BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem

Target Test Prep · GMAT

Choose how you want to prepare

Learn live with an expert or move at your own pace. Every option includes the complete TTP study system.

★★★★★5.0559 reviews
GMATLiveTeach Starts Oct 17
Chris Peckover, Target Test Prep GMAT expert
LIVE ONLINE CLASSES

Get Ready for GMAT Test Day Faster with Live Online Classes

with Chris Peckover, 100th-Percentile GMAT Scorer

Oct 17 · Chris Peckover
Sat · 11:00 AM to 2:00 PM ET
Oct 20 · Chris Peckover
Tue, Thu · 8:00 to 10:00 PM ET
Oct 25 · Josh Braslow
Sun · 1:00 to 4:00 PM ET
Included
40 hours of live online classes + 6 months of TTP OnDemand
  • Attend the first class for free
  • Every class is recorded, so you never fall behind
View classes & enroll
Limited seats availableTarget Test Prep
EALiveTeachOnDemand 5 seats left Start anytime
EXECUTIVE ASSESSMENT

Target Test Prep EA OnDemand

Self-paced EA prep. Study on your schedule.

Logan Thompson
EXECUTIVE ASSESSMENT

Sep 6 to Dec 6, 2026

with Logan Thompson

165+ EA score guarantee
$05-day trial no automatic billing
Schedule
Sun · 9:30 AM to 12:30 PM ET
Included
40 hours of live online classes plus six months of access to the complete TTP EA OnDemand course.
  • 165+ EA Score Guarantee
  • 4,100+ Quant, Verbal, and Integrated Reasoning practice questions
  • 400+ hours of in-depth video lessons
  • 3,000+ step-by-step video solutions
View EA class & enroll Start free 5-day trial
Limited cohort · enrollment openTrial includes full course accessTarget Test Prep
GMATOnDemand Start anytime
SELF-PACED MASTERCLASS

Target Test Prep GMAT OnDemand

Complete access from day one. Study on your schedule.

715+ score guarantee
$0to start then $127/mo
  • Personalized study plan and analytics
  • Thousands of lessons and practice questions
Start free 5-day trial
Read 559 reviewsTarget Test Prep

Compare the format, schedule, and included access before enrolling. Prices and seat counts shown reflect the supplied offer details.

What is the smallest integer \(n\) for which \(25^n > 5^{12}?\)

Expert replies
Post new topic Post Reply
Previous Topic Next Topic
Source: — Problem Solving |

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 16207
Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members
Location: Vancouver, BC
Thanked: 5254 times
GMAT Score:770

Re: What is the smallest integer \(n\) for which \(25^n > 5^{12}?\)

by Brent@GMATPrepNow » Sun Jan 10, 2021 6:16 am
Gmat_mission wrote: ↑
Fri Jan 08, 2021 1:55 am
 What is the smallest integer \(n\) for which \(25^n > 5^{12}?\)

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

Answer: B

Source: Official Guide
We have: 25^n > 5^12

To rewrite this inequality with the SAME base, we'll replace 25 with 5².
When we do so, we get: (5²)^n > 5^12
Apply the Power of a Power law to get: 5^(2n) > 5^12

This means that it must be the case that 2n > 12
Divide both sides of the inequality by 2 to get: n > 6

What is the smallest integer n for which 25^n > 5^12 ?
We now know that n > 6
So, 7 is the smallest possible INTEGER value that satisfies this inequality.

Answer: B

Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Image
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 8208
Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members
Location: Los Angeles, CA
Thanked: 43 times

Re: What is the smallest integer \(n\) for which \(25^n > 5^{12}?\)

by Scott@TargetTestPrep » Tue Jan 19, 2021 7:39 am
Gmat_mission wrote: ↑
Fri Jan 08, 2021 1:55 am
 What is the smallest integer \(n\) for which \(25^n > 5^{12}?\)

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

Answer: B

Source: Official Guide
Solution:

We re-express 25 as 5^2:

25^n > 5^12

5^(2n) > 5^12

When we have the same base, we can compare the exponents:

2n > 12

n > 6

The smallest integer greater than 6 is 7.

Answer: B

Scott Woodbury-Stewart
Founder and CEO
[email protected]

Image

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

ImageImage
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1