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## Official Guide Explanation:Data Sufficiency #167

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: 167
Page: 288
Difficulty: 5 (Moderate)
Category 1: Arithmetic > Properties of Integers > Other

Explanation: Statement (1) is sufficient. Look at what happens to the digits when we multiply a number by 10:

x = 3,456

10x = 34,560

Each digit moves one space to the left. The units digit becomes the tens digit, and so on. In reverse, the hundreds digit of 10x is 5, which is the same as the tens digit of x. Thus, if the hundreds digit of 10n is 6, 6 moves one step to the right when we divide by 10, so we know the tens digit of n.

Statement (2) is not sufficient. If the tens digit of n + 1 is 7, n + 1 could be any number between 70 and 79, inclusive. (Or 170 and 179, or 270 and 279, but all of those possibilities don't have any effect on the reasoning that follows.) If n + 1 = 70, then n = 69, and the tens digit is 6. But if n + 1 is 71 or greater, n is 70 or greater, meaning that the tens digit is 7. Choice (A) is correct.

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