It is currently 18 Nov 2017, 16:37

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A five digit number is to be formed using each of the digits

Author Message
TAGS:

### Hide Tags

Intern
Joined: 03 Aug 2013
Posts: 15

Kudos [?]: 41 [5], given: 46

A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

05 Sep 2013, 22:29
5
KUDOS
2
This post was
BOOKMARKED
00:00

Difficulty:

35% (medium)

Question Stats:

71% (01:19) correct 29% (01:20) wrong based on 273 sessions

### HideShow timer Statistics

A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?

(A) 48
(B) 36
(C) 72
(D) 60
(E) 120
[Reveal] Spoiler: OA

Kudos [?]: 41 [5], given: 46

VP
Joined: 02 Jul 2012
Posts: 1216

Kudos [?]: 1691 [6], given: 116

Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

05 Sep 2013, 22:46
6
KUDOS
1
This post was
BOOKMARKED
No. of ways the 5 digit number can be formed = 5! = 120

Let us fuse 1 & 2.
No. of ways in which 1 and 2 are together = 4! x 2! (Multiplying by 2! because 1 and 2 can be arranged in 2! ways) = 24*2 = 48

No. of ways 1 & 2 wont be together = 120 - 48
=72
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Kudos [?]: 1691 [6], given: 116

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132617 [4], given: 12326

Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

06 Sep 2013, 00:06
4
KUDOS
Expert's post
3
This post was
BOOKMARKED
MacFauz wrote:
A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?

(A) 48
(B) 36
(C) 72
(D) 60
(E) 120

No. of ways the 5 digit number can be formed = 5! = 120

Let us fuse 1 & 2.
No. of ways in which 1 and 2 are together = 4! x 2! (Multiplying by 2! because 1 and 2 can be arranged in 2! ways) = 24*2 = 48

No. of ways 1 & 2 wont be together = 120 - 48
=72

Great solution. +1.

Just to elaborate the case when 1 and 2 are together:

Glue 1 and 2 together and consider them as one unit: {12}.

Now, 4 units {12}, {3}, {4}, and {5} can be arranged in 4! ways and 1 and 2 within their unit can be arranged in 2 ways ({12} or {21}), thus total = 4!*2.
_________________

Kudos [?]: 132617 [4], given: 12326

Intern
Joined: 03 Aug 2013
Posts: 15

Kudos [?]: 41 [0], given: 46

Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

06 Sep 2013, 04:55
Awesome solutions MacFauz and Bunuel, +1 kudos for both. Thanks a lot

Kudos [?]: 41 [0], given: 46

Intern
Status: Taking the GMAT
Affiliations: ?
Joined: 05 Dec 2011
Posts: 16

Kudos [?]: 0 [3], given: 0

Location: Spain
Concentration: Finance, Entrepreneurship
Schools: Wharton '16, CBS '16
GMAT Date: 10-09-2013
GPA: 3.3
WE: Analyst (Investment Banking)
Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

06 Sep 2013, 04:59
3
KUDOS
Great learning on this one!! thank you very much!

Kudos [?]: 0 [3], given: 0

Intern
Joined: 03 Aug 2013
Posts: 15

Kudos [?]: 41 [0], given: 46

Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

06 Sep 2013, 05:07
manuelpalomares wrote:
Great learning on this one!! thank you very much!

No KUDOS?

Kudos [?]: 41 [0], given: 46

Math Expert
Joined: 02 Sep 2009
Posts: 42249

Kudos [?]: 132617 [1], given: 12326

Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

06 Sep 2013, 07:19
1
KUDOS
Expert's post
arakban99 wrote:
manuelpalomares wrote:
Great learning on this one!! thank you very much!

No KUDOS?

Good questions deserves kudos as much as a good solution. +1.
_________________

Kudos [?]: 132617 [1], given: 12326

VP
Joined: 02 Jul 2012
Posts: 1216

Kudos [?]: 1691 [1], given: 116

Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

06 Sep 2013, 07:32
1
KUDOS
Bunuel wrote:
arakban99 wrote:
manuelpalomares wrote:
Great learning on this one!! thank you very much!

No KUDOS?

Good questions deserves kudos as much as as good solution. +1.

Haha... I second that....
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Kudos [?]: 1691 [1], given: 116

Manager
Status: Persevering
Joined: 15 May 2013
Posts: 218

Kudos [?]: 101 [0], given: 34

Location: India
GMAT Date: 08-02-2013
GPA: 3.7
WE: Consulting (Consulting)
Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

07 Sep 2013, 06:19
C

Just subtract from the total number of cases.

total number of combinations=5*4*3*2*1=120
When two numbers are together, we will have pack the two numbers together, therefore combinations=4!*2(numbers can be arranged themselves)

The cases where they are not together=total-cases when they are together

120-48=72
_________________

--It's one thing to get defeated, but another to accept it.

Kudos [?]: 101 [0], given: 34

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 282 [0], given: 0

Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

10 Apr 2015, 14:18
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.
_________________

Kudos [?]: 282 [0], given: 0

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 282 [0], given: 0

Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

30 May 2016, 21:09
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.
_________________

Kudos [?]: 282 [0], given: 0

Senior Manager
Joined: 18 Jan 2010
Posts: 257

Kudos [?]: 157 [0], given: 9

Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

30 May 2016, 21:33
arakban99 wrote:
A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?

(A) 48
(B) 36
(C) 72
(D) 60
(E) 120

Reqd ways = (Total No. of ways - cases when both 1 and 2 are together)

5 numbers can be arranged in 5 places in 5! ways. Now tie 1 and 2 together so effectively there are 4 nos. they can be arranged in 4! ways. 1 and 2 can be arranged within themselves in 2!ways.

Reqd. Answer = 5! - 4!2! = 120 - (24*2) = 72

Kudos [?]: 157 [0], given: 9

Non-Human User
Joined: 09 Sep 2013
Posts: 15704

Kudos [?]: 282 [0], given: 0

Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

21 Jun 2017, 15:46
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.
_________________

Kudos [?]: 282 [0], given: 0

Senior Manager
Joined: 22 Aug 2013
Posts: 474

Kudos [?]: 155 [0], given: 268

Location: India
Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

21 Jun 2017, 22:04
Another way to ensure that 1 and 2 are not together is to use 'