PSAT Math Multiple-Choice Question 124: Answer and Explanation

Question: 124

Dana buys a shirt, a pair of shoes, and a purse at the store. Her bill is $81, and the shoes cost 25 percent more than the purse and shirt combined. How much were the shoes?

• A. $26
• B. $36
• C. $45
• D. $54

Correct Answer: C

Explanation:

C

The question asks for the cost of the shoes that Dana purchased. Since the question asks for a specific value and the answers contain numbers in increasing order, plug in the answers. Begin by labelling the answers as "cost of shoes," and start with (B), $36. If the shoes were $36, then the shirt and purse together were the rest of the bill, or $81 - $36 = $45. However, the shoes cost 25 percent more than the shirt and purse combined, so this cost of the shoes is too low. Eliminate (A) and (B). Try (C), $45. If the shoes were $45, then the shirt and purse together were $81 - $45 = $36. To see if the shoes were 25 percent more than the other two items, find the difference in the costs, which is $45 - $36 = $9. This amount is 25% of $36, so these values fit the requirements of the question. The correct answer is (C).