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What is the smallest positive integer n for which 324 is a
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Updated on: 01 Jun 2014, 08:38
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What is the smallest positive integer n for which 324 is a factor of 6^n? A. 2 B. 3 C. 4 D. 5 E. 6
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Originally posted by chintzzz on 19 Jun 2010, 00:09.
Last edited by Bunuel on 01 Jun 2014, 08:38, edited 1 time in total.
Edited the question.




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Re: please confirm answer
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19 Jun 2010, 00:30




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Re: What is the smallest positive integer n for which 324 is a
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04 Mar 2014, 01:36
6^n / 324 324 = 6*6*3*3 We would require minimum n =4 so that 6*6*3*3 divides the number Answer = C
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Re: please confirm answer
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19 Jun 2010, 00:49
Hi Bunuel, Even I thought there was some problem with the question. Good that you were able to find the mistake Thanks.
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Re: What is the smallest positive integer n for which 324 is a
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04 Mar 2014, 01:49
Clearly n = 2 and n = 3 would result in smaller numbers for 6^n/324. You can strike them off.
Put n = 4, and divide 324 into further factors, we get 6*6*6*6/6*6*3*3. Hence, the answer is C.



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Re: What is the smallest positive integer n for which 324 is a
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01 Jun 2014, 07:14
Hi,
Bunuel, so the problem stem changed to "2" instead of "n"?
thanks.



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Re: What is the smallest positive integer n for which 324 is a
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01 Jun 2014, 08:40



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Re: please confirm answer
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13 Jun 2014, 09:43
I understand the part where "6^n=2^n*3^n=324*k=2^2*3^4*k " however I don't understand how you get k = 4 in "> n_{min}=4 (for k=2^2=4)." I understand the other solutions, however I would like to understand this one better, please. Thank you. Bunuel wrote: chintzzz wrote: I tried solving the following question and arrived at (a). Please confirm if my answer is correct or the official answer (c) is correct.
What is the smallest positive integer n for which 324 is a factor of 6 to the power of 2.
A.2 B.3 C.4 D.5 E.6 Guess should be 6 to the power of \(n\). Given: if \(6^n=324*k\), then \(n_{min}=?\) \(6^n=2^n*3^n=324*k=2^2*3^4*k\) > \(n_{min}=4\) (for \(k=2^2=4\)). Answer: C.



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Re: please confirm answer
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13 Jun 2014, 09:59
farhanabad wrote: I understand the part where "6^n=2^n*3^n=324*k=2^2*3^4*k " however I don't understand how you get k = 4 in "> n_{min}=4 (for k=2^2=4)." I understand the other solutions, however I would like to understand this one better, please. Thank you. Bunuel wrote: chintzzz wrote: I tried solving the following question and arrived at (a). Please confirm if my answer is correct or the official answer (c) is correct.
What is the smallest positive integer n for which 324 is a factor of 6 to the power of 2.
A.2 B.3 C.4 D.5 E.6 Guess should be 6 to the power of \(n\). Given: if \(6^n=324*k\), then \(n_{min}=?\) \(6^n=2^n*3^n=324*k=2^2*3^4*k\) > \(n_{min}=4\) (for \(k=2^2=4\)). Answer: C. \(6^n=2^n*3^n\). \(324=2^2*3^4\). Now, 6^n to be a multiple of 324, the powers of its primes must be at least as large as powers of primes in 324. Thus the least value of n for which 6^n is a multiple of 324 is 4. Does this make sense?
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Re: please confirm answer
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13 Jun 2014, 10:08
Yes, I guess I thought there was a magic formula where K = (2^n * 3^n)/((2^2*3^4). I wanted to learn how you would solve that.
Thanks again.



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Re: What is the smallest positive integer n for which 324 is a
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19 Jan 2015, 15:27
Bunuel wrote: chintzzz wrote: I tried solving the following question and arrived at (a). Please confirm if my answer is correct or the official answer (c) is correct.
What is the smallest positive integer n for which 324 is a factor of 6 to the power of 2.
A.2 B.3 C.4 D.5 E.6 Guess should be 6 to the power of \(n\). Given: if \(6^n=324*k\), then \(n_{min}=?\) \(6^n=2^n*3^n=324*k=2^2*3^4*k\) > \(n_{min}=4\) (for \(k=2^2=4\)). Answer: C. Hi, The question asks for minimum value of n^th power of 6. Because 324 = 2^2*3^2 i.e. 324 = 6^2*3^2. So shouldn't n = 2? TO



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What is the smallest positive integer n for which 324 is a
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19 Jan 2015, 18:44
Hi All, This question can be solved with a bit of Number Property knowledge and TESTing THE ANSWERS. We're asked for the SMALLEST positive integer N for which 324 is a FACTOR of 6^N. In other words, which of these answers is SMALLEST and makes 6^N/324 is an integer. Since we're dealing with positives, and the answer choices are numbers, we can just "brute force" the answer choices until we find a match.... A: N = 2 6^2 = 36 36/324 is NOT an integer. Eliminate A. B: N = 3 6^3 = 216 216/324 is NOT an integer. Eliminate B. C: N = 4 6^4 = 1296 1296/324 might "look" tough, but consider the patterns.... "12" is divisibly by "3" (4 times) and "96" is divisibly by "24" (also 4 times), so 1296/324 = 4. This IS an integer, so C MUST be the answer. Final Answer: GMAT assassins aren't born, they're made, Rich
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Re: What is the smallest positive integer n for which 324 is a
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05 Feb 2016, 09:23
The simplest way for me to solve the question is:
Prime factorisation of 324 = 2^2x3^4 Prime factorisation of 6 = 2x3
We need to have at least four factors of 2 and 3 on the number 6^N in order to end with an integer.
Answer C.



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Re: What is the smallest positive integer n for which 324 is a
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05 Feb 2016, 10:30
chintzzz wrote: What is the smallest positive integer n for which 324 is a factor of 6^n?
A. 2 B. 3 C. 4 D. 5 E. 6 324 = 4*81 = 2^2*3^4 i.e. 6^n=2^n*3^n must have atleast 2^2*3^4 i.e. n Min must be 4 Answer: Option C
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Re: What is the smallest positive integer n for which 324 is a
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16 Sep 2018, 00:59
chintzzz wrote: What is the smallest positive integer n for which 324 is a factor of 6^n?
A. 2 B. 3 C. 4 D. 5 E. 6 Dear Moderator, Please retag this question from " Work /rate problems " to " Arithmetic ". Thank you.
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Re: What is the smallest positive integer n for which 324 is a
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16 Sep 2018, 01:01



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What is the smallest positive integer n for which 324 is a
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16 Sep 2018, 01:21
chintzzz wrote: What is the smallest positive integer n for which 324 is a factor of 6^n?
A. 2 B. 3 C. 4 D. 5 E. 6 factorize 324 > \(2^2*3^4\) factorize 6 > \(2^1*3^1\) \(\frac{2^1*3^1}{2^2*3^4}\) now so that \(6^n\) is divisible by 324 we need to add at least as many powers as 324 has i.e. \(2^1*3^1\) = \(2^2*3^4\) (must be equal) > \(6^n\) = \(2^1*2^1*3^1*3^3\) = \(2^2*3^4\) YAY



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Re: What is the smallest positive integer n for which 324 is a
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16 Sep 2018, 15:02
chintzzz wrote: What is the smallest positive integer n for which 324 is a factor of 6^n?
A. 2 B. 3 C. 4 D. 5 E. 6 6^3=216=2/3*324 6^4=6*2/3*324=1296 1296/324=4 C




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