Explanation

Now the thing to remember here is that

even number - even number = even number or odd number - odd number = even number.

Assume a pair of values j = 4 k = 2 and j =3 and k= 1

Options	j = 4 and k = 2	j =3 and k= 1
k	2	1
jk	8	3
j + 2k	8	5
jk + j	10	6
jk — 2j	0	1

Hence only option D fits.
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Let's test some values

GIVEN: j - k is even
So, it COULD be the case that j = 1 and k = 1 (since 1 - 1 = 0, which is even)

Now replace j and k with 1s to get:
A) \(1\) NOT EVEN

B) \((1)(1)=1\) NOT EVEN

C) \(1 + 2(1)=3\) NOT EVEN

D) \((1)(1) + 1=2\) EVEN

E) \((1)(1) — 2(1) = -1\) NOT EVEN

Answer: D

Cheers,
Brent
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