"A Factory Has 500 Workers, 15% of Whom Are Women..." — GMAT® Worked Solution

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

A factory has 500 workers, 15% of whom are women. If 50 additional workers are to be hired and all of the present workers remain, how many of the additional workers must be women in order to raise the percent of women employees to 20%?

(A) 3

(B) 10

(C) 25

(D) 30

(E) 35

Try it before reading on.

Step 1: Compute the Current Number of Women

The problem tells us there are 500 workers and 15% of them are women. We need to find that actual number.

Using fractions for the calculation:

$\frac{15}{100} \times 500 = \frac{15 \times 500}{100} = \frac{7500}{100} = 75$

So there are currently 75 women employed at the factory.

Step 2: Compute the Target Number of Women

After hiring 50 additional workers, the total workforce will be:

$500 + 50 = 550$

We want 20% of those 550 workers to be women. Computing that target:

$\frac{20}{100} \times 550 = \frac{20 \times 550}{100} = \frac{11000}{100} = 110$

So we need 110 women out of 550 total workers.

Step 3: Find the Difference

We already have 75 women. We need 110. The number of additional women to hire:

$110 - 75 = 35$

The answer is (E).

Why This Problem Matters

This is a warm-up problem, and the math is straightforward. The miss rate is relatively low compared to the other problems in this episode, and the wrong-answer distribution doesn't show a dominant trap answer. Most errors come from computation mistakes rather than a conceptual gap.

The value of this problem is in the approach. Three valid methods exist: the step-by-step logical approach we used above, an algebraic equation approach, and guess-and-test with the answer choices. All three produce the same answer, but they have different risk profiles.

The step-by-step approach doesn't require setting up or solving an equation, which means there's no variable to lose track of and no algebra to fumble. You compute three things in sequence: the current number of women, the target number of women, and the difference. Each step is a single calculation you can verify.

If you're aiming for a score below 645, picking one reliable approach per problem type and sticking with it is a reasonable strategy. Above that threshold, practicing multiple approaches on the same problem builds the flexibility to pivot mid-problem on harder questions, where the test writers add layers or twists that make a single approach insufficient.

The broader habit: do percent calculations as fractions. Writing $\frac{15}{100} \times 500$ instead of $0.15 \times 500$ gives you visual cancellation that reduces arithmetic errors. This compounds across every percent problem you'll see on the GMAT®.

Want the full strategy behind this problem? Read: GMAT® Quant: Three Systems for Percents, Exponents, and Rounding

From Episode 31 of Real GMAT® Problems (The GMAT® Strategy Podcast).

Ready for the next one? "What Is the Value of (10⁴ − 10²) × 0.0012̄?" — GMAT® Worked Solution.