Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 21 Jan 2009
Posts: 4

A password to a certain database consists of digits that can
[#permalink]
Show Tags
Updated on: 17 Sep 2012, 06:34
Question Stats:
42% (02:30) correct 58% (02:24) wrong based on 382 sessions
HideShow timer Statistics
A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of at least 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database? A. 8!/5 B. 8!/2 C. 8! D. 10!/2 E. 5/2.10!
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by sumana on 08 Jun 2010, 11:14.
Last edited by Bunuel on 17 Sep 2012, 06:34, edited 3 times in total.
Renamed the topic and edited the question.




Math Expert
Joined: 02 Sep 2009
Posts: 59157

Re: Permutation and Combination
[#permalink]
Show Tags
08 Jun 2010, 12:45
sumana wrote: Quote: Hi, and welcome to the Gmat Club. Below is the solution for your problem.
Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute.
Hope it's clear
Thank you  But the answer choices are as follows 
a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10! Quote: Answer to the question you've posted is \(\frac{P^8_{10}}{5}\), which can also be written as \(\frac{10!}{10}=9!\). But still no match with any of the answer choices. Pleas check the question (maybe some info from the stem is missing) or site the source.
Source is Veritas material I did check the question and following info is missing  If the password is known to consist of at least 8 digits  "at least" is missing I see. This "at least" changes everything, it means that password can have 8, 9 or 10 digits (more than 10 is not possible as per stem digits must be distinct). Total # of passwords possible for 8 digits is \(P^8_{10}=\frac{10!}{2}\); Total # of passwords possible for 9 digits is \(P^9_{10}=10!\); Total # of passwords possible for 10 digits is \(P^{10}_{10}=10!\). Time needed to guarantee access to database is \((\frac{10!}{2}+10!+10!)*\frac{1}{5}=\frac{10!}{2}\) minutes. Answer: D.
_________________




Math Expert
Joined: 02 Sep 2009
Posts: 59157

Re: Permutation and Combination
[#permalink]
Show Tags
08 Jun 2010, 11:39
sumana wrote: A password to a certain database consists of digits that cannot be repeated.If the password is known to consist of 8 digits and it takes 12 seconds to try one combination , what is the amount of time , in minutes , necessary to guarantee access to database? Hi, and welcome to the Gmat Club. Below is the solution for your problem. Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute. Hope it's clear.
_________________



Intern
Joined: 21 Jan 2009
Posts: 4

Re: Permutation and Combination
[#permalink]
Show Tags
08 Jun 2010, 11:53
Bunuel wrote: sumana wrote: A password to a certain database consists of digits that cannot be repeated.If the password is known to consist of 8 digits and it takes 12 seconds to try one combination , what is the amount of time , in minutes , necessary to guarantee access to database? Hi, and welcome to the Gmat Club. Below is the solution for your problem. Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute. Hope it's clear. Thank you  But the answer choices are as follows  a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10!



Math Expert
Joined: 02 Sep 2009
Posts: 59157

Re: Permutation and Combination
[#permalink]
Show Tags
08 Jun 2010, 12:08
sumana wrote: Bunuel wrote: sumana wrote: A password to a certain database consists of digits that cannot be repeated.If the password is known to consist of 8 digits and it takes 12 seconds to try one combination , what is the amount of time , in minutes , necessary to guarantee access to database? Hi, and welcome to the Gmat Club. Below is the solution for your problem. Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute. Hope it's clear. Thank you  But the answer choices are as follows  a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10! Answer to the question you've posted is \(\frac{P^8_{10}}{5}\), which can also be written as \(\frac{10!}{10}=9!\). But still no match with any of the answer choices. Pleas check the question (maybe some info from the stem is missing) or site the source.
_________________



Intern
Joined: 21 Jan 2009
Posts: 4

Re: Permutation and Combination
[#permalink]
Show Tags
08 Jun 2010, 12:34
Quote: Hi, and welcome to the Gmat Club. Below is the solution for your problem.
Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute.
Hope it's clear
Thank you  But the answer choices are as follows 
a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10! Quote: Answer to the question you've posted is \(\frac{P^8_{10}}{5}\), which can also be written as \(\frac{10!}{10}=9!\). But still no match with any of the answer choices. Pleas check the question (maybe some info from the stem is missing) or site the source.
Source is Veritas material I did check the question and following info is missing  If the password is known to consist of at least 8 digits  "at least" is missing



Manager
Joined: 14 Apr 2010
Posts: 140

Re: Permutation and Combination
[#permalink]
Show Tags
08 Jun 2010, 22:01
Bunuel, I used combination for this problem since the qs uses the word comb. I thought when the qs doesn't indicate anything about the order then we have to assume that it doesn't matter. Please correct me.



