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

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Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4417

Kudos [?]: 8417 [1], given: 102

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

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09 Jul 2013, 10:23
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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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Mike McGarry
Magoosh Test Prep

Kudos [?]: 8417 [1], given: 102

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Director
Status: Done with formalities.. and back..
Joined: 15 Sep 2012
Posts: 636

Kudos [?]: 653 [0], given: 23

Location: India
Concentration: Strategy, General Management
Schools: Olin - Wash U - Class of 2015
WE: Information Technology (Computer Software)
Re: Given that xy > 0, which of the following must also be [#permalink]

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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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Kudos [?]: 653 [0], given: 23

Director
Joined: 05 Mar 2015
Posts: 964

Kudos [?]: 287 [0], given: 41

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

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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.....

Kudos [?]: 287 [0], given: 41

Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4417

Kudos [?]: 8417 [0], given: 102

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

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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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Mike McGarry
Magoosh Test Prep

Kudos [?]: 8417 [0], given: 102

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Joined: 09 Sep 2013
Posts: 16795

Kudos [?]: 273 [0], given: 0

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

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26 Sep 2017, 03:05
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Kudos [?]: 273 [0], given: 0

Re: Given that xy > 0, which of the following must also be   [#permalink] 26 Sep 2017, 03:05
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