PSAT Math Multiple-Choice Question 652: Answer and Explanation

Question: 652

In a science class, for every two people who are failing, there are three people who have C's and D's. For every one person who has C's and D's, there are two people who have A's and B's. What is the ratio of those who are failing the class to those who have A's and B's?

• A. 1 to 1
• B. 1 to 3
• C. 2 to 3
• D. 1 to 6

Correct Answer: B

Explanation:

(B) Let's imagine the simplest version of this and say that there are two people failing. Since for every two failing, three have C's and D's, that means that three in this class do have C's and D's. We also know that for every one person who has a C or a D, two people have A's and B's. Since three have C's and D's, 3(2) = 6 have A's and B's.

Therefore, the ratio of those failing to those with A's and B's is 2 to 6, or 1 to 3, which is choice (B).