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 Analysis: Let the number of students in the class be 'n'. The initial average is given as 'x'. When the first student's score is rectified from 0 to 100, the total sum of the class scores increases by 100. We are given that this correction increases the class average by 4. According to the mathematical definition of arithmetic mean: Increase in Average = (Total Increase in Sum) / n 4 = 100 / n Therefore, the number of students n = 25.

Later, a second student's score is rectified from an incorrectly recorded 81 to the actual 56. This results in a sum decrease of 25 (since 56 - 81 = -25). The net change in the total sum of scores from the initial uncorrected state is: +100 - 25 = +75.

The final corrected average is designated as 'y'. The net change in the average from the initial 'x' is simply the net change in the sum divided by the number of students: Change in average (y - x) = (Net Change in Sum) / n y - x = 75 / 25 = 3. Thus, Option B is the mathematically correct choice.

Why the other options are incorrect:

• Option A (2): This is incorrect. Deriving an average increase of 2 would imply a net score change of +50, which does not match the actual net change of +75.
• Option C (5): This is incorrect. An aspirant might arrive at 5 by mistakenly adding the second correction (+25 instead of subtracting it), leading to a faulty net sum change of 125 (125 / 25 = 5).
• Option D (6): This is incorrect. It would require a net score increase of +150, entirely contradicting the given parameters.

Takeaway: For aptitude questions involving the rectification of averages, directly apply the principle: Net Change in Average = (Net Change in Total Sum) / (Total Number of Entities). You do not need to assume or calculate the initial total sum.