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

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Current Student
Joined: 11 May 2008
Posts: 555

Kudos [?]: 222 [0], given: 0

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

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22 Jul 2008, 00:10
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

Kudos [?]: 222 [0], given: 0

Director
Joined: 27 May 2008
Posts: 541

Kudos [?]: 363 [1], given: 0

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22 Jul 2008, 00:25
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)

Kudos [?]: 363 [1], given: 0

Current Student
Joined: 11 May 2008
Posts: 555

Kudos [?]: 222 [0], given: 0

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22 Jul 2008, 00:45
KUDOS... +1 DURGESH

Kudos [?]: 222 [0], given: 0

Senior Manager
Joined: 06 Apr 2008
Posts: 429

Kudos [?]: 165 [0], given: 1

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22 Jul 2008, 02:33
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

Kudos [?]: 165 [0], given: 1

Re: which is true   [#permalink] 22 Jul 2008, 02:33
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