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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: 4650
Given that xy > 0, which of the following must also be [#permalink]

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09 Jul 2013, 09:23
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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

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

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09 Jul 2013, 09:49
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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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Posts: 962
Re: Given that xy > 0, which of the following must also be [#permalink]

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25 Dec 2015, 06:33
[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.....
Magoosh GMAT Instructor
Joined: 28 Dec 2011
Posts: 4650
Re: Given that xy > 0, which of the following must also be [#permalink]

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25 Dec 2015, 08:25
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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Magoosh Test Prep

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

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

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26 Sep 2017, 02:05
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Re: Given that xy > 0, which of the following must also be   [#permalink] 26 Sep 2017, 02:05
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