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## Official Guide Explanation:

Problem Solving #202

**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.

Click here for an example of the PDF booklets. Click here to purchase a PDF copy.

**Solution and Metadata**

**Question****: 202**

Page: 181

Difficulty: **6** (Moderately Difficult)

Category 1: Algebra > Equations >

Category 2: Algebra > Simplifying Algebraic Expressions >

Category 3: Arithmetic > Percents > other

**Explanation:** Percents are a little tricky to work into equations. Just remember that "x percent" means ((x)/100), and you should be fine. Translating "x is m percent of y" gives you x = ((m)/100)(y) . If we call the percent we're looking for q, the question can be written y = ((q)/100)(x). To find q, rearrange the first equation to give y in terms of x, rather than the other way around:

x = ((m)/100)(y)

((x)/(y)) = ((m)/100)

(1/(y)) = ((m)/(100x))

y = ((100x)/(m)) = ((100/(m)))(x)

Thus, ((q)/100) = (100/(m)). To solve for the answer, multiply both sides by 100: q = (100/(m))(100) = ((10,000)/(m)), choice (E).

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