ASVAB - Practice math problems

Micheal bought 2 1/4 pounds of lumber at $4.00 per pound. If a 7% sales tax was added, how much did Micheal pay? (a) $9.63 (b) $9.98 (c) $10.70 (d) $11.77

(a) $9.63 2 1/4 pounds of lumber cost 2.25 x $4.00 = $9.00. (9.00)(1 + .07) = $9.63

If 50% of (x) is 150, what is 75% of (x)? (a) 225 (b) 250 (c) 275 (d) 300

(a) 225 .50/150 = .75/x cross multiply .5x = 112.5 x = 225

A painter charges $12 an hour while his son charges $6 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 x = number of hours worked 12x + 6x = 108 18x = 108 108 / 18 = 6.

The cost of a protein bar increased from $2.50 to $2.80. The percent increase to the $2.80 rate was how much? (a) 16% (b) 10% (c) 15% (d) 12%

D) 12% (new price - old price)/old price = .12 = 12%

How many square feet of carpeting are needed to carpet a 12-foot × 12-foot room? (a) 24 (b) 120 (c) 48 (d) 144

D) 144 To determine sq. footage, multiply length by width. 12 x 12 = 144

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 The probability of rolling a 5 is a 1 out of 6 chance, so the probability of NOT rolling a 5 is 5 out of 6. With two die the probability is ⁵/₆ × ⁵/₆ = ²⁵/₃₆

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

D) 48 gross = 144 3 bottles/1 day = 144 bottles/x days 3x = 144 x = 48

June's weekly salary is $70 less than Kelly's, which is $50 more than Eileen's. If Eileen earns $280 per week, how much does June earn per week? (a) $160 (b) $260 (c) $280 (d) $300

(b) $260 If Eileen earns $280, Kelly earns $330 June earns $330 - $70 = $260 per week

A certain box contains baseballs and golf balls. If the ratio of baseballs to golf balls is 2:3 and there are 30 baseballs in the box, how many golf balls are in the box? (a) 18 (b) 20 (c) 36 (d) 45

(d) 45 Express the ratio of baseballs to golf balls as 2/3. 2/3 = 30/ (x number of golf balls) cross-multiply to get 2(x) = 90, or x = 45.

Solve for x: If the scale on a road map is 1 inch = 250 miles, how many inches would represent 1,250 miles?

1/250 = x/1250 Cross multiply 250 x = 1250 x = 5

Six pizzas are pepperoni, seven are hamburger, four are cheese, and three are "with everything". What's the probability that a randomly selected pizza is pepperoni?

1/4. There are 6 + 7 + 4 + 3 = 20 pizzas total. So the probability is 6/20, which is 1/4.

Your car uses gasoline at a 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 First determine the distance (7hr × 48mph = 336) divide by the rate per gallon, 21. 336/21 = 16 So now you know you need 16 gallons at $2.82 per gallon to pay for the trip. 16 × $2.82 = $45.12

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 mile. Approximately how many miles per hour is Karl traveling? (a) 47 (b) 120 (c) 50 (d) 53

B) 47 1 km/(5/8 mile) = 75 km/x miles x = (75)(5/8) = 46.875

Jack loaned Bob $1,500 at an annual interest rate of 7%. After one year, how much will Bob owe Jack? (a) $105 (b) $1,500 (c) $1,605 (d) $1,507

C) $1,605 $1,500 ×(1 + 0.07) = 1,605

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

C) $42.00 Multiply 12 miles by $3.50 per mile. 12 x $3.50 = $42.00

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 $8.15 x (1 +0.07)=$ 8.7205 round to $8.72

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 2 pints in a quart, 4 quarts to a gallon. Therefore 8 pints are to a gallon or 16 half-pints, ¹/₁₆.

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

C) 22.50 minutes 8 blocks/30 min = 6 blocks/x min 8x =180 x = 22.5

Marty has exactly 5 blue pens, 6 black pens, and 4 red pens in his backpack. If he pulls out one pen at random from his backpack, what is the probability that the pen is either red or black? (a) 2/3 (b) 3/5 (c) 2/5 (d) 1/3

(a) 2/3 = number of red + black pens/total number of pens = (4 + 6)/ (4+6+5) = 10/15=2/3

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 There are 60 seconds in a minute and 60 minute in one hour; therefore, there are 60 x 60, or 3,600, seconds in an hour. In one second the car travels 1/100 kilometers; in one hour the car will travel 3,600 x 1/100 or 36 kilometers.

