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## Official Guide Explanation:

Data Sufficiency #38

**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.

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**Solution and Metadata**

**Question****: 38**

Page: 276

Difficulty: **5** (Moderate)

Category 1: Arithmetic > Ratio and Proportion >

**Explanation:** The ratios of populations to numbers of representatives are given as follows:

((p_{1})/(r_{1})) and ((p_{2})/(r_{2}))

We need to determine which is bigger.

Statement (1) is insufficient. The population of district 1 is bigger, but we can't compare ratios without knowing something about the numbers of representatives.

Statement (2) is also insufficient. This time we learn that district 2 has more representatives, but we can't compare ratios without information on populations.

Taken together, the statements are sufficient. District 1 has a larger population (the numerator of the fraction) and a smaller number of representations (the denominator of the fraction). Thus, that fraction/ratio must be larger than that of District 2, with the smaller numerator and larger denominator. Choice (C) is correct.

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