Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 23 May 2017, 22:08

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# What is the smallest integer n for which 25^n > 5^12 ?

Author Message
TAGS:

### Hide Tags

Manager
Joined: 02 Dec 2012
Posts: 178
Followers: 6

Kudos [?]: 2689 [4] , given: 0

What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

10 Dec 2012, 10:37
4
KUDOS
4
This post was
BOOKMARKED
00:00

Difficulty:

5% (low)

Question Stats:

81% (01:27) correct 19% (00:30) wrong based on 1214 sessions

### HideShow timer Statistics

What is the smallest integer n for which 25^n > 5^12 ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 38846
Followers: 7719

Kudos [?]: 105942 [2] , given: 11602

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

10 Dec 2012, 10:41
2
KUDOS
Expert's post
What is the smallest integer n for which 25^n > 5^12 ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

Work with the common base: $$25^n=(5^2)^n=5^{2n}$$.

Thus we have that $$5^{2n}>5^{12}$$ --> $$2n>12$$ --> $$n>6$$ --> $$n_{min}=7$$.

_________________
Moderator
Joined: 01 Sep 2010
Posts: 3166
Followers: 855

Kudos [?]: 7298 [3] , given: 1063

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

10 Dec 2012, 13:40
3
KUDOS
Here we have to be careful

because we know that n is > 6. So be on the lookout to not choose 6 as answer$$BUT 7$$

During the test such error could be common
_________________
Intern
Joined: 04 Mar 2012
Posts: 21
Followers: 0

Kudos [?]: 4 [0], given: 0

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

06 Apr 2013, 23:48
When i worked this problem I did the following:

5^12 -> 5*5^11 but why is 5*5^11 not equal 25^11?

I am stuck on this part, and im sure it is simply to do with order of operations but i cant wrap my mind around it.
Senior Manager
Joined: 16 Dec 2011
Posts: 433
Followers: 11

Kudos [?]: 214 [0], given: 70

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

07 Apr 2013, 01:06
specialxknc wrote:
When i worked this problem I did the following:

5^12 -> 5*5^11 but why is 5*5^11 not equal 25^11?

I am stuck on this part, and im sure it is simply to do with order of operations but i cant wrap my mind around it.

5*5^11 = 5^1 * 5^11 = 5*(1+11)

25^11 = (5^2)^11 = 5^(2*11) = 5^22

Rules for exponents are as follows:

(1) $$x^m * x^n = x^(m+n)$$
(2) $$x^m / x^n = x^(m-n)$$
(3) $$x^(-m)$$ = $$1/x^m$$
(4) $$x^0$$ =1
(5) $$(x^m)^n$$ = $$x^(mn)$$
(6) $$x^m * y^m$$ = $$(xy)^m$$

Last edited by doe007 on 10 Apr 2013, 23:20, edited 4 times in total.
Intern
Joined: 07 Apr 2013
Posts: 1
Location: Bulgaria
Concentration: Human Resources, Marketing
GMAT 1: 780 Q51 V47
Followers: 0

Kudos [?]: 6 [1] , given: 0

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

07 Apr 2013, 07:25
1
KUDOS
specialxknc wrote:
When i worked this problem I did the following:

5^12 -> 5*5^11 but why is 5*5^11 not equal 25^11?

I am stuck on this part, and im sure it is simply to do with order of operations but i cant wrap my mind around it.

Because you dropped parenthesis. 5*5^11 is ambiguous, so on one hand it could equal (5*5)^11, which is 25^11. But on the other hand it might mean 5*(5^11), which is 5^12.

Kind Regards,

Misterholmes
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1857
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 51

Kudos [?]: 2163 [0], given: 193

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

27 Feb 2014, 01:47
5^12 can be written as 25^6
When n=6, the equation becomes equal, so 7 should be the answer

_________________

Kindly press "+1 Kudos" to appreciate

Manager
Joined: 07 Apr 2014
Posts: 141
Followers: 1

Kudos [?]: 24 [0], given: 81

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

11 Sep 2014, 10:53
What is the smallest integer n for which 25^n > 5^12 ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

25^n > 5^12

5^2n>5^12

2n>12

n has to be minimum 7
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15412
Followers: 648

Kudos [?]: 206 [0], given: 0

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

25 Dec 2015, 21:34
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).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Target Test Prep Representative
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 895
Followers: 34

Kudos [?]: 505 [1] , given: 2

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

09 Jun 2016, 14:10
1
KUDOS
Expert's post
What is the smallest integer n for which 25^n > 5^12 ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

To solve, we want to get the bases the same. Thus we need to break 25^n into prime factors.

25^n = (5^2)^n = 5^(2n) (Remember that when we have a power to a power, we multiply the exponents.)

We can use the new value in the given inequality:

5^(2n)> 5^12

Since we have the same bases on either side of the inequality we can drop the bases and set up an equation involving just the exponents.

2n > 12

n > 6

Because n is greater than 6, the smallest integer that satisfies the inequality 25^n > 5^12 is 7.

_________________

Jeffery Miller

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Senior Manager
Joined: 18 Jan 2010
Posts: 257
Followers: 5

Kudos [?]: 102 [0], given: 9

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

09 Jun 2016, 22:46
What is the smallest integer n for which 25^n > 5^12 ?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

$$25^n$$ > $$5^12$$
$$5^2n$$ > $$5^12$$

Since 5 is a positive number

2n> 12

n > 6

Smallest integer value for which n> 6: 7.

Manager
Joined: 03 Jan 2017
Posts: 204
Followers: 0

Kudos [?]: 2 [0], given: 4

Re: What is the smallest integer n for which 25^n > 5^12 ? [#permalink]

### Show Tags

25 Mar 2017, 06:19
be careful here, we are not looking for an answer that would give us >=0, but >=
5^2n>5^12
n is 7
Re: What is the smallest integer n for which 25^n > 5^12 ?   [#permalink] 25 Mar 2017, 06:19
Similar topics Replies Last post
Similar
Topics:
5 What is the smallest positive integer n for which √n*7! is an integer? 4 15 Apr 2017, 17:27
4 What is the smallest positive integer n for which n!/9^9 is an integer 6 21 Feb 2017, 10:27
1 What is the smallest integer k for which 64^k > 4^14? 4 13 Aug 2016, 11:33
What is the smallest integer a for which 27^a>3^24? 4 09 Mar 2016, 23:43
24 What is the smallest positive integer n for which 324 is a 16 16 Feb 2017, 02:03
Display posts from previous: Sort by