Math Expert
Joined: 02 Sep 2009
Posts: 59157

Re: Permutation and Combination
[#permalink]
Show Tags
09 Jun 2010, 06:17
bibha wrote: Bunuel, I used combination for this problem since the qs uses the word comb. I thought when the qs doesn't indicate anything about the order then we have to assume that it doesn't matter. Please correct me. Most combinatorics questions can be solved with different approaches. Did you get correct answer with your approach? If yes, then it doesn't matter which formula you used. Next, it's a password, of course order matters: 12345678 is different from 87654321. \(P^8_{10}\) directly gives the total # of 8 digit passwords (when digits are distinct), because it counts every case of 8 digits possible from 10 (eg the case of "12345678") as many times as the digits can be arranged there (87654321, 56781234, ...). Different way to get the same answer: \(C^8_{10}\) # of ways to choose 8 digits out of 10 multiplied by 8! to get different arrangements of these digits, so \(C^8_{10}*8!\), which is the same as \(P^8_{10}\) (\(C^8_{10}*8!=P^8_{10}\)). Combinatorics questions are often confusing for many and there are numerous resources with really strange (not to say more) advices, like "if there is some specific word in stem (eg "combination") then use C" or "if there is a direct indication that order matters then use P" and so on. I think one should understand the formula and not just memorize it. When solving the question we should first understand what it is about and only after that choose the proper tool (formula) and not first choose formula (based on one word) and then trying to squeeze numbers in it. Hope it helps.
_________________



Current Student
Joined: 31 Mar 2010
Posts: 165
Schools: Tuck Class of 2013

Re: Permutation and Combination
[#permalink]
Show Tags
09 Jun 2010, 07:44
sumana wrote: Thank you. Could you please correct your first port ? As you said, the stem is missing the "at least" and you forgot to put the answer choices. Thanks.



Intern
Joined: 24 Jul 2010
Posts: 8

P and C ... how to do?
[#permalink]
Show Tags
19 Aug 2010, 00:26
A password contains at least 8 distinct digits. It takes 12 seconds to try one combination, what is the minimum amount of time required to guarantee access to the database?



Manager
Joined: 16 Apr 2010
Posts: 175

Re: P and C ... how to do?
[#permalink]
Show Tags
19 Aug 2010, 01:03
The questions seems awkward... Anyways, I will consider that password consists of 8 distinct digits (and of 8 numbers only). So there will be 8! different passwords and hence the minimum time to access the database is 8! * 12.



Manager
Joined: 25 Jun 2009
Posts: 226

Re: P and C ... how to do?
[#permalink]
Show Tags
19 Aug 2010, 01:51
praveengmat wrote: A password contains at least 8 distinct digits. It takes 12 seconds to try one combination, what is the minimum amount of time required to guarantee access to the database? Key word here is AT LEAST 8 digits, case (1): When we have exactly 8 digits in the password Then the number of passwords = \(10_P_8\) case (2) : When we have 9 digits in the password Then the number of passwords = \(10_P_9\) case (3) : When we have all the digits i.e 10 digits in the password Then the number of passwords = \(10_P_{10}\) Total number of passwords to\(10_P_8 + 10_P_9 + 10_P_{10}\) Time taken to crack 1 password \(= 12 seconds\) Thus, total time \(= (10_P_8 + 10_P_9 + 10_P_{10})*12\)



Manager
Status: Do till 740 :)
Joined: 13 Jun 2011
Posts: 79
Concentration: Strategy, General Management
GPA: 3.6
WE: Consulting (Computer Software)

Re: Permutation and Combination
[#permalink]
Show Tags
17 Sep 2012, 05:14
Hi bunuel,
In this question we consider 10 digits 09
but for a 8 digit number, the first digit cannot be 0 so there would be only 9 ways to select the first digit.
Have we missed that here?? Please explain...



Director
Joined: 22 Mar 2011
Posts: 584
WE: Science (Education)

Re: Permutation and Combination
[#permalink]
Show Tags
17 Sep 2012, 11:20
shankar245 wrote: Hi bunuel,
In this question we consider 10 digits 09
but for a 8 digit number, the first digit cannot be 0 so there would be only 9 ways to select the first digit.
Have we missed that here?? Please explain... It is a password which consists of at least 8 digits, not an eightdigit number, so it can also start with a 0.
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Senior Manager
Joined: 03 Apr 2013
Posts: 262
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: A password to a certain database consists of digits that can
[#permalink]
Show Tags
27 Nov 2016, 00:05
sumana wrote: A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of at least 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?
A. 8!/5 B. 8!/2 C. 8! D. 10!/2 E. 5/2.10! I think the question is flawed. Let me chalk out the conditions according to the question's language. Condition 1  Password contains at least 8 digits Condition 2  All the digits of the password are different. For both the conditions to be satisfied, there can be three cases. Case 1  8 distinct digits. Bunuel has solved this part. Case 2  9 distinct digits. This will be given by \(10*9*8*.....*2\) = \(10!\) To try each permutation 1/5 of a minute is needed. Case 3  10 distinct digits. Same as Case 2. So the worst case scenario for our "testing machine" will be 8 digits testing  No joy! 9 digits testing  No joy! 10 digits testing  exactly the last one tested turns out to be the match. Bunuel Please see. I may be overthinking too much about this!
_________________
Spread some love..Like = +1 Kudos