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% There are 75 ounces of new solution. How many ounces are alcohol? 20% of the original 25-ounces solution was alcohol. 20% is 1/5, so 1/5 of 25, or 5 ounces are alcohol. Now you can find the percent of alcohol in the new solution: % alcohol = alcohol/total solution x 100% = 5/75 x 100% = 20/3% = 6 2/3%

At garage (A), it cost $8.75 to park a car for the first hour and $1.25 for each additional hour. At garage (B), it costs $5.50 to park a car for the first hour and $2.50 for each additional hour. What is the difference between the cost of parking a car for 5 hours at garage (A) and parking it for the same length of time at garage (B)? (a) $2.25 (b) $1.75 (c) $1.50 (d) $1.25

(b) $1.75 The total cost for parking at garage (A) = $8.75 + 5.00 = $13.75 The total cost for parking at garage (B) = $5.50 + $2.50(4) = $5.50 + $10.00 = $15.50 So the difference in cost = $15.50 - $13.75 = $1.75,

A subway car passes 3 stations every 10 minutes. At this rate, how many stations will it pass in one hour? (a) 15 (b) 18 (c) 20 (d) 30

(b) 18 3 stations/10 minutes = (x) stations/60 minutes Cross multiply and solve for (x). 180 = 10(x) so 18 = (x)

On a certain map, 3/4 inch represents one mile. What distance, in miles, is presented by 1 3/4 inches? (a) 1 1/2 (b) 2 1/3 (c) 2 1/2 (d) 5 1/4

(b) 2 1/3 (3/4 )/1 = 7/4 inches / x number of miles Cross-multiply: 7/4(1) = 3/4 (x number of miles) Multiply both sides by 4 : 7 = 3x x = 7/3 = 2 1/3

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 half of the exam? (a) 20 (b) s4 (c) 27 (d) 36

(b) 24 If (S) represents the time spent on the second half, then the total time spent is 2/3(S) + (S) or 5/3 (S). 5/3(S) = 60 multiply both sides by 3/5 (S) = 36 2/3 times 36 24

If a man earns $200 for his first 40 hours of work in a week and then is paid one-and-one-half times his regular rate for any additional hours, how many hours must he 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 man 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.

John bought a camera on sale that normally costs $160. If the price was reduced 20% during the sale, what was the sale price of the camera? (a) $120 (b) $124 (c) $128 (d) $140

(c) $128 $160 (1-.20) = 160(.8) = 128

Ms. Smith drove a total of 700 miles on a business trip. If her car averaged 35 miles per gallon of gasoline and gasoline cost $1.25 per gallon, what was the cost in dollars of the gasoline for the trip? (a) $20.00 (b) $ 24.00 (c) $ 25.00 (d) $40.00

(c) $25.00 Find how many gallons are needed. To go 700 miles she will need 700/35, or 20 gallons of gasoline. The price of gasoline was $1.25 per gallon, so she spent 20 x $1.25, or $25, for her trip.

After spending 5/12 of his salary, a man has $420 left. What is his salary? (a) $175 (b) $245 (c) $720 (d) $1,008

(c) $720 x = starting salary x( 1 - 5/12) = 420 x(7/12) = 420 multiply both sides by 12/7 x = 720

Joan can shovel a certain driveway in 50 minutes. If Mary can shovel the same driveway in 20 minutes, how long will it take them, to the nearest minute, to shovel the driveway if they work together? (a) 12 (b) 13 (c) 14 (d) 15

(c) 14 Joan can shovel the whole driveway in 50 minutes, so each minute she does 1/50 of the driveway. Mary can shovel the whole driveway in 20 minutes: each minute she does 1/20 of the driveway. In one minute they do: 1/50 + 1/20 + = 2/100 + 5/100 = 7/100 (x min)(7/100) = 1 (1 stands for the finished job) x = 100/7 and 100/7= 14 2/7 rounds to 14.

