Mean: Essential Concepts for Competitive Exam Success

Mean

Q. If the mean of a set of numbers is 30 and the total number of elements is 6, what is the total sum of the elements? (2023)

A. 180
B. 150
C. 120
D. 200

Solution

Total sum = Mean * Number of elements = 30 * 6 = 180.

Correct Answer: A — 180

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Q. If the mean of a set of numbers is 50 and there are 5 numbers, what is the total sum of the numbers? (2020)

A. 200
B. 250
C. 300
D. 350

Solution

Total sum = Mean * Number of items = 50 * 5 = 250.

Correct Answer: A — 200

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Q. If the mean of five numbers is 20, what is their total sum? (2020)

A. 80
B. 100
C. 120
D. 140

Solution

Mean = Total Sum / Number of Items. Therefore, Total Sum = Mean * Number of Items = 20 * 5 = 100.

Correct Answer: A — 80

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Q. If the mean of the first five prime numbers is 6, what is the sum of these numbers? (2020)

A. 30
B. 25
C. 35
D. 20

Solution

Mean = Sum / 5. Therefore, Sum = Mean * 5 = 6 * 5 = 30.

Correct Answer: A — 30

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Q. If the mean of the first n natural numbers is 10, what is the value of n?

A. 20
B. 19
C. 18
D. 15

Solution

Mean = n(n + 1) / (2n) = 10.\n\n(n + 1) / 2 = 10\n\n(n + 1) = 20\n\nn = 19.

Correct Answer: A — 20

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Q. If the mean of the first n natural numbers is 15, what is the value of n? (2019)

A. 29
B. 30
C. 31
D. 32

Solution

Mean = n(n + 1) / (2n) = (n + 1) / 2 = 15. Therefore, n + 1 = 30, so n = 29.

Correct Answer: B — 30

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Q. In a class of 30 students, the average height is 160 cm. If the height of one student is 170 cm, what is the new average height after removing that student?

A. 159 cm
B. 160 cm
C. 161 cm
D. 162 cm

Solution

Total height = 30 * 160 = 4800 cm. New total = 4800 - 170 = 4630 cm. New average = 4630 / 29 = 159.66 cm.

Correct Answer: A — 159 cm

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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 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, 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 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 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 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 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 numbers is 15. If one number is increased by 5, what will be the new average?

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

Solution

Total of three numbers = 3 * 15 = 45.\n\nNew total = 45 + 5 = 50.\n\nNew average = 50 / 3 = 16.67.

Correct Answer: B — 16

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Q. The average of three numbers is 40. If the first number is increased by 10, what will be the new average?

A. 42
B. 43
C. 44
D. 45

Solution

The sum of the three numbers is 3 * 40 = 120. Increasing the first number by 10 gives a new sum of 120 + 10 = 130. The new average is 130 / 3 = 43.33, which rounds to 42.

Correct Answer: A — 42

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Q. The average of two numbers is 30. If one number is 20, what is the other number?

A. 40
B. 50
C. 60
D. 70

Solution

Mean = (20 + x) / 2 = 30.\n\n20 + x = 60\n\nx = 60 - 20 = 40.

Correct Answer: A — 40

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

A. 52
B. 50
C. 48
D. 46

Solution

Total of 10 numbers = 10 * 50 = 500. Total of 9 numbers = 9 * 48 = 432. Removed number = 500 - 432 = 68.

Correct Answer: A — 52

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Q. The mean of 10, 20, 30, 40, and x is 25. What is the value of x? (2022)

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

Solution

Mean = (10 + 20 + 30 + 40 + x) / 5 = 25. Therefore, 100 + x = 125, so x = 25.

Correct Answer: A — 10

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

A. 4
B. 6
C. 8
D. 10

Solution

Mean = (4 + 6 + 8 + x) / 4 = 7. Thus, 18 + x = 28, so x = 10.

Correct Answer: D — 10

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Q. The mean of 5, 10, 15, 20, and x is 12. What is the value of x?

A. 5
B. 10
C. 15
D. 20

Solution

Mean = (5 + 10 + 15 + 20 + x) / 5 = 12.\n\n50 + x = 60\n\nx = 60 - 50 = 10.

Correct Answer: A — 5

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Q. The mean of 5, 10, 15, and 20 is what?

A. 10
B. 12.5
C. 15
D. 17.5

Solution

Mean = (5 + 10 + 15 + 20) / 4 = 50 / 4 = 12.5.

Correct Answer: C — 15

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Q. The mean of 5, 10, 15, and x is 12. What is the value of x?

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

Solution

Mean = (5 + 10 + 15 + x) / 4 = 12. Therefore, 30 + x = 48, so x = 18.

Correct Answer: A — 8

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Q. The mean of 5, 15, 25, and x is 20. Find the value of x. (2023)

A. 20
B. 25
C. 30
D. 35

Solution

Mean = (5 + 15 + 25 + x) / 4 = 20. Solving gives x = 30.

Correct Answer: C — 30

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Q. The mean of 5, 15, and x is 10. What is the value of x? (2020)

A. 5
B. 10
C. 15
D. 20

Solution

Mean = (5 + 15 + x) / 3 = 10. Therefore, 20 + x = 30, so x = 10.

Correct Answer: D — 20

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Q. The mean of 6, 8, 10, and x is 9. What is the value of x? (2022)

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

Solution

Mean = (6 + 8 + 10 + x) / 4 = 9. Therefore, 24 + x = 36, so x = 12.

Correct Answer: D — 12

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

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

Solution

Mean = (7 + 9 + 11 + 13 + x) / 5 = 10. Solving gives x = 5.

Correct Answer: A — 5

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Mean

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