Bookshelf
Total GMAT Math Jeff's complete Quant guide, on sale now! |
Total GMAT Verbal Everything you need to ace GMAT Verbal! |
New: GMAT 111 Improve every aspect of your GMAT prep! |
1,800 Practice Math Questions
GMAT Official Guide
OG Math | OG Verbal
Guides To the Official Guide
Free: OG12 explanations!
GMAT Question of the Day
Beginner's Guide to the GMAT
GMAT Hacks Affiliate Program
Categories
- General Study Tips
- Goals and Planning
- CAT Strategy
- The Mental Game
- GMAT Math Strategy
- GMAT Math Topics
- Mental Math
- Data Sufficiency
- Critical Reasoning
- Reading Comprehension
- Sentence Correction
- Analytical Writing Assessment
- Business School Admissions
- GMAT Prep Resources
- Practice Questions
- Total GMAT Math
- Total GMAT Verbal
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.
Click here for an example of the PDF booklets. Click here to purchase a PDF copy.
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.
Click here for the full list of GMAT OG12 explanations.
You should follow me on Twitter. While you're at it, take a moment to subscribe to GMAT Hacks via RSS or Email. |
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! |