 32 = 96 2) 4.5 hours = 72 miles/hr We multiply 4.5 x 72 = 324 Add both 324 + 96 = 420 420 - total travel Now we need to divide by the time 3 hours + 4.5 hours = 7.5 hours 420/7.5 = 56 miles per hour.

A printing plant that produces baseball cards has a monthly overhead of $6,000. It costs 18 cents to print each card, and the cards sell for 30 cents each. How many cards must the printing plant sell each month in order to make a profit? A. 30,000 B. 40,000 C. 50,000 D. 60,000

Answer: C. We need to know how many cards they need to sell to make a profit. 1) Cards cost 18 cents to print and they sell for 30 cents. Remember cents means there is a decimal before the whole number. .30-.18 = .12 -How much they make per card. 2) So how many cards (.12) will it take to get to 6,000. 6,000 ÷ .12 -make decimal whole. What you change in the decimal you change in the number being divided. 600,000 ÷ 12 = 50,000 which is C.

The basal metabolic rate (BMR) is the rate at which our bodies use calories. The BMR for a man in his twenties is about 1,700 calories per day. If 204 of those calories should come from protein, about what percentage of this man's diet should be protein? A. 1.2% B. 8.3% C. 12% D. 16% E. 18%

Answer: C. The problem is solved by dividing 204/1700. Now 204 is closer to 200, we can think this way as the question states that it is "about what percentage". 200/1700 can be reduced by 100 to get 2/17, Now 17 is closer to 20 so if we do 2/20 we get 10%, 2/17 would be a bit higher so the closest is C. 12%

Out of 100 shoppers polled, 80 said they buy fresh fruit every week. How many shoppers out of 30,000 could be expected to buy fresh fruit every week? A. 2,400 B. 6,000 C. 22.000 D. 24,000

Answer: D 100/80 = 30,000/x - cross multiply 100x = 240,000.0 - divide by 100 x = 24,000 which is D.

A sales manager buys antacid in bottles the gross. If he goes through 3 bottles antacid everyday, how long will the gross last? (a) 144 days (b) 3 days (c) 20 days (d) 48 days

Answer: D A gross is a 12 x 12 skid. 12 x 12 = 144 If he goes through 3 a day so we need to divide 144 by 3 which is 48. 48 days until the gross of Antacid runs out.

Basic cable television service, which includes 16 channels, costs $15 a month. The initial labor fee to install the service is $25. A $65 deposit is required but will be refunded within two years if the customer's bills are paid in full. Other cable services may be added to the basic service: the movie channel service is $9.40 a month; the news channels are $7.50 a month; the arts channels are $5 a month; the sports channels are $4.80 a month. A customer's cable television bill totaled $20 a month. Using the passage above, what portion of the bill was for basic cable service? A. 25% B. 33% C. 50% D. 75%

Answer: D Basic cable is $15 a month. The person's bill totaled at $20 a month We simply have to divide 15/20 and reduce 15/20 = 3/4 which is the same as saying 75%

Without factoring in hourly wages, a restaurant server makes an average of 18% tips on $570 in sales over the course of a 6 hour shift. How much did the server make in tips (total) during said shift? A. $570 B. $131.60 C. $31.67 D. $102.60 E. $10.26

Answer: D. 570 x 18% - Make the percent into decimal and move 2 spaces to make whole .18 → 18 570 x 18 = 10,260 - Move 2 decimal points back 102.60 Which is D.

Joan is taking an admissions examination. If she has to get at least 40 of the 60 questions right to pass, what percent of the questions does she need to answer correctly? A. 30% B. 40% C. 66 1/3 % D. 66 2/3%

Answer: D. She needs 40/60 to pass so lets solve 1) 40/60 - reduced by 10 = 4/6 2) 4/6 - reduce by 2 = 2/3 Now 1/3 = .3333 repeated 2/3 = .666 repeated We know its either C or D. We've established 1/3 is .333 repeated so we are left with D the answer.

One lap on a particular outdoor track measures a quarter of a mile around. To run a total of three-and-a-half miles, how many laps must a person complete? A. 7 B. 9 C. 11 D. 12 E. 14

Answer: E. 1 lap = 1/4 We need to run a total of 3.5 miles. So think how many 1/4's do we need to get to 3.5 1/4x = 3.5 - Multiply both sides by 4 to isolate the x 1x = 3.5 x 4 - Move decimal of 3.5 to the right to multiply 35 x 4 = 140 - Move decimal back to the left once 1x = 14.0 = x = 14 which is E.

If 1 pound, 12 ounces of fish costs $2.24, what is cost of the fish per pound? A. $1.20 B. $1.28 C. $1.24 D. $1.40

B. $1.28 1) Express the total weight of the fish in ounces 2) 1 pound = 16 ounces 3) 16 ounces + 12 ounces = 28 ounces 4) Find the cost of 1 ounce and multiply it by 16 to find the cost of 1 pound 5) $2.24 ÷ 28 ounces = $0.08 (for one ounce) 6) $0.08 x 16 ounces (1 pound) = $1.28 per pound which is B.

Travis Lee has an ordinary life insurance policy with a face value of 10,000. At his age, the annual premium is $24.00 per $1,000. What is the total premium paid for this policy every 6 months? A. $100 B. $120 C. $240 D. $400

B. $120 We first get the annual. Every 1,000 its $24 so for 10,000 we have 10 units. 24 x 10 is 240. Since we only want to know every months we cut the 240 in half giving us $120.

A nursery employee mixes 10 pounds of hardy grass seed worth $1.20 per pound with 8 pounds of premium grass seed worth $3.00 per pound. At what price per pound should she sell the mixture? A. $2.10 B. $2.00 C. $1.90 D. $2.50

B. $2.00 10 pounds hardy grass worth $1.20 per pound 10 x $1.20 = $12.00 8 pounds of premium grass seed worth $3.00 per pound 8 x $3.00 = $24.00 She mixes the 10 pounds of grass with the 8 pounds of seed so tis 18 pounds total. $24.00 +$12.00 = $36.00 = 18 pound mixture. 18 x = $36.00 = $2.00 per pound

If a two gallon bucket of liquid floor polish cost $19.20, how much should a one-quart can cost? A. $4.90 B. $2.40 C. $1.20 D. $0.60

B. $2.40 1 gallon = 4 quarts 2 gallons =8 quarts 8 quarts = $19.20 $19.20 / 8 = $2.40 each quart

In a store four clerks each receive $255.00 per week, while two part timers each earn $120.00. What is the average weekly salary paid these six workers? A. $200.00 B. $210.00 C. $187.50 D. $190.00

B. $210.00 6 clerks total 1) 255.00 x 4 clerks = $1,020 2) 120 x 2 = $240 3) $1,020 + $240 = 1,260 4) 1,260/6 = 210

Shawn purchased a shirt of $22.05. If the sale tax was 5%, what was the total price of the shirt? A. $1.10 B. $23.15 C. $24.15 D. $20.95

B. $23.15 We're looking for the total price of the shirt before the sales tax. 1) 22.05 make whole - 2 steps. 2) 5% make whole - 2 steps 3) 4 steps total. 4) 2205 x 5 = 11025 go back 4 5) $1.10 - add this back into the purchased price to get the total. 6) $22.05 +$1.10 = B. $23.15

A merchant buys radios listed wholesale for $60 a piece at a 25% discount. He sells these radios at a 20% markup above the original wholesale price. What is his profit on each radio? A. $9.00 B. $27.00 C. $12.00 D. $18.00

B. $27.00 He buys the radios at a 25% discount of $60 $60 x 25% = $15.00 $60 - 15 = $45 what he bought them for He is selling them at 20% above the original price $60 x 20% = $12.00 $60 +12.00 = $72 dollars So what is his profit? Bought them for 45 and sold them for 72 $72-$45 = $27

While working in he Floors 'R' Us. suburban store, four customer service representatives each receive $320 a week, while two sales managers each earn $12 per hour plus an average $100 per day commission. What is the total weekly compensation paid to these six employees for a 5-day, 40 hour work week? A. $2,420 B. $3,240 C. $2,260 D. $4,520

B. $3,240 They want to know a weeks worth, 40 hour work week payment for all 6 employees. 1) First 4 customer service representatives. $320 x 4 = $1,280 total for 4 representatives. 2) 2 sales managers $12 an hour 40 x 12 = $480 for one Since there's 2 480 x 2 = $960 total Also get $100 per day. 5 days = 500 dollars. 2 people = 500 x 2 = $1000 $1,960 total for 2 managers. Now add both $1,960 + $1,280 = $3,240

Mr. Winter brought a $500 TV that was marked at a 15% discount. He made a down payment of $65 an agreed to pay the balance in 12 equal monthly installments. How much was each installment? A. $25.00 B. $30.00 C. $42.50 D. $360.00

B. $30.00 First we are only taking into account 15% of the $500 dollars. 1) $500 x 0.15 = $75.00 $500-$75 = $425 2) A down payment of $65 was made. $425-$65 = $360 3) 12 monthly installments $360/12 = $30 a month.

A taxi cab ride is $2.50 for the first 1/4 mile, and $0.40 for each additional 1/4 mile. How much would it cost to go 6/5 mile? A. $4.20 B. $4.10 C. $4.15 D. 4.12

B. $4.10 1) 1/4 mile = 0.25 mile 2) 6/5 = 1.2 or 1 mile and .20 miles 3) 1 mile accounts for 4 (1/4 miles) 4) We have .20 miles left for which we will consider in the 0.40 calculation. 5) The first 1/4 mile will cost $2.50 and all the remaining ones will cost $0.40. The remaining 0.2 miles should be charged as if it was for 0.25 miles Cost = (1 x $2.50) + (3 x $0.40) + (1 x $0.40) Cost = $2.50 + 1.2 + $0.4 = $4.10

It cost a couple $27 to go out for the evening. Sixty percent of this was for theater tickets. What was the cost for each ticket? A. $7.90 B. $8.10 C. $10.80 D. $16.20

B. $8.10 27 x 60% = $16.20 total cost of the tickets They want to know the cost of one ticket. 16.2/2 = $8.10

The ingredients in a cake recipe include 4 1/2 cups of flour and 3/4 cups of sugar. It is desired to make a cake that will require only 1/4 cup of sugar. How much flour should be used? A. 1 1/4 cups B. 1 1/2 cups C. 4 cups D. 1 3/4 cups

B. 1 1/2 cups Create a proportion Make 4 1/2 into an improper fraction = 9/2 9/2 flour/ 3/4 sugar = x / 1/4 sugar - solve for x 9/2 / 3/4 = 9/2 x 4/3 = 6 6 = x / 1/4 - multiply 1/4 both sides x = 6/4 = 3/2 or 1 1/2 cups

An inch on a map represents 200 miles. On the same map, a distance of 375 miles is represented by A. 1 1/2 inches. B. 1 7/8 inches. C. 2 1/4 inches. D. 2 3/4 inches.

B. 1 7/8 inches. 1/200 miles = x/375 miles 375/200 = 1.875 or 1 7/8 inches

A swimming pool is 20 yards wide and 50 yards long. A tile border is built around the outside of the pool using tiles that are 1 square foot each. If the border is 3 feet wide, how many tiles are needed? A. 639 B. 1,296 C. 8,639 D. 9,296

B. 1,296 There are 3 feet in a yard Because tiles are 1 square foot each, convert the measurements of the pool from yards to feet. 20 x 3 = 60 feet 50 x 3 = 150 feet Area = 150 x 60 = 9,000 square feet They add the border that is 3 feet Add 6 more feet to the width and 6 more feet to the length dimension to get the area of the pool with the tile border included 60 = 66 feet 150 = 156 feet 156 x 66 = 10,296 So 10,296 - 9000 = 1,296 needed.

The Pentagon in Washington, D.C., has five sides, each 281 meters long. What is the perimeter of the building to the nearest tenth of a kilometer? A. 1.1 km B. 1.4 km C. 14.1 km D. 56.2 km

B. 1.4 km 281 x 5 = 1,405 meters However, the question asks for the perimeter in kilometers, not meters. Since 1,000 meters = 1 kilometer If they want km we divide 1,405 /1000 = 1.4km

If it takes 30 minutes to type 6 pages, how many hours will it take to type 126 pages at the same rate? A. 6.3 B. 10.5 C. 15 D. 25

B. 10.5 If it takes 30 minutes for 6 pages One hour will be 12 pages. 126/12 = 10.5 hours.

A mapmaker is told to prepare a map with a scale of 1 inch = 50 miles. If the actual ground distance between two points is 120 miles, how far apart should the mapmaker show them on the map? A. 0.4 inch B. 2.4 inches C. 1.2 inches D. 4.8 inches

B. 2.4 inches 1 inch = 50 miles Can set this as an equation of x 1inch/50 miles = x/120miles 1/50 x 120 = 120/50 = 12/5 = 2.4 inches.

A heart attack victim can be saved 90 percent of the time if a defibrillator is used within 5 minutes of the heart attack's onset. Of the people who have heart attacks, defibrillators are nearby 40 percent of the time, but they are only used 60 percent of the time even when they are available. How many people who suffer a heart attack are saved because of the use of a defibrillator? A. 20% B. 22% C. 42% D. 30%

B. 22% Remember read the question first. How many people are saved from a defibrillator? It says that 90 percent of the time defib saves them. But its only nearby 40% of the time. Thus, 90% x 40% = 36% will have the opportunity. Now only 60% of the time defibs are used Thus, 36% x 60% =.0216 or 22%

My friend bought some skateboards for $195. He sold them for $770 making $25 profit on each skateboard. How many skateboards were there? A. 20 B. 23 C. 32 D. 36

B. 23 Bout for $195, sold for $770 $770 - $195 = $575 $575 ÷ 25 = 23 skateboards

A businesswoman spends 1/5 of her income for office rent, and 3/8 of the remainder of her income for salaries. What part of her income does she spend for salaries? A. 23/40 B. 3/10 C. 1/2 D. 3/4

B. 3/10 Remember its out of 100. If she spends 1/5 of her income that means she has 4/5 left. She then spends 3/8 on salaries. 4/5 x 3/8 = 12/40 or 3/10 which is B.

Charles wants to wrap a gift that's in the shape of a rectangular prism. The present is 10 inches long, 20 inches wide, and 50 inches tall. How many square inches of wrapping paper will Charles need to completely cover the present? A. 2814 square inches B. 3400 square inches C. 10000 square inches D. 1854 square inches

B. 3400 square inches They are not asking for Volume! There asking for Surface area of a prism. Remember prism is a key word Formula: S.A = 2(LW) + 2(WH) + 2(LH) 2 (10x20) + 2 (20x50) + 2 (50x10) 400 + 2000 + 1000 = 3400 square inches

At a concert, orchestra seats sell for $20 each, and balcony seats sell for $10 each .If 324 orchestra seats were occupied, and the box office collected $10,000,how many balcony seats were sold? A. 375 B. 352 C. 330 D. 310

B. 352 Find the amount taken in for orchestra seats. 324 x $20 = $6,480 Out of 10,000, the remaining amount came from balcony seats. $10,000 - $6,480 = $3,520 Divide this amount by 10 to find the number of balcony seat tickets there were sold. $3,520 ÷ $10 = 352 balcony seats which is answer B.

Leroy wants to tile the floor in his kitchen. The floor is 10 feet by 12 feet. Each tile is 6 by 8 inches. How many tiles will he need to finish the job? A. 124 tiles B. 360 tiles C. 412 tiles D. 514 tiles

B. 360 tiles First convert the feet to inches of the floor 10 x 12 = 120 inches 12 x 12= 144 inches 120 x 144 = 17,280 inches² tiles = 6x8 = 48 inches ² 17,280/48 = 360 tiles

A scale blueprint drawing of a building has a scale of 1 inch to 40 feet many inches on the drawing represent a distance of 175 feet on the blueprint ? A. 4 (1/8) B. 4 (3/8) C. 4 (1/2) D. 4 (3/4)

B. 4 (3/8) Divide the distance by the number of feet (40) to an inch. 1) 175 feet / 40 feet - reduce by 5 2) 35 / 8 = 4 (3/8) is the answer which is B.

If a barrel has a capacity of 100 gallons, how many gallons will it contain when it is two-fifths full? A. 20 B. 40 C. 60 D. 80

B. 40 2/5 x 100 = 40 gal

The circumference of a circle that has a radius of 70 feet is most nearly A. 220 feet. B. 440 feet. C. 660 feet. D. 690 feet.

