GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 23 May 2019, 22:10

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

# What is the smallest positive integer n for which 324 is a

Author Message
TAGS:

### Hide Tags

Intern
Joined: 16 Jun 2010
Posts: 14
What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

Updated on: 01 Jun 2014, 09:38
1
17
00:00

Difficulty:

45% (medium)

Question Stats:

62% (01:28) correct 38% (01:21) wrong based on 896 sessions

### HideShow timer Statistics

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

Originally posted by chintzzz on 19 Jun 2010, 01:09.
Last edited by Bunuel on 01 Jun 2014, 09:38, edited 1 time in total.
Edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 55276

### Show Tags

19 Jun 2010, 01:30
3
4
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 $$k=2^2=4$$).

_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1812
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

04 Mar 2014, 02:36
2
4
6^n / 324

324 = 6*6*3*3

We would require minimum n =4 so that 6*6*3*3 divides the number

_________________
Kindly press "+1 Kudos" to appreciate
##### General Discussion
Manager
Joined: 07 Oct 2006
Posts: 58
Location: India

### Show Tags

19 Jun 2010, 01:49
Hi Bunuel,

Even I thought there was some problem with the question. Good that you were able to find the mistake

Thanks.
_________________
-------------------------------------

For English Grammar tips, consider visiting http://www.grammar-quizzes.com/index.html.
Manager
Joined: 18 Nov 2013
Posts: 62
Location: India
GMAT Date: 12-26-2014
WE: Information Technology (Computer Software)
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

04 Mar 2014, 02:49
1
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.
Intern
Joined: 13 Dec 2013
Posts: 36
GMAT 1: 620 Q42 V33
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

01 Jun 2014, 08:14
Hi,

Bunuel, so the problem stem changed to "2" instead of "n"?

thanks.
Math Expert
Joined: 02 Sep 2009
Posts: 55276
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

01 Jun 2014, 09:40
Intern
Joined: 10 Mar 2013
Posts: 11

### Show Tags

13 Jun 2014, 10:43
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 $$k=2^2=4$$).

Math Expert
Joined: 02 Sep 2009
Posts: 55276

### Show Tags

13 Jun 2014, 10:59
2
1
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 $$k=2^2=4$$).

$$6^n=2^n*3^n$$.

$$324=2^2*3^4$$.

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?
_________________
Intern
Joined: 10 Mar 2013
Posts: 11

### Show Tags

13 Jun 2014, 11:08
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.
Manager
Joined: 03 Jan 2015
Posts: 59
Concentration: Strategy, Marketing
WE: Research (Pharmaceuticals and Biotech)
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

19 Jan 2015, 16:27
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 $$k=2^2=4$$).

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
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 14198
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

19 Jan 2015, 19:44
2
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.

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Current Student
Joined: 18 Jul 2015
Posts: 39
Location: Brazil
Concentration: General Management, Strategy
GMAT 1: 640 Q39 V38
GMAT 2: 700 Q47 V38
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

05 Feb 2016, 10:23
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.

CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2931
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

05 Feb 2016, 11:30
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

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Director
Joined: 27 May 2012
Posts: 787
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

16 Sep 2018, 01:59
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.
_________________
- Stne
Math Expert
Joined: 02 Sep 2009
Posts: 55276
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

16 Sep 2018, 02:01
stne wrote:
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.

________________________
Edited. The tags. Thank you.
_________________
VP
Joined: 09 Mar 2016
Posts: 1284
What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

16 Sep 2018, 02:21
1
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
VP
Joined: 07 Dec 2014
Posts: 1192
Re: What is the smallest positive integer n for which 324 is a  [#permalink]

### Show Tags

16 Sep 2018, 16:02
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
Re: What is the smallest positive integer n for which 324 is a   [#permalink] 16 Sep 2018, 16:02
Display posts from previous: Sort by