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## Official Guide Explanation:Data Sufficiency #16

Background

This is just one of hundreds of free explanations I've created to the quantitative questions in The Official Guide for GMAT Quantitative Review (2nd 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: 16
Page: 154
Difficulty: 6 (Moderately Difficult)
Category 1: Arithmetic > Properties of Integers > Remainder
Category 2: Arithmetic > Powers and Roots of Numbers > Powers

Explanation: The value of 10x will be 10, 100, 1,000, or something similar. Statement (1) is insufficient. Knowing that 10x = 100,000 doesn't answer the question; if 10x + y = 100,001, it is not divisible by 3; if it is 100,002, it is divisible by 3. (It's helpful to remember that we can determine whether a number is divisible by 3 by adding the digits together. If the sum of the digits is divisible by 3, the number itself is divisible by 3. If not, it's not.)

Statement (2) is sufficient. Given that y = 2, 10x + y will always be 102, 1,002, 10,002, or something to that effect. The important point is that the sum of the digits will always be 3. Given the sum of the digits, we can determine whether the result is divisible by 3, even if we don't know the value of x. Choice (B) is correct.

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