Arithmetic Reasoning Practice Set 1

  2. Select the best answer for each question. This section has 16 questions, which is the number of Arithmetic Reasoning questions you will see if you take the CAT-ASVAB.

  1. If |y − 3| = 3, what is the greatest possible value of y?
    1. 2
    2. 4
    3. 6
    4. 8
  2. Two teams are having a contest in which the prize is a box of candy that the members of the winning team will divide evenly. If team A wins, each player will get exactly 3 pieces of candy, and if team B wins, each player will get exactly 5 pieces of candy. Which of the following could be the number of pieces of candy in the box?
    1. 325
    2. 353
    3. 425
    4. 555
  3. What is the least common multiple of 7, 9, and 21?
    1. 21
    2. 63
    3. 147
    4. 189
  4. What is the value of ?
  5. What is the value of
    1. 5
    2. 7
    3. 14
    4. 35
  6. A copier can make 150 copies per minute. At this rate, how many minutes would it take to make 4,500 copies?
    1. 20
    2. 25
    3. 30
    4. 35
  7. The average (arithmetic mean) age of the members in a five-person choir is 34. If the ages of four of the members are 47, 31, 27, and 36, what is the fifth member’s age?
    1. 29
    2. 32
    3. 34
    4. 37
  8. In the past year, XYZ Corporation reported sales of $1.17 × 106. The year before, the company’s sales were $9.00 × 105. What was the percentage change in sales?
    1. 30% decrease
    2. 27% decrease
    3. 27% increase
    4. 30% increase
  9. What is the value of 30 − 5 × 4 + (7 − 3)2 ÷ 8?
    1. 4
    2. 12
    3. 36
    4. 102
  10. A group of five workers want to have a fair way of deciding who has to perform a difficult task, so they place 4 green balls and 1 red ball into an opaque box from which each worker will draw a ball at random. The person who draws the red ball will have to perform the task. What is the probability that the last (5th) person will get the red ball?
    1. 0.10
    2. 0.15
    3. 0.20
    4. 0.25

  11. John's grade for a class is determined by the results of 3 tests and 1 final exam. If the exam counts twice as much as each of the tests, what fraction of the final grade is determined by the final exam?


  12. If  , what is the value of  ?

    1. 160
    2. 200
    3. 400
    4. 500

  13. A full 10-liter container of diluted orange juice contains 20% water and 80% pure juice. After half of the diluted orange juice is consumed, 1 liter of pure juice is added to sweeten the taste. What is the ratio of liters of water to liters of pure juice after the liter of pure juice is added?

    1. 1:5
    2. 1:4
    3. 4:5
    4. 1:1

  14. For all integers x, which of the following must be true about 4x + 4?

    1. Must be even
    2. Must be odd
    3. Must be a multiple of 3
    4. Must be a multiple of 5

  15. A car is moving at 60 miles per hour. At this rate, how many hours will it take for the car to travel 420 miles?

    1. 5
    2. 6
    3. 7
    4. 8

  16. A building has   of its floors above ground. What is the ratio of the number of floors below ground to the number of floors above ground?

    1. 5:2
    2. 3:2
    3. 2:3
    4. 2:5

Arithmetic Reasoning Practice Set 2

  2. Select the best answer for each question. This section has 16 questions, which is the number of Arithmetic Reasoning questions you will see if you take the CAT-ASVAB.

  3. What is 28% of 25?

    1. 4
    2. 5
    3. 6
    4. 7

  4. What is the average of  ,  , and  ?

    4. 1

  5. How many ways are there to choose an outfit from 3 shirts and 4 pairs of pants, assuming an outfit consists of one shirt and one pair of pants?

    1. 4
    2. 7
    3. 12
    4. 20

  6. What is the value of  ?

    1. 6
    2. 9
    3. 10
    4. 25

  7. What is the value of  ?

    1. 0
    2. 15
    3. 47
    4. 72

  8. If  , what is the smallest possible value of  ?

    3. 15
    4. 25

  9. The average of x and y is 30. If z = 15, what is the average of the three terms x, y, and z?

    1. 3
    2. 15
    3. 25
    4. 30

  10. What is the value of  ?

    3. 1

  11. What is the greatest common factor of 50, 60, and 75?

    1. 2
    2. 5
    3. 10
    4. 25

  12. A $200 watch is on sale for $160. What is the percent change in the price of the watch?

    1. 25% decrease
    2. 20% decrease
    3. 20% increase
    4. 25% increase

  13. Michael can wash a car in two hours, and Jim can wash the same car in four hours. How long will it take the two of them working together to wash two of the same cars?

    1. 1 hour, 20 minutes
    2. 2 hours, 40 minutes
    3. 3 hours
    4. 6 hours

  14. What is the prime factorization of  ?

  15. In the set of numbers {1, 4, 7, 10, 13, 16, 19, 22, 25}, what is the arithmetic mean?

    1. 13
    2. 14.5
    3. 24.5
    4. 25

  16. If  , which of the following is a possible value of  ?

    3. 4
    4. 24

  17. For all positive values of x < 50, how many values are divisible by both 3 and 5?

    1. 0
    2. 1
    3. 2
    4. 3

  18. Three teams are having a contest in which the winning team will split a cash prize equally among all the members of the team. If Team 1 wins, each member will receive 10 dollars. If Team 2 wins, each member will receive 15 dollars. If Team 3 wins, each member will receive 25 dollars. Which of the following could be the number of dollars in the cash prize?

    1. 120
    2. 375
    3. 750
    4. 1,250