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:
Problem Solving #219
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: 219
Page: 184
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Evens and Odds
Category 2: Arithmetic > Properties of Integers > Factors and Multiples
Explanation: It may be useful to think of some examples for the three consecutive integers, such as 2, 3, and 4, or 7, 8, and 9. Or, you can think of them algebraically, as x, x + 1, and x + 2. Look at each roman numeral in turn:
I. This must be true: (x + 2) - x = 2. Alternatively, 4 - 2 = 2 , and 9 - 7 = 2.
II. At least one of the three integers will always be even, and any integer multiplied by an even results in an even product. Thus, this must also be true.
III. This is where the algebra comes in handy. You can write ((a + b + c)/3) as ((x + (x + 1) + (x + 2))/3) = ((3x + 3)/3) = x + 1. Since x is an integer, x + 1 must be an integer, as well.
All three statements must be true, so the correct answer is (E).
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! |