Last visit was: 18 Nov 2025, 14:10 It is currently 18 Nov 2025, 14:10
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,062
 [31]
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,062
 [31]
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 14 Apr 2020, 08:51
2
Kudos
Add Kudos
29
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

47% (03:06) correct 54% (02:28) wrong based on 200 sessions

History

Date
Time
Result
Not Attempted Yet
If n is a positive integer and \(n!\) is a multiple of \(2^{20}\) but not \(3^{20}\), then how many value can n take ?

A. 21
B. 20
C. 16
D. 11
E. 10


Are You Up For the Challenge: 700 Level Questions
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 18 Nov 2025
Posts: 5,793
Own Kudos:
5,508
 [13]
Given Kudos: 161
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,793
Kudos: 5,508
 [13]
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 14 Apr 2020, 11:01
5
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
Bunuel
If n is a positive integer and \(n!\) is a multiple of \(2^{20}\) but not \(3^{20}\), then how many value can n take ?

A. 21
B. 20
C. 16
D. 11
E. 10


Are You Up For the Challenge: 700 Level Questions
Show more

Asked: If n is a positive integer and \(n!\) is a multiple of \(2^{20}\) but not \(3^{20}\), then how many value can n take ?

Highest power of 2 in 23! = 11 + 5 + 2 + 1 = 19
Highest power of 2 in 24! = 12 + 6 + 3 + 1 = 22

Minimum value of n = 24

Highest power of 3 in 44! = 14 + 4 + 1 = 19
Highest power of 3 in 45! = 15 + 5 + 1 = 21

Maximum value of n = 44

Number of values of n feasible = 44-24 + 1 = 21

IMO A
General Discussion
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 18 Nov 2025
Posts: 5,793
Own Kudos:
5,508
 [2]
Given Kudos: 161
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,793
Kudos: 5,508
 [2]
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 14 Apr 2020, 10:47
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If n is a positive integer and \(n!\) is a multiple of \(7^{20}\) but not \(3^{20}\), then how many value can n take ?

A. 21
B. 20
C. 16
D. 11
E. 75


Are You Up For the Challenge: 700 Level Questions
Show more

Asked: If n is a positive integer and \(n!\) is a multiple of \(7^{20}\) but not \(3^{20}\), then how many value can n take ?

Highest power of 7 in 126! = 18 + 2 = 20
Highest power of 3 in 126! = 42 + 14 + 4 + 1 = 61

Hi Bunuel
Please check whether question is correct. Since there may not be any value of n such that \(n!\) is a multiple of \(7^{20}\) but not \(3^{20}\)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 18 Nov 2025
Posts: 105,355
Own Kudos:
778,062
Given Kudos: 99,964
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,355
Kudos: 778,062
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 14 Apr 2020, 10:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Kinshook
Bunuel
If n is a positive integer and \(n!\) is a multiple of \(7^{20}\) but not \(3^{20}\), then how many value can n take ?

A. 21
B. 20
C. 16
D. 11
E. 75


Are You Up For the Challenge: 700 Level Questions

Asked: If n is a positive integer and \(n!\) is a multiple of \(7^{20}\) but not \(3^{20}\), then how many value can n take ?

Highest power of 7 in 126! = 18 + 2 = 20
Highest power of 3 in 126! = 42 + 14 + 4 + 1 = 61

Hi Bunuel
Please check whether question is correct. Since there may not be any value of n such that \(n!\) is a multiple of \(7^{20}\) but not \(3^{20}\)
Show more

________________
Fixed. Thank you.
User avatar
Alextus93
User avatar
Joined: 21 Mar 2020
Last visit: 16 Dec 2024
Posts: 4
Own Kudos:
2
 [1]
Given Kudos: 8
Products:
My Reviews
Posts: 4
Kudos: 2
 [1]
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 14 Apr 2020, 11:15
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
So I’m getting the concept here but is there a quicker way to find N than just trial and error? I had to start with 20 and just try numbers until it fit. I’m trying to determine if there’s a more efficient way to solve this.

Posted from my mobile device
avatar
harishmobile
avatar
Joined: 28 Nov 2016
Last visit: 17 Jun 2022
Posts: 1
Own Kudos:
3
 [3]
Given Kudos: 8
Posts: 1
Kudos: 3
 [3]
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 14 Apr 2020, 13:43
3
Kudos
Add Kudos
Bookmarks
Bookmark this Post
hi

plz explain this
Highest power of 2 in 23! = 11 + 5 + 2 + 1 = 19 ????- how you came to this equation.

can you please share concept of this too ???
User avatar
Alextus93
User avatar
Joined: 21 Mar 2020
Last visit: 16 Dec 2024
Posts: 4
Own Kudos:
2
 [1]
Given Kudos: 8
Products:
My Reviews
Posts: 4
Kudos: 2
 [1]
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 14 Apr 2020, 13:49
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
23/2^1+23/2^2+23/2^3+23/2^4=19

So the formula is basically to figure out how many of a given factor are in n!, divide that number by that factor to 1,2,3, etc. power until it no longer will go into that number( ignore the remainder). Then find the sum of those numbers.

