• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

OG -106

tagged by: Brent@GMATPrepNow

This topic has 3 expert replies and 2 member replies
neeg Junior | Next Rank: 30 Posts
Joined
26 Feb 2013
Posted:
12 messages

OG -106

Sat Mar 30, 2013 11:43 am
Elapsed Time: 00:00
• Lap #[LAPCOUNT] ([LAPTIME])
What is the smallest integer n for which 25^n > 5^12?

a)6
b)7
c)8
d)9
e)10

If I try solving this by rewriting the right side rather than the left side as a common base i.e. 5 ^12 --> 25^ 11 then n would have to be greater than 11 ?

Need free GMAT or MBA advice from an expert? Register for Beat The GMAT now and post your question in these forums!

GMAT/MBA Expert

Brent@GMATPrepNow GMAT Instructor
Joined
08 Dec 2008
Posted:
10763 messages
Followed by:
1212 members
Thanked:
5144 times
GMAT Score:
770
Sat Mar 30, 2013 12:04 pm
neeg wrote:
What is the smallest integer n for which 25^n > 5^12?

a)6
b)7
c)8
d)9
e)10

First recognize that 5^12 = (5^2)^6 = 25^6
What is the smallest integer n for which 25^n > 25^6?
We need n>6
So, n = 7 is the smallest integer.

Cheers,
Brent

_________________
Brent Hanneson – Founder of GMATPrepNow.com
Use our video course along with

Check out the online reviews of our course
Come see all of our free resources

Thanked by: neeg
GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months!
rintoo22 Senior | Next Rank: 100 Posts
Joined
06 May 2012
Posted:
73 messages
Thanked:
6 times
Target GMAT Score:
650+
Sat Mar 30, 2013 12:05 pm
25^n > 5^12 => 5^2n > 5^12

Therefore 2n=12 => n=6. So for n=6 both sides will match.

But the question asks the smallest integer n for which 25^n > 5^12. So the the left hand side shodl be greater. So the answer in my opinion should be b.7.

GMAT/MBA Expert

Anju@Gurome GMAT Instructor
Joined
11 Aug 2010
Posted:
511 messages
Followed by:
86 members
Thanked:
344 times
Sat Mar 30, 2013 10:33 pm
neeg wrote:
If I try solving this by rewriting the right side rather than the left side as a common base i.e. 5 ^12 --> 25^ 11 then n would have to be greater than 11 ?
Arithmetic of powers do not work that way.
5^12 = 5*(5^11) NOT 25^11
Or, 5^12 = (5^6)*(5^6) = (5*5)^6 = 25^6

To clear your confusion, let us go back to the very definition of powers,
a^n = a multiplied with it self n times = a*a*a*... (n times)
a^m = a multiplied with it self m times = a*a*a*... (m times)

Now,
a^(m + n) = (a^m)*(a^n)
a^(mn) = (a^m)^n = (a^n)^m

Hope that helps.

_________________
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §

Thanked by: neeg
neeg Junior | Next Rank: 30 Posts
Joined
26 Feb 2013
Posted:
12 messages
Sun Mar 31, 2013 5:27 pm
Brilliant as always. I can see the error, Thank you.

Anju@Gurome wrote:
neeg wrote:
If I try solving this by rewriting the right side rather than the left side as a common base i.e. 5 ^12 --> 25^ 11 then n would have to be greater than 11 ?
Arithmetic of powers do not work that way.
5^12 = 5*(5^11) NOT 25^11
Or, 5^12 = (5^6)*(5^6) = (5*5)^6 = 25^6

To clear your confusion, let us go back to the very definition of powers,
a^n = a multiplied with it self n times = a*a*a*... (n times)
a^m = a multiplied with it self m times = a*a*a*... (m times)

Now,
a^(m + n) = (a^m)*(a^n)
a^(mn) = (a^m)^n = (a^n)^m

Hope that helps.

GMAT/MBA Expert

GMATGuruNY GMAT Instructor
Joined
25 May 2010
Posted:
13361 messages
Followed by:
1779 members
Thanked:
12885 times
GMAT Score:
790
Sun Mar 31, 2013 7:34 pm
neeg wrote:
What is the smallest integer n for which 25^n > 5^12?

a)6
b)7
c)8
d)9
e)10

If I try solving this by rewriting the right side rather than the left side as a common base i.e. 5 ^12 --> 25^ 11 then n would have to be greater than 11 ?
An alternate approach would be to plug in the answers, starting with the smallest answer choice.

If n=6, we get:
25⁶ > 5¹²
(5²)⁶ > 5¹²
5¹² > 5¹².
Since n=6 makes the lefthand side EQUAL to the righthand side, the smallest possible value of n must be 7.

_________________
Mitch Hunt
GMAT Private Tutor
GMATGuruNY@gmail.com
If you find one of my posts helpful, please take a moment to click on the "Thank" icon.
Available for tutoring in NYC and long-distance.

Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

Best Conversation Starters

1 Vincen 180 topics
2 lheiannie07 65 topics
3 Roland2rule 49 topics
4 ardz24 40 topics
5 LUANDATO 16 topics
See More Top Beat The GMAT Members...

Most Active Experts

1 Brent@GMATPrepNow

GMAT Prep Now Teacher

146 posts
2 Rich.C@EMPOWERgma...

EMPOWERgmat

103 posts
3 GMATGuruNY

The Princeton Review Teacher

100 posts
4 EconomistGMATTutor

The Economist GMAT Tutor

92 posts
5 Jay@ManhattanReview

Manhattan Review

79 posts
See More Top Beat The GMAT Experts