rajarshee wrote:

Is x+y>0 where x and y are non zero integers?

(1) |x|>y

(2) |y|>x

Answer: (C)

Question gives us some idea that the answer may be different for positive and negative integers. So let us think only along these lines.

Statement 1: INSUFFICIENT

Suppose x and y both are positive. Is it possible that |x| be greater than y? Yes, say x = 3 and y = 2. Is x+y>0?

YESIf x and y both are negative, is it possible that |x| be greater than y? Yes again, say x = -3 and y = -2. Is x+y>0?

NOStatement 2: INSUFFICIENT

Same reasoning as before except that x and y are interchanged now.

Statements can also be analyzed as:

Statement 1 -> If magnitude of x is greater than y, then we have 2 possibilities:

y = positive: then distance of x from 0 is greater than the value of y.

y = negative: then x can be any integer.

Statement 2 -> If magnitude of y is greater than x, then the 2 possibilities are:

x = positive: then distance of y from 0 is greater than the value of x.

x = negative: then y can be any integer.

Hence after combining ->

x = negative and y = negative: consistent with both statements. Is x+y>0?

NOx = positive and y = negative: Since x is positive, so distance of y from 0 must be greater than the value of x (as per statement 2). Hence, y can be negative but will have a larger magnitude compared to x. Hence x + y is negative. Is x+y>0?

NOx = negative and y = positive: Since y is positive, so distance of x from 0 must be greater than the value of y (as per statement 1). Hence, x can be negative but will have a larger magnitude compared to y. Hence x + y is negative. Is x+y>0?

NOx = positive and y = positive: inconsistent with the 2 statements because in this case, either |x| > y or |y| > x. Both can't hold true together.

Hence, there is unique answer for the question asked after combining the 2 statements.