Arithmetic Reasoning ASVAB

A bread recipe calls for 3 1/4 cups of flour. If you only have 2 1/8 cups, how much more flour is needed? A. 1 1/8 B. 1 1/4 C. 1 3/8 D. 1 3/4

A. 1 1/8 A. 3 1/4 - 2 1/8= 13/4 - 17/8= 26/8 - 17/8 = 9/8 = 1 1/8 more cups of flour.

You use a $20 bill to buy a magazine for $3.95. What change do you get back? A. $16.05 B. $16.95 C. $17.05 D. $17.95

A. $16.05 A. $20 - $3.95 = $16.05.

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 A. Using the ratio ?, the proportion ? models this situation, where x represents the height of the pole. Cross multiply. ?, so 84 = 6x, and ? feet.

An aquarium is 12 inches high, 24 inches long, and 10 inches wide. A goldfish needs 144 cu bic inches of space to live. How many goldfish can this aquarium support? A. 15 B. 20 C. 22 D. 24

B

Robby is twice as old as Greg. If Robby is 46 years old, how old is Greg? A. 15 B. 23 C. 25 D. 27

B

A cardboard box has a length of 3 feet, height of 2½ feet, and depth of 2 feet. If the length and depth are doubled, by what percent does the volume of the box change? A. 200% B. 300% C. 400% D. 600%

B. 300% B. The volume of the original box is ?. The volume of the box with the length and depth doubled is ?. The amount of change in volume is 60 - 15 = 45. The percent change is the amount of change in volume divided by the original volume:

A machine can produce 8,000 widgets in 3 hours. How many widgets are produced in 1 day? A. 96,000 B. 64,000 C. 32,000 D. 8,000

B. 64,000 B. If a machine produces 8,000 widgets in 3 hours, it produces ? widgets in 1 hour. There are 24 hours in a day, so ? or 64,000 widgets are produced in 1 day.

During the first year of life, a whale gains about 30 tons of weight. What is the average weight gain per month? A. 1.2 tons B. 2.5 tons C. 2.9 tons D. 3.1 tons

B. To calculate the average, take the number of tons and divide by the number of months. 30/12 = 2.5 tons per month

Karin is as old as her two cousins combined. If Karin is 54 and one cousin is 21, how old is the second cousin? A. 13 B. 22 C. 33 D. 37

C

Sylvia wants to plant flowers in a window box that measures 48 inches long, 10 inches high, and 18 inches wide. If a bag of potting soil holds 1,440 cubic inches of soil, how many bags should she purchase? A. 2 B. 4 C. 6 D. 8

C

Mr. Triber earns a weekly salary of $300 plus 10% commission on all sales. If he sold $8,350 last week, what were his total earnings? A. $835 B. $865 C. $1,135 D. $1,835

C. $1,135 C. The amount of commission is 10% × $8,350 = $835. Total earnings are $300 + $835 commission = $1,135.

If Gary earns $53/hour during a regular workday of 8 hours and $57/hour for any work he does after 5 P.M., how much does he earn if he worked 5 regular work days and 6.5 overtime hours? A. $1,870.50 B. $2,292.25 C. $2,490.50 D. $2,597.50

C. Multiply the number of hours worked by the regular rate of $53 per hour and add that to the overtime hours multiplied by the overtime rate. The number of regular hours worked is 5 × 8 or 40. 40($53) + 6.5($57) = $2,490.50

Staci earns $9.50 an hour plus 3% commission on all sales made. If her total sales during a 30-hour work week were $500, how much did she earn? A. $15 B. $250 C. $285 D. $300

D. $300 D. For a 30-hour week with $500 in sales, total earnings are (30 × $9.50) + (3% × $500) = $285 + $15 = $300.

Roxanne deposited $300 into a savings account earning 5¼% annually. What is her balance after 1 year? A. $15.75 B. $315 C. $315.25 D. $315.75

D. $315.75 D. Interest earned in 1 year is ?. The total amount of the account after 1 year is $300 + $15.75 = $315.75.

There are 72 freshmen in the band. If freshmen make up 1/3 of the entire band, the total number of students in the band is A. 24 B. 72 C. 144 D. 216

