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# If (ax)16(by)12(cxy)17(dxy)11>0, and all the variables are non-zero,

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Intern
Joined: 05 Dec 2017
Posts: 21
GPA: 3.35
If (ax)16(by)12(cxy)17(dxy)11>0, and all the variables are non-zero, [#permalink]

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18 Mar 2018, 01:57
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Question Stats:

59% (01:20) correct 41% (01:07) wrong based on 49 sessions

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If $$(ax)^{16}(by)^{12}(cxy)^{17}(dxy)^{11}>0$$, and all the variables are non-zero numbers, which of the following must be true?

A. ab>0
B. ab<0
C. cd>0
D. cd<0
E. None of the above.
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Aug 2009
Posts: 5777
Re: If (ax)16(by)12(cxy)17(dxy)11>0, and all the variables are non-zero, [#permalink]

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18 Mar 2018, 05:23
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Expert's post
Jamil1992Mehedi wrote:
Hi Bunuel, i am confused about the OA. Perhaps my provided ans is wrong. Please Would you share the right ans and difficulty level.
If $$(ax)^{16}(by)^{12}(cxy)^{17}(dxy)^{11}>0$$, and all the variables are non-zero numbers, which of the following must be true?
A. ab>0
B. ab<0
C. cd>0
D. cd<0
E. None of the above.

Hi,

The OA is flawed. What is the source?

Solution..
$$a^{16}*b^{12}*c^{17}*d^{11}*x^{16+17+11}*y^{12+17+11}>0........a^{16}*b^{12}*c^{17}*d^{11}*x^{44}*y^{40}>0$$..
Now a, b, x and y have even power, so raised to even power, they would always be POSITIVE. BUT without power, each could be positive or negative. Therefore we cannot comment on their PRODUCT without powers.
So we cannot comment on ab....

Now all other terms with a,b,x and y are positive, so $$c^{17}*d^{11}$$ also should be > 0..
Therefore cd>0..
Ans C..
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Joined: 22 May 2017
Posts: 120
Re: If (ax)16(by)12(cxy)17(dxy)11>0, and all the variables are non-zero, [#permalink]

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18 Mar 2018, 10:54
It should be C .
But OA given is A
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Posts: 44655
Re: If (ax)16(by)12(cxy)17(dxy)11>0, and all the variables are non-zero, [#permalink]

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18 Mar 2018, 11:00
akshata19 wrote:
It should be C .
But OA given is A

OA edited. For clarification is given in the post just above yours.
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Joined: 16 Sep 2016
Posts: 212
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Re: If (ax)16(by)12(cxy)17(dxy)11>0, and all the variables are non-zero, [#permalink]

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18 Mar 2018, 11:11
Jamil1992Mehedi wrote:
If $$(ax)^{16}(by)^{12}(cxy)^{17}(dxy)^{11}>0$$, and all the variables are non-zero numbers, which of the following must be true?

A. ab>0
B. ab<0
C. cd>0
D. cd<0
E. None of the above.

By pairing of the powers for all other terms.. it turns out c^17 and d^11 are only terms with odd power.
Rest all terms ( including the XY term end up with even powers )
(XY)^17 * (XY)^11 = (XY)^28.

So c and d must have same parity. Either both positive or both negative.

Hence cd > 0.
Option C.
Intern
Joined: 05 Dec 2017
Posts: 21
GPA: 3.35
Re: If (ax)16(by)12(cxy)17(dxy)11>0, and all the variables are non-zero, [#permalink]

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20 Mar 2018, 20:00
Thanks Chetan2u and Bunuel for your utmost response.
First of all, in terms of question's source asked by chetan2U, basically i found it in a local GMAT-GRE preparation book. But the question maker claims that product of ab will be positive always due to positive exponent exponent of both a & b. Any cogent argument from your end. Thank you
Re: If (ax)16(by)12(cxy)17(dxy)11>0, and all the variables are non-zero,   [#permalink] 20 Mar 2018, 20:00
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# If (ax)16(by)12(cxy)17(dxy)11>0, and all the variables are non-zero,

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