PSAT Math Multiple-Choice Question 447: Answer and Explanation

Question: 447

A rectangular prism has a height of x, a width of 7 less than the height, and a length 14 more than the width. What is the volume of the prism?

• A.
• B.
• C.
• D.

Correct Answer: D

Explanation:

D

Difficulty: Medium

Getting to the Answer: The volume equation for a rectangular prism is V = lwh, so work with one variable at a time and then plug all of the dimensions in. The height will just be x, so h = x. The width is 7 less than the height, so subtract 7 from the height, or x, which gives w = x - 7. The length is 14 more than the width, so l = (x - 7) + 14 = x + 7. Plug all of these values into the volume formula and recognize a difference of squares to get x(x - 7)(x + 7) = x(x² - 49). Thus, (D) is correct.