Digital PSAT Math Practice Question 276: Answer and Explanation

Question: 276

If 3 As equal 2 Bs, and 3 Cs equal one B, how many Cs will there be for each A?

• A. 1
• B. 2
• C. 3
• D. 6

Correct Answer: B

Explanation:

(B) Take this step by step. You are told that 3 As equal 2 Bs, or 3A = 2B, and 3 Cs equal one B, or 3C = 1(B). You want to know how many Cs there will be if you have just one (A). You don't know the relationship between (A) and (C) right away, but you do know how (A) is related to (B) and how (C) is related to (B). You can, therefore, use these relationships with (B) to find the relationship between (A) and (C). Since you want to know how many Cs there are for one A, you should first find out how (B) relates to one (A). Since 3A = 2B, it follows that . But, you also know 3C = B, so plugging this expression in for (B) in your previous equation, you obtain . Thus, 2 Cs equal one A, which corresponds to choice (B).