Official Guide Explanation:
Data Sufficiency #16




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Solution and Metadata

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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