D. 216 D. Let n represent the number of students in the band. Then 1/3n = 72, so n = 72 × 3 = 216.

A manufacturer can produce 112 shirts per hour. If a work day is 8 hours, how many shirts can be produced in 3.5 days? A. 392 B. 1,125 C. 1,236 D. 3,136

D. Set this up as a proportion. If 112 shirts can be produced in 1 hour, then [ x ] shirts can be pro duced in 8 hours. The proportion would look like this: 112 = x . 18 Cross-multiply and solve for x . 1 x = 896. So 896 shirts can be produced in one 8-hour day. The question asks how many can be produced in 3.5 days, so multiply 896 by 3.5 to get the final answer of 3,136

Rachel ran ½ mile in 4 minutes. At this rate, how many miles can she run in 15 minutes? A. 1 7/8 B. 4 C. 30 D. 60

A. 1 7/8 A. The proportion ? models this situation. Cross multiply. ?, so ? and x = ? miles.

The length of a rectangle is three times its width. If the perimeter of the rectangle is 48, what is its area? A. 108 B. 96 C. 54 D. 48

A. 108 A. The perimeter of a rectangle is l + w + l + w = 48. Since l = 3w, the perimeter is 3w + w + 3w + w = 48 so 8w = 48 and w = 6. Therefore, the length is 3 × 6 or 18 and the area of the rectangle is l × w = 18 × 6 = 108.

A sweater originally priced at $40 is on sale for $30. What percent has the sweater been discounted? A. 25% B. 33% C. 70% D. 75%

A. 25% A. The amount of discount is $40 - $30 = $10. The percent of discount is the amount of discount divided by the original price. 10/40 = 1/4 = 25%.

Jamie collects 300 stamps one week, 420 stamps the next week, and 180 stamps the last week. He can trade the stamps for collector coins. If 25 stamps earn him one coin, how many coins can Jamie collect? A. 36 B. 50 C. 900 D. 925

A. 36 A. The total number of stamps collected is 300 + 420 + 180 = 900. The number of coins that can be collected is 900/25 = 36.

At an electronics store, Sal bought a CD for $14.99, another CD for $19.99, a CD player for $49.75, and a software program for his com- puter for $56.59. What was his total bill? A. $121.45 B. $125.42 C. $139.72 D. $141.32

D. This is a simple addition problem. Add the amounts to get the total of $141.32.

Simon's garden is 12 by 24 feet. He will plant bushes that require 8 sq ft of space. How many bushes can he plant? A. 16 B. 24 C. 27 D. 36

D. To calculate the area of Simon's garden, use the formula A = lw . =× = A A 12 ft 24 ft 288 ft 2 If each bush needs 8 ft 2 of space, divide 288 by 8. = 288 ft 8 36 bushes

A restaurant had a delivery of 12 cartons of vegetables and 36 cartons of fruit. What is the ratio of vegetable cartons to fruit cartons? A. 1 4 B. 1 8 C. 1 3 D. 6 12

C. To find the ratio of one number to another, create a fraction to show the relationship. In this problem 12 cartons of vegetables are compared to 36 cartons of fruit. The resulting fraction is 12 36 . Simplifying this fraction results in a ratio of . You might see this as 1:3 on the ASVAB test. 1 3 1 3 and 1:3 mean the same thing.

Dana receives $30 for her birthday and $15 for cleaning the garage. If she spends $16 on a CD, how much money does she have left? A. $29 B. $27 C. $14 D. $1

A. $29 A. Add the amount of money received and subtract the amount spent. $30 + $15 - $16 = $29.

Jake is riding a bicycle on a circular track. The distance from the center of the track to the outside of the circle is 10 meters. How far will Jake ride if he goes around the track one time? A. 62.8 m B. 145.5 m C. 157.8 m D. 162.8 m

A. To find the circumference of a circle, use the formula C = 2 p r . The radius is given as 10 meters. Substitute that information into the formula C = 2(3.14)10. Solve for C. C = 62.8 meters.

