Official Guide Explanation:
Data Sufficiency #167




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Solution and Metadata

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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