Official Guide Explanation:
Problem Solving #83




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Solution and Metadata

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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