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

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Manager
Joined: 24 Oct 2016
Posts: 243
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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03 Jul 2018, 17:18
6
00:00

Difficulty:

55% (hard)

Question Stats:

61% (02:36) correct 39% (02:30) wrong based on 61 sessions

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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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Intern
Joined: 03 Apr 2018
Posts: 11
Re: If x and y are positive integers, which of the following is NOT a poss  [#permalink]

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03 Jul 2018, 17:55
1
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
Director
Status: Learning stage
Joined: 01 Oct 2017
Posts: 931
WE: Supply Chain Management (Energy and Utilities)
Re: If x and y are positive integers, which of the following is NOT a poss  [#permalink]

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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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