B. 440 feet. Remember Circumference is 2πr do not use π x D unless it is given. It will take too long too do it that way. π = 22/7 2 x 22/7 x 70 = 440 feet

What is the value of 3a² - 2a + 5 when a = 4? A. 43 B. 45 C. 61 D. 21

B. 45 1) Simply input the 4 where there is an A. 3(4)^2 - 2(4) + 5 2) Follow PEMDAS do parentheses first. 3) 48 - 8 + 5 - Go left to right 4) 40+5 = 45 which is B.

A mail carrier can deliver mail to 800 addresses in one day. In the city of Woodway, there are 36,800 residents. How many mail carriers must be hired to deliver mail to all of the woodway citizens each day? A. 36 B. 46 C. 92 D. 138

B. 46 36800/800 = 46

A man owns 50 shares of stock worth $30 each. The corporation declared a dividend of 6% payable in stock. How many shares did he then own? A. 47 shares B. 53 shares C. 56 shares D. 62 shares

B. 53 shares 50 shares: $30 each 50 x 30 = $1500 6% payable stock => it means 6% of the total value of 50 shares => 1500 × 6% = $90. With $90, the man can buy 3 more shares, so the total he owns then are 53 shares.

A diver's score is determined by the degree of difficulty of each dive multiplied by the points awarded for that dive. The table below shows the points Wayne earned for five dives and the degree of difficulty for each dive. What was Wayne's total score? Points Difficulty 8.2 1.2 9.0 1.4 8.3 1.5 9.5 1.4 9.5 1.2 A. 47.59 B. 59.59 C. 64.29 D. 66.29

B. 59.59 For this problem, multiply the points by the difficulty and add the scores for each dive. (8.2 x1.2)+(9.0x1.4)+(8.3x1.5)+(9.5x1.4)+(9.5x1.2) = 9.84+12.60+12.45+13.30+11.4 = 59.59 pts

A movie Theater opens at 10:00 A.M and closes at 11:30 P.M if a complete showing of a movie takes 2 hours and 15 minutes, how many complete showings are given at the movies theater each day? A. 5 B. 6 C. 7 D. 8

B. 6 Find the number of hours the movie house is open. From 10:00am to 10:00pm is 12 hours. From 10:00pm to 11:30pm is 1 (1/2) hours 12+ 1(1/2) = 13 (1/2) hours Lets focus on the 2 hours first So we can get 5 (2 hours) Which would be 10 hours. We have 5 (15 minutes) 15 x 5 = 75 minutes or 1 hour and 15 minutes So that's 11 hours and 15 minutes. That's 5 movies and a little more so we can round up so the only answer with that is B. Another movie and it will go over so the only option is B.

The cost of sending a telegram is $1.50 for the first 10 words and 0.05 for each additional word. How many words can be sent by telegram for $4.00? A. 50 B. 60 C. 81 D. 90

B. 60 First 10 words is $1.50 $4.00-$1.50 = $2.50 Now every word after 10 is $0.05 each. $2.50/$0.05 = 50 words. 10+50 = 60 words for $4.00

The midway panthers high school football quarterback attempted 82 passes and completed 57 of them while the team ran up a 8-1 record. What was his completion percentage? A. 30.4% B. 69.5% C. 43.8% D. 81.7%

B. 69.5% 57/82 = .695 or 69.5%

The manufacturer's suggested retail price of the new Guzzler 300 SEV (Sport Everything Vehicle) went from $22,399 last year to $23,999 for this year's model. About what percentage increase was this? A. 2.07% B. 7.1% C. 9.3% D. 11.4%

B. 7.1% $23,999 - $22,399 = 1,600 22,399x = 1,600 Round up to make it easier 1,600/22400 = 16/224 = 0.071 or 7.1%

An airplane travels a distance of x miles in y hours. What is its average rate of speed in miles per hour? A. xy/y B. x/y C. y/x D. x+y/2

B. x/y Think 50miles/hour. x miles/ y hours

What is the name of the indicated part of Vector B?

B: The answer is Choice B because the part of the vector that the arrow points to is the tail. The end of a vector with the arrow is called the head. The opposite end, without the arrow, is called the tail.

In a theater audience of 500 people, 80 percent were adults. How many children were in the audience? A. 20 B. 50 C. 100 D. 125

C. 100 Take 80 percent of 500. 500 x .80 = 400 adults. 500-400 is 100 kids.

What is the next term in this series : 3(1/2), 2(1/4), 13(1/4), 12,______? A. 1 (1/4) B. 10 (3/4) C. 23 D. 14 (1/2)

C. 23 1) 3(1/2), 2(1/4) They just subtracted 1 (1/4) to the 3(1/2). 2) 2(1/4), 13(1/4) they just added 11 to 2(1/4). 3) 13(1/4), 12 They once again subtracted 1 (1/4) to get 12 4) Next only make sense. There gonna add 11. Which means 12+11 is 23 answer C.

Anderson and Brandon's combined age is 40 years. Anderson is 16 years older than Brandon. How old is Anderson? A. 12 B. 27 C. 28 D. 32

C. 28 Let x = Brandon's age. x + x +16 = 40 2x + 16 = 40 2x = 24 x = 12 Brandon's age. With brandon's age added with 16 should give us Anderson. 16 + 12 = 28 Anderson's age. 28 + 12 = 40 so 28 is the answer

A part-time employee worked a total of 16 (1/2) hours during 5 days of the past week. What was this employee's average workday? A. 3 hours B. 3 hours, 15 minutes C. 3 hours, 18 minutes D. 3 hours, 25 minutes

C. 3 hours, 18 minutes 16 (1/2) =16.5 16.5/5 = 3.3 hours/day. Lets convert 3.3 to time. Only look at what's after the decimal. In this case .3 Formula .x x 60/1 = minutes .3 x 60 = 18 minutes. 3 hours and 18 minutes

The minute hand fell off a watch but the watch continued to work accurately. What time was it when the hour hand was at the 17-minute mark? A. 3:02 B. 3:17 C. 3:24 D. 4:17

C. 3:24 5 = 1 hour mark 10 = 2 hour mark 15 = 3 hour mark We know its between 3 and 4. After 15 minutes , 17 minutes is 2/5 the way to the 4 hour mark. So, 60 x 2/5 = 24 or 3:24 minutes

Using the formula I = √P/R, find the value of I when P=48 and R = 3 A. 12 B. 8 C. 4 D. 4/3

C. 4 Remember PEMDAS √48/3 48/3 = 16 √16 = 4

Of a thousand dogs at a dog show , 54 percent were male. Among these males, 4 out of 5 were over the age of 3. How many of the dogs were males 3 years old or order? A. 216 B. 332 C. 432 D. 540

C. 432 1) 1000 x 54% = 540 are male 2) 4/5 = 80% 540 x 80% = 432 are male and over the age of 3

On Black Friday, a refrigerator with a $500 original price was discounted by 20 percent. When no one bought it, the store reduced the sale price by an additional 30 percent. What was the total percent discount on the refrigerator's price? A. 56 percent B. 50 percent C. 44 percent D. 40 percent

C. 44 percent A discount of 20 percent means you pay 80 percent of the original price, and 0.80 × $500 = $400. An additional discount of 30 percent means you pay 70 percent of the sale price, so 0.70 × $400 = $280. So, after the two discounts, the $500 refrigerator costs only $280, or $220 less. The total percent discount on the refrigerator is 220/500 , or 44 percent.

Christy orders 1 pound of meat from the butcher. She wants it cut into slices each weighing 0.25 oz. About how many slices will Christy receive? A. 24 B. 44 C. 64 D. 84

C. 64 16 ounces = 1 pound How many 0.25 oz go into 16 ounces 16/0.25 = 64 slices

A snapshot 8 inches long and 6 inches wide is to be enlarged so that it length will be 12 inches. How many inches wide will the enlarged snapshot be? A. 8 inches B. 6 inches C. 9 inches D. 10 inches

C. 9 inches Since the picture nad its enlargement are similar, the lengths have the same ratio as the widths. Length of picture/ length of enlargement = width of picture/width of enlargement 1) 8/12 = 6/x - cross multiply 2) 8x = 12 (6) 3) 8x = 72 4) x = 72/8 = 9 inches width.

After five science tests, Sonya's average score is 89. If she gets a 95 on the sixth test, what is her new average? A. 89.50 B. 89.90 C. 90.00 D. 90.50

C. 90.00 If Sonya's average over five tests is 89, she has earned a total of 445 points for the five tests. Because 89 x 5 = 445 If she received a 95 on the sixth test, that brings her total points to 540. 445 + 95 = 540. Dividing that by the six tests gives a new average of 90. 540/6 = 90

The whole list price of a watch is $50. A dealer bought a shipment of watches at a discount of 20 percent above the wholesale list price. what was the profit on each watch? A. $8 B. $10 C. $12 D. $15

D. $15 Find the discounted price paid by the dealer 1) $50 x 20% 2) $50 x 0.2 = $10 (discount) 3) $50 -$10 = $40 (price paid by dealer) Then find the dealer's selling price based on an increase over the original wholesale list price. 4) $50 x 10% 5)$50 x 0.1 = $5 ( increase over list price) 6) $50 + $5 = $55 ( dealer's selling price) Finally, find the dealers profit $55-$40 = $15 ( dealer's profit) which is answer D.

While working her way through college, Amanda earns an average of $22 an hour in tips as a supervising waitress at the best steak in town. If her hourly wage is $2.50 and she has to pay a 10 percent tip share to the hostesses and busboys, how much does she take home at the end of a day where she worked from 10:30am to 5:30pm? A. $32.90 B. $121.11 C. $138.60 D. $156.10

D. $156.10 10:30am -5:30pm = 7 hours Tips = $22 x 7 = $154 Wage = $2.50 x 7 = $17.5 1) They take 10% of the tips. $154 x 0.10 = $15.4 $154.0 - $15.4 = $138.6 2) Add the wage. $138.6 + 17.5 = $156.10

The Deli in the local super grocery store sells 2 pounds of smoked deli turkey breast for $13.98. What would the cost be of a 5-ounce portion? A. $0.44 B. $0.87 C. $1.40 D. $2.20

D. $2.20 1lb = 16 ounces 32 ounces = $13.98 1) Divide both sides 13.98/32 = $0.44 each ounce They want 5 ounces 0.44 x 5 = $2.20

Jason bought 5 pairs of sunglasses and 9 hats for $257. Joseph bought 10 pairs of sunglasses and 7 hats for $261. What is the cost of one hat? A. $26.50 B. $27 C. $10 D. $23

D. $23 Think of this as a system of equations. s = sunglasses h = hats Jason = 5s +9h = 257 Joseph = 10s + 7h = $261 5s +9h = 257 10s + 7h = $261 Now we need to know the cost of one hat. Cancel out the sunglasses. Multiply Jason's equation by -2 -2 (5s +9h = 257) -10s -18h = -515 10s +7h = 261 Combine like terms -11h = -253 Solve for h h = 26 the cost of one hat.

A painter and a helper spent 3 days painting a house. The painter received twice as much as much as the helper. If the two men were paid $375 total for the job, how much did the painter receive? A. $175 B. $200 C. $225 D. $250

D. $250 1) Let x equal the amount the helper receives. 2) Let 2x equal the amount the painter receives 3) Write an equation to show that, together, they receive $375 for painting the house. 4) 2x + x = $375 5) Now Solve to first find the helper's cut 6) 3x = 375 - solve for x x = $125 (helpers cut) 7) Now subtract that to the main total and you will get the painter's cut 8) $375 - $125 = $250 which is answer D.

Mackenzie's bank balance was $2,674. Her next four transactions were as followers: -$348, + $765, +$802, -$518 What was her bank balance after the fourth transaction had a posted ? A. $5,107 B. $4,241 C. $3,475 D. $3,375

D. $3,375 1) Find the sum of the deposits and withdrawals 2) 765 + 802 = 1,567 (deposits) 3) 348 + 518 = 866 (withdrawals) 4) Find the difference between deposits and withdrawals 5) 1,567 - 866 = 701 6) Add this gain to the original price 7) 2,674 + 701 = $3,375 answer D.

Jose bought a $3,000 savings bond that earns 5 percent compounded interest per year. How much will his bond be worth after 3 years? A. $3,150.00 B. $3,307.50 C. $3,348.88 D. $3,472.88

D. $3,472.88 Simple interest problems use the formula I = prt Year One Principal = $3,000 Rate = 0.05 Interest = 3000 x 0.05 = $150 Add the interest to the principal to get $3,150. Year Two Principal = $3,150 Rate = 0.05 Interest = $3,150 x 0.05 = $157.50 Add the interest to the principal to get $3,307.50. Year Three Principal = $3,307.50 Rate = 0.05 Interest = $3,307.50 x 0.05 = $165.38 Add the interest to get the principal of $3,472.88, the amount Jose would have after three years.

What is the cost of 3 yards, 2 feet of an upholstery edging material that cost's $9 per yard? A. $30 B. $36 C. $29 D. $33

D. $33 3 feet = 1 yard 1 foot = 0.33 yards or 1/3 We have 2 feet so it will be 2/3 yards. 3 (2/3) yards $9 x 3 (2/3) yards = $33

An employee's net pay is equal to her total earnings less all deductions. If an employee's total earnings in a pay period are $497.05, what is her net pay if she has the following deductions: federal income tax, $90.32; FICA, $28.74; state tax, $18.79; city tax, $7.25; and pension, $1.88? A. $351.17 B. $351.07 C. $350.17 D. $350.07

D. $350.07 federal income tax $ 90.32 FICA 28.74 state tax 18.79 city tax 7.25 pension + 1.88 = $ 146.98 497.05 - 146.98 = 350.07

Tile chosen for a kitchen floor costs $2.85 per square foot. What is the cost to tile a kitchen whose dimensions are 3 yards by 5 yards? A. $42.75 B. $128.25 C. $289.00 D. $384.75

D. $384.75 3 yards x 3 = 9 feet 5 x 3 = 15 feet 15 x 9 = 135 feet 285 x 135 = 38,475 go back 2 384.75

The total fare for two adults and three children on an excursion boat is $14. If each child's fare is one half of each adult's fare, what is the adult fare? A. $2.00 B. $3.00 C. $3.50 D. $4.00

D. $4.00 Let x be the child's ticket. 1) There are 3 kids. 3x 2) The adults are double the kids since the kids are half off. So the adults will be 4x. Two adults = 4x. 3) 3x+4x=14 4) 7x =14 x = $2 (kids ticket) Now the adults are double the kids ticket so it will be $4 each.

Jorge paid $300 for an item at the store that was 40% off the original price. What was the original price? A. $400 B. $540 C. $510 D. $500

D. $500 100%-40% = 60% 300 is 60% of what number? 0.60x = 300 - solve for x 300/.60 30000/60 = $500

If you invest in an account that pays 2.5 percent simple interest and receive $187.50 in interest at the end of the first year, how much did you invest? A. $411 B. $750 C. $4,110 D. $7,500

D. $7,500 I = PRT 187.50 = p (0.025)(1) 187500/25 = 7,500

Kate earns $8.50 per hour with time and a half paid for overtime in excess of 8 hours on any one day. One day she worked 10 hours. How much did she earn on that day? A. $85.00 B. $117.50 C. $97.75 D. $93.50

D. $93.50 The first 8 hours is $8.50 $8.50 x 8 = $68.00 She gets paid a time and a half any hours after 8 hours. Half of $8.50 = $4.25 Time and a half is $8.50 + $4.25 = $12.75 She has 2 hours excess so $12.75 x 2 = $25.50 Add to the 8 hours. $68.00 + $25.50 = $93.50

What is the average of these temperature readings, taken on a cold day last winter? 6:00am: -12 degrees 7:00am: -7 degrees 8:00am: -2 degrees 9:00am: 0 degrees 10:00am: +6 degrees A. 0 degrees B. 2 degrees C. -1 degrees D. -3 degrees

D. -3 degrees -12+-7+-2 = -21 -21+6 = -15 -15/5 = -3

What is the Quotient when 0.675 is divided by 0.9? A. 7.5 B. 0.075 C. 75 D. 0.75

D. 0.75 1) The quotient means the answer in division. (Clear the decimal in the divisor before doing the arithmetic.) 2)0.675/0.9 - make whole 3) 6.75/9 4) 9 cant go into 6 so put a zero up. 5) Subtract 6 by 0 bring it down and then bring down the 7 to get 67. 6) 9 can go into 67, 7 times. 7) At this point you know its 0.7 only answer with that is D.

