Arithmetic Reasoning ASVAB

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 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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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%

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.

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.

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.

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.

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.

What is the value of 3a^2 - 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 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.

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.

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.

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.

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

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 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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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%.