GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 09 Dec 2019, 10:38

### 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

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

# A popular website requires users to create a password consis

Author Message
TAGS:

### Hide Tags

Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 243

### Show Tags

25 Nov 2010, 18:49
2
15
00:00

Difficulty:

55% (hard)

Question Stats:

60% (01:52) correct 40% (02:05) wrong based on 206 sessions

### HideShow 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!

_________________
I'm the Dumbest of All !!
Math Expert
Joined: 02 Sep 2009
Posts: 59623

### Show Tags

26 Nov 2010, 10:26
5
5
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.

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 $$10!+10!=2*10!$$.

_________________
##### General Discussion
Director
Joined: 03 Sep 2006
Posts: 613

### Show Tags

25 Nov 2010, 19:48
2
1
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
Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 243

### Show Tags

26 Nov 2010, 10:16
why 9! is multiplied with 10 ?

thanks
_________________
I'm the Dumbest of All !!
Manager
Status: Do and Die!!
Joined: 15 Sep 2010
Posts: 243

### Show Tags

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
_________________
I'm the Dumbest of All !!
Manager
Joined: 27 Jul 2010
Posts: 132
Location: Prague
Schools: University of Economics Prague

### Show Tags

26 Nov 2010, 12:42
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!
Manager
Joined: 27 Aug 2014
Posts: 53
Concentration: Strategy, Technology
GMAT 1: 660 Q45 V35
GPA: 3.66
WE: Consulting (Consulting)
Re: A popular website requires users to create a password consis  [#permalink]

### Show Tags

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..
Senior Manager
Joined: 03 Apr 2013
Posts: 259
Location: India
Concentration: Marketing, Finance
GMAT 1: 740 Q50 V41
GPA: 3
Re: A popular website requires users to create a password consis  [#permalink]

### Show Tags

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?
Math Expert
Joined: 02 Sep 2009
Posts: 59623
Re: A popular website requires users to create a password consis  [#permalink]

### Show Tags

12 Jun 2017, 02:43
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?

_________________
Manager
Joined: 19 Aug 2015
Posts: 84
Location: India
GMAT 1: 650 Q49 V30

### Show Tags

12 Jun 2017, 09:56
9 digit passwords = $$10_C_9$$ * 9! = 10!
10 digit passwords = $$10_C_{10}$$ * 10!= 10!
sum = 2*10!
Intern
Joined: 21 Mar 2016
Posts: 1
Re: A popular website requires users to create a password consis  [#permalink]

### Show Tags

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
Target Test Prep Representative
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 8645
Location: United States (CA)
Re: A popular website requires users to create a password consis  [#permalink]

### Show Tags

14 Jun 2017, 16:26
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!).

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Non-Human User
Joined: 09 Sep 2013
Posts: 13731
Re: A popular website requires users to create a password consis  [#permalink]

### Show Tags

22 Mar 2019, 02:45
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.
_________________
Re: A popular website requires users to create a password consis   [#permalink] 22 Mar 2019, 02:45
Display posts from previous: Sort by
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}