A half-cup of pudding has 150 calories. The same amount of broccoli has 60 calories. How much broccoli can a person eat to equal the same number of calories in the 1/2 cup of pudding? A. 2 cups B. 2 (1/2) cups C. 1 (1/2) cups D. 1 (1/4) cups

D. 1 (1/4) cups Divide the number of calories in the pudding by the number of calories in the broccoli: 150 ÷ 60 = 2.5 The calorie-counter can eat 2.5 times the amount of broccoli as they can eat pudding for the same number of calories. Multiply 2.5 by 0.5 cup (the amount of pudding that contains 150 calories) to find how many cups of broccoli this person can eat for 150 calories:

What is the difference between a 50% discount and a discount of 33(1/3)%? A. 0.17 B. 1/3 C. 0.25 D. 1/6

D. 1/6 1) Find the difference between the two percentages. 2) Divide the answer by 100 percent to change it to a simple fraction 3) 50% = 1/2 4) 1/3 = .33 repeating or 33.33% when you make into a percent. Hence what we are looking at is 1/2 - 1/3 5) We need to subtract 1/2 - 1/3 and which will give us 1/6 the answer. So the answer is D.

Five years ago, Ruth made a deposit of $500 into a savings account that pays simple interest. She made no further deposits, and now her account is worth $750. What was the rate of interest per year? A. 2% B. 4% C. 9% D. 10%

D. 10% Simple interest formula = I= prt I = amount of interest p = principal or the amount saved or invested r = rate of interest t = time In this problem you are asked to find the rate of interest given that Ruth has earned $250 in interest over 5 years. $750 - $500 = $250 I = $250 p = $500 r = what they want t = 5 years Substitute the information into the formula to get $250 = $500(r)5 and solve for r. $250 = $2,500r; r = 0.10 or 10%

George ships merchandise and sends boxes of product to a distribution center. Each box is in the shape of a rectangular prism and measures 4x12x20 and each unit of product is a 2 -foot cube. How many units fit in each box? A. 100 B. 150 C. 110 D. 120

D. 120 There not asking for surface area How many units fit in each box? = Division. Small box into the big box. In this case Volume of big box/Volume of 2-foot cube. Remember cube means all sides the same. (4x12x20)/(2x2x2) = 960/8 120

A scale on a map is 1 inch to 50 miles. On the map, two cities are 2 1/2 inches apart. What is the actual distance between the two cities? A. 75 mile B. 100 miles C. 225 miles D. 125 miles

D. 125 miles 1 inch = 50 2 = 100. 1/2 = 25 100+25 = 125

Mrs. D found a chandelier for the dining room for $1,400. However, since the model had been discontinued and the display had no factory packaging material, the store manager discounted the price to $1,150. What was the percentage of the reduction? A. 1.78% B. 13.0% C. 15.0% D. 17.9%

D. 17.9% 1,400 - 1,150 = $250 difference 1,400x = $250 25/140 = .1785 or 17.9%

A front Lawn measures 25 feet in length and 15 in width. The back lawn of the same house measures 50 feet in length and 30 in width. What is the ratio of the area of the front lawn to the area of the back lawn ? A. 1:2 B. 2:3 C. 3:4 D. 1:4

D. 1:4 1) Find the area of each lawn 2) 25 feet x 15 feet = 375 square feet ( front) 3) 50 feet x 30 feet = 1500 square feet ( front) 4) To find the ratio divide one area by the other 5) 375/1500 = 1/4 which is D.

If 1/2 cup of spinach contains 80 calories and the same amount of peas contains 300 calories, how many cups of spinach have the same caloric content as a 2/3 cup of peas? A. 2/5 B. 1 (1/3) C. 2 D. 2 (1/2)

D. 2 (1/2) 1/2 cup of spinach = 80 calories 1 cup of spinach = 160 calories 1/2 cup of peas = 300 calories 1 cup of peas = 600 calories Take 2/3 of 600 = 400 2/3 cup of peas = 400 calories Now lets see how many cups of spinach go into the cups of peas 400 ÷ 160 = 2.5 or D. 2 (1/2)

One phone plan charges a $20 monthly fee and 8¢ per minute on every phone call made. Another phone plan charges a $12 monthly fee and 12¢ per minute for each call. After how many minutes would the charge be the same for both plans? A. 60 minutes B. 90 minutes C. 120 minutes D. 200 minutes

D. 200 minutes First plan = 20 +0.08m Second plan = 12 +0.12m Let one plan equal the other 20 +0.08m = 12 +0.12m - solve for m 8 = 0.04m m = 200

From 1980 through 1990, the population of country X increased by 100%. From 1990 to 2000, the population increased by 50%. What was the combined increase for the period 1980-2000? A. 150% B. 166 (2/3)% C. 175% D. 200%

D. 200% X = Population of the country 1) 1980 through 1990, 100% increase essentially its doubled X→2x 2) 1990 to 2000, 50% increase. So if 2x is 100% half of that would just be another X X→2x→3x It took a 2x increase for X to get to 3x in other words 200% to get to 3x. Which is D.

An employee has of his 2/9 salary withheld for income tax. The percent of his salary that is withheld is most nearly A. 16%. B. 18%. C. 20%. D. 22%.

D. 22%. Simply divide 2/9 = .222 or 22%

In 1968 the population of the Chicago metropolitan area was 8,435,978. In 1998, the population was 10,544,972. By about what percent did the population increase in 30 years? A. 13% B. 18% C. 21% D. 25%

D. 25% 10,544,972 - 8,435,978 = 2,108,994 2,108,994/8,435,978 = 0.2499 or 25%

A regional waste disposal expediter company wants to calculate a price to charge for their new super-duper dumpster. In order to do that, the operations manager needs to calculate the volume of the new container. What is the volume of the container if it is 23 feet long, 15 feet wide, and 11 feet high? A. 2,530 square feet B. 3,450 cubic feet C. 3,795 square feet D. 3,795 cubic feet

D. 3,795 cubic feet Volume = L x W x H 23ft x 15ft x 11ft = 3,795 cubic feet

A women budgets her income so that she spends 1/4 of it for rent and 2/5 of the remainder for food. What part of the total income does she budget for food? A. 1/10 B. 1/5 C. 3/20 D. 3/10

D. 3/10 She spends 1/4 for rent which means we have 3/4 left. We are only taking into account the 3/4 of the total since 1/4 of it is going to rent. She uses 2/5 for food so take 3/4 from the 2/5 and this will be the part of the total income she budgets for food. 2/5 x 3/4 = 6/20 or 3/10

Mr. Green drove for 12 hours at a speed of 55 miles per hour. If his car covered 22 miles for each gallon of gas used, How many gallons of gas did he use? A. 32 gallon B. 34 gallons C. 36 gallons D. 30 gallons

D. 30 gallons 55 x 12 = 660 miles 660/22 = 30 gallons used.

Find the perimeter of the follow figure 5in _________________ I I I I x 8 in 6in I I_________________ I I 2in I_________________________________ I x A. 21 inches B. 25 inches C. 33 inches D. 38 inches

D. 38 inches As you may notice perimeter we add all the sides. We are missing 2 sides. Look at the shape going clockwise. One side next to the 5, another bottom of the shape. What we know The first x looks like half of the 6in side. So we'll set it as 3 The second x looks like a combination of the 5inch and 8 inch side. So 13 5 + 3 + 8 + 2 + 13 + 6 = 37 inches. Only answer close is D.

The area of one circle is four times larger than the area of a smaller circle with a radius of 2 inches. The radius of the larger circle is A. 12 inches B. 9 inches C. 8 inches D. 4 inches

D. 4 inches Let x = the radius of the larger circle. Then, πr² = 4 (π x 2²) πx² = 16π x² = 16 x = 4 or -4

If 8 workers are needed to run 4 machines, how many workers are needed to run 20 machines? A. 16 B. 32 C. 36 D. 40

D. 40 For this since their asking for the number of workers. You can solve using x. 8/4 = x/20 - solve for x 20x8 = 160 160/4 = 40

A baker made 20 pies. A Boy Scout troop buys one-fourth of his pies, a preschool teacher buys one-third of his pies, and a caterer buys one-sixth of his pies. How many pies does the baker have left? A. 3/4 B. 15 C. 12 D. 5

D. 5 One person buys 1/4 of pies Another buys 1/3 of pies another buys 1/6 of the pies 1) 1/4+1/3+1/6- find common denominator 12 is common denominator so lets change the fractions 3/12 + 4/12 + 2/12 = 9/12 - reduce to 3/4 or 75% 2) Now take 75% of 20. 75/100 x 20/1 -reduce 75/5 x 1/1 75/5 = 15 pieces Now we take 15 from 20 and that is how much is left which will be 5.

The total length of fencing needed to enclose a rectangular area 46 feet by 34 feet is A. 26 yards, 1 foot. B. 26 (2/3) yards. C. 52 yards, 2 feet. D. 53 (1/3) yards.

D. 53 (1/3) yards. The question is asking for the perimeter in yards. Perimeter = 2l + 2w 2 (46) + 2 ( 34) = 92 + 68 = 160 ft 3 ft = 1 yard 160/3 = 53 (1/3) yards

A square measures 9 feet on a side. If each side of the square is increased by 3 feet , how many square feet are added to the area? A. 144 square feet B. 81 square feet C. 60 square feet D. 63 square feet

D. 63 square feet 1) Multiply one side of a square by itself to find the area. 2) Thus 9 feet x 9 feet = 81 square ft ^2 3) By adding 3 feet to each side of the 9-foot square, you produce a 12-foot square. 4) Thus 12 feet x 12 feet = 144 ft^2 5) Find the difference between the areas of the two squares. 6) 144 - 81 = 63 square feet which is D.

Find the numerical value of 1+5xy²-3x²y if x =3 and y =2 A. 25 B. 18 C. 739 D. 7

D. 7 Remember PEMDAS

A farmer uses 2 gallons of insecticide concentrate to spray each 1/4 acre of his land. How many gallons of the concentrate will he need to spray 10 (1/2) acres? A. 80 B. 80 1/4 C. 82 D. 84

D. 84 2 gallons = 1/4 4 gallons = 2/4 or 1/2 6 gallons =3/4 8 gallons will cover 1 whole acre. 10 acres = 8 x 10 = 80 gallons. 1/2 = 4 80+4 = 84

A women has $5,000 invested at 8 percent annual interest. At what rate must she invest an additional $10,000 so that her annual income from both investments is equivalent to 9 percent of her total investment? A. 10% B. 10.5% C. 9% D. 9.5%

D. 9.5% For 5,000 at 8% 5,000 x 0.08 = $400/ annual Now her total investment will be $15,000 since she is adding another $10,000 to the equation. She wants it at a 9% Thus, $15,000 x 0.09 = $1,350 Subtract the income from the first investment to find out how much income she must get from the second. $1,350 - $400 = $950 Divide the income, $950, by the investment, $10,000 to find the rate of interest. $950 / $10,000 = 0.095 or 9.5%

Logan is making a picture frame for a photo of his family. The photo is 8 inches by 10 inches. If the wood for the frame costs 50 cents an inch, how much will the wood for the frame cost? A. $9.00 B. $12.00 C. $15.00 D. $18.00

D. To answer this question, you need to know the perimeter of the frame. For a rectangle, the perimeter is 2l + 2w. If w = 8 and l = 10, then the perimeter = 2(8) + 2(10) = 36 inches. At $0.50 per inch, multiply 36 × $0.50 to get the price of the wood. 36 × $0.50 = $18.00

Mrs. Jacobs is making a large circular rug with a radius of 10 feet. Every square foot of material used to make the rug costs her $0.50. Approximately how much will the material for the entire rug cost? (A) $157 (B) $167 (C) $628 (D) $314

(A) $157 Area of a circle is A = πr² The radius is 10 3.14 (10)² Move decimal to the right 2 times 314 ft² 0.50 (314) = $157

A carpenter needs to cut four sections, each 3 feet, 8 inches long, from a piece of molding. If the board is only sold by the foot, what's the shortest length of board the carpenter can buy? (A) 15 feet (B) 14 feet (C) 16 feet (D) 12 feet

(A) 15 feet Give a foot to the 8 to make this easier 1 ft = 12 inches 2 feet, 20 inches Multiply by 4 each 2x4 = 8 feet. 20 inches x 4 = 80 inches 80inch/12 = 6.6 feet 8+6.6 = 14.6 feet. We need 15 feet the smallest cut to fill this requirement.

Amy wants to fence in a yard using 400 feet of fencing. If she wants the yard to be 30 feet wide, what will its length be? (A) 170 feet (B) 175 feet (C) 180 feet (D) 185 feet

(A) 170 feet 2L +2W = 400 They give us the Width 2L + 2(30) = 400 2l + 60 = 400 2L = 340 L = 170

Karl is driving in Austria, where the speed limit is posted in kilometers per hour. The car's speedometer shows that he's traveling at a rate of 75 kilometers per hour. Karl knows that a kilometer is about 5/8 of a mile. Approximately how many miles per hour is Karl traveling? (A) 47 (B) 120 (C) 50 (D) 53

(A) 47 75 x 5/8 = 375/8 = 46.8 or 47 miles per hour

Angela has 15 coins (quarters and dimes) in the cash register. The total value of the quarters and dimes is $2.55. How many dimes are in the cash register? (A) 8 dimes (B) 7 dimes (C) 3 dimes (D) 10 dimes

(A) 8 dimes Let q equal the number of quarters and d equal the number of dimes. The value of the quarters is 25q, and the value of the dimes is 10d. So the value of dimes and quarters is 25q + 10d = 255 You also know that the total number of coins is 15, so q + d = 15. You can rearrange this equation to isolate q: q = 15 - d. Now you can substitute that for the q in the first equation and solve for d: 25 (15-d) + 10d = 255 375 - 25d +10d = 255 375 - 15d = 255 -15d = -120 d = 8

A pair of farmers sold 3 pints of strawberries for $1.98 each, 5 pints of raspberries for $2.49 each, and a bushel of peaches for $5.50 at their roadside stand. How much money did the farmers make? (A) $9.97 (B) $23.89 (C) $18.39 (D) $18.91

(B) $23.89 1) Multiply 3 pints of strawberries at $1.98 3 x $1.98 = $5.94 2) 5 pints of raspberries at $2.49 5 x 2.49 = $12.45 3) 1 bushel of peaches 1 x 5.50 = $5.50 4) Add the products $5.94 + $12.45 + $5.50 = $23.89

A student buys a science textbook for $18.00, a math textbook for $14.50, and a dictionary for $9.95. What's the total cost of the books? (A) $27.95 (B) $42.45 (C) $41.95 (D) $38.50

(B) $42.45 Just add all of them.

Your car uses gasoline at the rate of 21 miles per gallon. If gasoline costs $2.82 per gallon and you drive for 7 hours at a speed of 48 miles per hour, how much will you pay for gasoline for the trip? (A) $38.18 (B) $45.12 (C) $47.73 (D) $59.27

(B) $45.12 48 mph x 7 hrs = 336 miles 336 miles/21 miles = 16 gallons 2.82 x 16 = (B) $45.12

Delia has been walking at a constant speed of 2.5 miles per hour for 12 minutes. How many miles has she walked? (A) 0.2 mile (B) 0.5 mile (C) 2 miles (D) 4.8 miles

(B) 0.5 mile Convert the minutes to hours by dividing 12 by 60: 12 ÷ 60 = 0.2 hours. Use the distance formula, d=rt, to find the distance in miles that she walked: d = 2.5 (0.2) = 0.5 mile.

