If (x+y)^2<x^2, which of the following must be true? I. : Quant Question Archive [LOCKED]
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# If (x+y)^2<x^2, which of the following must be true? I.

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If (x+y)^2<x^2, which of the following must be true? I. [#permalink]

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21 Jul 2008, 23:10
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

If (x+y)^2<x^2, which of the following must be true?
I. x*y<0
II. y<x
III. y*(y+2x)<0
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III
Director
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21 Jul 2008, 23:25
1
KUDOS
E

(x+y)^2 < x^2
x^2 + y^2 + 2xy < x^2
y^2 + 2xy < 0
y*(y+2xy) < 0 -------------(III)

y^2 is always +ve
--> 2xy < 0
xy < 0 --------------(I)
Current Student
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21 Jul 2008, 23:45
KUDOS... +1 DURGESH
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22 Jul 2008, 01:33
arjtryarjtry wrote:
If (x+y)^2<x^2, which of the following must be true?
I. x*y<0
II. y<x
III. y*(y+2x)<0
(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

E)

The equation solves to y^2 + 2xy < 0 => y (y + 2x) < 0 or xy < 0 since y2 is always +ve
Re: which is true   [#permalink] 22 Jul 2008, 01:33
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