Question

The given question consists of a set of statements. Find out whether the data provided in the statements are sufficient to answer the question and mark the option:

Out of 64 students, 38 play both chess and cricket. How many students play only chess?
I. Out of 64 students, 22 students don’t play any game 4 students play only cricket.
II. Out of 64 students, 20 are girls and 10 of them don’t play any game

• A. If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.
• B. If the data in Statement II alone are sufficient to answer the question, while the data in Statement I alone are not sufficient to answer the question.
• C. If the data either in Statement I alone or Statement II alone are sufficient to answer the question.
• D. If the data given in both the Statements I and II together are not sufficient to answer the question.
• E. If the data in both the Statement I and II are together necessary to answer the question.

Answer 1

The correct option is A If the data in Statement I alone are sufficient to answer the question, while the data in Statement II alone are not sufficient to answer the question.

From Statement I, out of 64, 4 students play only cricket.
So, remaining 64 – 4 = 60 and 22 students don’t play any game
$\therefore$ Remaining students = 60 – 22 = 38
Now, according to the statement 38 play both chess and cricket. So, none plays chess only.
Hence, Statement I alone is sufficient.
From Statement II, out of 64, 10 don’t play any game,
so remaining 64 – 10 = 54 and according to the statement 38 play both chess and cricket.
So, finally, we have to find the number of students who play only cricket which is not given.
So, we cannot determine the number of students who play only chess.
Hence, Statement II alone is not sufficient.
Hence, Statement I alone is sufficient to answer the question.