Jim can repair a heating unit in 2 hours. Kyle can repair the same unit in 3 hours. How long will they take to repair the unit if they work together? (A) 1 hour and 10 minutes (B) 1 hour and 12 minutes (C) 48 minutes (D) 50 minutes

(B) 1 hour and 12 minutes 1/2 + 1/3 = 1/t 5/6 = 1/t 6/5 = t Now we need to know how long it will take to repair the unit. 6/5 is 1 (1/5) We know it will take an hour so we've got A and B as choices. What is 1/5 of an hour 60x 1/5 = 12 minutes So its 1 hour and 12 minutes

A bag has 8 pennies, 5 dimes, and 7 nickels. A coin is randomly chosen from the bag. What is the probability that the coin chosen is a dime? (A) 1/20 (B) 1/4 (C) 1/3 (D) 3/10

(B) 1/4 The probability of randomly selecting a dime is equal to the number of dimes in the bag, 5, divided by the total number of coins in the bag, 20: 5 ÷20 =1/4

Pam cuts a pie in half in a straight line. She then cuts a line from the center to the edge, creating a 55-degree angle. What's the supplement of that angle? (A) 55 degrees (B) 125 degrees (C) 70 degrees (D) 35 degrees

(B) 125 degrees She cuts the pie in half. Half of 360 is 180. We are only talking about that one piece. When the sum of two angles is 180 degrees, the angles are said to be supplementary to each other. To find the supplement, subtract 55 from 180: 180-55 = 125.

Debbie receives a weekly salary of $80, plus a 5% commission on any sales. During the week, she has $800 in total sales. What's the ratio of her commission to her salary? (A) 2:1 (B) 1:2 (C) 3:1 (D) 1:3

(B) 1:2 Her commission for the week was $40 (because 0.05 x 800 = 40). The ratio of her commission to her salary is 40:80, which can be reduced to 1:2

Daniel is driving to an event that starts at a certain time. He knows that if he drives at 70 mph, he will arrive 1 hour early to the event. However, if he drives at 55 MPH, he will arrive 2 hours late. How long is it until the event is set to start? A. 12 hours B. 15 hours C. 11 hours D. 10 hours

When you see time and rate. You know it will be a distance rate problem. D = R x T D = distance to the event T = time until event starts R = mph If he drives at 70 mph he will arrive 1 hour early. 1) D = 70 (T-1) - its -1 because he is arriving 1 hour early before the event starts. 2) D = 55 (T+2) - its +2 because he is arriving 2 hours late. 3) Create a probability and solve for T. 70 (T-1) = 55 (T+2) 4) 70t - 70 = 55t +110 add 70 both sides. subtract 55 t both sides 15t = 180 t = 180/15 = 12 hours

If one gallon of milk costs $3.84, what is the cost of three pints? A. $1.44 B. $2.82 C. $2.04 D. $1.96

A. $1.44 8 pints per gallon. Convert gallon to pints. 1) 8 pints = $3.84 2) get the cost of 1 pint. 3) 3.84/8 = 0.48 4) 3 pints so 3 x 0.48 = 1.44

The price of a radio is $31.29, which includes a 5% sales tax. What was the price of the radio before the tax was added? A. $29.80 B. $29.85 C. $29.90 D. $29.95

A. $29.80 Let x = price of radio before tax was added. x + .05x = $31.29 1.05x = 31.29 x = $29.80

What is the result of diving 0.675 by 0.9? A. 7.5 B. 0.075 C. 75 D. 0.75

D. 0.75

A rectangular deck is 6 meters long and 8 meters wide. What is the distance from one corner of the deck to the opposite corner? 8m I-----------I I I I ? I 6m I I I-----------I (A) 10 m (B) 12 m (C) 14 m (D) 15 m

(A) 10 m Think of a triangle within the square. a² + b² = c² 6² + 8² = c² 36+64 = c² 100 = c² c = 10 m

Which of these is an example of similar figures? A. a plane and a scale model of that plane B. a pen and a pencil C. a motorcycle and a car D. an equilateral triangle and a right triangle.

A. a plane and a scale model of that plane They must have the same shape. Only thing that is completely similar is A.

A rectangular auditorium contain x rows, with y seats in each row. What is the number of seats in the auditorium? A. xy B. x + y C. x - y D. y- x

A. xy To find the number of seats in the auditorium, multiply the number of rows (x) by the number of seats in each row (y). This is expressed as xy answer A.

Randy is training to cycle in a 15-kilometer race. His training program starts at cycling 5 kilometers per day for the first week and increases that amount by 20 percent each week. How many kilometers will he be cycling per day in the fourth week? A. 7.20 km B. 8.64 km C. 9.33 km D. 9.98 km

B. 8.64 km Compound interest. Every week he adds 20% of his previous distance. Week one 5km Week two 5km +20%(5) = 6km Week 3 6km + 20%(6) = 7.2 km Week 4 7.2km + 20%(7.2) = 8.64 km

Many American cars feature speedometers that show kilometers per hour. If you are required to drive 500 miles, and you know that one kilometer is approximately 5/8 of a mile, how many kilometers would you cover in that journey? A. 625 B. 800 C. 850 D. 1,000

B. 800 Miles → km = Divide by 5/8 km → miles = multiply by 5/8 500 ÷ 5/8 = 500x 8/5 = 800

If ab = 10 and a²+b² = 30, solve for y in the equation y = (a+b)². A. 40 B. 45 C. 50 D. 55

C. 50 Expanding the equation y = (a+ b)² results in after FOIL y= a²+ab+ab+b² ab = 10 a²+b² = 30 2(10)+30 = 50

If the circumference of a circle is divided by the length of its diameter, what is the result? A. 2 B. 27 C. π D. 7

C. π C/D = (Dxπ)/D c/d = π

After eating 25% of the jelly beans, Brett had 72 left. How many jelly beans did Brett have originally? A. 90 B. 94 C. 95 D. 96

D. 96 From the question, we have: Proportion eaten = 25% Amount left = 72 If Brett eats 25%, then it means that Brett has 75% left. Let the original amount of jelly bean be x. So, we have: 75% * x = 72 Rewrite as: 0.75 * x = 72 Divide both sides by 0.75 x = 96

Which of the following is a correct mathematical statement?

E: The correct mathematical statement is the one in which the number to the left on the number line is less than the number to the right on the number line. It is written in answer E that , which is the same as a correct statement.

David biked to the beach and back home on the same route. On the way there. David at a rate of 9 miles per hour and biked at a rate of 30 miles per hour on the way back. How long did the trip to the beach take if the return trip took 3 hours? A. 12 hours B. 10 hours C. 11 hours D. 14 hours

First know the question. We're looking for how long it took for the person to get to the beach. We know how long it took him to get back. Distance = rate x time (Way back) Distance = 30 mph x 3 hours = 90 miles Since he took the same route. This the same amount of miles on his way to the beach. We have distance now. 90 miles = 9 mph x time to the beack 90/9 = 10 hours to the beach.

Lisa is now on page 483 after being on page 99 last week in her new book. If Lisa read at an average pace of 48 pages per hour, then for how many hours did she read? A. 6 hours B. 11 hours C. 8 hours D. 14 hours

Now: 483 Was: 99 rate: 49 pages/hour We can use Y = mx+b Y= end x = how long it takes B = begin m = slope 1) 483 = 48x + 99 Subtract 100 to both sides and add 1. to 483. Easier than just subtracting 99. 384 = 48x 384/48 = 8 hours

Carpet stain protector costs $0.65 per square yard to apply. How much will it cost to apply the protector to a 16-foot-x-18-foot carpet? (A) $187.20 (B) $62.40 (C) $20.80 (D) $96.00

(C) $20.80 Area = 16 x 18 = 288 sq ft Because we are dealing with square feet the 3 ft in 1 yard will be squared as well so it will be 9 ft per yard in this scenario. 288 sq ft / 9 yds = 32 sq yards 32 x 0.65 = $20.8

A dog trainer is building a rectangular dog run that measures 9 by 16 feet. If they want to fence the perimeter of the run, how many feet of chain link fence will they need? (A) 144 feet (B) 25 feet (C) 32 feet (D) 50 feet

(D) 50 feet Calculate perimeter by adding the lengths of all four sides of a quadrilateral: 9 + 9 + 16 + 16 = 50 feet.

A waitress earns an average tip of 12% of the cost of the food she serves. If she serves $375 worth of food in one evening, how much money in tips will she earn on average? A. $37 B. $45 C. $42 D. $420

Answer : B. We just need to multiply the percentage to dollar amount of food served. 375 x 12% - Change percent to decimal 375 x .12 - move decimal twice to make whole and multiply 375 x 12 = 4500 - move back 2 Answer is 45 B.

A folding chair regularly sells for $29.50. How much money is saved if the chair is bought at a 20% discount? A. $4.80 B. $5.90 C. $6.20 D. $7.40

B. $5.90 $29.50 × 20% = $29.50 × 0.20 = $5.90 saved.

Max earns $7.50 per hour. If he works from 8:45 a.m until 5:15pm with one hour off for lunch, How much does he earn in one day? A. $58.50 B. $56.25 C. $55.00 D. $53.75

B. $56.25 When it comes to time just go up. 1) 8:45 to 4:45 is 8 hours 2) How much does 4:45 need to get to 5:00? 15 minutes 3) Now we need 15 more to get to 5:15. So 15+15 is 30. 8:45 a.m until 5:15pm - 8 hours and 30 minutes Or 8 1/2 4) We take an hour off due to lunch so its 7 1/2 hours Or 7.5 5) 7.5 x 7.50 = 56.25

If 5 shirts and 3 ties cost $52 and each tie costs $4, what is the cost of a shirt? A. $6 B. $8 C. $10 D. $7.50

B. $8 3 ties and they cost 4 each. 4x3 = $12 $52 - $12 = $40 5 shirts. $40 left. 30/5 = $8 each

A pint of milk is what part of half a gallon? A. 1/8 B. 1/4 C.1/2 D.1/16

B. 1/4 There are 8 pts. in 1 gal Which means there are 4 pts for every 1/2 gallon. Every pts in half a gallon is 1/4. So there is one pint (1/4) in half a gallon.

There are 124 certified nursing assistants and 36 registered nurses working at a hospital. What percentage of the workforce are registered nurses? A. 18.7% B. 22.5% C. 36.0% D. 41.3%

B. 22.5% 124+36 = 160 36/160 = 22.5%

A student finishes the first half of an exam in 2/3 the time it takes him to finish the second half. If the entire exam takes him an hour, how many minutes does he spend on the first of the exam? A. 20 B. 24 C. 27 D. 36

B. 24 Let x=time to finish 2nd half of the exam. It took him 2/3 of the time for the first half as it did for the 2nd half. Thus, 2/3x + x = 60 1) 2/3x + x = 2/3+1 = 5/3 2) 5/3x = 60 - solve for x 3) x = 36, now this is the second half of the exam. 4) Lets take 36 from 60 which will give us 24.

Kiki has been asked to decorate a square room with an area of 576 sq feet. What is the length of each side of the room? A. 17 feet B. 24 feet C. 26 feet D. 29 feet

B. 24 feet Area of square = A = S² For problems like this, the fastest way to find the correct answer is to multiply each answer choice by itself and see which produces 576 ft².

A circular balloon has a diameter of 18 inches. What is the volume? A. 114.24 in³ B. 3,052.08 in³ C. 5,624.10 in³ D. 8,416.34 in³

B. 3,052.08 in³ Balloon is a sphere. Area is 4/3πr³ radius = half the diameter Area is 4/3π(9)³ (4 x 3.14 x 729) / 3 12.56 x 729 = 9,156.24/3 = 3,052.08 in³

Phil bought two hamburgers and a milkshake for $10.30. Janice bought three hamburgers and a milkshake for $14.80. What is the cost of the two milkshake? A. $1.30 B. $1.45 C. $2.60 D. $4.50

C. $2.60 First look at Phills order = 2 burgers and a milkshake Janice is three burgers and a milkshake. If we subtract both we'll get the cost of one burger since the milkshakes and the 1 burger cancel out. So $14.80 minus $10.30 = $4.50. Which is the cost of 1 burger. Phil ordered 2 burgers so $4.50 x 2 = $9 If we subtract 9 from Phils total we will get the cost of 1 milkshake. $10.30-$9 = $1.30 for one milkshake. They want to know the cost of 2 milkshakes. 1.30 x 2 = C. $2.60

A stock clerk had 600 pads on hand. He then issued 3/8 of his supply of pads to Division X, 1/4 to Division Y, and 1/6 to Division Z. The number of pads remaining in stock is. A. 48 B. 240 C. 125 D. 475

C. 125 3/8 + 1/4 + 1/6 = 19/24 were issued Add numerators = 3+1+1 = 5 Means 5/24 are left. 5/24 x 600 = 125

It takes a race car 54 seconds to go around a racetrack. If the car makes 20 laps around the track, how many minutes did it take? A. 14 minutes B. 16 minutes C. 18 minutes D. 20 minutes

C. 18 minutes 54 sec x 20 = 1080 seconds 1080 seconds/ 60 sec = 18 minutes.

Two cars start in the same spot and drive away from each other in opposite directions. One car travels at a speed of 25 miles per hour and the other car travels at 35 miles per hour. How long will it be until the cars are 150 miles a part? Distance = rate x time A. 1.5 hours B. 2 hours C. 2.5 hours D. 3 hours

C. 2.5 hours Objects facing opposite directions going a certain rate. Add the rates. They are covering the ground together Distance = rate x time 150 = (25+35) × time 150=60x x = 2.5

If a boat is towed at the rate of 4 miles per hour, how much time will be needed to tow the boat 17 miles? A. 5 hours, 15 minutes B. 4 hours, 30 minutes C. 4 hours, 15 minutes D. 5 hours, 30 minutes

C. 4 hours, 15 minutes Distance = rate x time 17 miles = 4mph x time Solve for time time = 17/4 = 4 1/4 4 hours and 1/4 x 60 = 60/4 = 15 minutes 4 hours and 15 minutes

Bindee is having a barbeque on Sunday and needs 12 packets of ketchup for every 5 guests. If 60 guests are coming, how many packets of ketchup should she buy? a. 100 b. 12 c. 144 d. 60 e. 300

C: This problem involves ratios and percentages. If 12 packets are needed for every 5 people, this statement is equivalent to the ratio The unknown amount x is the number of ketchup packets needed for 60 people. The proportion 12/5 = x/60 must be solved. Cross-multiply to obtain 12 x 60 =5x Therefore, 720=5x. Divide each side by 5 to obtain x = 144 packets.

A parcel delivery service charges $9.26 for the first 4 pounds of package weight and an additional $1.06 for each half pound over 4 pounds. What is the charge for a package weighing 6 (1/2) pounds? A. $2.65 B. $6.89 C. $11.91 D. $14.56

D. $14.56 First 4 pounds is $9.26 We have 2 (1/2) left of the 6 (1/2) pounds. How many half pounds are in 2 (1/2)? 5 half pounds 1.06 x 5 = 5.30 $9.26 + 5.30 = $14.56

Jonathan gets a bonus check and goes to the haberdasher's outlet. He finds that five shirts and four ties cost $173 and each tie costs $12. What is the cost of one shirt? A. $15.00 B. $22.60 C. $19.22 D. $25.00

D. $25.00 Ties = $12 each 4 ties = 12 x 4 = $48 $173 - $48 = $125 We have 5 shirts Thus, $125/5 shirts = $25 for each shirt

Upon his death, a man's life insurance policies paid $750,000 to his wife and three children. The policies were set up to pay the wife and children in the ratio of 5:1:1:1. How much did the children receive altogether? A. $150,000 B. $200,000 C. $250,000 D. $281,250

D. $281,250 Let x equal one share share. 5x+1x+1x+1x = $750,000 8x = $750,000 = To make it easier just divide 75/8 x = 9.3 9.3 x 3 = 28.1 or D.

A night watchman must check a certain storage area every 45 minutes. If he first checks the area as he begins a 9-hour tour of duty, how many times will he have checked this storage area? A. 10 B. 11 C. 12 D. 13

D. 13 First convert 9 hours to minutes 60 x 9 = 540 minutes 540/45 = 12 times. Now since he checked it once before the 9 hour tour it will be 13 times.

