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Given that xy > 0, which of the following must also be

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Given that xy > 0, which of the following must also be [#permalink]

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Given that xy > 0, which of the following must also be greater than zero?

(A) \(x + y\)
(B) \(x^2 + y\)
(C) \((x + y)^2\)
(D) \(x^2 - y^2 + 100\)
(E) \((x - y)^2\)

For a discussion of plugging in numbers, as well as a full solution to this question, see:
http://magoosh.com/gmat/2013/how-to-plu ... questions/

Mike :-)
[Reveal] Spoiler: OA

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Re: Given that xy > 0, which of the following must also be [#permalink]

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New post 09 Jul 2013, 10:49
mikemcgarry wrote:
Given that xy > 0, which of the following must also be greater than zero?

(A) \(x + y\)
(B) \(x^2 + y\)
(C) \((x + y)^2\)
(D) \(x^2 - y^2 + 100\)
(E) \((x - y)^2\)

For a discussion of plugging in numbers, as well as a full solution to this question, see:
http://magoosh.com/gmat/2013/how-to-plu ... questions/

Mike :-)


Actually if u just go through the options.. you'll notice that option C, is a perfect square.. which has to be greater than or equal to zero. Now looking back at the question, we know xy>0, which implies x and y are not equal to 0 and are of same sign. therefore x+y will be a non zero number and its square would be greater than 0.

Ans C it is.
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Re: Given that xy > 0, which of the following must also be [#permalink]

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Re: Given that xy > 0, which of the following must also be [#permalink]

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New post 25 Dec 2015, 07:33
[quote="mikemcgarry"]Given that xy > 0, which of the following must also be greater than zero?

(A) \(x + y\)
(B) \(x^2 + y\)
(C) \((x + y)^2\)
(D) \(x^2 - y^2 + 100\)
(E) \((x - y)^2\)

We are not told that X & Y were integers.
Consider X=Y=1/2

only option C fits in..... :)
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Magoosh GMAT Instructor
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Re: Given that xy > 0, which of the following must also be [#permalink]

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New post 25 Dec 2015, 09:25
rohit8865 wrote:
mikemcgarry wrote:
Given that xy > 0, which of the following must also be greater than zero?

(A) \(x + y\)
(B) \(x^2 + y\)
(C) \((x + y)^2\)
(D) \(x^2 - y^2 + 100\)
(E) \((x - y)^2\)

We are not told that X & Y were integers.
Consider X=Y=1/2

only option C fits in..... :)

Dear rohit8865,
Quite true, my friend: the values of x & y are not necessarily integers and not necessarily positive. The two perfect squares, (C) & (E), must be greater than or equal to zero. As you figured out, if the two variables are equal non-zero numbers (whether positive or negative), then (E) will equal zero and not work. Only (C) works.
Good job!
Mike :-)
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Re: Given that xy > 0, which of the following must also be   [#permalink] 25 Dec 2015, 09:25
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