The class average x in a test increases by 4 when the score of a student is rectified, whose corrected score is 100 instead of 0.…

Question

The class average x in a test increases by 4 when the score of a student is rectified, whose corrected score is 100 instead of 0. Later, the score of another student was found to have been recorded as 81 in place of 56. If there are no other corrections and the final corrected average is y, then y − x is

1. A. 2
2. B. 3 (Correct answer)
3. C. 5
4. D. 6

Correct Answer

Option B — 3

Detailed Solution & Explanation

The correct answer is Option B (3).

Key Points

• The first correction adds (100 − 0) = 100 to the total and raises the average by 4, so 100/N = 4 ⇒ N = 25 students.
• The second correction changes a recorded 81 to the true 56, i.e. −25 to the total, changing the average by −25/25 = −1.

Additional Information

• So the final average y = (x + 4) − 1 = x + 3, giving y − x = 3 → Option B.