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

Correct Answer: (B) 3

Let $N$ be the number of students. The first rectification replaced a score of 0 with 100 (a net increase of $+100$ in total marks), which increased the average by 4. Thus, $100 / N = 4$$\implies$ N = 25 students. The second rectification corrected a score recorded as 81 back to its true value 56 (a net decrease of $56 - 81 = -25$ in total marks). The overall net change in the class total from the original state is $+100 - 25 = +75$ marks. The final corrected average is $y = x +$$\frac{75}{25}$ = x + 3. Thus, $y - x = 3$.