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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]  21 Jul 2008, 23:10
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
Joined: 27 May 2008
Posts: 550
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Re: which is true [#permalink]  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
Joined: 11 May 2008
Posts: 562
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Kudos [?]: 55 [0], given: 0

Re: which is true [#permalink]  21 Jul 2008, 23:45
KUDOS... +1 DURGESH
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Re: which is true [#permalink]  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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