Question

A survey on games played by 400 college students, it is found that 15% play Hockey, 25% play football, 30% play cricket, 15% basketball and 15% 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 total students surveyed
Statement 2: 15% of the total students who play basketball and football are from college A

• A. Statement (1) alone is sufficient to answer the question
• B. Statement (2) alone is sufficient to answer the question
• C. Both the statements together are needed to answer the question
• D. Either statement (1) alone or statement (2) alone is sufficient to answer the question
• E. Neither statement (1) nor statement (2) suffices to answer the question.

Answer 1

Answer: (E)

Let's analyze the problem step by step using the provided statements:  

1. First, we are given the total number of students surveyed is 400.
2. The question asks us for the ratio of the minimum number of students from college A who play basketball to those who play football.
3. Statement 1 states that students from college A comprise 20% of the total students surveyed.

Let's calculate based on Statement 1:

• Students from college A: \(0.20 \times 400 = 80\).
• Basketball players: 15% of 400 = \(0.15 \times 400 = 60\).
• Football players: 25% of 400 = \(0.25 \times 400 = 100\).

However, Statement 1 does not tell us how many students from college A are among those who play basketball or football, making it insufficient alone to determine the ratio.

Now, let's assess Statement 2:

1. Statement 2 informs that 15% of the total students who play both basketball and football are from college A.

Without combining this with any details from Statement 1, we cannot directly infer the numbers of basketball or football players specifically from college A.

Thus, Statement 2 alone is also insufficient.

By evaluating both statements separately, it becomes clear:

• Statement 1 does not provide specific numbers regarding basketball or football-playing students from college A.
• Statement 2 cannot provide specific numbers either, without reference to total counts or percentages of college A students engaged in the sports.

In conclusion, neither statement alone can determine the required ratio; therefore, the correct answer is: Neither statement (1) nor statement (2) suffices to answer the question.