The correct answer is option (E):
Neither statement (1) nor statement (2) suffices to answer the question.
Here's a breakdown of why the answer is "Neither statement (1) nor statement (2) suffices to answer the question":
The problem asks for 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. To solve this, we need specific numbers for each group. Let's analyze the statements:
Statement 1: Students from college A comprise 20% of total students surveyed.
* This tells us the total number of students in college A: 400 students * 20% = 80 students.
* We know how many students play basketball (15% of 400 = 60 students) and football (25% of 400 = 100 students) *overall*.
* However, this statement gives us NO direct information on how those 60 basketball players or those 100 football players are distributed between college A and the other colleges. We don't know the breakdown.
* We can't determine the *minimum* number of basketball players and the *exact* number of football players from college A.
* Therefore, statement 1 is insufficient.
Statement 2: 15% of the total students who play basketball and football are from college A.
* This tells us that 15% of the combined group of basketball players and football players (15% of 60 + 100 = 160 students) are from college A.
* It doesn't tell us how many basketball players from college A or how many football players from college A.
* We can calculate: 15% of 160 students = 24 students. That means 24 students out of 160 play either basketball or football and are from college A.
* Since we need the minimum number of students, we can assume that college A students only play one sport to satisfy the conditions.
* We still can't determine the ratio. We can't distinguish how many students play basketball and football out of this 24 students in college A.
* Therefore, statement 2 is insufficient.
Combining both statements doesn't solve the problem:
* We know there are 80 students in college A (from statement 1).
* We know 15% of the basketball and football players are from college A (24 students).
* But, we still lack information. This 24 students could include any mix of basketball and football players, or other games.
* We cannot derive the minimum number of basketball players from college A or the number of football players from college A.
*Therefore, neither statement alone nor both statements together provide enough information to calculate the required ratio.* The answer is "Neither statement (1) nor statement (2) suffices to answer the question."