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Q. The average kinetic energy of gas molecules is proportional to which of the following?

A. Pressure
B. Volume
C. Temperature
D. Density

Solution

The average kinetic energy of gas molecules is directly proportional to the absolute temperature of the gas.

Correct Answer: C — Temperature

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Q. The average of 10 numbers is 50. If one number is removed, the average becomes 48. What is the removed number?

A. 60
B. 50
C. 40
D. 30

Solution

Total of 10 numbers = 10 * 50 = 500.\n\nTotal of 9 numbers = 9 * 48 = 432.\n\nRemoved number = 500 - 432 = 68.

Correct Answer: A — 60

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Q. The average of 10, 20, 30, and x is 25. What is the value of x?

A. 20
B. 30
C. 40
D. 50

Solution

Mean = (10 + 20 + 30 + x) / 4 = 25. Solving gives x = 50.

Correct Answer: C — 40

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Q. The average of 12 numbers is 15. If one number is removed, the average becomes 14. What is the removed number?

A. 16
B. 17
C. 18
D. 19

Solution

Total of 12 numbers = 12 * 15 = 180. Total of 11 numbers = 11 * 14 = 154. Removed number = 180 - 154 = 26.

Correct Answer: C — 18

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Q. The average of 12 numbers is 60. If one number is removed, the average becomes 58. What is the removed number?

A. 66
B. 60
C. 54
D. 62

Solution

Total of 12 numbers = 12 * 60 = 720. Total of 11 numbers = 11 * 58 = 638. Removed number = 720 - 638 = 82.

Correct Answer: D — 62

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Q. The average of 12 numbers is 60. If the average of the first 6 numbers is 70, what is the average of the last 6 numbers?

A. 50
B. 55
C. 60
D. 65

Solution

Total of 12 numbers = 12 * 60 = 720. Total of first 6 = 6 * 70 = 420. Total of last 6 = 720 - 420 = 300. Average of last 6 = 300 / 6 = 50.

Correct Answer: A — 50

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Q. The average of 12 numbers is 60. If the highest number is removed, the average of the remaining numbers is 58. What is the highest number?

A. 66
B. 68
C. 70
D. 72

Solution

Total of 12 numbers = 12 * 60 = 720. Total of 11 numbers = 11 * 58 = 638. Highest number = 720 - 638 = 82.

Correct Answer: C — 70

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Q. The average of 4 numbers is 15. If one number is increased by 5, what will be the new average? (2019)

A. 15
B. 16
C. 17
D. 18

Solution

Total of 4 numbers = 4 * 15 = 60. New total = 60 + 5 = 65. New average = 65 / 4 = 16.25.

Correct Answer: B — 16

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Q. The average of 4 numbers is 20. If one number is increased by 10, what will be the new average?

A. 20
B. 22.5
C. 25
D. 30

Solution

Total of 4 numbers = 4 * 20 = 80. New total = 80 + 10 = 90. New average = 90 / 4 = 22.5.

Correct Answer: B — 22.5

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Q. The average of 4 numbers is 25. If one number is increased by 5, what will be the new average?

A. 25
B. 26
C. 27
D. 28

Solution

Total of 4 numbers = 4 * 25 = 100. New total = 100 + 5 = 105. New average = 105 / 4 = 26.25.

Correct Answer: B — 26

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Q. The average of 4, 6, 8, and x is 7. What is the value of x?

A. 6
B. 8
C. 10
D. 12

Solution

Mean = (4 + 6 + 8 + x) / 4 = 7.\n\n18 + x = 28\n\nx = 28 - 18 = 10.

Correct Answer: C — 10

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Q. The average of 5 numbers is 12. If one number is removed, the average of the remaining numbers becomes 10. What is the number that was removed?

A. 8
B. 10
C. 12
D. 14

Solution

Total of 5 numbers = 5 * 12 = 60. Total of 4 numbers = 4 * 10 = 40. Number removed = 60 - 40 = 20.

Correct Answer: D — 14

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Q. The average of 5 numbers is 45. If the largest number is 60, what is the average of the other four numbers?

A. 40
B. 42
C. 44
D. 46

Solution

Total of 5 numbers = 5 * 45 = 225. Total of other four numbers = 225 - 60 = 165. Average of other four = 165 / 4 = 41.25.

Correct Answer: C — 44

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Q. The average of 5 numbers is 50. If one number is removed, the average becomes 45. What is the number that was removed?

A. 55
B. 60
C. 65
D. 70

Solution

Total of 5 numbers = 5 * 50 = 250. Total of 4 numbers = 4 * 45 = 180. Number removed = 250 - 180 = 70.

Correct Answer: A — 55

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Q. The average of 5 test scores is 76. If the highest score is removed, the average of the remaining scores is 72. What is the highest score?

A. 80
B. 84
C. 88
D. 92

Solution

Total score of 5 tests = 5 * 76 = 380. Total score of 4 tests = 4 * 72 = 288. Therefore, the highest score = 380 - 288 = 92.

