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## Official Guide Explanation:Data Sufficiency #52

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Review (12th ed.). Click the links on the question number, difficulty level, and categories to find explanations for other problems.

These are the same explanations that are featured in my "Guides to the Official Guide" PDF booklets. However, because of the limitations of HTML and cross-browser compatibility, some mathematical concepts, such as fractions and roots, do not display as clearly online.

Question: 52
Page: 277
Difficulty: 5 (Moderate)
Category 1: Word Problems > Profit >
Category 2: Arithmetic > Ratio and Proportion >
Category 3: Arithmetic > Percents > other

Explanation: If the cost is x and the selling price is y, the profit is y - x. We're looking for what percent the profit was of the cost, or:

(((y - x)/(x))) * 100%

Statement (1) is insufficient. It tells us that the profit was \$20, but without knowing the exact cost, we can't answer the question.

Statement (2) is sufficient. If the ratio of the selling price to the cost is (5/4), the selling price is 25% higher than the cost. The profit, then, is 25% of x, which we can plug in for y - x:

(((.25x)/(x))) * 100%

= .25 * 100%

= 25%

Choice (B) is correct.

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