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.
Jun 1012:30 AM EDT
-01:30 AM EDT
Thought your job leaves no time for GMAT prep? After multiple GMAT attempts and a demanding consulting job, Kshitij improved to 695 in under 2 months. Learn the mindset shifts, study strategy, and execution changes that made the breakthrough possible.
Jun 1006:00 AM PDT
-06:15 PM PDT
Register for the GMAT Club Virtual MBA Spotlight Fair – the world’s premier event for serious MBA candidates. This is your chance to hear directly from Admissions Directors at nearly every Top 30 MBA program..- Jun 10
10:00 AM PDT
-11:00 AM PDT
Scoring 715 on the GMAT Focus Edition requires more than just learning formulas, memorizing concepts, or solving hundreds of questions. In this episode, Nishant shares how he improved his GMAT preparation by focusing on application of concepts, and more. 
Jun 1101:30 AM EDT
-02:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Jun 1111:00 AM EDT
-01:00 PM EDT
TTP GMAT OnDemand gives serious students 400+ hours of expert video instruction, the full TTP course, AI support, weekly office hours, and a 715+ score guarantee—all built for elite GMAT score improvement.
Jun 1603:00 PM PDT
-04:00 PM PDT
Free- full-length test + 15 concept videos + 150+ short videos + study plan!
Jun 2207:30 PM EDT
-09:30 PM EDT
Master the GMAT with expert live instruction, a personalized study plan, and real-time support. Includes 40 hours of online classes plus 6 months of access to the TTP GMAT OnDemand video course. Class date: Mon/Wed June 22, 2026 →August 26, 2026
16 Oct 2024, 00:41
Kudos
Bookmarks
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
(N/A)
Question Stats:
0% (00:00) correct
0%
(00:00)
wrong
based on 0
sessions
History
Date
Time
Result
Not Attempted Yet
I have just solved two similar assignments and I am confused about the answer guides. Both assignments require the same solution method, however, one answer guide says the solution must be multiplied by the number of digits in the numerator, and the other doesn't. So for the 20 factorial assignment, we must multiply the answer of 4 by two and for the 500 factorial, we do not need to multiply the 124. What is the reasoning?
Problem 1:
Solution:
We are given that 20!×20!/20n is an integer, and we need to determine the largest possible integer value of n. Breaking 20n20^n20n into prime factors, we have:
We see that since there are fewer 5’s than 2’s in 20!20!20!, the greatest possible integer value of n is dependent on the number of 5’s in 20!20!20!. To determine the number of 5’s in 20!20!20!, we use the factorial division shortcut:
20/5 = 4
We see that there are 4 fives in the first 20!20!20! and another 4 fives in the second 20!20!20!. In other words, there are 8 fives in 20!×20!20! \times 20!20!×20!. Thus, the largest integer value of n is 8.
Problem 2:
Solution:
We are given that 500!×500!×500!/500n is an integer, and we need to determine the largest possible integer value of n.
In other words, the question is asking us to perform the factorial division shortcut:
We see that there are 100+20+4=124 fives in 500!. Thus, there are another 124 fives in the next 500!500!500! and another 124 fives in the third 500!500!500!. In other words, there are 124×3=372.
We must remember that we need to determine the maximum integer value of n such it is an integer. Thus:
3n≤372 --> n≤124
Therefore, the largest integer value of n is 124.
In problem 1, why do I not need to do 2n < 8 as in the solution guide for problem 2? THANK YOU to anyone who can help!!
Problem 1:
Solution:
We are given that 20!×20!/20n is an integer, and we need to determine the largest possible integer value of n. Breaking 20n20^n20n into prime factors, we have:
We see that since there are fewer 5’s than 2’s in 20!20!20!, the greatest possible integer value of n is dependent on the number of 5’s in 20!20!20!. To determine the number of 5’s in 20!20!20!, we use the factorial division shortcut:
20/5 = 4
We see that there are 4 fives in the first 20!20!20! and another 4 fives in the second 20!20!20!. In other words, there are 8 fives in 20!×20!20! \times 20!20!×20!. Thus, the largest integer value of n is 8.
Problem 2:
Solution:
We are given that 500!×500!×500!/500n is an integer, and we need to determine the largest possible integer value of n.
In other words, the question is asking us to perform the factorial division shortcut:
We see that there are 100+20+4=124 fives in 500!. Thus, there are another 124 fives in the next 500!500!500! and another 124 fives in the third 500!500!500!. In other words, there are 124×3=372.
We must remember that we need to determine the maximum integer value of n such it is an integer. Thus:
3n≤372 --> n≤124
Therefore, the largest integer value of n is 124.
In problem 1, why do I not need to do 2n < 8 as in the solution guide for problem 2? THANK YOU to anyone who can help!!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
