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The MCQs below are drawn from the Mathematics subject category.
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7481
A batsman makes 87 runs in his 17th inning and thereby increases his average by 3. What is his new average?
A. 36
B. 39
C. 42
D. 33
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Correct Option
Explanation
Let the new average be x. The previous average for 16 innings was (x − 3). Total runs after 16 innings = 16(x − 3). Adding 87 runs gives 16(x − 3) + 87 = 17x. Solving gives x = 39.
7482
Find the average of the first five multiples of 3.
A. 15
B. 9
C. 12
D. 18
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Correct Option
Explanation
The first five multiples of 3 are 3, 6, 9, 12, and 15. Their sum is 45. Dividing by the number of terms (5) gives the average: 45 ÷ 5 = 9.
7483
If the average of x, y, z is 15 and x+y=20, then z equals:
A. 15
B. 20
C. 25
D. 30
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Correct Option
Explanation
The sum x+y+z = 3 * 15 = 45. We know x+y = 20. Therefore, 20 + z = 45, which gives z = 25.
7484
Average of 5 consecutive integers is 21. If the highest and lowest numbers are removed, what is the average of the remaining numbers?
A. 19
B. 20
C. 21
D. 22
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Correct Option
Explanation
For any symmetric sequence, removing the highest and lowest values symmetrically does not change the average. The middle term remains the same. The average remains 21.
7485
The average of 8, 11, 6, 14, x, and 13 is 10. Find the value of x.
A. 6
B. 8
C. 10
D. 12
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Correct Option
Explanation
The sum of the 6 numbers is 6 * 10 = 60. Sum of given 5 numbers = 8 + 11 + 6 + 14 + 13 = 52. So, x = 60 - 52 = 8.
7486
What is the average of the squares of the first 3 natural numbers?
A. 4
B. 4.67
C. 5
D. 6
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Correct Option
Explanation
The squares of the first 3 natural numbers are 1, 4, 9. Their sum is 1+4+9=14. Average = 14 / 3 = 4.666..., which rounds to 4.67.
7487
If the average of two numbers is ab and one number is a, the other number is:
A. 2ab - a
B. ab - a
C. 2ab + a
D. ab + a
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Correct Option
Explanation
Let the two numbers be x and y. Their average is (x+y)/2 = ab. Therefore, x+y = 2ab. If x = a, then a + y = 2ab, so y = 2ab - a.
7488
The average of 5 positive numbers is 100. If the first number is 20, what is the average of the remaining 4 numbers?
A. 100
B. 110
C. 120
D. 130
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Correct Option
Explanation
Total sum = 5 * 100 = 500. Sum of the remaining 4 numbers = 500 - 20 = 480. Average of the remaining 4 = 480 / 4 = 120.
7489
If the average of 5 terms is 10 and the average of 10 terms is 5, what is the combined average of these 15 terms?
A. 5
B. 6.67
C. 7.5
D. 8
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Correct Option
Explanation
Total sum = (5 * 10) + (10 * 5) = 50 + 50 = 100. Total terms = 15. Combined average = 100 / 15 = 20 / 3 = 6.67.
7490
The average marks of 30 students are 45. A student who scored 80 marks is mistakenly entered as 50. Find the correct average.
A. 44
B. 45
C. 46
D. 47
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Correct Option
Explanation
Difference = Correct Mark - Incorrect Mark = 80 - 50 = +30. This difference is distributed among the 30 students. Increase in average = 30 / 30 = +1. Correct average = 45 + 1 = 46.