Intern
Joined: 21 Mar 2017
Posts: 49

Re: A password to a certain database consists of digits that can
[#permalink]
Show Tags
28 Jul 2017, 06:15
Bunuel wrote: sumana wrote: Quote: Hi, and welcome to the Gmat Club. Below is the solution for your problem.
Total # of passwords possible is \(P^8_{10}=10*9*8*7*6*5*4*3\) (picking 8 different digits out of ten when order of the digits matters, or another approach 10 choices for the 1st digit, 9 choices for the second and so on), 1/5 minute (12 seconds) for one combination, means that time needed to guarantee access to database is \(\frac{P^8_{10}}{5}\) minute.
Hope it's clear
Thank you  But the answer choices are as follows 
a) 8!/5 b) 8!/2 c) 8! d) 10!/2 and e) 5/2.10! Quote: Answer to the question you've posted is \(\frac{P^8_{10}}{5}\), which can also be written as \(\frac{10!}{10}=9!\). But still no match with any of the answer choices. Pleas check the question (maybe some info from the stem is missing) or site the source.
Source is Veritas material I did check the question and following info is missing  If the password is known to consist of at least 8 digits  "at least" is missing I see. This "at least" changes everything, it means that password can have 8, 9 or 10 digits (more than 10 is not possible as per stem digits must be distinct). Total # of passwords possible for 8 digits is \(P^8_{10}=\frac{10!}{2}\); Total # of passwords possible for 9 digits is \(P^9_{10}=10!\); Total # of passwords possible for 10 digits is \(P^{10}_{10}=10!\). Time needed to guarantee access to database is \((\frac{10!}{2}+10!+10!)*\frac{1}{5}=\frac{10!}{2}\) minutes. Answer: D. But as we need to solve a certain password should not we take the no. of highest possibility that is 10! ??!!!! Plz explain ********************* Plz give kudos, buddies!!!!



Manager
Joined: 01 Feb 2017
Posts: 244

A password to a certain database consists of digits that can
[#permalink]
Show Tags
22 Oct 2017, 22:31
Total distint digits in one password: Minimum 8 & Maximum 10.
For 8 digits password, no. of distinct combinations possible= 8!*10C8= 10!/2!= 10!/2
For 9 digits password, no. of distinct combinations possible= 9!*10C9= 10!/1!= 10!
For 10 digits password, no. of distinct combinations possible= 10!*10C10= 10!/0!= 10!
Total possible passwords= 10!*0.5 + 10! + 10!= 10!*2.5
Time required to try one password= 12sec= 1/5 min.
Therefore, Time required to try 10!*2.5 password= 10!*2.5/5 min= 10!/2 mins.
Hence, Ans D



Senior Manager
Joined: 22 Feb 2018
Posts: 415

Re: A password to a certain database consists of digits that can
[#permalink]
Show Tags
25 Aug 2018, 10:21
sumana wrote: A password to a certain database consists of digits that cannot be repeated. If the password is known to consist of at least 8 digits and it takes 12 seconds to try one combination, what is the amount of time, in minutes, necessary to guarantee access to database?
A. 8!/5 B. 8!/2 C. 8! D. 10!/2 E. 5/2.10! OA:DThere are \(10\) possibilities for \(1\) st digit i.e \(1\) st digit can be \(0,1,2,3,4,5,6,7,8,9\). After the \(1\) st digit, the number of possibilities keeps decreasing by \(1\) as digits cannot be repeated. Number of possibilities when there are \(8\) digits in the password: \(10*9*8*7*6*5*4*3=\frac{10!}{2}\) Number of possibilities when there are \(9\) digits in the password : \(10*9*8*7*6*5*4*3*2 =\frac{10!}{1}\) Number of possibilities when there are \(10\) digits in the password : \(10*9*8*7*6*5*4*3*2*1 = 10!\) Total Number of possibilities : \(\frac{10!}{2} +10!+10!=\frac{5*10!}{2}\) Time taken for trying \(1\) password: \(12\) seconds \(= \frac{12}{60}\quad minutes=\frac{1}{5}\quad minutes\) Time taken for trying \(\frac{5*10!}{2}\) passwords \(= \frac{1}{5}*\frac{5*10!}{2}= \frac{10!}{2}\)minutes
_________________
Good, good Let the kudos flow through you



NonHuman User
Joined: 09 Sep 2013
Posts: 13610

Re: A password to a certain database consists of digits that can
[#permalink]
Show Tags
15 Sep 2019, 23:07
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 password to a certain database consists of digits that can
[#permalink]
15 Sep 2019, 23:07






