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## Official Guide Explanation:

Data Sufficiency #124

**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****: 124**

Page: 284

Difficulty: **6** (Moderately Difficult)

Category 1: Word Problems > Sets >

Category 2: Arithmetic > Sets > 3+ sets

**Explanation:** Since only 30 of the 100 people answered "Favorable" regarding N, the maximum number of people who answered "Favorable" regarding both is 30, and that is only the case if all of those were answered "Favorable" regarding N did the same regarding M. The minimum size of the overlap is 0, if none of the same people viewed the candidates favorably.

Statement (1) is sufficient. If the number of people who did not answer Favorable regarding either candidate was 40, that means 60 of the 100 people answered Favorable regarding at least one of the candidates. There were 70 total Favorable answers, but some of those must have come from the same people. We can express this as an equation:

FavorableM + FavorableN - FavorableBoth = 60

40 + 30 - FB = 60

FB = 10

That's the number we're looking for--the number who responded Favorable regarding both candidates.

Statement (2) is not sufficient. The reason why (1) was sufficient is that is limited the answers to two choices: Favorable or "not favorable." The chart splits the "not favorable" into two categories. Since we care about the "Favorable" answers, we need to be able to isolate that one. Knowing a detail about the "Unfavorable" answers leaves us with two answers' worth of variables--those for "Favorable" answers and those for "Not Sure" answers. Choice (A) is correct.

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