NEW HERE? LEARN MORE
closeclose
Last visit was: 25 Apr 2024, 13:15 It is currently 25 Apr 2024, 13:15
Decision Tracker
My Rewards
New posts
New comers' posts

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

A popular website requires users to create a password consis

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
shrive555
Manager
Manager
Joined: 15 Sep 2010
Status:Do and Die!!
Posts: 207
Own Kudos [?]: 2134 [37]
Given Kudos: 193
 Q29  V6 GMAT 3: 430  Q31  V19
Send PM
A popular website requires users to create a password consis [#permalink] New post   25 Nov 2010, 18:49
3
Kudos
32
Bookmarks
00:00
A
B
C
D
E

Difficulty:

55% (hard)

Question Stats:

61% (01:44) correct 39% (01:52) wrong based on 439 sessions
Hide Show timer Statistics
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!
ShowHide Answer
Official Answer
B
Most Helpful Reply
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619009 [13]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: P1 [#permalink] New post   26 Nov 2010, 10:26
7
Kudos
6
Bookmarks
Expert Reply
shrive555 wrote:
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?

9! + 10!
2 x 10!
9! x 10!
19!
20!

i got it right with slot method, but wasn't sure. :roll:


shrive555 wrote:
why 9! is multiplied with 10 ?

thanks


Note that we are told that no digit may be repeated.

There are total of 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9.

As password must be at least 9 digits long then it can consist of either 9 or all 10 digits.

If password consists of 9 digits then # of passwords possible is \(C^9_{10}*9!=10*9!=10!\): \(C^9_{10}\) - # of ways to choose 9 digits which will be used in password and \(9!\) arranging these digits (or in another way \(P^9_{10}=10!\) - choosing 9 digits out of 10 when the order matters);

If password consists of all 10 digits then # of passwords possible is simply \(10!\);

So total # of passwords possible is \(10!+10!=2*10!\).

Answer: B.
User avatar
LM
Senior Manager
Senior Manager
Joined: 03 Sep 2006
Posts: 446
Own Kudos [?]: 6776 [6]
Given Kudos: 33
Send PM
GMAT ToolKit User
Re: P1 [#permalink] New post   25 Nov 2010, 19:48
4
Kudos
1
Bookmarks
If we choose the 10 different digits then they can be arranged (permutations) in 10! ways.
But the question asks at least 9 digits. So we have the possibility of choosing only 9 digits for the password ( but digit shouldn't repeat), so we can have a total of 10 different combinations and each combination can be arranged in 9! ways.
Therefore
10 x 9! + 10!

= 10! + 10!

= 2 x 10!

Therefore B
General Discussion
User avatar
shrive555
Manager
Manager
Joined: 15 Sep 2010
Status:Do and Die!!
Posts: 207
Own Kudos [?]: 2134 [0]
Given Kudos: 193
 Q29  V6 GMAT 3: 430  Q31  V19
Send PM
Re: P1 [#permalink] New post   26 Nov 2010, 10:16
why 9! is multiplied with 10 ?

thanks
User avatar
shrive555
Manager
Manager
Joined: 15 Sep 2010
Status:Do and Die!!
Posts: 207
Own Kudos [?]: 2134 [0]
Given Kudos: 193
 Q29  V6 GMAT 3: 430  Q31  V19
Send PM
Re: P1 [#permalink] New post   26 Nov 2010, 11:07
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
Manager
Manager
Joined: 27 Jul 2010
Posts: 108
Own Kudos [?]: 253 [4]
Given Kudos: 15
Location: Prague
Concentration: Finance
Schools:University of Economics Prague
Send PM
GMAT ToolKit User
Re: P1 [#permalink] New post   26 Nov 2010, 12:42
1
Kudos
2
Bookmarks
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
S
praneet87
Intern
Intern
Joined: 27 Aug 2014
Posts: 45
Own Kudos [?]: 16 [0]
Given Kudos: 6
Location: Canada
Concentration: Strategy, Technology
Schools: Tepper '20 Johnson '20 Ross '20 Ivey '19
GMAT 1: 660 Q45 V35
GPA: 3.66
WE:Consulting (Consulting)
Send PM
Re: A popular website requires users to create a password consis [#permalink] New post   15 May 2017, 21:39
Would have been brutal if 10! would have been one of the answers. It's easy to ignore the word atleast..
User avatar
G
ShashankDave
Manager
Manager
Joined: 03 Apr 2013
Posts: 222
Own Kudos [?]: 239 [0]
Given Kudos: 872
Location: India
Concentration: Marketing, Finance
Schools: McDonough '21 (A) Kelley '21 ISB '21 (I)
GMAT 1: 740 Q50 V41
GPA: 3
Send PM
GMAT ToolKit User
Re: A popular website requires users to create a password consis [#permalink] New post   12 Jun 2017, 01:40
shrive555 wrote:
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
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92915
Own Kudos [?]: 619009 [2]
Given Kudos: 81595
Send PM
CAT Tests Forum Quiz Mode
Re: A popular website requires users to create a password consis [#permalink] New post   12 Jun 2017, 02:43
1
Bookmarks
Expert Reply
ShashankDave wrote:
shrive555 wrote:
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
B
dabhishek87
Manager
Manager
Joined: 19 Aug 2015
Posts: 64
Own Kudos [?]: 13 [0]
Given Kudos: 24
Location: India
GMAT 1: 650 Q49 V30
Send PM
A popular website requires users to create a password consis [#permalink] New post   12 Jun 2017, 09:56
9 digit passwords = \(10_C_9\) * 9! = 10!
10 digit passwords = \(10_C_{10}\) * 10!= 10!
sum = 2*10!
Answer B
avatar
B
Sayari
Intern
Intern
Joined: 21 Mar 2016
Posts: 1
Own Kudos [?]: [0]
Given Kudos: 63
Send PM
Re: A popular website requires users to create a password consis [#permalink] New post   13 Jun 2017, 03:41
praneet87 wrote:
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
L
ScottTargetTestPrep
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 18761
Own Kudos [?]: 22052 [0]
Given Kudos: 283
Location: United States (CA)
Send PM
Re: A popular website requires users to create a password consis [#permalink] New post   14 Jun 2017, 16:26
Expert Reply
shrive555 wrote:
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
P
Crytiocanalyst
Director
Director
Joined: 16 Jun 2021
Posts: 994
Own Kudos [?]: 183 [0]
Given Kudos: 309
Send PM
A popular website requires users to create a password consis [#permalink] New post   12 Oct 2021, 23:39
shrive555 wrote:
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
Intern
Intern
Joined: 14 Apr 2023
Posts: 3
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: A popular website requires users to create a password consis [#permalink] New post   19 Apr 2023, 11:07
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!
GMAT Club Bot
gmatclubot
Re: A popular website requires users to create a password consis [#permalink]
19 Apr 2023, 11:07
Moderators:
Bunuel
Math Expert
92914 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions