How many students in a class play football? Statements: I. Only boys play…
2024
How many students in a class play football?
Statements:
I. Only boys play football.
II. There are forty boys and thirty girls in the class.
Answer: D. Neither statement alone nor the two statements together are sufficient. — Concept In data-sufficiency questions, a statement is sufficient only when it fixes one unique answer to the question asked. A restriction on who may belong…
- A.
Statement I alone is sufficient, but Statement II alone is not sufficient.
- B.
Statement II alone is sufficient, but Statement I alone is not sufficient.
- C.
Both statements together are sufficient, but neither statement alone is sufficient.
- D.
Neither statement alone nor the two statements together are sufficient.
Attempted by 59 students.
Show answer & explanation
Correct answer: D
Concept
In data-sufficiency questions, a statement is sufficient only when it fixes one unique answer to the question asked.
A restriction on who may belong to a group does not by itself determine how many people actually belong to that group.
Application
Statement I says that every football player is a boy, but it gives no count of boys who actually play football.
Statement II gives the class composition—forty boys and thirty girls—but gives no participation information.
Together, the statements only constrain the number of football players to an integer between zero and forty; no condition selects one unique number.
Cross-check
Two different classes satisfy both statements: in one, no boy plays football; in another, all forty boys play. Since the same information permits different answers, the required number cannot be determined.
Therefore, neither statement alone nor the two statements together are sufficient.