Digital PSAT Math Practice Question 338: Answer and Explanation

Question: 338

A company has four different stores at four different locations throughout a large city. The company gathered data on the initial prices, sale prices, and respective quantities sold of a particular item.

Store	Price Before Sale	Quantity Sold Before Sale	Sale Price	Quantity Sold During Sale
Store A	$12.50	350	$11.00	400
Store B	$13.25	260	$10.00	520
Store C	$11.75	550	$9.50	625
Store D	$14.00	220	$10.25	460

Which of the following equations properly expresses the functional relationship given by this expression?

"Take an input variable and divide it by 4; then subtract 5 from the result."

• A. $f\left(x\right)=\frac{x-5}{4}$
• B. $f\left(x\right)=\frac{x}{4}-5$
• C. $f\left(x\right)=5-\frac{x}{4}$
• D. $f\left(x\right)=\frac{5-x}{4}$

Correct Answer: B

Explanation:

(B) When you are told, "Take an input variable," that refers to x. Then divide the x by 4 and subtract 5 from this, which gives the function $f\left(x\right)=\raisebox{1ex}{$x$}\!\left/ \!\raisebox{-1ex}{$4$}\right.-5$.