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There are 2 variables ( x and y) in the original condition. Hence, there is high chance that C is the correct answer. Using both the condition 1) and the condition 2), we get x=17, y=1. The answers are unique and the conditions are sufficient. However, since this is one of key questions, an integer question, we need to apply the common mistake type 4(A).
In case of the condition 1), from (x,y)=(1,17),(17,1),(-1,-17),(-17,-1), the answer is always |x|+|y|+xy=35. The answer is unique and the condition is sufficient. Hence, the correct answer is A.
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Hello from the GMAT Club BumpBot!

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