Official Guide Explanation:
Problem Solving #125

Background

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Solution and Metadata

Question: 125
Page: 78
Difficulty: 5 (Moderate)
Category 1: Algebra > Linear Equations-One Unk >
Category 2: Arithmetic > Properties of Integers > Factors and Multiples

Explanation: If x is an integer, then 3x is a multiple of 3. To rephase the equation, y is 2 greater than a multiple of 3. That means that y itself cannot be a multiple of 3. Since the only numbers that are divisible by 6 are multiples of 3, y cannot be divisible by 6, which means that (C) is correct.

If you aren't able to make those connections, it is always an option to come up with a series of possible values for y: when x = 1, y = 5, when x = 2, y = 8, etc. Eventually, that series of numbers will eliminate four of the five choices. However, it's much quicker to think about the set of possible y values more abstractly.

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