How many omelets can be made from 2 dozen eggs if an omelet contains 3 eggs? A. 1 B. 3 C. 6 D. 8

D. 8 D. There are 24 eggs in 2 dozen eggs. If 3 eggs are in an omelet, then 24 ÷ 3, or 8 omelets, can be made.

Ned works after school. When he cuts grass, he earns $6.25 per hour. When he delivers papers, he earns $5.95 per hour and when he runs er rands for people, he earns $5.50 per errand. If in one week he cut grass for 6 hours, delivered papers for 11 hours, and ran 6 errands, how much money did he earn? A. $114.95 B. $135.95 C. $144.15 D. $156.05

B. Create an equation to solve this problem. This problem requires both multiplication and addition. 6($6.25) + 11($5.95) + 6($5.50) = $37.50 + $65.45 + $33.00 = $135.95

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

.C

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 be fore the deductions? A. $3,550.50 B. $3,665.72 C. $4,175.50 D. $4,278.50

A

Ellen baked 112 cookies and shared them equally with her 23 classmates. How many whole cookies each can Ellen and her classmates have? A. 4 B. 5 C. 6 D. 7

A. If Ellen baked 112 cookies for herself and her 23 classmates, divide 24 into 112 to get 4.67. The question asks for the number of whole cookies, so there are 4 per person plus some fraction of a cookie left over. The correct answer is 4

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 ft 2 . How many gallons of paint must he purchase? A. 6 B. 8 C. 12 D. 15

A. Leon has four walls that are 8 ft by 30 ft. That's an area of 240 f t 2 for each of four walls. For all four walls, multiply 240 by 4, giving a total square footage of 960 f t 2 . If a quart of paint covers 40 f t 2 , then you need to divide 960 by 40, which results in 24 quarts of paint. The question asks for the number of gallons. Since there are 4 quarts in a gallon, divide 24 by 4 to get 6 gallons.

Gerard throws a discus distances of 10 meters, 14.5 meters, 14.8 meters, 16.7 meters, and 15.4 meters. On his last attempt he faults, which counts as 0 meters. What is his average throwing distance? A. 11.9 meters B. 12.8 meters C. 13.78 meters D. 14.28 meters

A. To find the average, add the numbers and di vide by the number of numbers. In this prob- lem add 10, 14.5, 14.8, 16.7, 15.4, and 0 to get 71.4. Divide this by 6. = 71.4 6 11.9 Caution: Don't forget that the zero counts as a number, so be sure to divide by 6, not 5.

Sam buys three candy bars for 45 cents each and two packs of gum for 79 cents each. What is the total cost of this purchase? A. $1.24 B. $2.93 C. $6.20 D. $6.24

B. $2.93 B. The total cost of the purchase is (3 × $0.45) + (2 + $0.79) = $1.35 + $1.58 = $2.93.

An employee earns $8.25 an hour. In 30 hours, what earnings has the employee made? A. $240.00 B. $247.50 C. $250.00 D. $255.75

B. $247.50 B. The earnings for 30 hours are $8.25 × 30 = $247.50.

If 400 people can be seated in eight subway cars, how many people can be seated in five subway cars? A. 200 B. 250 C. 300 D. 350

B. 250 B. If 400 people fit in eight subway cars, then 400 ÷ 8, or 50, people fit in one subway car. Therefore, 50 × 5, or 250, people fit in five subway cars.

A family goes to a restaurant, and the bill is $112.00. If the parents want to leave the waitperson a 15 percent tip, how much should they leave? A. $15.40 B. $16.80 C. $17.25 D. $17.85

B. If the bill is $112.00, a tip of 15% is calcu- lated by multiplying $112.00 by 0.15. $112.00 × 0.15 = $16.80

Elaine was born on December 15 and has lived in Minneapolis, MN, all her life. Weather records show that over the last 100 years, it has snowed on December 15 60 percent of the time. If this trend continues and Elaine lives to be 85, on how many birthdays will she probably have snow? A. 47 B. 51 C. 54 D. 62

B. Multiply 85 years by 0.60 to get 51 years with snow

Sally's rent is $750.00 each month. After two years of paying rent, how much has she spent? A. $12,000 B. $18,000 C. $21,000 D. $24,000

B. Multiply the monthly rent by the number of months. There are 24 months in two years. 24 × $750 = $18,000

Vanessa has a drawer full of headbands. Twenty are pink , 32 are blue, and 16 are black. If she reaches into the drawer and picks out a head- band at random, what is the probability that the headband will not be black? A. 17 32 B. 13 17 C. 16 32 D. 1 2

B. Probability = number of favorable outcomes/ number of possible outcomes. In this problem the number of possible outcomes equal 0 + 32 + 16 = 68. The number of favorable out- comes is the sum of pink and blue or 20 + 32 = 52. = , 52 68 13 17 the correct answer when simplified.

