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Official Guide Explanation:Problem Solving #83

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: 83
Page: 72
Difficulty: 6 (Moderately Difficult)
Category 1: Geometry > Coordinate Geometry > Other
Category 2: Arithmetic > Properties of Integers > Other

Explanation: This is a kind of function question. Given an integer value for x, which of the following equations will NEVER give an integer value for y?

(A)    If x is an integer, y will always be an integer--they are the same number!

(B)    If x is an integer, y will always be (1/2) greater than an integer--NEVER an integer. This is correct.

(C)    If x is an integer, y will be 5 greater than an integer, which is itself always an integer.

(D)    If x is even, then y will be one - half an even number, which is always an integer. It's possible that y is not an integer, but only sometimes.

(E)    As in (E), if x is even, y will be an integer, as (1/2)x is an integer, and 5 greater than an integer is also an integer.

Choice (B) is correct.

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