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# If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol

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GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
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Kudos [?]: 1612 [0], given: 375

If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol [#permalink]  23 Jun 2018, 12:40
Expert's post
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Question Stats:

71% (01:00) correct 28% (01:27) wrong based on 14 sessions
If $$a = (x + y)^2$$ and $$b = x^2 + y^2$$ and $$xy > 0$$, which of the following must be true?
Indicate all such statements.

A. a = b
B. a > b
C. a is positive
[Reveal] Spoiler: OA

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Sandy
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GRE Forum Moderator
Joined: 29 May 2018
Posts: 117
Followers: 0

Kudos [?]: 77 [1] , given: 3

Re: If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol [#permalink]  24 Jun 2018, 06:53
1
KUDOS
sandy wrote:
If $$a = (x + y)^2$$ and $$b = x^2 + y^2$$ and $$xy > 0$$, which of the following must be true?
Indicate all such statements.

A. a = b
B. a > b
C. a is positive

We are given that xy > 0 , i.e. both xy are -ve or both +ve.

A. When we expand a and b.

finally we get 2xy = 0 , and we know that 2xy is not equal to 0...eliminate.

B. 2xy > 0 , as xy>0 , then 2xy must be greater than 0 ... yes

C. a is +ve , when we take x and y both -ve or both +ve , finally we get a has +ve itself...Yes

B and C.
GMAT Club Legend
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

Re: If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol [#permalink]  28 Jul 2018, 16:15
Expert's post
Explanation

Distribute for a: $$a = (x + y)^2 = x^2 + 2xy + y^2$$. Since $$b = x^2 + y^2$$, a and b are the same except for the “extra” 2xy in a.

Since xy is positive, a is greater than b. The 1st statement is false and the 2nd statement is true.

Each term in the sum for a is positive: xy is given as positive, and $$x^2$$ and $$y^2$$ are definitely positive, as they are squared and not equal to zero. Therefore, $$a = x^2 + 2xy + y^2$$ is positive. The 3rd statement is true.
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Sandy
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Re: If a = (x + y)2 and b = x2 + y2 and xy > 0, which of the fol   [#permalink] 28 Jul 2018, 16:15
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