BTGmoderatorDC wrote:Which of the following describes the set of all possible values of the positive integer k such that, for each positive odd integer n, the value of n/k is midway between consecutive integers?

A. All positive integers greater than 2
B. All prime numbers
C. All positive even integers
D. All even prime numbers
E. All positive even multiples of 5

OA D

Source: Official Guide

Let's first write the consecutive integers. They are 0, 1, 2, 3, 4, 5, 6, ... The midway between consecutive integers is 0.5, 1.5, 2.5, 3.5, ...

Odd positive integers 1, 3, 5, 7, 9, ..., when divided by 2, would give 0.5, 1.5, 2.5, 3.5, ...

So, k = 2. Integer 2 is the only even prime number. Option D correctly defines it.

The correct answer: D

Hope this helps!

-Jay
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BTGmoderatorDC wrote:Which of the following describes the set of all possible values of the positive integer k such that, for each positive odd integer n, the value of n/k is midway between consecutive integers?

A. All positive integers greater than 2
B. All prime numbers
C. All positive even integers
D. All even prime numbers
E. All positive even multiples of 5

OA D

Source: Official Guide

We see that n can be 1, 3, 5, and so on. If k = 2, then 1/2 is midway between 0 and 1, 3/2 is midway between 1 and 2, 5/2 is midway between 2 and 3, and so on. Since any other value of k would not have such a property, k must be 2. Note that 2 is the only even prime number, so choice D is correct.

Answer: D