Question

A survey on games played by 400 college students found that 15% play Hockey, 25% play Football, 30% play Cricket, 15% play Basketball and 15% play Tennis. What is the ratio of the minimum number of students from college A who play Basketball to the number of students from college A who play Football?

Statement 1: Students from college A comprise 20% of the total students surveyed.
Statement 2: 15% of the total students who play Basketball and Football are from college A.

• A. If the data in statement (1) alone is sufficient to answer the question
• B. If the data in statement (2) alone is sufficient to answer the question
• C. If the data in both the statements together are needed to answer the question
• D. If neither statement (1) nor statement (2) suffices to answer the question

Hint:

Notice the survey covers multiple colleges, and see if either statement isolates college A's split by sport.

Answer 1

The Correct Option is D

Step 1: Note the overall numbers.
Out of 400 students, Basketball players number \( 15\% \times 400 = 60 \) and Football players number \( 25\% \times 400 = 100 \).
The survey covers students from more than one college, and we need figures for college A only.

Step 2: Check statement 1 alone.
Statement 1 gives college A as 20% of the surveyed students, that is 80 students in total.
It does not say how many of those 80 play Basketball or Football specifically.
Statement 1 alone is not sufficient.

Step 3: Check statement 2 alone.
Statement 2 gives a combined figure of 15% for students who play Basketball and Football together who belong to college A.
This does not separate how many of college A's students play Basketball versus Football individually.
Statement 2 alone is not sufficient.

Step 4: Combine both statements.
Even with college A fixed at 80 students and a combined 15% figure for the two games, there is no way to split that percentage between Basketball and Football alone.
Several colleges took part in the survey, so the true minimum split for college A cannot be pinned to one number from this data.
The combined data still cannot produce the required ratio.

Final Answer:
Neither statement, alone or together, fixes the minimum ratio asked for. \[ \boxed{\text{Neither statement suffices (option e)}} \]