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

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Math Expert
Joined: 02 Sep 2009
Posts: 56257
Does x = y ? (1) x^2 - y^2 = 0 (2) (x + y)^2 = 0  [#permalink]

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11 Oct 2015, 05:24
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Difficulty:

85% (hard)

Question Stats:

30% (01:22) correct 70% (01:08) wrong based on 108 sessions

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Does x = y ?

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

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Status: tough ... ? Naaahhh !!!!
Joined: 08 Sep 2015
Posts: 63
Location: India
Concentration: Marketing, Strategy
WE: Marketing (Computer Hardware)
Re: Does x = y ? (1) x^2 - y^2 = 0 (2) (x + y)^2 = 0  [#permalink]

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11 Oct 2015, 06:27
(1) x^2 - y^2 = 0
x^2 = y^2, x can be + or - and y can also be + or -. Insufficient
(2) (x + y)^2 = 0
0^2 = 0 , so x+y=0 or x=-y, sufficient

Ans: B
Manager
Joined: 11 Sep 2013
Posts: 108
Re: Does x = y ? (1) x^2 - y^2 = 0 (2) (x + y)^2 = 0  [#permalink]

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11 Oct 2015, 13:42
Bunuel wrote:
Does x = y ?

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

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

Insufficient

(2) (x + y)^2 = 0
=> x+y=0
=> x=-y
But when x = 0, y=0 => x=y=0
When x not equal 0 => x = -y

Insufficient

(1) (2) => X+ Y = 0

INSUFFICENT

Ans: E
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Does x = y ? (1) x^2 - y^2 = 0 (2) (x + y)^2 = 0  [#permalink]

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11 Oct 2015, 14:52
1
Bunuel wrote:
Does x = y ?

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

Per statement 1, $$x^2=y^2$$ ---> $$x= \pm y$$ . Thus this statement is not sufficient to answer "is x=y".

Per statement 2, (x+y)^2=0 ---> either x=y=0 , then a "yes" for is x=y but if x=1 and y=-1, then a"no" for "is x=y". This statement is not sufficient.

Combining, still get x=y=0 and x=1 and y=-1 satisfying both the statements ($$x=\pm y$$) giving you an insufficient answer.

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Re: Does x = y ? (1) x^2 - y^2 = 0 (2) (x + y)^2 = 0  [#permalink]

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22 Dec 2018, 11:39
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Re: Does x = y ? (1) x^2 - y^2 = 0 (2) (x + y)^2 = 0   [#permalink] 22 Dec 2018, 11:39
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