PSAT Math Multiple-Choice Question 382: Answer and Explanation

Question: 382

A store starts a sale to attract more customers. Mandy notices in the newspaper that the store has comforters on sale for 40 percent less than the original price. If Mandy pays $89.10 after the discount and a 10 percent sales tax on the discounted price, what is the original price of the comforter?

• A. $133
• B. $135
• C. $139
• D. $141

Correct Answer: B

Explanation:

B

Difficulty: Hard

Category: Percent Change

Getting to the Answer: Set up an equation with the original price having the variable C. Instead of subtracting the 40% discount, use the complement and multiply by that: 100% - 40% = 60% = 0.6, so the discounted price is 0.60C. The sales tax is a percentage of this discounted price, so multiply by 100% + tax (10%) = 110% = 1.1, which gives 1.1(0.60C). This amount should equal what Mandy actually paid: 1.1(0.60C) = 89.10. Solve for C:

Thus, (B) is correct. You could also solve this question using Backsolving.