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The OA is C, however I didn't agree with the OA because it doesn't appear to account for fractions and negative fractions.

For example, if X=1/2 and Y=1/2, then (1) is fine because 1/2 * 1/2 <0; and (2) is fine because X=Y. Back to the main question, 1/2 + 1/2 does NOT equal 0.

However, if X=1/2 and Y=-1/2, then (1) is still fine; and (2) is still fine because (1/2)^2 = (-1/2)^2. Back to the main question 1/2 +(-1/2) DOES equal 0.

In the first case, X+Y does not equal 0, while in the second case X+Y=0.

The problem does not state that X & Y are intergers or whole numbers or anything, so when accounting for negatives and fractions, I think the answer should be E.

Heman, you give examples of where X is positive, and Y is negative, but with if both are positive fractions?

Can someone point out my mistake, I am confused by this question/answer. Thanks.

For example, if X=1/2 and Y=1/2, then (1) is fine because 1/2 * 1/2 <0; and (2) is fine because X=Y. Back to the main question, 1/2 + 1/2 does NOT equal 0.

1/2*1/2=1/4 which is less than 1 but still greater than zero. Hence in your example 0<xy<1. Hence Statement I is not satisfied.

From 1, xy<0 implies x & y are of opposite sign INSUFF

From 2, (x^2-y^2) = 0 i.e. (x-y)(x+y) = 0 i.e either x=y or x=-y INSUFF

Combined, from 1 x&y have to be of opposite sign hence x=-y is the only possibility. SUFF

The stem says nothing about x or y having to be whole numbers, natural numbers, etc. let alone integers. Even if we considered x={(-sqrt2)} and y=1.414.... ?

The answer should be (C)

Last edited by GMATT73 on 03 Sep 2006, 22:50, edited 1 time in total.

tricky question
IMHO E it is
1)clearly insuff
x can be -ve and y+ve
and so y can be-ve and x+ve
2)x^2=y^2 no info about the sugn of x or y
1st and 2 combined
we know x is the opposite sign of y and that their absolute values are equal But the solutiion can be -x=y or x=-y
Hence E it is _________________

tricky question IMHO E it is 1)clearly insuff x can be -ve and y+ve and so y can be-ve and x+ve 2)x^2=y^2 no info about the sugn of x or y 1st and 2 combined we know x is the opposite sign of y and that their absolute values are equal But the solutiion can be -x=y or x=-y Hence E it is

in both cases, x+y = 0 , hence serves the purpose to answer the question.

tricky question IMHO E it is 1)clearly insuff x can be -ve and y+ve and so y can be-ve and x+ve 2)x^2=y^2 no info about the sugn of x or y 1st and 2 combined we know x is the opposite sign of y and that their absolute values are equal But the solutiion can be -x=y or x=-y Hence E it is

in both cases, x+y = 0 , hence serves the purpose to answer the question.