[SOLVED] even integer and odd integer

SAT math page 860 #20 on the OG Book

If k is a positive integer, which of the following must represent an even integer that is twice the value of an odd integer?

a) 2k
b) 2k+3
c)2k+4
d)4k+1
e)4k+2



Thanks in advance!!

The correct answer is e). Why so? Also is this question asking for an even integer or odd integer?

To be clear, the question is asking for an even integer.

Let's eliminate some options. b) and d) are clearly odd integers, so they cannot be correct answers.

For a): Half of 2k is k, which may or may not be odd.

For c): Half of 2k + 4 is k+2, which may or may not be odd.

For e): Half of 4k + 2 is 2k + 1, which must be odd.

So e) is the only correct answer.