Which of the following statements is/are CORRECT?
I. The average of 6 numbers is 42. If one number is removed, the average of the remaining 5 numbers becomes 40, so the removed number is 52.
II. If instead, the removed number was 38, the average of the remaining 5 numbers would be 43.
Show answer & explanation
Correct answer: A
Explanation
Given:
Average of 6 numbers = 42
Total sum = 6 × 42 = 252
Statement 1
Average of 5 numbers = 40
Sum of 5 numbers = 5 × 40 = 200
The removed number = 252 − 200 = 52
Therefore, Statement 1 is correct.
Statement 2
If the removed number = 38
Remaining sum = 252 − 38 = 214
New average = 214 / 5 = 42.8
≠ 43
Therefore, Statement 2 is incorrect.
Only Statement 1 is correct.