A mapmaker is told to prepare a map with a scale of 1 inch to 40 miles. If actual distance between 2 points is 110 miles, how far apart should the mapmaker show them on the map? A. 7 inches B. 3 1/2 inches C. 2 1/2 inches D. 2 3/4 inches

D. 2 3/4 inches Just make this into a variable problem. 1 inch = 40 miles How many inches is 110 miles? 1/40 = x/110 - multiply 110 to both sides 1/40 x 110/1 - reduce by 10 1/4 x 11/1 = 11/4 or 2 3/4

The number of half-pound packages of tea that can be made up from a box that holds 10.25 lbs of tea is A. 5 B. 10 1/2 C. 20 D. 20 1/2

D. 20 1/2 10 1/4 ÷ 1/2 = 41/4 x 2/1 = 20 1/2 boxes

It takes 4 men 14 days to do a certain job. How long should it take 7 men working at the same rate to do the same job? A. 5 days B. 6 days C. 7 days D. 8 days

D. 8 days 4 men = 14 days 4 x 14 = 56 days per man Now that we have 7 men. 56 days / 7 men = 8 days.

A college student scored 74,97,88,83 and 86 on his physics tests during the course of the semester. His professor will drop the lowest test grade to compute each student's average for the semester. What is the student's final average in the class? A. 82.0% B. 85.6% C. 86.0% D. 88.5%

D. 88.5% 97+88+83+86 = 354 354/4 = 88.5%

Mr. Lee is high tech cutlery salesman. On a sales trip, he first drives for two hours at 70 miles per hour. He then drives for another one and half hours at 65 miles per hour. If his car gets 25 miles per gallon on the highway in this speed range, how many gallons of gas did he use for the trip? A. 5.4 gallons B. 8.2 gallons C. 8.4 gallons D. 9.5 gallons

D. 9.5 gallons 70mph x 2 hrs = 140 miles 65 x 1.5 = 97.5 miles 140 +97.5 = 237.5 miles Round up and divide. 238/25 = 9.5

What is the result of dividing 24 by 8/5 ?

D: Division is completed by multiplying by the reciprocal. Therefore: 24 divided 8/5 = 24/1 x 5/8 (3x8)/1 x 5/8 = 15/1 = 15

A rectangle has a perimeter of 36 inches. Its length is 3 inches greater than twice the width. What's the rectangle's length? (A) 5 inches (B) 13 inches (C) 18 inches (D) 20 inches

(B) 13 inches Length = 3 + 2w P = 2L + 2W Solve for W first 36 = 2 (3+2w) + 2w 36 = 6 + 4w + 2w 30 = 6w w = 5 3 + 2(5) = 13

A recruiter travels 1,100 miles during a 40-hour workweek. If they 2/5 of their time traveling, how many hours do they spend traveling? (A) 22 (B) 5 (1/2) (C) 16 (D) 8

(C) 16 Don't let the number of miles traveled confuse you. You don't use them to solve the problem. Finding 2/5 of a 40-hour workweek is the same thing as multiplying 40 times 2, which is 80, and then dividing 80 by 5, which equals 16 hours the recruiter travels week.

The price of daily admission at an amusement park is $36. The park sells an unlimited season pass for $240. How many trips would you need to make with the season pass in order for it to cost less than paying the daily admission rate? (A) 6 (B) 7 (C) 8 (D) 9

36 x 6 = $216 To low. 36 x 7 = $252 over the season pass cost so that means that it would take 7 trips for the Season pass to be worth getting instead of buying the daily admission.

Every day, Bert spends totally an hour commuting to and from his office, driving at an average speed of 50 mph and taking the same route each way. How far does Bert live from his office? A. 25 miles B. 50 miles C. 30 miles D. .5 miles

A. 25 miles

Two cars start at the same place and drive in the same direction. One car travels at an average speed 50 miles per hour while the other car travels at 40 miles per hour. How far a part will the cars be after 7 hours? A. 70 miles B. 280 miles C. 350 miles D. 630 miles

A. 70 miles Distance = rate x time Same direction going at the same time means we are subtracting the rates. Distance = (50-40) x 7 Distance = 70 miles

You measure the distance around a hula hoop and observe that it is 25.12 feet. What is the diameter of the hula hoop? A. 8 feet B. 2 feet C. 50.24 D. 4 feet

A. 8 feet "Distance around the hula hoop" = circumference Circumference of a circle = π x Diameter (What we need) 25.12 = π x d - Solve for D 25.12/3.14 = 8 feet

What is the product of and 5/14 and 7/20?

A: A product is found by multiplication. Multiplying two fractions together is easier when common factors are cancelled first to avoid working with larger numbers. 5/14 x 7/20 = 5/2x7 x 7/5x4 1/2 x 1/4 = 1/8

What is the cost of 5 feet, 3 inches of plastic material that sells for $8.00 per foot? A. $4.00 B. $42.00 C. $23.00 D. $21.12

B. $42.00 Each foot is 8 dollars. There are 5 feet so we know its more than 40. Only option is B.

What is the value of this expression? (0.05 x 4)/0.1 A. 20 B. 2 C. 0.2 D. 0.02

B. 2 1) 0.05 x 4 =0.20 2) 0.20/.1 is the same as saying 2/1 3) 2/1 is just 2 answer B.

The perimeter of a square is 13 feet, 8 inches. What is the length of one side of the square? A. 3feet, 2 inches B. 3 feet, 5 inches C. 3 feet, 3 inches D. 3 feet, 6 inches

B. 3 feet, 5 inches Since its a square we need to divide 13 feet, 8 inches by 4. Since 4 can't go into 13, lets give a foot to the 8 inches. 1 foot = 12 inches 8+12 = 20 inches. 12 feet, and 20 inches divided by 4 3 feet and 5 inches for each side of the square.

Find the numerical value of 5a²b - 3ab² if a =7 and b = 4 A. 846 B. 644 C. 488 D. 224

B. 644

At the arcade, Nick spent 203 tokens on video games in seven days. Each day he spent five more tokens than the previous day. How many tokens did Nick spend on the third day at the arcade? A. 20 B. 29 C. 24 D. 104

C. 24 Suppose nick spent x number of tokens on day 1 So he spent x + 5 on day 2 He spent x + 10 on day 3 He spent x + 15 on day 4 He spent x + 20 on day 5 On day 6 he spent x + 25 And on day 7 he spent x + 30 So in all he spent x + (x + 5) + (x + 10) + (x + 15) + (x + 20) + (x + 25) + (x + 30) = 203 Simplifying the equation: 7x + 105 = 203 7x = 203 - 105 7x = 98 x = 98 / 7 x = 14 Now we sub 14 back into the third day. x + 10 = 14+10 = 24 tokens.

The toll on the Island Bridge is $1 for car and driver and 75¢ for each additional passenger. How many people were riding in a car for which the toll was $3.25? A. 1 B. 2 C. 3 D. 4

C. 3 Basic toll = $1 $3.25 - $1 = $2.25 for extra passengers $2.25 ÷ .75 = 3, Since we only want to know about the people riding and not the driver it will just be 3 and not 4.

A plane left New York at 3:30 p.m. EST and arrived in Los Angeles at 4:15 p.m. PST. How long did the flight take? A. 7 hours, 15 minutes B. 6 hours, 45 minutes C. 3 hours, 45 minutes D. 3 hours, 15 minutes

C. 3 hours, 45 minutes This question deals with time difference. Time difference between New York and Los Angeles is 3 hours 3:30pm - 4:15pm - 45 minutes. So it will be 3 hours, and 45 minutes.

Five girls each ate 3 cookies from a box containing 2 dozen. What part of a dozen was left? A.1/8 B. 5/8 C. 3/4 D. 8/8

C. 3/4 2 dozen = 24 5 girls each eat 3 = 5x3 = 15 cookies 24 - 15 = 9 cookies left 9 = 3/4s of a dozen Because (12 x 3)/4 = 9

Shaniqua spent 2 (1/7) hours on her homework Monday night. On Tuesday night, she spent only 1 (9/14) hours on her homework. How much less time did Shaniqua spend on her Tuesday homework than on her Monday homework? A. 10 minutes B. 20 minutes C. 30 minutes D. 40 minutes

C. 30 minutes Make the mixed fractions into improper fractions 2 (1/7) = 15/7 1 (9/14) = 23/14 15/7-23/14 - find same denominator which is 14 in this case. 30/14-23/14 = 7/14 1/2 1/2 of an hour is 30 minutes.

Felipe can run 25 laps in 34 minutes. At this rate, approximately how long will it take him to run 30 laps? A. 37 minutes B. 39 minutes C. 41 minutes D. 43 minutes

C. 41 minutes You keep everything same level. Do not change the position of the proportion 25 laps / 34 minutes = 30 laps/ x minutes Cross multiply 25x = 1,020 x = 1,020/25 = 40.8 or 41

While home one weekend from college, Jonathan spent 4 hours studying, 1 hour playing with the dogs, 30 minutes doing his laundry, and 2 hours watching TV. What percentage of his time was spent studying? A. 46.6 % B. 50.0% C. 53.3% D. 57.1%

C. 53.3% Total hours = 7 hours, 30 minutes. Or 7.5 hours total. 4 hours studying/ 7.5 = 0.533 or 53.3%

Newly hired nurses have to buy duty shoes at the full price of 84.50, but nurses who have served at least a year get a 15% discount. Nurses who have served at least three years get an additional 10% off the discounted price. How much does a nurse who has served at least three years have to pay for shoes? A. $63.78 B. $64.65 C. $71.83 D. $72.05

First we get 15% from the 84.50 and then get the 10% off of that. Important: DO NOT mix the percentages thinking it will work. Percentages off does not work this way. First Lets split 15% into 2 parts Taking 10% of something makes the decimal place move over to the left. So 10% x 84.50 is 8.45 5% means cutting it in half 8.45 x 5% = 4.23 cents Now we add them both 8.45 +4.23 = 12.68 Now lets subtract 84.50 by 12.68 84.50-12.68 = 71.82 - this is the 15% discount. Now we need to take 10% off of 71.82. Well we know 10% means move the decimal to the left once 71.82 x 10% = 7.18 Now lets take 7.18 from 71.82 71.82 -7.18 = 64.65 which is answer B

Basic cable television service, which includes 16 channels, costs $15 a month. The initial labor fee to install the service is $25. A $65 deposit is required but will be refunded within two years if the customer's bills are paid in full. Other cable services may be added to the basic service: the movie channel service is $9.40 a month; the news channels are $7.50 a month; the arts channels are $5 a month; the sports channels are $4.80 a month. A customer's first bill after having cable television installed totaled $112.50. This customer chose basic cable and one additional cable service. Which additional service was chosen? a. the news channels b. the movie channels c. the arts channels d. the sports channels e. none of the above

First we know a $65 dollar deposit is required at the start so we can take 65 from 112.50 and go from there. 112.50 - 65 = 47.5 Install service is 25 dollars so lets take that from the 47.5 47.5-25= 22.5 Basic cable is 15 so we can take that as well 22.5-15= 7.50 Only channel that fits that bill is the news channel which is exactly 7.50 so A is the answer.

14% of your monthly income goes towards your car payment and 32% goes toward savings. If $420 goes toward your car payment, then how much goes toward savings? A. $971 B. $362 C. $420 D. $960

This is a proportion problem What we know 14% of the income goes to car payment. They say $420 is going to car payment so 14% = $420 They want the savings in which 32% of the income goes towards. Set up the problem. x/32 = 420/14 420/14 = 30 x/32 = 30 - multiply 32 both sides 30 x 32 = 960

A grocery store sold 48 bags of apples in one day, and 9 of the bags contained Granny Smith apples. The rest contained Red Delicious apples. What is the ratio of bags of Granny Smith to bags of Red Delicious that were sold? a. 48:9 b. 39:9 c. 9:48 d. 9:39 e. 39:48

D: There were 48 total bags of apples sold. If 9 bags were Granny Smith and the rest were Red Delicious, then 48 - 9 = 39 bags were Red Delicious. Therefore, the ratio of Granny Smith to Red Delicious is 9:39.

The Ice Cream Manufacturers Association is conducting a survey of favorite ice cream flavors. The results so far are as follow: Flavor Number of Persons Chocolate 602 Rocky Road 411 Vanilla 589 Strawberry 214 Peach 78 Pistachio 514 If these numbers are representative, what is the probability that the next randomly selected person will say that their favorite flavor is chocolate? A. 1/4 B. 1/3 C. 4/5 D. 6/7

A. 1/4 This is the same question like the ones for Jellybeans. Add everything and divide what they want (Chocolate) to the whole. 602 + 411 + 589 + 214 + 78 + 514 = 2,408 surveyors. 602 like chocolate. 602/2408 - reduce by 602. First try with what they give you when it is very large like this. 1/4

What is the greatest number of half-pint bottles that can be filled from a 10-gallon can of milk? A. 160 B. 170 C. 16 D. 17

A. 160 8 pints = 1 gallon 80 pints = 10 gallons Half meaning double 160 half pints = 10 gallons

Devin throws a football 7 (1/3) yards. Carl throws it 4 (1/2) yards. How much farther did Devin's throw travel than Carl's? A. 2 (5/6) yards B. 3 (1/6) yards C. 11(5/6)yards D. 28 (1/6) yards

A. 2 (5/6) yards Convert mixed fracitons into improper fractions 7 (1/3) = 22/3 4 (1/2) = 9/2 22/3 -9/2 44/6 - 27/6 17/6 or 2 (5/6)

What is the value of (0.02 x3)/0.001 A. 60 B. 6 C. 0.6 D. 0.06

A. 60 Remember PEMDAS Do multiplication first then divide 0.02 x 3 = 0.06 0.06/0.001 = 60/1 = 60

Miriam bought five cases of motor oil on sale. A case of motor oil normally costs $24.00, but she was able to purchase the oil for $22.50 a case. How much money did Miriam save on her entire purchase? (a) $7.50 (b) $1.50 (c) $8.00 (d) $22.50

Answer A. 1) 24.00 - 22.50 = 1.50 - this is how much she saves per case. 2) Now we multiply 1.50 x 5 which will be 7.50. We multiply by 5 as its the amount of cases she bought total.

Of the 80 employees working on the road construction crew, 35% worked overtime this week. How many employees did not work overtime. A. 28 B. 45 C. 52 D. 56

Answer C. Now we know 35% worked overtime. Well 35% of 100% is 65%. So if 65% of the workers did not work overtime we just need to find the percent of that from 80. So .65 x 80= 52.00 which is C.

In the freshman class, the ratio of in-state students to out-of-state students is 15 to 2. If there are 750 in-state students in the class, how many out-of-state students are there? A. 100 B. 112 C. 130 D. 260

Answer: A First we know ratios so when they say 15 to 2 we know they mean 15/2 So we can look at this problem with a missing variable. 15/2 = 750/x - cross multiply 15x = 1500 - solve for x divide 15 both sides x = 100 which is answer A.

Body max index (BMI) is equal to weight in kilograms/(height in meters)^2. A man who weighs 64.8 kilograms has a BMI of 20. How tall is he? A. 1.8 meters B. 0.9 meters C. 2.16 meters D. 3.24 meters

Answer: A We know the weight = 64.8 We know the BMI which is 20 Lets plug it into the formula 64.8/x^2 = 20 - Solve for x Now lets first get rid of the fraction. We can multiply x^2 both sides 64.8 = 20x^2 Divide both sides by 20 64.8/20 = 3.24 3.24 = x^2 - Square root each side to get rid of the square x = √3.24 Now we must know what squared will give us 3.24. Well we know 0.9 is too low and 2.16 is too high. 3.24 is a trick to fool us since we got 3.24. The answer must be 1.8.

An outdoor swimming pool at the Shulkind residence can be filled with water from the garden hose at a rate of three and a half inches per hour. If the Shulkinds want to fill the empty pool with 49 inches of water, how many hours will it take to get to this level? A. 3.5 hours B. 5.25 hours C. 14 hours D. 16.3 hours

Answer: C So we know the hose goes at 3.5inches/hour. We need to get to 49. We simply divide 49 by 3.5 49/3.5 - remember we need to make the 3.5 whole. What we do the the left we do to the right. 490/35 = 14 which is answer C.

Maya is using written instructions to create an airplane made out of thin balsa wood. Her instructions are drawn to scale so that every 1/8 inch in the drawing represents 1 (1/2) inches of balsa wood. How tall will the tail of the airplane be if it is 2 (3/4) inches tall in the drawing? A. 12 inches B. 22 inches C. 26 inches D. 33 inches

Answer: D We know that 1/8 inch in the drawing represents 1 (1/2) inches of balsa wood. The drawing is 2 (3/4) so that means we need to first divide the 2 (3/4) by 1/8 to see how many units we have . 2(3/4) ÷ 1/8 - remember dividing by a fraction means multiply by its reciprocal. 2 (3/4) x 8/1 = Make the 2 (3/4) into an improper fraction. 11/4 x 8/1 = 22 units. Now we can multiply the 22 by the 1 (1/2) 1 (1/2) x 22 - make improper 3/2 x 22/1 = 33 which is answer D.

