Mean: Essential Concepts for Competitive Exam Success

Mean

Q. A class has 30 students with an average score of 75. If 5 new students join with an average score of 80, what is the new average? (2023)

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

Solution

Total score of 30 students = 30 * 75 = 2250. Total score of 5 new students = 5 * 80 = 400. New total = 2250 + 400 = 2650. New average = 2650 / 35 = 76.43.

Correct Answer: C — 78

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Q. A class has 30 students with an average score of 75. If a new student joins and the average becomes 76, what is the score of the new student? (2023)

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

Solution

Total score of 30 students = 30 * 75 = 2250. New total = 31 * 76 = 2356. Score of new student = 2356 - 2250 = 106.

Correct Answer: B — 85

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Q. A class has an average score of 75. If one student scored 90, what is the average score of the remaining students if there are 20 students in total?

A. 74
B. 75
C. 76
D. 77

Solution

The total score of the class is 75 * 20 = 1500. Removing the student who scored 90 gives a new total of 1500 - 90 = 1410. The average of the remaining 19 students is 1410 / 19 = 74.21, which rounds to 74.

Correct Answer: A — 74

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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 age of 20 years. If a new student aged 22 joins the group, what will be the new average age if there were originally 15 students?

A. 20.5
B. 20.6
C. 20.7
D. 20.8

Solution

The total age of the original group is 20 * 15 = 300. Adding the new student gives 300 + 22 = 322. The new average age is 322 / 16 = 20.125, which rounds to 20.6.

Correct Answer: B — 20.6

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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 height of 160 cm. If one student with a height of 170 cm leaves, what will be the new average height if the group size was 10?

A. 158 cm
B. 159 cm
C. 160 cm
D. 161 cm

Solution

Total height = 160 * 10 = 1600 cm. New total = 1600 - 170 = 1430 cm. New average = 1430 / 9 = 158.89 cm, approximately 159 cm.

Correct Answer: B — 159 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 15. If one number is removed, the new mean becomes 12. What was the removed number? (2022)

A. 9
B. 12
C. 15
D. 18

Solution

Let the number of items be n. Then, 15n - x = 12(n - 1). Solving gives x = 18.

Correct Answer: D — 18

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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 scored 70, 80, and 90 in three exams. What score is needed in the fourth exam to achieve a mean of 85?

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

Solution

Let the fourth score be x. Mean = (70 + 80 + 90 + x) / 4 = 85. Thus, 240 + x = 340, so x = 100.

Correct Answer: D — 95

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Q. A student scored 80, 85, 90, and 95 in four subjects. What score does he need in the fifth subject to achieve an average of 90?

A. 90
B. 95
C. 100
D. 105

Solution

Mean = (80 + 85 + 90 + 95 + x) / 5 = 90. Solving gives x = 100.

Correct Answer: C — 100

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Q. A student scores 80, 85, 90, and 95 in four exams. What score does he need in the fifth exam to achieve an average of 90?

A. 90
B. 95
C. 100
D. 85

Solution

Mean = (80 + 85 + 90 + 95 + x) / 5 = 90.\n\n350 + x = 450\n\nx = 450 - 350 = 100.

Correct Answer: C — 100

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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. A student scores 80, 90, and 70 in three subjects. If he wants to achieve an average of 85 after scoring in a fourth subject, what score does he need?

A. 90
B. 95
C. 100
D. 85

Solution

The current total score is 80 + 90 + 70 = 240. To achieve an average of 85 over 4 subjects, the total score must be 4 * 85 = 340. Therefore, the score needed in the fourth subject is 340 - 240 = 100.

Correct Answer: B — 95

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Q. If the average of 10 numbers is 50, what is the sum of these numbers?

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

Solution

Sum = Average * Number of items = 50 * 10 = 500.

Correct Answer: A — 500

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Q. If the average of 6 numbers is 30, what is the average if one number is increased by 10?

A. 30
B. 32
C. 34
D. 36

Solution

Total of 6 numbers = 6 * 30 = 180.\n\nNew total = 180 + 10 = 190.\n\nNew average = 190 / 6 = 31.67.

Correct Answer: B — 32

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Q. If the average of 7, 9, 11, and 13 is x, what is the value of x? (2023)

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

Solution

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

Correct Answer: B — 10

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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 average of five numbers is 60, what is the total of these numbers?

A. 300
B. 250
C. 350
D. 400

Solution

The total of the five numbers is calculated as average * number of items = 60 * 5 = 300.

Correct Answer: A — 300

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Q. If the mean of 10 numbers is 50, what is the mean of the first 5 numbers if their sum is 200?

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

Solution

Mean of 10 numbers = 50, so total sum = 500. Sum of last 5 numbers = 500 - 200 = 300. Mean of last 5 = 300 / 5 = 60.

Correct Answer: D — 60

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Q. If the mean of 12 numbers is 25, what is the sum of these numbers?

A. 250
B. 300
C. 275
D. 225

Solution

The sum of the numbers is calculated as mean * number of items = 25 * 12 = 300.

Correct Answer: A — 250

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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 10 numbers is 50, what is the mean if one number is increased by 10? (2021)

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

Solution

The total sum is 500. Increasing one number by 10 gives a new total of 510. New mean = 510 / 10 = 51.

Correct Answer: B — 51

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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 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 = 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 12 and there are 8 numbers in the set, what is the total sum of the numbers?

A. 96
B. 100
C. 80
D. 88

Solution

Total sum = Mean * Number of items = 12 * 8 = 96.

Correct Answer: A — 96

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Q. If the mean of a set of numbers is 25 and there are 12 numbers in the set, what is the total sum of the numbers?

A. 300
B. 250
C. 275
D. 325

Solution

Total sum = Mean * Number of items = 25 * 12 = 300.

Correct Answer: A — 300

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Q. If the mean of a set of numbers is 25 and there are 8 numbers, what is the total of these numbers? (2022)

A. 150
B. 200
C. 250
D. 300

Solution

Total = Mean * Number of Items = 25 * 8 = 200.

Correct Answer: C — 250

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