Last visit was: 12 Jul 2025, 06:04 It is currently 12 Jul 2025, 06:04
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
User avatar
shrive555
Joined: 15 Sep 2010
Last visit: 26 Jun 2016
Posts: 202
Own Kudos:
2,467
 [50]
Given Kudos: 193
Status:Do and Die!!
 Q29  V6 GMAT 3: 430  Q31  V19
Posts: 202
Kudos: 2,467
 [50]
3
Kudos
Add Kudos
45
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,636
Own Kudos:
Given Kudos: 98,172
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,636
Kudos: 740,652
 [14]
7
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
User avatar
LM
Joined: 03 Sep 2006
Last visit: 04 Apr 2015
Posts: 445
Own Kudos:
7,464
 [6]
Given Kudos: 33
Posts: 445
Kudos: 7,464
 [6]
4
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
General Discussion
User avatar
shrive555
Joined: 15 Sep 2010
Last visit: 26 Jun 2016
Posts: 202
Own Kudos:
Given Kudos: 193
Status:Do and Die!!
 Q29  V6 GMAT 3: 430  Q31  V19
Posts: 202
Kudos: 2,467
Kudos
Add Kudos
Bookmarks
Bookmark this Post
why 9! is multiplied with 10 ?

thanks
User avatar
shrive555
Joined: 15 Sep 2010
Last visit: 26 Jun 2016
Posts: 202
Own Kudos:
Given Kudos: 193
Status:Do and Die!!
 Q29  V6 GMAT 3: 430  Q31  V19
Posts: 202
Kudos: 2,467
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Got it.
012345678 is one password 123456789 is another, by combination method we can find how many arrangements of 9 digits are possible, which is 10
Thanks B
User avatar
craky
Joined: 27 Jul 2010
Last visit: 29 Jan 2013
Posts: 103
Own Kudos:
303
 [4]
Given Kudos: 15
Location: Prague
Concentration: Finance
Schools:University of Economics Prague
GMAT 1: 700 Q48 V38
Posts: 103
Kudos: 303
 [4]
1
Kudos
Add Kudos
2
Bookmarks
Bookmark this Post
It's good to realize the permutation formula: n! / (n-k)!

We then got:

10! / (10-9)! = 10!/1! = 10!
and
10! / (10-10)! = 10!/0! = 10! = 10!/1! = 10! (

The answer is than: 2 * 10!
avatar
praneet87
Joined: 27 Aug 2014
Last visit: 03 Jun 2018
Posts: 43
Own Kudos:
Given Kudos: 6
Location: Canada
Concentration: Strategy, Technology
GMAT 1: 660 Q45 V35
GPA: 3.66
WE:Consulting (Consulting)
GMAT 1: 660 Q45 V35
Posts: 43
Kudos: 16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Would have been brutal if 10! would have been one of the answers. It's easy to ignore the word atleast..
User avatar
ShashankDave
Joined: 03 Apr 2013
Last visit: 26 Jan 2020
Posts: 218
Own Kudos:
279
 [1]
Given Kudos: 872
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
GMAT 1: 740 Q50 V41
Posts: 218
Kudos: 279
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shrive555
A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible?

A. 9! + 10!
B. 2 x 10!
C. 9! x 10!
D. 19!
E. 20!
The question must mention that the password can start with a '0'. Bunuel, if my reasoning is correct, would you please edit the question? :)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 11 Jul 2025
Posts: 102,636
Own Kudos:
740,652
 [2]
Given Kudos: 98,172
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,636
Kudos: 740,652
 [2]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
ShashankDave
shrive555
A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible?

A. 9! + 10!
B. 2 x 10!
C. 9! x 10!
D. 19!
E. 20!
The question must mention that the password can start with a '0'. Bunuel, if my reasoning is correct, would you please edit the question? :)

A password/code can start with 0, it goes without saying.
avatar
dabhishek87
Joined: 19 Aug 2015
Last visit: 02 Oct 2017
Posts: 62
Own Kudos:
14
 [1]
Given Kudos: 24
Location: India
GMAT 1: 650 Q49 V30
GMAT 1: 650 Q49 V30
Posts: 62
Kudos: 14
 [1]
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
9 digit passwords = \(10_C_9\) * 9! = 10!
10 digit passwords = \(10_C_{10}\) * 10!= 10!
sum = 2*10!
Answer B
avatar
Sayari
Joined: 21 Mar 2016
Last visit: 02 Mar 2018
Posts: 1
Given Kudos: 63
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
praneet87
Would have been brutal if 10! would have been one of the answers. It's easy to ignore the word atleast..
Couldn't agree more.

Posted from my mobile device
User avatar
ScottTargetTestPrep
User avatar
Target Test Prep Representative
Joined: 14 Oct 2015
Last visit: 11 Jul 2025
Posts: 21,091
Own Kudos:
Given Kudos: 296
Status:Founder & CEO
Affiliations: Target Test Prep
Location: United States (CA)
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 21,091
Kudos: 26,141
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shrive555
A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible?

A. 9! + 10!
B. 2 x 10!
C. 9! x 10!
D. 19!
E. 20!

The number of ways to create a 10-digit password from 10 digits is 10P10 = 10!.

Thus, the number of ways to create the codes is 10! + 10! = 2(10!).

Answer: B
User avatar
Crytiocanalyst
Joined: 16 Jun 2021
Last visit: 27 May 2023
Posts: 951
Own Kudos:
Given Kudos: 309
Posts: 951
Kudos: 202
Kudos
Add Kudos
Bookmarks
Bookmark this Post
shrive555
A popular website requires users to create a password consisting of digits only. If no digit may be repeated and each password must be at least 9 digits long, how many passwords are possible?

A. 9! + 10!
B. 2 x 10!
C. 9! x 10!
D. 19!
E. 20!

9 digits long can be arranged in 10! ways and ends with 2 possibilities

10 digit can be arranged in 10! ways ending with 1 possibility

Total ways = 2*10!

Therefore IMO B
User avatar
ryangcii2
Joined: 14 Apr 2023
Last visit: 01 May 2023
Posts: 3
Posts: 3
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
For the 10-digit password: Arrange 10 digits in 10 spots, order matters, therefore 10P10 = 10!
For the 9-digit password: Arrange 9 digits in 10 spots, order matters, therefore 10P9 = 10!
Total is 10! + 10! = 2 x 10!
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 37,375
Own Kudos:
Posts: 37,375
Kudos: 1,010
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:
Math Expert
102636 posts
PS Forum Moderator
688 posts