What is the prime factorization of 140? (a) 2 x 70 (b) 2 x 3 x 5 x 7 (c) 2 x 2 x 5 x 7 (d) 2 x 2 x 2 x 5 x 7

(c) 2 x 2 x 5 x 7 140 = 2 x 70 140 = 2 x 2 x 35 140 = 2 x 2 x 5 x 7

A stock decreases in value by 20%. By what percent must the stock price increase to reach its former value? (a) 15% (b) 20% (c) 25% (d) 40%

(c) 25% x = the stock price increase that you're finding (1 -.2)(1 + x ) = 1 (equals starting value) (.8)(1+x) =1 1 + x = 1.25 x = .25 or 25%

Jan types at an average rate of 12 pages per hour. At that rate, how long will it take Jan to type 100 pages? (a) 8 hours and 10 minutes (b) 8 hours and 15 minutes (c) 8 hours and 20 minutes (d) 8 hours and 30 minutes

(c) 8 hours and 20 minutes 12 pages/1 hour = 100 pages/ (x) hours 12(x) = 100 (x) = 100/12 = 8 1/3 One third of an hour is 20 minutes. So 8 1/3 hours is 8 hours and 20 minutes.

Four people shared a taxi to the airport. The fare was $36.00, and they gave the driver a tip equal to 25% of the fare. If they equally shared the cost of the fare and tip, how much did each person pay? (a) $9.75 (b) $10.25 (c) $10.75 (d) $11.25

(d) $11.25 Total cost of the taxi ride equals $36(1 + .25)= $45. If four people split the cost equally, then each person paid $45/4, or $11.25 each.

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 x = adult fare, .5x = child's fare 2x + (3)(.5x) = 14 2x + 1.5x = 14 3.5x = 14 x = 4

The ratio of 3 1/4 t0 5 1/4 is equivalent to the ratio of __. (a) 3 to 5 (b) 4 to 7 (c) 8 to 13 (d) 13 to 21

(d) 13 to 21 3 1/4 : 2 1/4 = 13/4: 21/4 Multiply both sides of the ratio by 4. = 13:21

Two large sodas contain the same amount as three medium sodas. Two medium sodas contain the same amount as three small sodas. How many small sodas contain the same amount as eight large sodas? (a) 24 (b) 18 (c) 16 (d) 12

(d) 18 2 large/3 medium = 8 large/x medium 2x = 24, x = 12 medium 2 medium/3small = 12 medium/x small 2x =36, x = 18 small

A cat is fed 3/8 of a pound of cat food every day. For how many days will 72 pounds of this cat food feed the cat? (a) 160 (b) 172 (c) 180 (d) 192

(d) 192 3/8 lb / 1 day = 72 lbs / (x) days Cross multiply. 3/8 (x) = 72 (x) = 72 x 8/3 (x) = 192

If each digit 5 in the number 258,546 is replaced with the digit 7, by how much will the number be increased? (a) 2,020 (b) 2,200 (c) 20,020 (d) 20,200

(d) 20,200 If you change each digit 5 into a 7 in the number 258,546, the new number would be 278,746. The difference between these two numbers would be 278,746 - 258,546 = 20,200.

From 1980 through 1990, the population of Country X increased by 100%. From 1990 to 2000, the population increased by 50%. What was the continued increase for the period 1980-2000? (a) 150% (b) 166 2/3% (c) 175% (d) 200%

(d) 200% ( x # of people)(1 + 1)(1 + .5) = x(2)(1.5) = 3x new - old / old (3x - x)/x = 2 so percent is 200% Or let 1990 population =100, then a 100% increase would put the 1990 population at 200. And a 50% increase over 200 would be 200 + 100 = 300. (300 - 100)/100 = 2 X 100 = 200%

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 You're given the percent decrease (25%) and the new number (72), and you're asked to reconstruct the original number. (original number)(1 - .25) = new number (x)(.75) = 72 x = 96.

Which of the following fractions is the largest? 2/3 , 5/8, 11/16 or 3/4?

3/4 Find a common denominator - which is 48 2/3 = 32/48, 5/8 = 30/48, 11/16 = 33/48, 3/4 = 36/48 The largest numerator is 36 so 3/4 is the largest

Kiya had only one coupon for 10% off one frozen turkey breast. The turkey breast costs $8.50 each, and Kiya wanted to buy two. How much did she pay? (a) $16.15 (b) $17.00 (c) $15.30 (d) $7.65

A) $16.15 First find the discounted turkey's price ($8.50)(1 - .10) = $7.35 then add another $8.50 for the 2nd turkey breast. $7.35 + $8.50 = $16.15

