Question

Out of 76 students, 48 play both chess and cricket. How many students play only chess?

I. Out of 76 students, 19 students don't play any game, 5 students play only cricket.

II. Out of 76 students, 30 are girls and 15 of them don't play any game.

• A. If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question
• B. If the data in statement II alone is sufficient to answer the question, while the data in statement I alone is not sufficient to answer the question
• C. If the data either in statement I alone or in statement II alone are sufficient to answer the question
• D. If the data in both statements I and II together are necessary to answer the question

Answer 1

The correct option is A

If the data in statement I alone is sufficient to answer the question, while the data in statement II alone is not sufficient to answer the question

From Statement I, out of 76, 5 students play only cricket.

So, remaining students = 76 − 5 = 71 and 19 students among them don't play any game.

$\therefore$ Remaining students = 71 − 19 = 52

Now, according to the statement given, 48 play both chess and cricket. So, 4 play only chess.

Hence, Statement I alone is sufficient.

From Statement II, out of 76, 15 don't play any game, so remaining students who play = 76 − 15 = 61 and according to the statement 48 play both chess and cricket.

So, we have to find the number of students who play only cricket, which is not given. Hence, we cannot determine the number of students who play only chess.

Hence, Statement II alone is insufficient, but Statement I alone is sufficient to answer the question.