Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Nov 1912:30 PM EST
-01:30 PM EST
Learn how Keshav, a Chartered Accountant, scored an impressive 705 on GMAT in just 30 days with GMATWhiz's expert guidance. In this video, he shares preparation tips and strategies that worked for him, including the mock, time management, and more
Nov 2007:30 AM PST
-08:30 AM PST
Learn what truly sets the UC Riverside MBA apart and how it helps in your professional growth
Nov 2001:30 PM EST
-02:30 PM IST
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Nov 2211:00 AM IST
-01:00 PM IST
Do RC/MSR passages scare you? e-GMAT is conducting a masterclass to help you learn – Learn effective reading strategies Tackle difficult RC & MSR with confidence Excel in timed test environment- Nov 23
11:00 AM IST
-01:00 PM IST
Attend this free GMAT Algebra Webinar and learn how to master the most challenging Inequalities and Absolute Value problems with ease. 
Nov 2407:00 PM PST
-08:00 PM PST
Full-length FE mock with insightful analytics, weakness diagnosis, and video explanations!
Nov 2510:00 AM EST
-11:00 AM EST
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors.
25 Feb 2020, 02:04
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
66% (02:04) correct
34%
(02:21)
wrong
based on 336
sessions
History
Date
Time
Result
Not Attempted Yet
If n is a positive integer and \(\frac{100!}{72^n}\) is a positive integer, what is the greatest possible value of n ?
A. 20
B. 21
C. 22
D. 23
E. 24
Are You Up For the Challenge: 700 Level Questions
A. 20
B. 21
C. 22
D. 23
E. 24
Are You Up For the Challenge: 700 Level Questions
25 Feb 2020, 03:14
Kudos
Bookmarks
If n is a positive integer and \(\frac{100!}{72^{n}}\) is a positive integer, what is the greatest possible value of \(n\) ?
\(72^{n}= (8*9)^{n}= 2^{3n}*3^{2n}\\
\)
--> In order to get the greatest possible value of n, finding the number of 3s in 100! is enough:
\([\frac{100}{3}]+[\frac{100}{9}]+[\frac{100}{27}]+[\frac{100}{81}]+...= \\
\)
=\(33+11+3+1= 48 \) --> the number of \(3s\) in \(100!\)
-->\( 48= 2n\) --> \(n =24 \)
The answer is E.
\(72^{n}= (8*9)^{n}= 2^{3n}*3^{2n}\\
\)
--> In order to get the greatest possible value of n, finding the number of 3s in 100! is enough:
\([\frac{100}{3}]+[\frac{100}{9}]+[\frac{100}{27}]+[\frac{100}{81}]+...= \\
\)
=\(33+11+3+1= 48 \) --> the number of \(3s\) in \(100!\)
-->\( 48= 2n\) --> \(n =24 \)
The answer is E.
25 Feb 2020, 07:35
Kudos
Bookmarks
Bunuel
72 = 2^3*3^2
So, 72 will have more 2's than 3's and to find the highest power of 72 find the highest power of 3 in 100
100/3 = 33
33/3 = 11
11/3 = 3
3/1 = 1
Total is 33 + 11 + 3 + 1 = 48
Since, power of 3 is 2 we need to divide 48/2 = 24 , Answer must be (E)
