Author 
Message 
TAGS:

Hide Tags

Manager
Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 152
Location: India
Concentration: Finance, Human Resources
GMAT 1: 570 Q47 V21 GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)

Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
07 Jan 2013, 06:55
6
This post was BOOKMARKED
Question Stats:
75% (02:22) correct
25% (01:56) wrong based on 222 sessions
HideShow timer Statistics
Each digit 1 through 5 is used exactly once to create a 5digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5digit integers are possible? (A) 48 (B) 66 (C) 72 (D) 78 (E) 90
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
Don't give up on yourself ever. Period. Beat it, no one wants to be defeated (My journey from 570 to 690) : http://gmatclub.com/forum/beatitnoonewantstobedefeatedjourney570to149968.html



Manager
Joined: 12 Mar 2012
Posts: 93
Location: India
Concentration: Technology, Strategy
GPA: 3.2
WE: Information Technology (Computer Software)

Re: Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
07 Jan 2013, 07:10
Total number of 5 digit numbers that can be formed = 5! = 120. Total number of 5 digit numbers in which 3 and 4 are adjacent = 48. This can be calculated by taking 3 and 4 as a pair and considering positions where they can appear. Number of 5 digit numbers in which 3 and 4 are not adjacent = Total number of 5 digit numbers  Total number of 5 digit numbers in which 3 and 4 are adjacent. Ans = 120  48 = 72.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
07 Jan 2013, 10:32
daviesj wrote: Each digit 1 through 5 is used exactly once to create a 5digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5digit integers are possible?
(A) 48 (B) 66 (C) 72 (D) 78 (E) 90 Such questions are best solved using the complement approach. You need to find arrangements in which 3 and 4 are not adjacent. Instead, work on finding the arrangements in which they are together since it is much easier to do. Number of arrangements using 5 distinct digits = 5! Number of arrangements in which 3 and 4 are adjacent  consider 3 and 4 together as one group. Now you have 4 numbers/groups to arrange which can be done in 4! ways. In each of these arrangements, 3 and 4 can be arranged as 34 or 43. So we need to multiply 4! by 2 to give all arrangements where 3 and 4 are adjacent to each other e.g. 34251, 43251, 23415, 32415 ... Number of arrangements in which 3 and 4 are not adjacent = 5!  2*4! = 72 Check out my detailed post on this concept: http://www.veritasprep.com/blog/2011/10 ... tsparti/
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 04 Oct 2011
Posts: 218
Location: India
Concentration: Entrepreneurship, International Business
GPA: 3

Re: Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
14 Jan 2013, 04:46
daviesj wrote: Each digit 1 through 5 is used exactly once to create a 5digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5digit integers are possible?
(A) 48 (B) 66 (C) 72 (D) 78 (E) 90 Total number of arrangements of 5 digit integer = 5! = 120 Let 3 and 4 be single digit like { 1 2 X 5 } This set arrangement is 4! = 24 As 3 and 4 can be interchanged between them 2(24) = 48 So 12048 =72 Pls correct me if my solution is wrong!
_________________
GMAT  Practice, Patience, Persistence Kudos if u like



Manager
Joined: 04 Jan 2013
Posts: 80

Re: Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
14 Jan 2013, 12:45
daviesj wrote: Each digit 1 through 5 is used exactly once to create a 5digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5digit integers are possible?
(A) 48 (B) 66 (C) 72 (D) 78 (E) 90 combinatorics and permutations eish..how do you guys make out on which way to use,whether combination or permutation,when you have such problem to solve?..when do you use permutation and when do you use combination? Posted from my mobile device



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
14 Jan 2013, 20:50
chiccufrazer1 wrote: daviesj wrote: Each digit 1 through 5 is used exactly once to create a 5digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5digit integers are possible?
(A) 48 (B) 66 (C) 72 (D) 78 (E) 90 combinatorics and permutations eish..how do you guys make out on which way to use,whether combination or permutation,when you have such problem to solve?..when do you use permutation and when do you use combination? Posted from my mobile device Discussed this dilemma here: http://www.veritasprep.com/blog/2011/11 ... binations/
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15980

Re: Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
28 Nov 2014, 05:51
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15980

Re: Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
01 Sep 2016, 00:35
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 05 Aug 2012
Posts: 20
WE: Project Management (Pharmaceuticals and Biotech)

Re: Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
12 Nov 2016, 05:53
VeritasPrepKarishma wrote: Now you have 4 numbers/groups to arrange which can be done in 4! ways. VeritasPrepKarishma can you please explain how you draw the conclusion that there are 4 numbers/groups to arrange? There are only 2 numbers and the second part of your answer addresses switching their order. I am not understanding this conclusion. Thank you!



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: Each digit 1 through 5 is used exactly once to create a 5di [#permalink]
Show Tags
14 Nov 2016, 05:36
raeann105 wrote: VeritasPrepKarishma wrote: Now you have 4 numbers/groups to arrange which can be done in 4! ways. VeritasPrepKarishma can you please explain how you draw the conclusion that there are 4 numbers/groups to arrange? There are only 2 numbers and the second part of your answer addresses switching their order. I am not understanding this conclusion. Thank you! You need to create a 5 digit integer using digits from 1 to 5. You will do that in various ways such as 12345, 23145, 45231 etc If you club 3 and 4 together, you get a group {34}. Now you have 3 leftover digits: 1, 2 and 5. You have arrange 1, 2, 5 and {34}. So you have to arrange 4 digits/groups. You can do this in various ways such as 12534, 21345 etc... Since instead of {34}, you can have {43} too, you multiply by 2.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews




Re: Each digit 1 through 5 is used exactly once to create a 5di
[#permalink]
14 Nov 2016, 05:36








Similar topics 
Author 
Replies 
Last post 
Similar Topics:


6


If each digit in the set A = {1, 2, 3, 4, 5} is used exactly once, in

Bunuel 
8 
29 Jan 2016, 09:26 

4


By using the numbers 1, 2, 3, 5 and 7 only once, how many

salsal 
3 
14 May 2014, 02:06 

2


If each digit in the set of A = (1,2,3,4,5) is exactly used once, in

efet 
2 
16 Aug 2016, 10:19 

2


A security company can use number 1 7 to create a 5 digit

TheSituation 
5 
16 Aug 2016, 10:17 

21


In a 5 digit ID number, what is the probability of exactly t

Bunuel 
31 
19 Apr 2017, 23:34 



