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my guess is (C)
my reasoning is complicated though...I'm not sure

1) WX + YZ = ODD
translate: either WX or YZ is odd, which means at least a couple of numbers is odd, either W&X or Y&Z
seems insufficient to answer

2) WZ + XY = ODD
translate: either WZ or XY is odd, which means at least a couple of numbers is odd, either W&Z or X&Y
seems insufficient to answer

Combine: 3 are odd and 1 even (will explain more if correct)
It is sufficient to answer NO to the question, because the ratio of an even number to an odd one is EVEN.

If W,X,Y, and Z are integers such that W/X and Y/Z are integers, is W/X and Y/Z odd?

(1) WX + YZ is odd (2) WZ + XY is odd

sometime it is easy to plaug in: suppose, w=6, x=3, y = 5 and z = 1

(1) WX + YZ = 18+5=23, an odd integer. insuff. (2) WZ + XY = 6+3=9, an odd integer again. insuff.

togather also insuff.

In this case, you have W/X that is EVEN, so you should also prove that there is a case in which both ratios are ODD, otherwise the answer should be NO, making (1)+(2) sufficient to answer

If W,X,Y, and Z are integers such that W/X and Y/Z are integers, is W/X and Y/Z odd?

(1) WX + YZ is odd (2) WZ + XY is odd

sometime it is easy to plaug in: suppose, w=6, x=3, y = 5 and z = 1

(1) WX + YZ = 18+5=23, an odd integer. insuff. (2) WZ + XY = 6+3=9, an odd integer again. insuff.

togather also insuff.

In this case, you have W/X that is EVEN, so you should also prove that there is a case in which both ratios are ODD, otherwise the answer should be NO, making (1)+(2) sufficient to answer

hmm.. make sense, that is what i was looking for. i will look on it in detial later.