Brad placed several calls on his cell phone dur- ing the first half of the month. The calls were 15 minutes, 46 minutes, 59 minutes, 83 minutes, and 114 minutes. If his plan authorizes 400 min- utes, how many minutes does he have left? A. 47 B. 83 C. 113 D. 147

B. This problem has two steps. First you need to add the number of minutes Brad used. Then you need to subtract that amount from his al location of 400 minutes. The total number of minutes used was 317, so subtracting that from 400 leaves 83 minutes.

Trinidad earns $2,700 per month. If she spends $1,100 on the rent for her apartment, to the nearest percent what percent is spent on rent? A. 20% B. 41% C. 51% D. 65%

B. To determine the percent, you need to divide the amount Trinidad spends on rent by the amount that she earns. In this problem, $1,100 is divided by $2,700 with the result coming to 40.7%. Rounding to the nearest percent gives the correct answer of 41%

Tim has run a 500-meter race four times. His times are 169 seconds, 212 seconds, 198 sec- onds, and 201 seconds. What is his average speed? A. 182 seconds B. 195 seconds C. 198 seconds D. 201 seconds

B. To find the average, add the numbers and divide by the number of numbers. In this problem Tim's times add up to 780 seconds. Dividing that number by 4 gives an average of 195 seconds.

At the local department store, a flat screen television retails for $4,250. Manuel finds the same television for sale on the Internet for $450 less. What percent will Manuel save if he purchases the television via the Internet site? A. 5.2% B. 10.6% C. 12.8% D. 15%

B. Use the following formula: percent of change = amount of change/starting point. In this problem we know that the amount of change is $450 if Manuel purchases the TV online. The starting point is the cost of the TV at the local department store, $4,250. Substitute that information into the formula: percent of change = $450.00/4250.00 = 0.106. Change the result to a percent by moving the decimal place two places to the right and adding the percent sign. 0.106 = 10.6%

Rae earns $8.40 an hour plus an overtime rate equal to 1½ times her regular pay for each hour worked beyond 40 hours. What are her total earnings for a 45-hour work week? A. $336 B. $370 C. $399 D. $567

C. $399 C. The overtime rate is $8.40 × 1.5 = $12.60. Five hours of overtime were completed, so the total earnings are ($8.40 × 40) + ($12.60 × 5) = $336 + $63 = $399.

Davis donates 4/13 of his paycheck to his favorite charity. If he donates $26.80, what is the amount of his paycheck? A. $8.25 B. $82.50 C. $87.10 D. $348.40

C. $87.10 C. Let p represent the amount of the paycheck. 4/13p? = , so ?.

Devin throws a football 7 1/3 yards. Carl throws it 2 1/2 times farther. How much farther did Carl's throw travel than Devin's? A. 2 1/2 yards B. 3 1/3 yards C. 11 yards D. 18 1/3 yards

C. 11 yards C. Carl's throw went ? yards. The difference between the two throws is ? yards.

On a map, 1 centimeter represents 4 miles. A distance of 10 miles would be how far apart on the map? A. 1¾ centimeters B. 2 centimeters C. 2½ centimeters D. 4 centimeters

C. 2½ centimeters C. The proportion ? models this situation. Cross multiply. 1 × 10 = 4x, so 10 = 4x and ?.

Two runners finished a race in 80 seconds, another runner finished the race in 72 seconds, and the final runner finished in 68 seconds. The average of these times is A. 73 seconds. B. 74 seconds. C. 75 seconds. D. 76 seconds.

C. 75 seconds. C. Since two runners finished in 80 seconds, the average of 80, 80, 72, and 68 must be found. This average is ? seconds.

This morning, Taryn drove 13 miles to the library and then returned home. In the afternoon, she drove 9 miles to the movies and returned home. How much farther did Taryn travel in the morning? A. 4 miles B. 6 miles C. 8 miles D. 9 miles

C. 8 miles C. The total distance traveled in the morning was 13 × 2 = 26 miles. The total distance traveled in the afternoon was 9 × 2 = 18 miles. The difference between the two distances is 26 - 18 = 8 miles.

