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Usually, A.V questions are easy to solve using Picking numbers technique:

Is |x| = |y|?

(1) x - y = 6. If x=8 and y=2, then the answer is NO but if x=3 and y=-3, then the answer is YES. Not sufficient.

(2) x + y = 0 --> x = -y --> |-y| = |y| or |-5| = |5|, the answer is only YES so is Sufficient.

Answer: B.
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Is |x| = |y|?

question basically ask distance from x to 0 is the same as the distance from y to 0.

(1) x - y = 6. Not sufficient.

(2) x + y = 0 --> x = -y --> |x| = |y|. Sufficient.

B is correct
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