Finer Fabric International sells a total of $880,600.00 in fabrics during the course of the year. If 32% of the company's sales went to pay for labor to make those fabrics how much money did Finer Fabric International spend on this labor? A. $27,518.75 B. $32,000.00 C. $275,600.00 D. $281,792.00

Answer: D We need to get 32% of the sells total. An easier way of doing this instead of multiplying the whole total by .32 is by splitting the .32 into 2 parts and then adding those totals together. .3 x 880600 .02 x 880600 Now instead of multiplying everything we'll just focus on the 88 of the total since all the choices are different. .3 x 88 = 264 move back 1 = 26.4 .02 x 88 = 176 move back 2 = 1.76 26.4+1.76 = 281 which is D the closest answer.

A typist uses lengthwise a sheet of paper 9 inches by 12 inches. She leaves a 1-inch margin on each side and a 1 (1/2) inch margin on top and bottom. What fractional part of the page is used for typing? A. 21/22 B. 7/12 C. 5/9 D. 3/4

B. 7/12 First recognize the question. We need to know the fraction of what is being used after we remove margins from the original piece. First get the area of the original 9 inch x 12 inch = 108 inch² Now lets remove the margins and put that new area over the original. At the start we have a 9 inches by 12 inches sheet of paper. 1) She removes 1 inch on each side. Length. So 2 inches since there are two. 9-2 = 7 inches 2) She then removes 1 (1/2) inch margin top and bottom. Width. 2 as well 1 (1/2) x 2 = 3/2 x 2 = 3 She removes 3 from the width. 12 - 3 = 9 inches 7 inches by 9 inches is what is used. 7 x 9 = 63 inch² Now we get the fraction form the original. 63 inch²/108 inch² = reduce by 9. 7/12 is what is being used for typing.

A piece of wood 35 feet 6 inches long was used to make 4 shelves of equal length. The length of each shelf was A. 9 feet, 1 (1/2) inches. B. 8 feet, 10 (1/2) inches. C. 7 feet, 10 1/2 inches. D. 7 feet, 1 (1/2) inches.

B. 8 feet, 10 (1/2) inches. There asking how many shelves can fit in 35feet and 6 inches. To make this easier lets convert 35 ft to inches 35 x 12 = 420 inches + 6 inches 426 inches Now lets divide that by the number of shelves which is 4 426/4 = 106.5 inches. Now lets divide that by 12 to get the feet. 106.5/12 = 8.8 Closest answer is B.

What is 12/60 converted to a percentage? a. 0.20 b. 20% c. 25% d. 12% e. 1.2%

The fraction 12/60 can be reduced to 1/5 , in lowest terms. First, it must be converted to a decimal. Dividing 1 by 5 results in 0.2. Then, to convert to a percentage, move the decimal point two units to the right and add the percentage symbol. The result is 20%.

A soup can is 6 inches high with a diameter of 4 inches. How much soup can it hold? A. 44.6 in.³ B. 57.2 in.³ C. 75.4 in.³ D. 81.3 in.³

There asking for volume of a cylinder. V = πr²h Radius = half the diameter Radius = 4/2 = 2 V = (3.14)(2²)(6) = (3.14)(4)(6) = 75.36 or 75.4 in.3

Terry earns three times more per hour than Tim. Tim earns $2 more per hour than Angie. As a group, they earn $43 per hour. What's Angie's hourly wage? (A) $7.00 (B) $8.00 (C) $9.00 (D) $10.00

(A) $7.00 Let x equal Angie's hourly wage; x +2 would then represent Tim's hourly wage, and 3( x+ 2) would represent Terry's hourly wage. Set up your equation and solve for x: x + (x+2) + 3 (x+2) = 43 x + x+ 2 + 3x +6 = 43 5x+8 = 43 5x = 35 x = 7

How many pounds of nails costing $7 per pound must be mixed with 6 pounds of nails costing $3 per pound to yield a mixture costing $4 per pound? (A) 2 pounds (B) 2.5 pounds (C) 3 pounds (D) 3.5 pounds

(A) 2 pounds Let x = the weight of nails costing $7 per pound. The total cost of the mixture (M) equals the sum of the cost for each type of nail, or M = A +B, where A = 7x , B = 3 (6) , and M = 4 (6+x) . Substitute the known values into the equation and solve for x: 4 (6+x) = 7x +18 24 +4x = 7x +18 24-18 = 7x - 4x 6 =3x x = 2

An office building has 30 employees and provides 42 square feet of work space per employee. If five more employees are hired, how much less work space will each employee have? (A) 6 square feet (B) 7 square feet (C) 7.5 square feet (D) 36 square feet

(A) 6 square feet 42 x 30 employees = 1,260 square feet of space. With 35 employees 1,260 space/35 employees = 36 sq feet of space for each 42 ft original -36 ft final = 6 feet less than the original.

David is at a car dealership trying to decide between buying a truck or a sedan. The truck is available in three colors, and the sedan is available in four colors. Each vehicle also has both a 2-wheel-drive and a 4-wheel-drive option in all available colors. How many different choices does he have? (A) 48 (B) 14 (C) 12 (D) 6

(B) 14 Truck comes in 3 colors Sedan comes in 4 colors They both have an option for 2WD or 4WD So that means there are 2 types with color options Trucks = 2 x 3 = 6 options Sedans = 2 x 4 = 8 options 8 + 6 = 14

Three apples and twice as many pears add up to one-half the number of grapes in a fruit basket. How many grapes are in the basket? (A) 8 (B) 18 (C) 28 (D) 38

(B) 18 3 (apples) + 6 (pears) = 1/2x Solve for x 9 = 1/2x 9 x 2 = x 18 = x

Kelly used to pay $500 a month for rent. Now she pays $525 a month for rent. By what percent did her rent increase? (A) 0.5 percent (B) 5 percent (C) 10 percent (D) 12.5 percent

(B) 5 percent The percent increase is the amount of increase, $25, divided by the original amount, $500: 25 ÷ 500 = 0.05. Convert 0.05 to a percent by multiplying 0.05 by 100 to get 5 percent.

Joe received an hourly wage of $8.15. His boss gave him a 7% raise. How much does Joe make per hour now? (A) $0.57 (B) $8.90 (C) $8.72 (D) $13.85

(C) $8.72 8.15 x 0.07 = $0.57 $0.57 + $8.15 = $8.72

How many gallons of water should you add to 4 gallons of a juice that is 20 percent water so the final mixture is 50 percent water? (A) 2.2 gallons (B) 2 gallons (C) 2.4 gallons (D) 1.4 gallons

(C) 2.4 gallons Let x represent the amount of water to be added to the 20 percent mixture, and then make a chart to help solve the problem. From the table, you know that the amount of added water is 100x, and the amount of juice is 4(20) . The sum of these two amounts is equal to the amount of mixture, 50(x+ 4) . Write and solve an equation to find x 100+4 (20) = 50 (x+4) 100x+80 = 50x +200 50 x = 120 x = 2.4

An accounting-firm employee is asked to shred 900 documents. If they can shred documents at a rate of 7 per minute, the number of documents remaining after 1 (1/2) hours of shredding is (A) 630 (B) 90 (C) 270 (D) 810

(C) 270 1 (1/2) hours = 90 minutes 7 per minute 90 x 7 = 630 900-630 = 270 documents in 1 (1/2) hours.

Your piggy bank contains $19.75 in dimes and quarters. There are 100 coins in all. How many dimes are there? (A) 25 (B) 30 (C) 35 (D) 40

(C) 35 Let x equal the number of dimes. Then 100- x represents the number of quarters. You have $0.10x in dimes and $0.25 (100-x) in quarters, so set up your equation and solve for x. 0.10x +0.25 (100-x) = 19.75 0.10x +25 -0.25x = 19.75 -0.15x = -5.25 x = 35

A patio measures 12 feet by 14 feet. How many 8-inch-square paving stones are needed to pave the patio? (A) 21 (B) 252 (C) 378 (D) 168

(C) 378 First figure out how many stones will be needed along the 12-foot side of the patio and then how many stones will be needed along the 14-foot side of the patio. Then multiply those two numbers together to get the total number of stones required. Here's the math: Convert 12 feet to inches: 12 ft. x 12 in./ft = 144 inches. The paving stones are 8 inches square, so divide 144 inches by 8 inches 144inches/8inches = 18 stones. Do the same math for the 14-foot length: 14 ft. x 12 n./ft. = 168 in 168/8 = 21stones. Therefore, 21 stones are needed on the 14-foot side. Now multiply the stones: 18 stones x 21 stones = 378 stones, which is Choice (C).

Tom is flying a kite at the end of a 500-foot string. His friend Kathy is standing directly under the kite 300 feet away from Tom. How high is the kite flying? (A) 300 feet (B) 350 feet (C) 400 feet (D) 450 feet

(C) 400 feet Think of a triangle A² + B² = C² 300² +B² = 500² 90,000 + b² = 250,000 b² = 160,000 b = 400

An aircraft flies over Boondock Air Force Base at 10:20 a.m. At 10:32 a.m., the aircraft passes over Sea Side Naval Air Station, 120 miles away. How fast is the aircraft traveling? (A) 400 mph (B) 500 mph (C) 600 mph (D) 700 mph

(C) 600 mph 10:20am - 10:32 am = 12 minutes In 120 miles it gets to the next spot in 12 minutes. Find out what it is in 1 minute. 120/12 = 10 miles/1 minute. They want in hours so 10 miles x 60 minutes = 600 miles per hour.

Miguel passed seven of his history quizzes and failed three. The fraction of quizzes he passed is correctly expressed as (A) 7/3 (B) 3/7 (C) 7/10 (D) 3/5

(C) 7/10 The total number of quizzes is 10. If he passed seven of them, the fraction would be expressed as 7 / 10

A street vendor sells $25.70 worth of pretzels on Friday, $32.30 on Saturday, and $31.80 on Sunday. They spend a fourth of the money over the weekend. How much money do they have left? (A) $89.80 (B) $22.45 (C) $44.90 (D) $67.35

(D) $67.35 Add the sales amounts together: $25.70+32.30 +31.80 = $89.80 When it says a fourth it means 1/4 of the total. Means they have 3/4 of it left. Then multiply the total sales by 3/4 to determine how much money the vendor has left: 89.80 x 0.75 = $67.35

The measure of angle P is 44°. Angle Q is 12° less than half the measure of the supplement of angle P. What is the measure of angle Q? (A) 136° (B) 80° (C) 124° (D) 56°

(D) 56° If two angles are supplementary, the sum of their measures is equal to 180°. To find the supplement of angle P, subtract its measure from 180°: 180 -44 = 136° Angle Q is 12° less than half the supplement of angle P, so divide 136° by 2 and then subtract 12°: (136/2)-12 = 68-12 = 56

Theodore has 24 baseball cards. He sells 1/4 of his cards to Tom and 1/3 of his cards to Larry, and his mom accidently throws away 1/6 of his cards. How many baseball cards does Theodore have left? (A) 2 (B) 18 (C) 12 (D) 6

(D) 6 You need to add the fractions, so convert the different denominators to a common denominator — 4, 3, and 6 all divide evenly into 12, so use 12 as the common denominator. 1/4 x 3/3 = 3/12 1/3 x 4/4 = 4/12 1/6 x 2/2 = 2/12 Add the fractions 9/12 Reduce by 3 3/4 So 1/4 of the cards remain. 1/4 of 24 is 1/4 x 24 = 6, so 6 cards remain.

If a crew of four people can paint the barn in three days, how long will it take a crew of two people? (A) 4 days (B) 1 (1/2) days (C) 8 days (D) 6 days

(D) 6 days Four members is twice as many as two members. Multiply the number of days it would take four people to paint by 2 (that is, 3x2= 6) to determine how long it would take two people to do the same task.

A painter has painted a picture on a piece of canvas that measures 10 by 14 inches. To accommodate a frame, they have left an unpainted margin of 1 inch all the way around. What part of the canvas has been painted? (A) 96% (B) 91% (C) 65% (D) 69%

(D) 69% The area of the entire piece of canvas = 10 inches x 14 inches = 140 square inches. The portion painted on equals 8 inches x 12 inches = 96 square inches. (This is determined by subtracting 2 inches — 1 inch on each side — from the length of each side to account for the margins.) Divide 96 by 140 to determine that about 68.5% of the canvas is covered with paint. You can round up to 69%.

Five years ago, Amy was three times as old as Mike. If Mike is 10 years old now, how old is Amy? A. 20 B. 30 C. 10 D. 5

A. 20 The 5 years ago means a lot in this question. Don't think time is the same and that we don't take it into account. Mike is 10 years old now, so he must have been 5 years old five years ago. Amy was 3 times as old as Mike five years ago, so Amy must have been 15 five years ago. Add 5 years to Amy's age five years ago to calculate her age now. Amy is 15 + 5 = 20 years old now.

Laura goes to the grocery store every 5 days and Tim goes to the same grocery store every 6 days. If Laura and Tim both went to the grocery store today, when is the next time they will both go to the grocery store on the same day? A. 30 days B. 11 days C. not enough information D. 60 days

A. 30 days The least common multiple of 5 and 6 is 30. This means that after 30 days, both Laura and Tim will go to the grocery store on the same day again.

A corner table is the shape of a right triangle. One side is 3 feet, another side is 4 feet, and the third side is 5 feet. What is the area of the table top? A. 6 ft2 B. 7.2 ft2 C. 8 ft2 D. 8.5 ft2

A. 6 ft2 Area of a triangle is 1/2 (b)(h) Nothing is giving try all and see if any of the answers match. In the end, 3 feet is the height and 4 feet is the base. 1/2 (4)(3) = A. 6 ft2

To complete the decoration of her new home, Kate bought a rectangular Persian rug that measured 45 feet around its outer edge. If the long sides measure 15 feet each, how long is each short side of the rug? A. 7.5 feet B. 10 feet C. 12.5 feet D. 15 feet

A. 7.5 feet P = 2l +2W If the long sides equal 15 feet than when using the equation both sides together will be 30 feet 15 x 2 = 30 Now we simply take 30 from 45 to get the short side. 45 - 30 = 15 feet (two sides added together) 15/2 = 7.5

During a season a professional basketball player tried 320 shots and made 272 of them. What percentage of the shots tried were successful? A. 85% B. 80% C. 75% D. 70%

A. 85% 1)Divide the number of successful shots by the total number of shots the player tried. Change your answer to a percent. 2) Reducing bit by bit is gonna take too long. We need to get something fast. 3) 272 is closer to 270 so lets do 270/320. 4) Reduce by 10 5) 27/32 = 0.84 = 84%. 6) If numerator is a bit higher the answer will be a bit higher as well only option is B which is the closest.

On May 15, an electric meter read 5,472 kilowatt-hour, The following month, on June 15, the meter read 5,687 kilowatt-hour. The utility charges the following rates for electric service. First 10 kilowatt-hours-- $2.48 Next 45 kilowatt-hours---$0.16 per kilowatt-hour Next 55 kilowatt-hours---$0.12 per kilowatt-hour More than 110 kilowatt- hour-- $0.07 per kilowatt-hour What was the total change for the kilowatt-hours consumed during the month from may 15 to June 15 ? A. $22.53 B. $23.63 C. $22.63 D. $24.43

B. $23.63 1)For the month between May 15 and June 15, the meter showed that the electric usage was 5,687 - 5,472 = 215 (kilowatt-hours) 2) The first 10 kilowatt hours cost $2.48 3)The next 45 kilowatt hours cost 0.60 per kilowatt hour. 45 x 0.60 = $7.20 4)The next 55 kilowatt hours cost 0.12 per kilowatt hour 55 x 0.12 = $6.60 5) All usage over the first 110 kilowatt-hours was charged at a lower rate. Thus, 215-110 = 105 kilowatt hours 6) Now lets multiply 105 by 0.07 105 x 0.07 = $7.35 7) Now lets add the total amounts $2.48 + $7.20 + $6.60 + $7.35 = $23.63 which is answer B.

Sydney deposited $4,000 in the bank at 5% interest. How much interest will you earn after 2 years? A. $4400 B. $400 C. $200 D. $4000

B. $400 I=Prt Interest I = $4,000 x 0.05 = 200 x 2 years = $400. We just want to know the interest not the total after 2 years.

