Arithmetic Reasoning

Question 1

1: 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

Answer 1

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.

Question 2

2: How many omelets can be made from 2 dozen eggs if an omelet contains 3 eggs?

A. 1
B. 3
C. 6
D. 8

Answer 2

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.

Question 3

3: 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.

Answer 3

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.

Question 4

4: 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

Answer 4

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.

Question 5

5: 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

Answer 5

B. $247.50

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

Question 6

6: 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

Answer 6

D. 216

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

Question 7

7: 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

Answer 7

A. $29

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

Question 8

8: 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

Answer 8

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.

Question 9

9: 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

Answer 9

D. $300

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

Question 10

10: 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.

Answer 10

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.

Question 11

11: 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

Answer 11

A. $16.05

A. $20 - $3.95 = $16.05.

Question 12

12: 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

Answer 12

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.

Question 13

13: 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

Answer 13

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.

Question 14

14: 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%

Answer 14

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%.

Question 15

15: 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%

Answer 15

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:

Question 16

16: 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

Answer 16

C. $1,135

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

Question 17

17: 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

Answer 17

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.

Question 18

18: 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

Answer 18

18: 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

Question 19

19: 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

Answer 19

C. $87.10

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

Question 20

20: 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

Answer 20

A. 1 7/8

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

Question 21

21: 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

Answer 21

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.

Question 22

22: 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

Answer 22

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.

Question 23

23: 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

Answer 23

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.

Question 24

24: 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

Answer 24

D. 200 minutes

Question 25

25: 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

Answer 25

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.

Question 26

26: 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

Answer 26

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.

Question 27

27: 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

Answer 27

B. $2.93

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

Question 28

28: 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

Answer 28

C. 11 yards

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

Question 29

29: 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

Answer 29

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

Question 30

30: 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

Answer 30

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.