Question

In a particular school, sixty students were athletes. Ten among them were also among the top academic performers. How many top academic performers were in the school?
A: Sixty per cent of the top academic performers were not athletes.
B: All the top academic performers were not necessarily athletes.

• A. if the question can be answered using the statement A alone but not by using the statement B alone.
• B. if the question can be answered using the statement B alone but not by using the statement A alone.
• C. if the question can be answered using either of the statements alone.
• D. if the question can be answered using both the statements together but not by either of the statements alone.
• E. if the question cannot be answered on the basis of the two statements.

Hint:

For ratio/percentage problems, if one statement gives a direct proportion and an absolute number, it’s usually sufficient.

Answer 1

The Correct Option is A

From A: 60% of top performers are not athletes → 40% are athletes.
Given 10 athletes are top performers → 40% corresponds to 10 → total top performers = \( 10 / 0.4 = 25 \). Hence A alone is sufficient.
From B: only says that some top performers may not be athletes, but no quantity → insufficient.