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# If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive

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If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive  [#permalink]

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27 May 2012, 09:21
1
00:00

Difficulty:

15% (low)

Question Stats:

81% (01:47) correct 19% (02:20) wrong based on 70 sessions

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If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive integers, what is the value of a?

A. 22
B. 11
C. 9
D. 6
E. 3
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Posts: 58347
Re: If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive  [#permalink]

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28 May 2012, 00:32
macjas wrote:
If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive integers, what is the value of a?

A. 22
B. 11
C. 9
D. 6
E. 3

$$18^a*9^{3a-1}=2^3*3^b$$ --> $$(2^a*3^{2a})*3^{6a-2}=2^3*3^b$$ --> $$2^a*3^{8a-2}=2^3*3^b$$ --> since both $$a$$ and $$b$$ are positive integers then the powers of 2 on both sides must be equal: $$a=3$$.

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Re: If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive  [#permalink]

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27 Feb 2014, 21:04
macjas wrote:
If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive integers, what is the value of a?

A. 22
B. 11
C. 9
D. 6
E. 3

(18^a) * 9^(3a – 1)= (2^3)(3^b)

= 2^a . 9^a . 9^(3a – 1) = (2^3)(3^b)

Just compare powers of 2 from both sides (no need to calculate powers of 3, 9 as value of b is not asked)

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Re: If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive  [#permalink]

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22 Sep 2019, 01:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If (18^a) * 9^(3a – 1)= (2^3)(3^b) and a and b are positive   [#permalink] 22 Sep 2019, 01:12
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