Gmatclub DS, liked the terse explanation

[arora007]

If a > 0 and b > 0 , is a/b an even integer?

1. ab is an even integer
2. b/a is an even integer


[spoiler] OA B, Statement (2) by itself is sufficient. S2 says that a/b is a reciprocal to an even integer and is therefore less than 1. Thus,a/b is not an even integer.[/spoiler]

[kvcpk]

If a > 0 and b > 0 , is a/b an even integer?

1. ab is an even integer

a=2, b=4
ab = 8
a/b = 1/2 .. NO
a=4,b=2
ab=8
a/b=2 ... YES

2. b/a is an even integer

b/a = 2x [x is postive integer]
b=2ax
a/b = 1/2x

(1/positive integer) will never be integer, except when 2x=1. but 2x is even and so cannot be 1.
Hence always NO

pick B