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Each digit 1 through 5 is used exactly once to create a 5-di

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Manager
Manager
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Status: Never ever give up on yourself.Period.
Joined: 23 Aug 2012
Posts: 138
Location: India
Concentration: Finance, Human Resources
Schools: Mays '16
GMAT 1: 570 Q47 V21
GMAT 2: 690 Q50 V33
GPA: 3.5
WE: Information Technology (Investment Banking)
Followers: 9

Kudos [?]: 94 [0], given: 35

Each digit 1 through 5 is used exactly once to create a 5-di [#permalink] New post 07 Jan 2013, 05:55
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Difficulty:

  35% (medium)

Question Stats:

72% (02:10) correct 28% (01:43) wrong based on 64 sessions
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit integers are possible?

(A) 48
(B) 66
(C) 72
(D) 78
(E) 90
[Reveal] Spoiler: OA

_________________

Don't give up on yourself ever. Period.
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Location: Pune, India
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Kudos [?]: 5329 [1] , given: 165

Re: Each digit 1 through 5 is used exactly once to create a 5-di [#permalink] New post 07 Jan 2013, 09:32
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Expert's post
daviesj wrote:
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit 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 ... ts-part-i/
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Manager
Manager
avatar
Joined: 12 Mar 2012
Posts: 95
Location: India
Concentration: Technology, Strategy
GMAT 1: 710 Q49 V36
GPA: 3.2
WE: Information Technology (Computer Software)
Followers: 9

Kudos [?]: 266 [0], given: 22

Re: Each digit 1 through 5 is used exactly once to create a 5-di [#permalink] New post 07 Jan 2013, 06:10
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.
Manager
Manager
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Joined: 04 Oct 2011
Posts: 225
Location: India
Concentration: Entrepreneurship, International Business
GMAT 1: 440 Q33 V13
GMAT 2: 0 Q0 V0
GPA: 3
Followers: 0

Kudos [?]: 27 [0], given: 44

Re: Each digit 1 through 5 is used exactly once to create a 5-di [#permalink] New post 14 Jan 2013, 03:46
daviesj wrote:
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit 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 120-48 =72
Pls correct me if my solution is wrong!
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Manager
Manager
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Joined: 04 Jan 2013
Posts: 82
Followers: 0

Kudos [?]: 6 [0], given: 1

Re: Each digit 1 through 5 is used exactly once to create a 5-di [#permalink] New post 14 Jan 2013, 11:45
daviesj wrote:
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit 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 Image
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 4868
Location: Pune, India
Followers: 1145

Kudos [?]: 5329 [0], given: 165

Re: Each digit 1 through 5 is used exactly once to create a 5-di [#permalink] New post 14 Jan 2013, 19:50
Expert's post
chiccufrazer1 wrote:
daviesj wrote:
Each digit 1 through 5 is used exactly once to create a 5-digit integer. If the 3 and the 4 cannot be adjacent digits in the integer, how many 5-digit 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 Image


Discussed this dilemma here:
http://www.veritasprep.com/blog/2011/11 ... binations/
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Save $100 on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.

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Re: Each digit 1 through 5 is used exactly once to create a 5-di   [#permalink] 14 Jan 2013, 19:50
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