If (ax)16(by)12(cxy)17(dxy)110, and all the variables are non-zero,

Question

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.

chetan2u · Answer

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.
 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..

akshata19 · Answer

It should be C .
But OA given is A 
some please clarify

Bunuel · Answer

OA edited. For clarification is given in the post just above yours.

Gladiator59 · Answer

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.

Jamil1992Mehedi · Answer

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

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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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