Averages: Essential Concepts for Competitive Exam Success

Averages

Q. A bag contains 3 red, 5 blue, and 2 green balls. What is the average number of balls per color?

A. 3
B. 5
C. 2
D. 4

Solution

Total balls = 3 + 5 + 2 = 10. Average = Total balls / Number of colors = 10 / 3 = 3.33.

Correct Answer: D — 4

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Q. A class has an average score of 65. If a new student with a score of 85 joins, how does the average change if the class size increases by one?

A. 66
B. 67
C. 68
D. 65

Solution

Total score = 65 * n + 85. New average = (65n + 85) / (n + 1).

Correct Answer: B — 67

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Q. A student has scores of 60, 70, and 80 in three tests. If he wants an average of 75 after the fourth test, what score does he need?

A. 90
B. 85
C. 80
D. 75

Solution

Let the fourth score be x. (60 + 70 + 80 + x) / 4 = 75 => 210 + x = 300 => x = 90.

Correct Answer: A — 90

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Q. A student scored 80, 90, and 70 in three subjects. If the fourth subject is scored 100, what will be the weighted average of the scores?

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

Solution

The average is (80 + 90 + 70 + 100) / 4 = 85.

Correct Answer: B — 90

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Q. If the average of 4 numbers is 50 and one number is 60, what is the average of the remaining three numbers?

A. 45
B. 50
C. 55
D. 60

Solution

Total of 4 numbers = 4 * 50 = 200. Remaining total = 200 - 60 = 140. Average of remaining = 140 / 3 = 46.67.

Correct Answer: A — 45

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Q. If the average of five numbers is 20, what is the total sum of these numbers?

A. 80
B. 100
C. 60
D. 40

Solution

Total sum = Average * Number of items = 20 * 5 = 100.

Correct Answer: A — 80

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Q. In a class of 40 students, the average score in Mathematics is 75. If 10 new students join with an average score of 85, what will be the new average?

A. 78
B. 80
C. 82
D. 76

Solution

Total score of 40 students = 40 * 75 = 3000. Total score of 10 new students = 10 * 85 = 850. New average = (3000 + 850) / 50 = 77.

Correct Answer: C — 82

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Q. In a survey, the average age of 10 people is 30 years. If one person aged 40 leaves, what will be the new average age?

A. 28
B. 29
C. 30
D. 31

Solution

Total age = 10 * 30 = 300. New total age = 300 - 40 = 260. New average = 260 / 9 = 28.89.

Correct Answer: B — 29

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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 numbers is 30. If one number is removed, the average becomes 25. What is the removed number?

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

Solution

Let the three numbers be x, y, z.  (x + y + z) / 3 = 30 => x + y + z = 90. After removing one number, (x + y) / 2 = 25 => x + y = 50. Therefore, removed number = 90 - 50 = 40.

Correct Answer: A — 35

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Averages

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