GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

It is currently 22 Feb 2020, 22:14

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If (20!*20!)/20^n is an integer

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
S
Joined: 18 Oct 2018
Posts: 91
Location: India
Concentration: Finance, International Business
GMAT 1: 710 Q50 V36
GPA: 4
WE: Business Development (Retail Banking)
If (20!*20!)/20^n is an integer  [#permalink]

Show Tags

New post 07 Jan 2019, 09:52
1
6
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

57% (01:32) correct 43% (01:42) wrong based on 102 sessions

HideShow timer Statistics

If (20!*20!)/20^n is an integer, what is the largest possible value of n?

A. 6
B. 8
C. 10
D. 11
E. 12


Please Press Kudos if you find the question worth it.
Manager
Manager
avatar
S
Joined: 08 Oct 2018
Posts: 61
Location: India
GPA: 4
WE: Brand Management (Health Care)
If (20!*20!)/20^n is an integer  [#permalink]

Show Tags

New post Updated on: 07 Jan 2019, 23:10
2
anshkool4u wrote:
If (20!*20!)/20^n is an integer, what is the largest possible value of n?

A. 6
B. 8
C. 10
D. 11
E. 12


Please Press Kudos if you find the question worth it.


\(\frac{(20!*20!)}{20^n}\)
Greatest possible value of 'n' for which the fraction will be an integer means finding the total number of "20s" in 20! x 20!

20 = 5 x \(2^2\)
Since the number of 2s will always be more than number of 5s, we calculate only the number of 5s in 20!

Number of 5s in 20! = \(\frac{20}{5}\) = 4
Since there are 2 20! in numerator, the number of 5s in 20^n will be 2x4 = 8

Hence option B.

Alternate Method


\(20!*20! = (20!)^2\)
\(\frac{(20!)^2}{20^n}\) is an integer and value of 'n' will be the same as the maximum number of 20s in \((20!)^2\)

Number of 20s means finding number of 5s.
Therefore, 20/5 = 4
So n=4
i.e \(20^4\)
Number of 5s (or 20s) in \((20!)^2 = (20^4)^2 = 20^8\)

i.e n=8. Option B
_________________
We learn permanently when we teach,
We grow infinitely when we share.

Originally posted by Darshi04 on 07 Jan 2019, 10:53.
Last edited by Darshi04 on 07 Jan 2019, 23:10, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 11 Dec 2018
Posts: 60
Re: If (20!*20!)/20^n is an integer  [#permalink]

Show Tags

New post 07 Jan 2019, 12:14
Finding out number of 5's in 20! Will give us 4.
And as 20! Is given twice we take 4+4=8.
Hence, B.

Why we look for 5 and not 2?
→ because there will always be a greater no of 2's so we look for exact number of 5's to know the perfect answer.

Posted from my mobile device
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 14126
Re: If (20!*20!)/20^n is an integer  [#permalink]

Show Tags

New post 09 Jan 2020, 05:02
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.
_________________
GMAT Club Bot
Re: If (20!*20!)/20^n is an integer   [#permalink] 09 Jan 2020, 05:02
Display posts from previous: Sort by

If (20!*20!)/20^n is an integer

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne