Mean: Essential Concepts for Competitive Exam Success

Mean

Q. A class of 30 students has an average score of 75. If one student scores 90, what will be the new average? (2022)

A. 76
B. 77
C. 78
D. 79

Solution

Total score = 75 * 30 = 2250. New total = 2250 - 75 + 90 = 2265. New average = 2265 / 30 = 75.5.

Correct Answer: B — 77

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Q. A group of students has an average height of 150 cm. If one student leaves the group and the average height becomes 148 cm, what is the height of the student who left?

A. 152 cm
B. 154 cm
C. 156 cm
D. 158 cm

Solution

Let the number of students be n. Total height = 150n. After one leaves, total height = 148(n - 1). Setting the equations gives 150n - 148(n - 1) = height of student.

Correct Answer: A — 152 cm

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Q. A group of students has an average score of 75. If one student with a score of 90 leaves, what will be the new average if the group size is 10?

A. 72
B. 73
C. 74
D. 75

Solution

Total score = 75 * 10 = 750. New total = 750 - 90 = 660. New average = 660 / 9 = 73.33.

Correct Answer: B — 73

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Q. A set of numbers has a mean of 20. If one number is removed, the mean becomes 18. What was the number removed? (2022)

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

Solution

Let the number of elements be n. Then, 20n - x = 18(n - 1). Solving gives x = 22.

Correct Answer: A — 22

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Q. A student scores 80, 85, and 90 in three subjects. If he wants an average of 85, what score does he need in the fourth subject?

A. 80
B. 85
C. 90
D. 95

Solution

Let the fourth score be x. (80 + 85 + 90 + x) / 4 = 85. Therefore, 255 + x = 340, so x = 85.

Correct Answer: B — 85

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Q. A student scores 80, 85, and 90 in three subjects. What score must he achieve in the fourth subject to have an average of 85?

A. 80
B. 85
C. 90
D. 95

Solution

Mean = (80 + 85 + 90 + x) / 4 = 85.\n\n255 + x = 340\n\nx = 340 - 255 = 85.

Correct Answer: B — 85

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Q. If the average of a set of numbers is 12 and there are 6 numbers, what is the total sum of the numbers?

A. 60
B. 72
C. 84
D. 96

Solution

Total sum = Average * Number of items = 12 * 6 = 72.

Correct Answer: B — 72

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Q. If the mean of a dataset is 50 and there are 10 numbers, what is the total sum of the numbers? (2021)

A. 500
B. 600
C. 550
D. 450

Solution

Total sum = Mean * Number of elements = 50 * 10 = 500.

Correct Answer: A — 500

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Q. If the mean of a set of numbers is 12 and there are 6 numbers in the set, what is the total sum of the numbers?

A. 60
B. 72
C. 84
D. 96

Solution

Total sum = Mean * Number of items = 12 * 6 = 72.

Correct Answer: A — 60

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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 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. 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, 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 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 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 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 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 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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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 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 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 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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