A 2-ton truck is taxed at a rate of $0.12 per pound. How much is the total tax bill? (a) $480 (b) $240 (c) $120 (d) $600

A) $480 2,000 pounds to a ton. 4,000 × .12 = 480

A carpenter earns $12.30 an hour for a 40-hour week. His overtime pay is 1¹/₂ times his base pay. If he puts in a 46-hour week, how much is his weekly pay? (a) $602.70 (b) $492.00 (c) $565.80 (d) $110.70

A) $602.70 $12.30 × 40hrs = $492 = base pay $12.30 × 1.5 = $18.45. = overtime pay per hour $18.45 × 6 hr. = $110.70 $492 + $110.7 = $602.70

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

A) $7.50 Subtract the sale price from the original price, $24.00 - $22.50 = $1.50. Now, multiply that number by the amount of cases to get the final answer. $1.50 x 5 = $7.50.

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 she can buy? (a) 15 feet (b) 14 feet (c) 16 feet (d) 12 feet

A) 15 feet Each section is 3²/₃ feet, times that by four and you get 14²/₃ so 15 is the shortest board possible.

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

A) 31 x +( x + 8) = 70 2x + 8 = 70 x = 31

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 ft. × 30 = 1260 sq ft = total work space Then divide the space by 35 employees 1260 / 35 = 36 They did have 42 each and now have 36 each difference = 6

Stan bought a monster truck for a $2,000 down payment and $450 a month for five years. What's the total cost of the monster truck? (a) $4,250 (b) $29,000 (c) $27,000 (d) $34,000

B) $29,000 Five years contains 60 months $450 payments at 60 months = $27,000. Now add the down payment, $27,000 + $2,000 = $29,000

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 weights 12 ounces and the lunch and dinner rations weight 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 each truck can hold 3 tons, each ton is 2,000 lb so the truck can carry 6,000 lb. One pound = 16 oz, (6000 lb)(16) = 96,000 oz Now find the daily total for each persons 12oz + 18oz + 18oz = 48oz. 96,000 / 48 = 2,000 daily rations. These rations need to last 10 days 2,000 ÷ 10 = 200.

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

B) 500,000 x= original prediction 600,00 = (1 + .2)x 600,000/1.2 = x x = 500,000.

Jenny's test grades are 93,89, 96, and 98. If she wishes to raise her average to 95, what does she need to score on her next test? (a) 100 (b) 99 (c) 97 (d) 95

B) 99 x = the unknown score. (93 + 89 + 96 + 98 + x) / 5 =95 (376 + x) / 5 =95 376 + x = 475 x= 99

MIchael needs 55 gallons if paint to paint an apartment building. He would like to purchase the paint for the least amount money possible. Which of the following should he buy? (a) two 25-gallon buckets at $550 each (b) eleven 5-gallon buckets at $108 each (c) six at 10-gallon buckets at $215 each (d) fifty-five 1-gallon bucket at $23 each

B) Eleven 5-gallon buckets at $108 each Choice (a) doesn't have enough paint (2 ×25 gal = 50 gal) so it's wrong. Choice (b): 11 × $108 = $1,188 Choice (c): 6 × $215 = $1,290 Choice (d): 55 × $23 = $1265

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 First expand the equation (a+b)² or (a+b)(a=b) into y = a² + 2ab +b² . You already know ab = 10 and a² + b² = 30, so substitute the known values and solve for y. 30 + 2(10) = 50

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

C) 52.5 mph First, find how far Alice had traveled 31/2 hours at 45 mph = 157.5 mph. Dave has three hours to cover this distance. Now find his speed. 157.5 mi / 3 hr = 52.5 mph.

An aircraft flies over Boondock Air Force Base at 10:20 a.m. At 10:32 a.m., the plane 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 120 miles/12 min = x miles/60 min 12x = 7200 x = 600

A train headed south for Wichita left the station at the same time a train headed north for Des Moines left the same station. The train headed to Wichita traveled 55 miles per hour. The train headed for Des Moines traveled at 70 miles per hour. How many miles apart are the trains at the end of three hours? (a) 210 miles (b) 165 miles (c) 125 miles (d) 375 miles

D) 375 miles take the distance traveled by the Wichita train (55mph × 3hr = 165 miles) then add that to the distance traveled by the Des Moines train (70mph × 3hr = 210 miles). The trains are 375 miles apart in 3 hours.