### 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:

Data Sufficiency #D25

**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****: D25**

Page: 24

Difficulty: **5** (Moderate)

Category 1: Arithmetic > Powers and Roots of Numbers > Powers

Category 2: Arithmetic > Properties of Integers > Other

**Explanation:** Note from the question that units digit cannot be 0, 1, or 2. Since it's a digit, it must be no greater than 9. Thus, the units digit of n must be between 3 and 9, inclusive.

Statement (1) is insufficient. Consider each of the possibilities from 3 to 9. If the units digit of n is 3, the units digit of n^{2} is 9, so it can't be 3. If the units digit of n is 4, the units digit of n^{2} is 6. Continue through the options: if 5, then 5; if 6, then 6; if 7, then 9; if 8, then 4; if 9, then 1. Thus, the units digit of n could be either 5 or 6.

Statement (2) is also insufficient. Again, consider each of the choices. When calculating the cube, don't bother with the actual cube, just focus on the units digit. For instance, if the units digit of n is 9, it doesn't matter that n^{3} = 729, just that the units digit of n^{3} is 9. The product of 9 and 9 is 81, so the units digit is 1. The product of 1 and 9 is 9, so the units digit of the cube must be 9.

Working through each of the options: if 3, then 7; if 4, then 4; if 5, then 5; if 6, then 6; if 7, then 3; if 8, then 2; if 9, then 9. Thus, the units digit of 9 could be 4, 5, 6, or 9.

Taken together, the statements are still insufficient. Even knowing both statements, the units digit of n could be 5 or 6. Choice (E) 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! |