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
Detailed Explanation:
Let the number of students be n. When one student's score is corrected from 0 to 100, the total increases by 100 and the average increases by 4. Thus: 100/n = 4, giving n = 25 students.
The second correction changes a score from 81 to 56, decreasing the total by 25. This decreases the average by 25/25 = 1.
After the first correction, average = x + 4. After the second correction, y = x + 4 − 1 = x + 3. Hence y − x = 3, making Option 2 the correct answer.
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