### Bookshelf

Total GMAT MathJeff's complete Quant guide, on sale now! |

Total GMAT VerbalEverything you need to ace GMAT Verbal! |

New: GMAT 111Improve 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 #7

**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****: 7**

Page: 153

Difficulty: **4** (Moderately Easy)

Category 1: Arithmetic > Properties of Integers > Primes

**Explanation:** The GMAT doesn't expect you to memorize every prime number up to 70, but it does expect that you know how to determine which numbers (out of a small group such as 60 to 70) are prime. Even numbers aren't prime, so the only possibilities are 61, 63, 65, 67, and 69. 63 and 69 are multiples of 3 (if the digits of the number add up to a multiple of 3, the number itself is a multiple of 3), and 65 is a multiple of 5. That leaves only 61 and 67. The only possible answer choices for us at this point are 67 and 128, so the question comes down to: is 61 prime? It isn't divisible by 2, 3, or 5, and it isn't divisible by 7. (If you know that 63 is divisible by 7, or even that 70 is divisible by 7, you can figure out that 61 isn't.) If a number is not prime, it must have at least one factor that is equal or less than its square root, and 61's square root is less than 8 (8 squared is 64), so we know that 61 is prime. Thus the answer is (B), 128, the sum of 61 and 67.

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! |