PSAT Math Multiple-Choice Question 109: Answer and Explanation

Question: 109

A patterned quilt uses 16 different squares of fabric. Each square of fabric must have an area of at least 340 square inches and no more than 360 square inches. What inequality represents all possible values of the total area of fabric, f, in square inches needed for the quilt?

• A. 5,740 ≤ f ≤ 5,760
• B. 5,440 ≤ f ≤ 5,760
• C. 5,440 ≤ f ≤ 5,460
• D. 340 ≤ f ≤ 360

Correct Answer: B

Explanation:

B

The question asks for an inequality that models a specific situation. Translate the question in Bite-Sized Pieces and eliminate after each piece. One piece of information says that each square of fabric must have an area of at least 340 square inches. Since the quilt uses 16 different squares of fabric, multiply 16 by 340 to get the minimum area of fabric needed for the quilt. This results in 5,440, so eliminate (A) and (D), where this minimum value does not appear. Compare the remaining answers. The difference between (B) and (C) is the maximum value. The question states that each square of fabric must have an area of no more than 360 square inches, so multiply 16 by 360 to get the maximum. That value is 5,760, which does not appear in (C), so eliminate it. The correct answer is (B).