Correct Answer: B — 84

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Q. The average of 5 test scores is 82. If the highest score is removed, the average becomes 80. What was the highest score?

A. 84
B. 85
C. 86
D. 87

Solution

Total score = 5 * 82 = 410. Total score without highest = 4 * 80 = 320. Highest score = 410 - 320 = 90.

Correct Answer: B — 85

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Q. The average of 6 numbers is 12. If one number is increased by 6, what will be the new average?

A. 12
B. 13
C. 14
D. 15

Solution

Total of 6 numbers = 6 * 12 = 72. New total = 72 + 6 = 78. New average = 78 / 6 = 13.

Correct Answer: B — 13

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Q. The average of 7 numbers is 14. If one number is added which is 10 more than the average, what will be the new average?

A. 15
B. 16
C. 17
D. 18

Solution

New total = 7 * 14 + (14 + 10) = 98 + 24 = 122. New average = 122 / 8 = 15.25.

Correct Answer: B — 16

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Q. The average of 8 numbers is 15. If one number is excluded, the average of the remaining numbers becomes 12. What is the excluded number?

A. 24
B. 20
C. 18
D. 16

Solution

The total sum of the 8 numbers is 8 * 15 = 120. Let the excluded number be x. The sum of the remaining 7 numbers is 120 - x, and their average is (120 - x)/7 = 12. Thus, 120 - x = 84, leading to x = 36.

Correct Answer: B — 20

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Q. The average of 8 numbers is 50. If one number is removed, the average becomes 48. What is the value of the removed number?

A. 56
B. 50
C. 48
D. 44

Solution

Total of 8 numbers = 8 * 50 = 400. Total of 7 numbers = 7 * 48 = 336. Therefore, the removed number = 400 - 336 = 64.

Correct Answer: A — 56

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Q. The average of a set of numbers is 50. If one number is removed, the average becomes 48. What was the number that was removed?

A. 50
B. 52
C. 54
D. 56

Solution

Let the number of items be n. Total sum = 50n. After removing one number, the new sum = 48(n - 1). Setting up the equation gives the removed number as 52.

Correct Answer: B — 52

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Q. The average of five consecutive integers is 12. What is the smallest of these integers?

A. 10
B. 11
C. 12
D. 13

Solution

Let the integers be x, x+1, x+2, x+3, x+4.\n\nMean = (5x + 10) / 5 = 12\n\n5x + 10 = 60\n\n5x = 50\n\nx = 10.

Correct Answer: B — 11

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Q. The average of five numbers is 18. If one number is excluded, the average becomes 16. What is the excluded number?

A. 20
B. 22
C. 24
D. 26

Solution

Total sum = 5 * 18 = 90. New sum = 4 * 16 = 64. Excluded number = 90 - 64 = 26.

Correct Answer: C — 24

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Q. The average of five numbers is 18. If one number is removed, the average becomes 16. What was the removed number?

A. 20
B. 22
C. 24
D. 26

Solution

Total of five numbers = 5 * 18 = 90. Total of four numbers = 4 * 16 = 64. Removed number = 90 - 64 = 26.

Correct Answer: C — 24

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Q. The average of five numbers is 20. If one number is excluded, the average of the remaining numbers becomes 18. What is the excluded number?

A. 22
B. 24
C. 20
D. 18

Solution

Total of five numbers = 5 * 20 = 100. Total of remaining four = 4 * 18 = 72. Excluded number = 100 - 72 = 28.

Correct Answer: A — 22

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Q. The average of five numbers is 20. If one number is removed, the average becomes 18. What is the number removed?

A. 22
B. 24
C. 20
D. 18

Solution

Total of five numbers = 5 * 20 = 100. Total of four numbers = 4 * 18 = 72. Number removed = 100 - 72 = 28.

Correct Answer: A — 22

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Q. The average of five numbers is 50. If one number is increased by 10, what will be the new average?

A. 52
B. 50
C. 51
D. 53

Solution

Total sum = 5 * 50 = 250. New total = 250 + 10 = 260. New average = 260 / 5 = 52.

Correct Answer: C — 51

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Q. The average of three consecutive integers is 15. What is the smallest of these integers?

A. 14
B. 15
C. 16
D. 17

Solution

Let the integers be x, x+1, x+2. Average = (x + (x+1) + (x+2)) / 3 = 15. Solving gives x = 14.

Correct Answer: A — 14

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Q. The average of three consecutive integers is 20. What are the integers?

A. 19, 20, 21
B. 18, 19, 20
C. 20, 21, 22
D. 17, 18, 19

Solution

Let the integers be x, x+1, x+2. (x + (x + 1) + (x + 2)) / 3 = 20. Therefore, 3x + 3 = 60, so x = 19.

Correct Answer: A — 19, 20, 21

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Q. The average of three consecutive integers is 20. What is the smallest of these integers? (2023)

A. 18
B. 19
C. 20
D. 21

Solution

Let the integers be x, x+1, x+2. The average is (x + (x + 1) + (x + 2)) / 3 = 20. Solving gives x = 18.

Correct Answer: A — 18

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Major Competitive Exams

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