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If x and y are positive integers, which of the following is NOT a poss

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GMAT 1: 670 Q46 V36
If x and y are positive integers, which of the following is NOT a poss  [#permalink]

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New post 03 Jul 2018, 17:18
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Question Stats:

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If x and y are positive integers, which of the following is NOT a possible value for \(\frac{3*2^x*18^x}{6^{(x+y)}}\)?


A. \(\frac{1}{12}\)

B. \(\frac{1}{2}\)

C. \(\frac{2}{3}\)

D. 3

E. 18

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Re: If x and y are positive integers, which of the following is NOT a poss  [#permalink]

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New post 03 Jul 2018, 17:55
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dabaobao wrote:
If x and y are positive integers, which of the following is NOT a possible value for (3 * 2^x * 18^x)/6^(x+y)?

A. \(\frac{1}{12}\)
B. \(\frac{1}{2}\)
C. \(\frac{2}{3}\)
D. 3
E. 18


C. The (3 * 2^x * 18^x)/6^(x+y) is shortened as 6^(x-y) x 3. Only C do not allow x, y as integers
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Re: If x and y are positive integers, which of the following is NOT a poss  [#permalink]

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New post 03 Jul 2018, 20:56
dabaobao wrote:
If x and y are positive integers, which of the following is NOT a possible value for \(\frac{3*2^x*18^x}{6^{(x+y)}}\)?


A. \(\frac{1}{12}\)

B. \(\frac{1}{2}\)

C. \(\frac{2}{3}\)

D. 3

E. 18


Given \(\frac{3*2^x*18^x}{6^{(x+y)}}\)
Or, \(\frac{3*2^x+3^{2x}*2^x}{6^{x+y}}\)
Or, \(\frac{3*6^{2x}}{6^{x+y}}\)
Or, \(3*6^{x-y}\)

Checking options for possible value of the expression:-
A.\(3*6^{x-y}\)=\(\frac{1}{12}\) Or, x-y=-2, since x and y are positive integers. hence this option is validated.
B.\(3*6^{x-y}\)=\(\frac{1}{2}\) Or, x-y=-1,this option is validated.
C.\(3*6^{x-y}\)=\(\frac{2}{3}\) Or, \(6^{x-y}\)=\(2*3^{-2}\) since x and y are positive integers. hence this option is not validated
D.\(3*6^{x-y}\)=\(3\) Or, \(6^{x-y}\)=\(6^0\) Or, x-y=0 Or, x=y.hence this option is validated.
E.\(3*6^{x-y}\)=\(18\) or, \(6^{x-y}\)=\(6^1\) Or,x-y=1,hence this option is validated.
Ans. C
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Re: If x and y are positive integers, which of the following is NOT a poss &nbs [#permalink] 03 Jul 2018, 20:56
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