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

Resources

MBA.com
GMAC Official Site
Free GMATPrep Practice Tests

Stacy Blackman Consulting
Book | Essay Guides

GRE HQ
Total GRE Math

Ultimate SAT Verbal

Official Guide Explanation:Problem Solving #174

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.

Question: 174
Page: 177
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Discrete Probability >
Category 2: Word Problems > Sets >

Explanation: The key words in this question are "at least." When you see those words, turn the question upside down: instead of solving for the probability of what they're asking for, solve for the opposite. In this case, the opposite of "at least one tail" is "all heads." The probability of any one toss turning up heads is (1/2), so the probability of three consecutive tosses coming up heads is ((1/2))((1/2))((1/2)) = (1/8). Since we found the opposite of what we were looking for, we need to subtract our answer from 1, as follows: 1 - (1/8) = (7/8), choice (D).

 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! Click to read more.