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# Is |x - y| > |x + y|? (1) x^2 - y^2 = 9 (2) x - y = 2

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Math Expert
Joined: 02 Sep 2009
Posts: 42631

Kudos [?]: 135880 [0], given: 12715

Is |x - y| > |x + y|? (1) x^2 - y^2 = 9 (2) x - y = 2 [#permalink]

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02 Dec 2017, 23:26
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Question Stats:

69% (01:05) correct 31% (00:53) wrong based on 35 sessions

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Is |x - y| > |x + y|?

(1) x^2 - y^2 = 9
(2) x - y = 2
[Reveal] Spoiler: OA

_________________

Kudos [?]: 135880 [0], given: 12715

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 627

Kudos [?]: 313 [0], given: 39

Location: India
GPA: 3.82
Is |x - y| > |x + y|? (1) x^2 - y^2 = 9 (2) x - y = 2 [#permalink]

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03 Dec 2017, 02:38
Bunuel wrote:
Is |x - y| > |x + y|?

(1) x^2 - y^2 = 9
(2) x - y = 2

$$|x-y|>|x+y|$$, square both sides to get

$$x^2+y^2-2xy>x^2+y^2+2xy => 4xy<0$$

so the question Is $$xy<0$$. Hence we need to know the value of $$x$$ & $$y$$

Statement 1: implies $$(x-y)(x+y)=9$$. two variable one equation not possible to solve. Insufficient

Statement 2: $$x-y=2$$. again two variable one equation not possible to solve. Insufficient

Combining 1 & 2 we get $$2(x+y)=9$$ so $$x+y=4.5$$ and $$x-y=2$$. Two variables and two equations we can calculate the value of $$x$$ & $$y$$. Sufficient

Option C

Kudos [?]: 313 [0], given: 39

PS Forum Moderator
Joined: 25 Feb 2013
Posts: 627

Kudos [?]: 313 [0], given: 39

Location: India
GPA: 3.82
Re: Is |x - y| > |x + y|? (1) x^2 - y^2 = 9 (2) x - y = 2 [#permalink]

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03 Dec 2017, 05:53
antztheman wrote:
Hmm.. why not B?

Hi antztheman

if x=1 & y =-1, then x-y=2 and x+y=0 so |x-y|>|x+y|

but if x=4 y=2, then x-y=2 and x+y=6 but |x-y|<|x+y|

Hence we have a Yes and a NO answer for B.

Kudos [?]: 313 [0], given: 39

Re: Is |x - y| > |x + y|? (1) x^2 - y^2 = 9 (2) x - y = 2   [#permalink] 03 Dec 2017, 05:53
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