A math class has 32 students. Fourteen are females. What percent of the class is female? A. 24.22% B. 37.25% C. 43.75% D. 52.75%

C. In order to calculate the percent, you need to divide the number of female students by the total number of students. In this case you would divide 14 by 32 to get 0.4375. To change that to a percent, move the decimal point two places to the right and add the percent sign to get the correct answer of 43.75%.

The movie Gladiator earned $6 million in the first week of its showing. All movies shown that week earned $114 million. Which of the following shows the ratio of the earnings of Gladiator to the earnings of all movies that week? A. 1:4 B. 2:13 C. 1:19 D. 3:8 24.

C. The ratio would be stated as 6:114 or . 6/114 Simplify this fraction to get 1/19

Jenny is 34 years old. Two years ago she was twice as old as her cousin. How old is her cousin now? A. 15 B. 17 C. 18 D. 21

C. Two years ago Jenny was 32 years old. She was twice the age of her cousin. Set this up as an equation. 2 c = 32. Solve for c. c = 16 Since we want the cousin's age now, which is two years later, it would be 18 (16 + 2).

Rita earns an annual salary of $30,000. Her boss promised her that next year she will earn $32,500. What percent increase is the new salary? A. 5.2% B. 6.3% C. 8.3% D. 9.1%

C. Use the formula percent of change = amount of change/starting point. The amount of change is the difference between $30,000 and $32,500 or $2,500. The starting point is the original salary of 30,000. Substitute the information into the formula. percent of change = $2500/$30,000= 0.083 or an 8.3% raise.

A television is on sale for 20% off. If the sale price is $800, what was the original price? A. $160 B. $640 C. $960 D. $1,000

D. $1,000 D. If an item is discounted 20%, the sale price is 80% of the original price. Let p represent the original price. Then $800 = 80% × p and p = 800/80% = 800/.80 = $1,000.

Tiling costs $2.89 per square foot. What is the cost to tile a kitchen whose dimensions are 4 yards by 5 yards? A. $57.80 B. $173.40 C. $289.00 D. $520.20

D. $520.20 D. There are 3 feet in a yard, so a kitchen 4 yards by 5 yards is equivalent to (4 × 3) feet by (5 × 3) feet, or 12 feet by 15 feet. The area of the kitchen is 12 × 15 = 180 square feet. The cost to tile is $2.89 × 180 = $520.20.

Heidi tallied the different car colors in the parking lot and summarized her results in a pie chart. There are 260 cars in the lot. How many cars are either red or black? A. 65 B. 78 C. 130 D. 143

D. 143 D. The percentage of cars that are either red or black are 25% + 30% = 55%. The total cars that are either red or black is 260 × 55% = 143.

One phone plan charges a $20 monthly fee and $0.08 per minute on every phone call made. Another phone plan charges a $12 monthly fee and $0.12 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

One-eighth of a bookstore's magazines are sold on a Friday. If ¼ of the remaining magazines are sold the next day, what fractional part of the magazines remains at the end of the second day? A. 1/32 B. 1/8 C. 7/32 D. 21/32

D. 21/32 D. At the end of the first day, there are ? of the magazines remaining. ? sold the next day. So at the end of the second day, there are ? of the magazines remaining.

The area of one circle is four times as large as a smaller circle with a radius of 3 inches. The radius of the larger circle is A. 12 inches. B. 9 inches. C. 8 inches. D. 6 inches.

D. 6 inches. D. The area of the circle with a radius of 3 is pr2 = p × r2 = 9p. The area of the larger circle is 4 × 9p = 36p. Therefore, r2 = 36, so r = √36 = 6. The radius of the larger circle is 6.

Five years ago, Ruth made a deposit of $500 into a savings account that pays simple inter- est. 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. Simple interest problems use the formula I = prt , where I is the amount of interest, p is the principal or the amount saved or invested, r is the rate of interest, and t is the amount of time in which the interest is accruing. In this problem you are asked to find the rate of inter- est given that Ruth has earned $250 in interest over 5 years. Substitute the information into the formula to get $250 = $500( r )5 and solve for r . $250 = $2,500 r ; r = 0.10 or 10%