Posted from my mobile device
User avatar
gurmukh
User avatar
Joined: 18 Dec 2017
Last visit: 24 Jan 2025
Posts: 259
Own Kudos:
260
 [1]
Given Kudos: 20
Posts: 259
Kudos: 260
 [1]
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 14 Apr 2020, 19:43
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
harishmobile
hi

plz explain this
Highest power of 2 in 23! = 11 + 5 + 2 + 1 = 19 ????- how you came to this equation.

can you please share concept of this too ???
Show more
23!= 23×22×21×---------3×2×1
All the multiple of 2 will give atleast one 2 so 11
All the multiple of 4 will give you extra one 2 so 5
All the multiple of 8 will give you extra one 2 so 2
All the multiple of 16 will give you extra one 2 so 1
11+5+2+1 =19

Posted from my mobile device
User avatar
gurmukh
User avatar
Joined: 18 Dec 2017
Last visit: 24 Jan 2025
Posts: 259
Own Kudos:
260
 [1]
Given Kudos: 20
Posts: 259
Kudos: 260
 [1]
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 14 Apr 2020, 19:46
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Alextus93
23/2^1+23/2^2+23/2^3+23/2^4=19

So the formula is basically to figure out how many of a given factor are in n!, divide that number by that factor to 1,2,3, etc. power until it no longer will go into that number( ignore the remainder). Then find the sum of those numbers.

Posted from my mobile device
Show more
My suggestion is to understand how this is working because you can't do it like this when you have to find out number of 10's in 23!.
User avatar
dave13
User avatar
Joined: 09 Mar 2016
Last visit: 12 Aug 2025
Posts: 1,108
Own Kudos:
1,113
Given Kudos: 3,851
Posts: 1,108
Kudos: 1,113
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 26 May 2020, 13:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Kinshook
Bunuel
If n is a positive integer and \(n!\) is a multiple of \(2^{20}\) but not \(3^{20}\), then how many value can n take ?

A. 21
B. 20
C. 16
D. 11
E. 10


Are You Up For the Challenge: 700 Level Questions

Asked: If n is a positive integer and \(n!\) is a multiple of \(2^{20}\) but not \(3^{20}\), then how many value can n take ?

Highest power of 2 in 23! = 11 + 5 + 2 + 1 = 19
Highest power of 2 in 24! = 12 + 6 + 3 + 1 = 22

Minimum value of n = 24

Highest power of 3 in 44! = 14 + 4 + 1 = 19
Highest power of 3 in 45! = 15 + 5 + 1 = 21

Maximum value of n = 44

Number of values of n feasible = 44-24 + 1 = 21

IMO A
Show more

hey Kinshook
how did you come up with highlighted numbers and why these numbers
thanks :)
User avatar
Kinshook
User avatar
Major Poster
Joined: 03 Jun 2019
Last visit: 18 Nov 2025
Posts: 5,793
Own Kudos:
5,508
Given Kudos: 161
Location: India
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Products:
My Reviews
Schools: HBS '26 CBS '26 Wharton '26
GMAT 1: 690 Q50 V34
Posts: 5,793
Kudos: 5,508
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 26 May 2020, 21:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dave13
Kinshook
Bunuel
If n is a positive integer and \(n!\) is a multiple of \(2^{20}\) but not \(3^{20}\), then how many value can n take ?

A. 21
B. 20
C. 16
D. 11
E. 10


Are You Up For the Challenge: 700 Level Questions

Asked: If n is a positive integer and \(n!\) is a multiple of \(2^{20}\) but not \(3^{20}\), then how many value can n take ?

Highest power of 2 in 23! = 11 + 5 + 2 + 1 = 19
Highest power of 2 in 24! = 12 + 6 + 3 + 1 = 22

Minimum value of n = 24

Highest power of 3 in 44! = 14 + 4 + 1 = 19
Highest power of 3 in 45! = 15 + 5 + 1 = 21

Maximum value of n = 44

Number of values of n feasible = 44-24 + 1 = 21

IMO A

hey Kinshook
how did you come up with highlighted numbers and why these numbers
thanks :)
Show more

Hi dave13
It is done by hit and try method
User avatar
Vibhatu
User avatar
Joined: 18 May 2021
Last visit: 18 Nov 2025
Posts: 183
Own Kudos:
51
Given Kudos: 186
Posts: 183
Kudos: 51
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 29 Sep 2023, 01:33
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Kinshook
Bunuel
If n is a positive integer and \(n!\) is a multiple of \(2^{20}\) but not \(3^{20}\), then how many value can n take ?

A. 21
B. 20
C. 16
D. 11
E. 10


Are You Up For the Challenge: 700 Level Questions

Asked: If n is a positive integer and \(n!\) is a multiple of \(2^{20}\) but not \(3^{20}\), then how many value can n take ?

Highest power of 2 in 23! = 11 + 5 + 2 + 1 = 19
Highest power of 2 in 24! = 12 + 6 + 3 + 1 = 22

Minimum value of n = 24

Highest power of 3 in 44! = 14 + 4 + 1 = 19
Highest power of 3 in 45! = 15 + 5 + 1 = 21

Maximum value of n = 44

Number of values of n feasible = 44-24 + 1 = 21

IMO A
Show more

Bunuel can you please write the concept behind this ?
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,586
Own Kudos:
1,079
Posts: 38,586
Kudos: 1,079
If n is a positive integer and n! is a multiple of 2^20 but not 3^20 02 Feb 2025, 07:05
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105355 posts
Krunaal
Tuck School Moderator
805 posts