Travis' hunting lodge does not have electrical lines run to it, but it does have gasoline generator that powers the lights, heater, and stove. The fuel tank of the generator holds enough to run the generator for 75 minutes. About how many times must the fuel tank be filled to run the generator from 6:15 pm to 7:00am? A. 9.4 B. 10.2 C. 10.8 D. 11.5

B. 10.2 1) 6:15pm - 7:00am 6:15am - 6:15pm = 12 hours 0:15 - 1:00 = 45 minutes 12 hours, 45 minutes total 2) Convert 12 hours to minutes 12 x 60 = 720 minutes 720 +45 = 765 minutes 765/75 - we know D is too big and A is too small. Its either B or C. In the end we should get B.

A shed with a square base 15 feet on each side is 8 feet high. All four sides are to be painted. One gallon of paint will cover 400 square feet. How many gallons of paint are needed? A. 1 B. 2 C. 3 D. 4

B. 2 Each side has an area of 15 × 8 = 120 square feet, so the four sides have a total area of 120 × 4 = 480 square feet. A gallon of paint will cover 400 square feet, but that is not enough; 2 gallons will be required.

A pole 15 feet high casts a shadow 5 feet long. A 6-foot man standing nearby would cast a shadow A. 1 (1/2) feet long. B. 2 feet long. C. 2 (1/2) feet long. D. 3 feet long.

B. 2 feet long. They want the shadow. 15feet/5 ft shadow = 6 feet / x ft shadow Solve for x 6x5 = 30/15 = 2 feet

If a worker earns $200 for the first 40 hours of work in a week and then is paid one and one half times her regular rate for any additional hours, how many hours must she work to make $230 in a week? A. 43 B. 44 C. 45 D. 46

B. 44 First figure out his regular rate of pay. Divide the amount of $200 / 40 hours = $5 per hour. The girl is paid 1 1/2 times his regular rate during overtime, so when working more than 40 hours he makes 3/2 x $5 per hour = $7.50 per hour. It takes him 40 hours to make the first $200. The last $30 are made at the overtime rate. Since it takes the man one hour to make $7.50 at this rate, you can figure out the number of extra hours by dividing $30 by $7.50 per hour. $30 / $7.50 per hour = 4 hours. The total time needed is 40 hours plus 4 hours, or 44 hours.

If a fire truck is 55 feet away from a hydrant, it is how many feet nearer to the hydrant than a truck that is 105 feet away? A. 40 feet B. 50 feet C. 55 feet D. 60 feet

B. 50 feet 105 - 55 feet = 50 feet

A shipment of 2,200 pounds of fertilizer is packed in 40 ounce bags. How many bags are needed for shipment? A. 800 B. 880 C. 780 D. 640

B. 880 convert 2,200 lbs to ounces 16 ounces per 1 lb/ 2200 x 16 = 35,200 35,200/40 = 880

In a quality control test at a factory of 280 products inspected at random, 266 were found to be acceptable. What percentage of the items inspected were found acceptable? A. 66% B. 95% C. 5% D. 86%

B. 95% To make it easier simply raise the 266 to 270 to make the division faster. The answer choices are far apart either way. 270/280 = 27/28 = .96 or 96%. Only answer chose close is B.

The paint that Amanda is using to paint Madalyn's room comes in two sizes, small (16 ounces) and large (one gallon/64 ounces). The only size paint can left at the hardware store is the small size. If she used up an entire large can painting 3/4 of Madlyn's room, how many cans does she need to buy to finish painting? A. one B. two C. three D. four

B. two One large 64 ounce paint can did 3/4 of the room. Means we need 1/4 left to complete it. 64/16 = 4 small size cans. Let x = small size cans. Let y equal the finished room. 4x=3/4y We need 1y the complete room so lets divide both sides by 3. 4/3x = 1y 4/3 = 1 1/3. That is more than 1 some we need 2 more small paint cans to complete the room.

Which of the following represents the correct sum of 14/15 and 2/5?

B: Common denominators must be used. The LCD is 15, and 2/5 = 6/15 Therefore, 14/15 + 6/15 = 20/15 , and in lowest terms, the answer is A common factor of 5 was divided out of both the numerator and denominator.

In a neighborhood, 15 out of 80 of the households have children under the age of 18. What percentage of the households have children? a. 0.1875% b. 18.75% c. 1.875% d. 15% e. 1.50%

B: First, the information is translated into the ratio 15/80. To find the percentage, translate this fraction into a decimal by dividing 15 by 80. The corresponding decimal is 0.1875. Move the decimal point two units to the right to obtain the percentage 18.75%.

If a car is purchased for $15,395 with a 7.25% sales tax, what is the total price? a. $15,395.07 b. $16,511.14 c. $16,411.13 d. $15,402 e. $16,113.10

B: If sales tax is 7.25%, the price of the car must be added by the this additional tax. To start, 1) Convert 7.25% to a decimal by dividing by 100. (Move left 2 spots) 7.25/100 = 0.0725 2) 1 must be added to 0.0725 to calculator the total price this is the equation. This is for all cases. Purchased price × (1+ sales tax decimal form) 15395 x 1.0725 (move decimal 4 times to the right to multiply) They are asking for an exact number so we have to multiply the long way. 15395 10725 x --------- 165,111, 375 ( Now go back 4 times) 16511.1375 ( Round to the hundredths) 16511.14 Answer comes out as $16,511.14 which is B the answer.

If Oscar's bank account totaled $4,000 in March and $4,900 in June, what was the rate of change in his bank account total over those three months? a. $900 a month b. $300 a month c. $4,900 a month d. $100 a month e. $4,000 a month

B: The average rate of change is found by calculating the difference in dollars over the elapsed time. Therefore, the rate of change is equal to $4,900-$4,000÷ 3 months, which is equal to $900÷3 or $300 a month.

How is a transposition of a matrix performed? a. Multiply each number by negative 1 rows and columns b. Switch the rows and columns c. Reverse the order of each row d. Find the inverse of each number e. Divide the first number in each row by the last number in the last column

B: because the definition of transposing a matrix says that the rows and columns should be switched. For example, the matrix 3 4 2 5 1 6 can be transposed into 3 2 1 4 5 6 Notice that the first row, 3 and 4, becomes the first column. The second row, 2 and 5, becomes the second column. This is an example of transposing a matrix.

Mike has $5.25 in quarters and dimes. He has exactly 15 dimes. How many quarters does he have? (A) 6 (B) 12 (C) 15 (D) 21

C) 15 If Mike has 15 dimes, he has (15) ($0.10) = $1.50 in dimes. Subtract that from the total to find out how much he has in quarters: $5.25 - $1.50 = $3.75. Then, divide that result by $0.25 to determine how many quarters he has: $3.75 ÷ $0.25 = 15.

A television priced at $400 was reduced 25 percent during a weekend sale. In addition, there was a 10 percent discount for paying cash. What was the cash price of the set during the sale? A. $130 B. $260 C. $270 D. $320

C. $270 400 x .25 = 100 400-100 = 300 300 x .10 = 30 300-30 = 270

This table gives the annual premiums for a life insurance policy based on the age of the holder when the policy is taken out. Age in years Premium per $1,000 22 $18 30 $22 38 $28 46 $38 Over 20 years, how much is saved by taking out a $1,000 policy at age 30, rather than at age 46? A. $16 B. $32 C. $320 D. $400

C. $320 1) Find the annual difference between the premium paid by someone who is 30 and the premium paid by someone who is 46. 2) $38 - $22 = $16 3) Multiply the answer by 20 to find the total amount saved over 20 years by taking out a policy at an early age. 4)$16 x 20 = $320 saved which is answer C.

A chair was marked for sale at $240. This sale price was 25 percent less than the original price. What was the original price? A. $300 B. $280 C. $320 D. $60

C. $320 1) On sale, the chair is 25% less than the original price. In other words, the sale price is a fraction of the original price. 2) 100%-25% = 75% (or 3/4) of the original price. 3) If x equals the original price, then the sale price can be written as an equation. 4) (3/4)x = $240 -solve for x Multiply both sides by 4 3x = 960 divide both sides by 3 x = 320 which is answer C.

A snack bar sold 12(1/2) Gallons of milks at 35 cents a pint. How much did the snack bar receive for the milk? A. $33.60 B. $34.00 C. $35.00 D. $32.20

C. $35.00 The number of pints sold is ... (12.5 gal)×(8 pt/gal) = 100 pt Then the total amount received for the milk is ... (100 pt)($0.35/pt) = $35.00

In the city of Hewitt, houses are assessed for tax purposes at 80 percent of the purchase price. If Mr. Thomas buys a house in Hewitt for $120,000 a real estate taxes are $4.75 per $100 of assessed valuation, how much property tax must he pay per year? A. $3,648 B. $5,472 C. $4,560 D. $4,845

C. $4,560 Only 80% is accounted for. 120 x 80 = 9,600 add one more zero = 96,000 $100 is being assessed each so take that from 96,000 960 x $4.75 = $4,560

A patient's hospice stay cost 1/4 as much as his visit to the emergency room. His home nursing cost twice as much as his hospice stay. If his total healthcare bill was $140,000, how much did his home nursing cost? A. $10,000 B. $20,000 C. $40,000 D. $80,000

C. $40,000 We need to first know how much his emergency room bill is to get the nursing cost. Hospice is 1/4 of the total Emergency is 4/4 since hospice is taking 1/4 of it. Nursing cost twice as much as hospice so 1/4 x 2 = 2/4 or 1/2 Lets add all fractions. Hospice Emergency Nursing 1/4E + 4/4E + 2/4E We get 7/4 E Now we know the total is $140,000 So, 7/4 E = $140,000, Solve for e Multiply both sides by 4 560,000 = 7E - divide 7 both sides Emergency cost = 80,000 They want nursing which is 1/2 of the total so 80,000/2 is 40,000 C.

A man left $72,000 to his and son. The ratio of the wife's share to the son's share was 5:3. How much did his wife receive? A. $ 27,000 B. $14,000 C. $45,000 D. $54,000

C. $45,000 x is the number of shares. 5x+3x = 72,000 - solve for x 8x = 72,000 x = 9,000 this is one share Mom got 5 shares so 9,000 x 5 = 45,000

During a 25% off sale, an article sells for $375. What was the original price of this article? A. $93.75 B. $468.75 C. $500 D. $575

C. $500 Since they took 25% of the original price. That means that $375 is 75% of the original price. Let x equal the original price. 75%x = 375 375/.75 = $500

The Hamiltons bought a table that was marked $400. On the installment plan, they made a down payment equal to 25 percent of the marked price plus 12 monthly payment of $30 each. How much more than the marked price did they pay by buying it this way? A. $25 B. $50 C. $60 D. $460

C. $60 1) 25% is 1/4 2) 25% x 400 = $100 3) Now lets add the monthly payments 4) 12 x 30 = 360 Add them both 5) $360 + $100 = 460 6) $460 - $400 = $60 which is how much more they paid doing the monthly payments.

The USS Texas (SSN 775) sails x miles the first day, y miles the second day, and z miles the third day. What is the formula for the average number of miles sailed per day? A. 3xyz B. 3 × (x +y+z) C. (x +y+z) ÷ 3 D. (x +y+z)

C. (x +y+z) ÷ 3

A line with a slope of 1 passes through the coordinates (10,14). What is the x-coordinate when y=4? A. -1 B. 2 C. 0 D. 3

C. 0 Slope = y2-y1/x2-x1 They tell us the slope is 1and they want the x of y2 So 1 = (4-14)/(x-10) 1 = -10/x-10 - multiply denominator both sides to isolate the x x-10 = -10 x = 0

What is the difference between the square of 49 and the square of 31? A. 18 B. 1.4322 C. 1,440 D. 2,056

C. 1,440 1) To square a number multiply it by itself 2) 49^2 = 49 x 49 = 2,401 3) 31^2 = 31 x 31 = 961 4) get the difference which is subtraction 5) 2,401 - 961 = 1,440 which is answer C.

At Chez Marie, one-fifth of the patrons are male and one-fourth of the patrons are from out of town. What proportion would you expect to be both male and from out of town? A. 1/4 B. 1/9 C. 1/20 D. 1/25

C. 1/20 1/5 of 1/4 = 1/5 x 1/4 = 1/20

A rectangular ottoman covers 6 square feet on its surface. If it is 2 feet wide, what is its perimeter? A. 9 feet B. 3 feet C. 10 feet D. 11 feet

C. 10 feet First we are dealing with a rectangle Area of a rectangle is length x width. They give us 6 square feet the length of the surface. This is the area of the rectangle from the square feet. We know 2 feet is the width. Perimeter = 2l + 2w Width = 2 feet Length = 3 because 3 x 2 = 6 square feet. 2 (3) + 2(2) = 6+4 = 10 feet

At a local YMCA. there are 5 males for every 45 females. How many females are there if 12 males are present? A. 103 B. 107 C. 108 D. 537

C. 108 Proportion 5 males/45 females = 12 males/ x Solve for x x = 108

Suzie has a piece of ribbon 6 yards long. She needs to cut the ribbon into lengths of 1(1 ⁄ 2) feet. How many pieces will she be able to cut? A. 10 B. 11 C. 12 D. 13

C. 12 Covert 6 yards to feet 3ft = 1 yard 6x3 = 18 feet 1(1/2) = 3/2 How many 3/2 cuts go into 18 feet? 18 ÷ 3/2 = 18 x 2/3 = 36/3 = 12

For an event at which they must seat 56 people, a restaurant uses 7 round tables. How many of this type of table would they need to seat 91 people? A. 10 B. 11 C. 12 D. 13

C. 12 If 7 tables will seat 56 people, you can seat 56 ÷ 7 = 8 people at each table. For 91 people, you will need tables. Because 11 tables will not be enough, the restaurant must use 12 tables.

The minute hand of a clock is missing, but the hour hand is on the 11 minute mark. What time was it when the clock broke? A. 5 minutes after 11 B. 11 minutes after 12 C. 12 minutes after 2 D. 20 minutes after 1

C. 12 minutes after 2 1) When the hour hand is on the 10-minute mark, it is actually on the number 2 ( for 2 o' clock). 2) The hour hand advanced to a new minute mark every 12 minutes of actual time. 3) Thus, when the hour hand stopped at the 11 - minute mark, it was 12 minutes after 2 - which is answer C.

A carpenter spent his 40-hour workweek as follows: 1/4 of his time ordering materials; 1/2 of his time doing the woodwork; and 1/8 of his time talking to customers. The rest of his time was devoted to cleanup. What is the approximate percentage of time the carpenter spent doing cleanup? A. 8% B. 10% C. 12.5% D. 15%

C. 12.5% 40 (1/4) + 40 (1/2) + 40 (1/8)= 10 + 20 + 5 = 35 40 - 35 = 5 being the time devoted to cleanup. 5/40 = 0.125 or 12.5%

The price of a used car was increased from $6,400 to $7,200. What was the percentage increase? A. 10% B. 11.25% C. 12.5% D. 15%

C. 12.5% 7,200 - 6,400 = 800 So lets get that original and see what percentage gets us 800 1) $6,400x = $800 - solve for x 2) 800/6400 - reduce by 100 3) 8/64 - reduce by 8 4) 1/8 = 0.125 move decimal twice to the right to make percent. 12.5% which is C.

The ratio of green items to red items in a bowl is 6:30. If there are 144 total items, how many red items are in the bowl? A. 41 B. 103 C. 120 D. 24

C. 120 6 green for every 30 red = in total its 36 total items. Since they want total red lets make the proportion. R/144 total = 30 red/36 total - solve for R. r/144 = 5/6 = 720/6 = 120

Although the table of organization and equipment specifies that an infantry rifle company has a total 131 soldiers authorized, B company (Bulldogs), 3rd Battalion, 144th Infantry Regiment has only 125 soldiers assigned, of whom 4 percent are officers. How many enlisted soldiers are assigned to the company? A. 114 B. 123 C. 120 D. 121

C. 120 There only asking how many soldiers are in B company which is the one with 125 soldiers assigned and 4 percent are officers. 125 x 0.04 = 5 officers in B company. 125 - 5 = 120 enlisted soldiers.

