"Nancy Earns a Salary of $240 Plus 5% of the Amount of Her Total Sales..." — GMAT® Worked Solution

Source: Official Guide for GMAT® Review, 11th Edition

In a certain furniture store, each week, Nancy earns a salary of $240 plus 5% of the amount of her total sales that exceed $800 for the week. If Nancy earned a total of $450 one week, what were her total sales that week?

(A) $2,200

(B) $3,450

(C) $4,200

(D) $4,250

(E) $5,000

Try it before reading on.

Step 1: Write Down What's Given and What's Asked

Before setting up an equation, write the given information in a mix of English and shorthand math. This is the half-math, half-English layer — a stepping stone that processes the logic before you have to structure it algebraically.

Total sales = ?
Salary = $240
Commission = 5% after $800
Total earned = $450

That's not an equation. It's not pure English either. But it catches the detail that matters most on this problem: the commission applies to sales that EXCEED $800, not to total sales.

If you go straight from reading to equation, that threshold is the thing you're most likely to miss. The half-math, half-English step makes it visible before the algebra begins.

Step 2: Translate Into an Equation

Let $x$ represent Nancy's total sales for the week.

The commission isn't 5% of $x$. It's 5% of the amount that exceeds $800 — which is $(x - 800)$.

So the commission is:

Add the base salary and set the total equal to $450:

Step 3: Solve

Subtract 240 from both sides:

Multiply both sides by $\frac{100}{5}$ (which is 20) to clear the fraction:

Add 800 to both sides:

The answer is (E).

Why This Problem Matters

About 25% of test takers miss this problem. The most common wrong answer is (C) — $4,200.

Here's what happens: you set up the equation correctly, solve correctly, and get $4,200. The math is right. The equation is wrong. You computed 5% of total sales instead of 5% of sales above $800.

The equation you solved:

The equation you should have solved:

The difference is one subtraction. The $-800$ is the threshold — the amount that gets subtracted before the commission kicks in. Miss it, and you're solving a different problem than the one on the page.

That's why the half-math, half-English step matters. If you write "Commission = 5% after $800" before building the equation, you're less likely to skip the subtraction. The stepping stone catches what the equation hides.

Want the full strategy behind this problem? Read: GMAT® Word Translations: The Step-By-Step Setup System

From Episode 25 of Real GMAT® Problems (The GMAT® Strategy Podcast).

Ready for the next one? The "Rule of 70" Retirement Problem — GMAT® Worked Solution.