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.

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

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:

((p₁)/(r₁)) and ((p₂)/(r₂))

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.

Click here for the full list of GMAT OG12 explanations.

Total GMAT Math The comprehensive guide to the GMAT Quant section. It's "far and away the best study material available," including over 300 realistic practice questions and more than 500 exercises! Click to read more.