A survey of a small group of people found that 3 of them each watched 2 hours of TV per day. Two of them watched 1 hour per day, and 1 watched 4 hours per day. What is the average number of hours of TV watched by members of this group? A. 1 1/3 hours B. 2 2/3 hours C. 2 hours D. 3 hours

C. 2 hours First calculate the hours. 3 each watch 2 hours. 3x2 = 6 hours 2 watch 1 hour = 2x1 = 2 hours 1 watches for 4 hours = 4 hours 6+2+4 = 12 hours total. Now calculate the number of people 6 people total. 12/6 = 2 hours which is the average.

A recipe calls for 2 1/2 ounces of chocolate and 1/2 cup of corn syrup. If only 2 ounces of chocolate are available, how much corn syrup should be used? A. 1/2 cup B. 1/3 cup C. 2/5 cup D. 3/10 cup

C. 2/5 cup Treat it like ratios. Set up the proportion with equal types. Chocolate/chocolate = syrup/syrup (we need) (2 1/2 ounces chocolate) / 2 pounces of chocolate = 5/2 / 2 = 5/4 5/4 ounces chocolate = 1/2 corn syrup/x (corn syrup) 1/2 / x = 1/2 x 1/x = 1/2x 5/4 ounces chocolate = 1/2x corn syrup cross multiply 10x = 4, x = 4/10 = 2/5

A 40 mL solution contains 20% juice is mixed with a 80 mL solution that contains 50% juice. What is the juice concentration of the resulting mixture? A. 43.00% B. 30.00% C. 40.00% D. 35.00%

C. 40.00% We're combining the mixtures together P = % of the mixture concentration of juice in the mixture 1) 80mL+40mL = 120ml 2) 20% x 40ml + 50% x 80 ml = P % x 120 ml 20% x 40 ml = 8 50% x 80 ml = 40 P % = p/100 since we're gonna have to turn it into a decimal so we put it over a 100 to explain that process. Remember 2 to the left. 40+8 = p/100 x 120 48 = p/100 x 120 - 100 and 120 can be reduced by 20 3) 48 = p/5 x 6 48 = 6p/5 - we can multiply by the reciprocal of 6/5 which is 5/6 to cancel out the 6/5 both sides. 48 x 5/6 = p p = 40

An airplane traveled 1000 miles in 2 hours and 30 min. What was the average rate or speed , in miles per, hour the trip? A. 200 miles per hour B. 300 mile per hour C. 400 miles per hour D. 500 miles per hour

C. 400 miles per hour 1) To find the average rate of speed, divide the distance covered (1,000 miles) by the time spent traveling (2 (1/2) or 2.5 hours. 2) 1000/2.5 - move decimal 3) 10,000/25 = 400 miles answer C.

A courier leaves an office driving at an average rate of 30 miles per hour but forgets part of the material he was supposed to take with him. An hour later, a second courier is dispatched with the missing material and is instructed to overtake the first courier in 2 hours more. How fast must the second courier travel? A. 90 miles per hour B. 60 miles per hour C. 45 miles per hour D. 40 miles per hour.

C. 45 miles per hour First courier will travel 1 hour + 2 hours, or a total of 3 hours, before he is overtaken. Traveling 30 miles per hour for 3 hours will take the first courier 30 x 3 or 90 miles away. The second courier must travel the 90 miles in 2 hours. Therefore, he must travel at a rate of 90/2 or 45 miles per hour.

In a certain city , taxicab fare is $0.80 for the first 1/4 mile, and $0.20 for each additional 1/4 mile. How far, in miles, can a passenger travel for $5.00? A. 5 miles B. 4 (1/4) miles C. 5 (1/2) miles D. 5 (3/4) miles

C. 5 (1/2) miles Since the first 1/4 mile cost $0.80, this leaves $4.20 for the balance of the trip. At $0.20 for each additional 1/4 mile, find the number of 1/4 miles that $4.20 will cover. $4.20/$0.20 - Make whole 420/20 - reduce by 10 42 ÷ 2 = 21 (additional 1/4 miles) Add the first 1/4 miles (at 0.80) to this total 21 + 1 = 22 (1/4 miles) Change the 1/4 miles to miles 22 ÷ 4 = 5 (1/2) (miles for $5) Which is answer C.

A pile of magazines is 4 feet high. If each magazine is 3/4 of an inch thick, the number of magazines in the pile is A. 36 B. 48 C. 64 D. 96

C. 64 4 feet = 12 x 4 = 48 inches Each magazine is 3/4 48 ÷ 3/4 = 48/1 x 4/3 = 64

A college football players parents spent $119 on tickets for family and friends to attend a conference playoff game. If the general admission tickets were $7 and $10, and they bought an equal number of both kinds of tickets, how many $7 tickets did they buy? A. 4 B. 5 C. 7 D. 11

C. 7 Let x be the number of tickets bought at each price. 7x + 10x = 119 1) 17x = 119 2) 119/17 = 7 x = 7

A basketball has a diameter of 12 inches. What is the volume? A. 76.2 in.³ B. 89.52 in.³ C. 904.32 in.³ D. 1068.12 in.³

C. 904.32 in.³ Volume of a sphere = 4/3π(6)³ Almost divide by 3 last. 6³ = 216 4(3.14)(216) / 3 2,712.96 / 3 = 904.32 in.³

The distance across the circular mouth of a volcano running through its center is 75 yards. What is the distance around its mouth? A. 145.5 yd B. 215.5 yd C. 235.5 yd D. 315.5 yd

C. To find the circumference of a circle, use the formula C = 2pr or p x diameter. Since the diameter is giving we will use the latter. C = 3.14 x 75 = 235.5 yd

Which of the following is incorrect?

C: -1/5 > 4/5 is incorrect. The expression on the left is negative, which means that it is smaller than the expression on the right. As it is written, the inequality states that the expression on the left is greater than the expression on the right, which is not true.

Subtract 5/14 from 5/24 Which of the following is the correct result?

C: Common denominators must be used. The LCD is 168, so each fraction must be converted to have 168 as the denominator. 5/24 - 5/14 = 5/24 x 7/7-5/14x12/12 35/168 - 60/168 = -25/168

Gina took an algebra test last Friday. There were 35 questions, and she answered 60% of them correctly. How many correct answers did she have? a. 35 b. 20 c. 21 d. 25 e. 18

C: Gina answered 60% of 35 questions correctly; 60% can be expressed as the decimal 0.60. Therefore, she answered 0.60 × 35 = 21 questions correctly.

What is the resultant matrix when addition is performed?

C: The correct answer is Choice C because matrices are added by adding the corresponding numbers in the two given matrices. For matrices to be added, they must have the same number of rows and columns. These two matrices have two rows and two columns. The first row, first column numbers are 1 and 3, and adding them together yields a total of 4. The second row, first column has numbers 4 and -2, which yields a sum of 2. The first row, second column has -5 and 2, which sum to -3. The second row, second column have 2 and 1, which yield a sum of 3. The resulting matrix after addition is: 4 -3 2 3

The price of a new car is $25,000. If the sales tax rate is 6.5% what is the total cost of the car, including tax? B. $23,150 B. $27,890 C. $21,720 D. $26,625

D. $26,625 1) 6.5% = 0.065 - 3 steps. 2) 25,000 x 65 = 1,625,000 - go back 3 times 3) 1,625 - add to the total 4) 25,000 + 1,625 = D. $26,625

James, the high tech electronics store owner, makes a deal to buy 20 DVD players for the listed wholesale price of $80 apiece, but receives a 25 percent discount because he is a frequent customer of the wholesale dealer. Being a shrewd entrepreneur, he then sells these DVD players at a 20 percent markup above the original wholesale price, What is his profit on each DVD player? A. $16 B. $720 C. $20 D. $36

D. $36 Buys 20 $80 each but gets a 25% discount $80 x .25 = 20 $80-20 = $60 bought He then sells at 20% above the markup price. $80 x .20 = $16 $80+16 = $96 sold each. Profit = 96-50 = $36

A man takes a trip in which he first drives for 3 hours at 50 miles per hour. He then drives for 2 hours more at 55 miles per hour. If his car gets 20 miles per gallon, how many gallons of gas did he use for the trip? A. 10 gallons B. 9.5 gallons C. 26 gallons D. 13 gallons

D. 13 gallons 3 hours at 50 miles/hr = 50 x 3 = 150 miles 2 hours at 55 miles/hr = 55 x 2 = 110 miles 150+110 = 260 20 miles per gallon 260/20 = 26/2 = 13 gallons

A mother is sending a box of brownies to her daughter. The box is 6 inches high, 6 inches wide, and 15 inches long. If each brownie is 2 inches wide, 1 ⁄ 2 inch high, and 3 inches long, how many brownies will fit into the box? A. 25 B. 55 C. 90 D. 180

D. 180 Volume of quadrilateral = L x w x H Question = How many brownies fit in the boxes. Get volume of brownies and divide the volume of the box by the volume of the brownies. Brownies = 3in x 2in x 1/2in = 3 in³ Box = 15in x 6in x 6in = 540 in³ Box/brownies = 540/3 = 180 brownies.

A pasta recipe calls for 2/3 cup of tomato paste for each batch of lasagna. If Victor has 18 cups of tomato paste, how many batches of lasagna can he make? A. 12 B. 21 C. 26 D. 27

D. 27 In this problem you need to find out how many 2/3 cups are in 18 cups. 2/3 cup = 1 batch of lasagna 18 cups ÷ 2/3 = 54/2 = 27 batches of lasagna.

A military unit has 360 members, and 20 percent are officers. How many members of the unit are enlisted personnel? A. 90 B. 270 C. 72 D. 288

D. 288 20 percent of the 360 are officers. 360 x .20 = 72 officers. 360-72 = 288 enlisted personnel

Jennifer is paid $143 for 4 hours of work. At this rate, how long will it take Jennifer to earn $1036.75? A. 17.5 hours B. 40 hours C. 70 hours D. 29 hours

D. 29 hours We know the rate. $143 for 4 hours of work If we multiply both by 10 40 hours = $1430 That is too big so we know its not B or C. Half of $1430 is around $700 so 20 hours. Means 17.5 is too small. Only answer left is 29.

Randy is training to run a 12-kilometer race. His training program starts at him running 3 kilometers per day for the first week and increasing that amount by 15% each week. How many kilometers will he be running per day in the fourth week? A. 3.45 km B. 3.97 km C. 4.12 km D. 4.57 km

D. 4.57 km 3 x 15% = .45 Week One 3 km Week Two 3 km + 0.15(3) = 3.45 km Week Three 3.45 km + 0.15(3.45) = 3.97 km Week Four 3.97 km + 0.15(3.97) = 4.57 km

You need 8 barrels of water to sprinkle 1/2 mile of roadway. How many barrels of water do you need to sprinkle 3 1/2 miles of roadway? A. 7 B. 15 C. 50 D. 56

D. 56 8 for every 1/2. Which means 16 for every 1 3 = 16+ 16+16 = 48 +8 = 56

A swimming pool is 3 meters deep, 50 meters long, and 25 meters wide. If it takes 0.25 pounds of chlorine for every 15 cubic meters of water to keep the pool clean and healthy, how many pounds of chlorine are needed? A. 27.2 pounds B. 35.7 pounds C. 45.4 pounds D. 62.5 pounds

D. 62.5 pounds Length x width x height 50 x 25 x 3 = 3,750 cubic meters 3,750 / 15 = 250 250 x 0.25 = 62.5 pounds

After reading 60 pages per hour over a period of 11 hours, Anthony now has only 60 pages left to read. How many pages did Anthony have left to read initially? A. 660 pages B. 346 pages C. 60 pages D. 720 pages

D. 720 pages 60 pages/hr 11 hours 60 x 11 = 660 pages Now has 60 left 660+60 = 720 pages total. Before the 11 hours he had 720 pages left to read.

Two numbers add up to 112. One number is 44 less than the other. What is the bigger number? A. 68 B. 88 C. 34 D. 78

D. 78 A + B = 112 We'll let A = B-44 since it says one number is 44 less than the other. Lets find the bigger number by substituting varaible. B-44+B = 112 2B -44 = 112 - Solve for B 2B = 156 B = 78

The local electronics store is holding a 20%-off sale on all its products. Marla selects 2 CDs at the original price of $16.99 each. What is the price of the two CDs after the 20% discount? A. $15.99 B. $22.50 C. $25.78 D. $27.18

D. Calculate the cost of the two CDs: $16.99 × 2 = $33.98 Reduce that amount by 20% by multiplying the total cost by 0.20: 0.20 × 33.98 = $6.80 Subtract $6.80 from the original cost: $33.98 - $6.80 = $27.18 A faster way to do this (and speed is important on the ASVAB) is to multiply the original cost by 80% or 0.80 because that is the cost of the items after the discount. 0.80 × $33.98 = $27.18

Which set of matrices represents the following system of equations?

D: The correct matrix to describe the given system of equations is the last matrix (Choice D) because it has values that correspond to the coefficients in the right order. The top row corresponds to the coefficient in the first equation, the second row corresponds to the coefficients in the second equation, and the third row corresponds to the coefficients in the third equation. The second matrix (Choice B) is filled with the three variables in the system. One thing to also look for is the sign on the numbers, to make sure the signs are correct from the equation to the matrix.

Which label describes the relationship between these vectors?

D: The picture shows how vectors are added. According to the definition, the vectors must be placed head to tail, then the resulting vector is drawn from the beginning head to the ending tail. Notice that the vector runs from the bottom left to the top right. Adding these vectors in the wrong direction would yield a vector starting at the top right, at the end of vector v, and ending at the bottom left.

Each year, a family goes to the grocery store every week and spends $105. About how much does the family spend annually on groceries? a. $10,000 b. $50,000 c. $500 d. $5,000 e. $1,200

D: There are 52 weeks in a year, and if the family spends $105 each week, that amount is close to $100. A good approximation is $100 a week for 50 weeks, which is found through the product 50x 100= $5,000.

Which of the following is the correct decimal form of the fraction 14/33 rounded to the nearest hundredth place? a. 0.420 b. 0.14 c. 0.424 d. 0.140 e. 0.42

E: If a calculator is used, divide 33 into 14 and keep two decimal places. If a calculator is not used, multiply both the numerator and denominator times 3. This results in the fraction 42/99, and hence an approximate decimal of 0.42.

Paul took a written driving test, and he got 12 of the questions correct. If he answered 75% of the total questions correctly, how many problems were on the test? a. 25 b. 15 c. 20 d. 18 e. 16

E: The unknown quantity is the number of total questions on the test. Let be equal to this unknown quantity. Therefore, 0.75x = 12 Divide both sides by 0.75 to obtain x = 16 .

When two vectors are added, what is the answer called? a. Ending vector b. Total vector c. Summation vector d. Resolved vector e. Resultant vector

E: When two vectors are added, the resulting vector is called the resultant. By definition, the vector found from addition of two or more vectors is the resultant. The other choices of ending vector and total vector could refer to one or more of the starting vectors, not the resultant.

What is the label given to a problem that multiplies a matrix by a constant? a. Vector multiplication b. Scalar multiplication c. Inverse of a matrix d. Transposition of a matrix e. Product of a matrix

The correct answer is Choice B because multiplying a matrix by a constant is called scalar multiplication. A scalar is a constant number, which means the only thing it changes about a matrix is its magnitude. For a given matrix, 3 4 6 5 scalar multiplication can be applied by multiplying by 2, which yields the matrix 6 8 12 10 Notice that the dimensions of the matrix did not change, just the magnitude of the numbers.

A rectangle is 1 inch longer than it is wide. Its diagonal is 5 inches. What's the width of the rectangle? (A) 2 inches (B) 3 inches (C) 4 inches (D) 5 inches

When you see Diagonal. Means were gonna have to use the Pythagorean theorem. A² + B² = C² C = Diagonal They tell us that the length is 1 inch longer than it is wide. Were gonna find the width with this. Length = (x+1)², x = Width. x² + (x+1)² = 5² (x+1)² = x²+2x+1 x² + x²+2x+1 = 25 2x² +2x+1 = 25 - subtract 25 both sides QUADRATIC EQUATION. Set it equal to zero 2x² +2x - 24 = 0 What does all of the factors have in common? Its 2 Factor out the 2 x² +x - 12 = 0 What 2 numbers equal 12 but when subtracted give you 1? 3 and 4 work. 0 = (x-3)(x+4) x = 3, x = -4. 3 is the only answer choice.