Mean: Essential Concepts for Competitive Exam Success

Mean

Q. The mean of 7, 9, 11, 13, and x is 10. What is the value of x?

A. 5
B. 7
C. 9
D. 11

Solution

Mean = (7 + 9 + 11 + 13 + x) / 5 = 10.\n\n40 + x = 50\n\nx = 50 - 40 = 10.

Correct Answer: A — 5

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Q. The mean of 7, 9, 11, and 13 is what? (2019)

A. 9
B. 10
C. 11
D. 12

Solution

Mean = (7 + 9 + 11 + 13) / 4 = 40 / 4 = 10.

Correct Answer: B — 10

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Q. The mean of 8, 12, 16, and 20 is what? (2019)

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

Solution

Mean = (8 + 12 + 16 + 20) / 4 = 56 / 4 = 14.

Correct Answer: B — 15

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Q. The mean of 8, 12, 16, and x is 14. Find the value of x.

A. 10
B. 12
C. 14
D. 16

Solution

Mean = (8 + 12 + 16 + x) / 4 = 14. Therefore, 36 + x = 56, so x = 20.

Correct Answer: A — 10

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Q. The mean of a set of numbers is 15. If one number is removed, the mean becomes 12. What was the removed number?

A. 18
B. 20
C. 24
D. 30

Solution

Let the total number of items be n. Then, 15n - x = 12(n - 1). Solving gives x = 24.

Correct Answer: C — 24

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Q. The mean of a set of numbers is 25. If one number is increased by 5, how does the mean change?

A. Increases by 1
B. Increases by 0.5
C. Remains the same
D. Decreases by 1

Solution

Increasing one number by 5 increases the total sum by 5. If there are n numbers, the mean increases by 5/n.

Correct Answer: A — Increases by 1

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Q. The mean of a set of numbers is 30. If one more number, 50, is added to the set, what will be the new mean if the original set had 10 numbers?

A. 32
B. 33
C. 34
D. 35

Solution

The original sum of the numbers is 30 * 10 = 300. Adding 50 gives a new sum of 300 + 50 = 350. The new mean is 350 / 11 = 31.82, which rounds to 32.

Correct Answer: B — 33

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Q. The mean 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. Mean = (5x + 10) / 5 = 12. Solving gives x = 10.

Correct Answer: A — 10

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Q. The mean of five numbers is 20. If one number is removed, the mean of the remaining numbers becomes 18. What is the number that was removed?

A. 10
B. 12
C. 14
D. 16

Solution

Let the sum of the five numbers be S. Then, S/5 = 20, so S = 100. Let the removed number be x. The new sum is S - x, and the new mean is (S - x)/4 = 18. Therefore, 100 - x = 72, which gives x = 28.

Correct Answer: C — 14

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Q. The mean of the first four prime numbers is what? (2019)

A. 2
B. 3
C. 5
D. 7

Solution

The first four prime numbers are 2, 3, 5, and 7. Mean = (2 + 3 + 5 + 7) / 4 = 17 / 4 = 4.25.

Correct Answer: C — 5

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Q. The mean of the numbers 4, 8, 10, 12, and x is 10. What is the value of x? (2021)

A. 10
B. 12
C. 14
D. 16

Solution

Mean = (4 + 8 + 10 + 12 + x) / 5 = 10. Solving gives x = 14.

Correct Answer: C — 14

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Q. The mean of the numbers 4, 8, 12, and x is 10. What is the value of x?

A. 10
B. 12
C. 16
D. 20

Solution

Mean = (4 + 8 + 12 + x) / 4 = 10. Therefore, 4 + 8 + 12 + x = 40. So, x = 40 - 24 = 16.

Correct Answer: C — 16

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

A. 19, 20, 21
B. 18, 19, 20
C. 20, 21, 22
D. 21, 22, 23

Solution

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

Correct Answer: A — 19, 20, 21

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Q. The mean of three numbers is 12. If one of the numbers is 8, what is the mean of the other two numbers? (2021)

A. 10
B. 12
C. 14
D. 16

Solution

Total of three numbers = 3 * 12 = 36. Sum of the other two numbers = 36 - 8 = 28. Mean of the other two = 28 / 2 = 14.

Correct Answer: B — 12

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Q. The mean of three numbers is 15. If one number is increased by 5, what will be the new mean?

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

Solution

New mean = (15*3 + 5) / 3 = 20/3 = 16.67.

Correct Answer: B — 16

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Q. The mean of three numbers is 15. If one of the numbers is 10, what is the mean of the other two numbers? (2020)

A. 15
B. 20
C. 25
D. 10

Solution

Let the other two numbers be a and b. Then, (10 + a + b) / 3 = 15. Solving gives (a + b) = 35, so Mean of a and b = 35 / 2 = 17.5.

Correct Answer: B — 20

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Q. The mean of three numbers is 30. If one of the numbers is 20, what is the mean of the other two numbers? (2023)

A. 25
B. 30
C. 35
D. 40

Solution

Let the three numbers be a, b, c. Then, (a + b + 20) / 3 = 30. Thus, a + b = 90, and the mean of a and b = 90 / 2 = 45.

Correct Answer: A — 25

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Mean

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