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# Does x = y ? (1) x^2-y^2=0 (2) (x+y)^2=0

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Does x = y ? (1) x^2-y^2=0 (2) (x+y)^2=0 [#permalink]  24 Jul 2011, 15:32
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Does x = y ?

(1) x^2-y^2=0

(2) (x+y)^2=0
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Re: DS - 700 level - equation [#permalink]  24 Jul 2011, 16:12
bschool83 wrote:
Does x = y ?

(1) x^2-y^2=0

(2) (x+y)^2=0

x=0, y=0
OR
x=1, y=-1

Not Sufficient

Ans: "E"
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Re: DS - 700 level - equation [#permalink]  24 Jul 2011, 21:58
Does x = y ?

(1) x^2-y^2=0

(2) (x+y)^2=0

ans: stmt1: x^2=y^2 doesn't tell us whether x = y as both positive and negative values are possible. insuff

Stmt2: x+y = 0 gives x = -y.

Note: Just saw fluke's answer, yes x and y can be both zero. Hence E.
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Re: Does x = y ? (1) x^2-y^2=0 (2) (x+y)^2=0 [#permalink]  04 Jan 2012, 02:05
Does x = y ?

(1) x^2-y^2=0

(2) (x+y)^2=0

Question: Does x = y?

Statement 1: x^2 = y^2
This can be true when x = y = 0 and when x = 1, y = -1. Two different answers can be derived. Thus INSUFFICIENT

Statement 2: x + y = 0 (Taking root on both sides)
Again, this can be true when x = y = 0 and when x = 1, y = -1. Two different answers can be derived. Thus INSUFFICIENT

Combining the two statements, we still have the same dilemma. Both the values of x and y shown above satisfy both the given statements. Two different answers can be derived. Thus INSUFFICIENT

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Re: Does x = y ? (1) x^2-y^2=0 (2) (x+y)^2=0 [#permalink]  04 Jan 2012, 08:25
the question just asks whether a=b ..If we are able to prove that a is not equal to b that will be enough .
From statement 2 ..we can deduce that a and b are of opposite signs .Hence they are not equal .
Hence statement 2 alone is sufficient .Answer is not E .

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Re: Does x = y ? (1) x^2-y^2=0 (2) (x+y)^2=0 [#permalink]  04 Jan 2012, 21:57
saikarthikreddy wrote:
the question just asks whether a=b ..If we are able to prove that a is not equal to b that will be enough .
From statement 2 ..we can deduce that a and b are of opposite signs .Hence they are not equal .
Hence statement 2 alone is sufficient .Answer is not E .

It is not necessary from Statement 2 for x and y to have opposite signs. If x = 0, y = 0, then x + y = 0. In this case, x = y. That is why the answer is E, not B.
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Re: Does x = y ? (1) x^2-y^2=0 (2) (x+y)^2=0 [#permalink]  06 Jan 2012, 18:45
Nice one.

1. Here, it could be x=y=0,1,2... or x=1 and y=-1. Insuff
2. Here, it could be x=y=0 or x=1, y=-1. Insuff.

Together, nothing conclusive. E.
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Re: Does x = y ? (1) x^2-y^2=0 (2) (x+y)^2=0   [#permalink] 06 Jan 2012, 18:45
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