"If x > 0, x/50 + x/25 Is What Percent of x?" — GMAT® Worked Solution

From Episode 39 of Real GMAT® Problems (The GMAT® Strategy Podcast). For the full strategy behind percent word problems on the GMAT®, read: Translating Percent Word Problems on the GMAT®: A One-Word-at-a-Time System.

The Problem

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

If x > 0, ^x⁄₅₀ + ^x⁄₂₅ is what percent of x?

(A) 6%

(B) 25%

(C) 37.5%

(D) 60%

(E) 75%

Translate the Problem One Word at a Time

Use the four-word translation system. Read the problem left to right and convert each piece as you go.

• ^x⁄₅₀ + ^x⁄₂₅ → ^x⁄₅₀ + ^x⁄₂₅
• "is" → =
• "what" → a new variable. Use P (P does not appear in the problem yet)
• "percent" → ÷ 100
• "of" → ×
• "x" → x

Stitching it all together:

^x⁄₅₀ + ^x⁄₂₅ = ^P⁄₁₀₀ × x

The setup is done. From here it is algebra.

Step 1: Combine the Fractions on the Left

Common denominator for ^x⁄₅₀ and ^x⁄₂₅ is 50. Multiply ^x⁄₂₅ by ²⁄₂:

^x⁄₂₅ = ^2x⁄₅₀

So:

^x⁄₅₀ + ^2x⁄₅₀ = ^3x⁄₅₀

The equation becomes:

^3x⁄₅₀ = ^P⁄₁₀₀ × x

Step 2: Clear the Fractions

Multiply both sides by 100 to get rid of the denominators on both sides:

100 × ^3x⁄₅₀ = 100 × ^P⁄₁₀₀ × x

On the left, ¹⁰⁰⁄₅₀ = 2:

2 × 3x = 6x

On the right, the 100 cancels:

P × x

So the equation simplifies to:

6x = Px

Step 3: Solve for P

Divide both sides by x. The problem tells us x > 0, so dividing by x is safe:

6 = P

So ^x⁄₅₀ + ^x⁄₂₅ is 6% of x.

The answer is (A).

Why This Problem Matters

About 10% of test takers miss this one. The math is light. The other answer choices each pick up only 1–2% of test takers, which suggests those wrong answers come from one-off arithmetic slips rather than a systematic mistake.

The reason this problem matters is not the math — it is the setup.

This is one of the cleanest places to learn the four-word translation system. The problem is short. Every word maps directly to an operation. By the time you get to the algebra, the equation is on the page and there is no ambiguity about what to solve for.

Once the habit is built here, it pays off on harder problems where the translation is where most test takers go wrong. The next problem in this episode — Problem 2 — is one of those. The miss rate jumps to 31%, mostly because of a translation issue that the four-word system catches automatically.

Two specific habits to take away from this problem:

When you see "what," create a new variable. Do not reuse x. The problem already has x with a specific role, and reusing the letter creates an equation that confuses two different quantities.

When you see "percent," write ÷ 100. The word percent is not the same as the percentage sign. Treat it as its own operation in the translation step, and the algebra stays clean.

Next problem: If x is m% of y, then in terms of m, y is what percent of x? — GMAT® Worked Solution

Back to the strategy article: Translating Percent Word Problems on the GMAT®: A One-Word-at-a-Time System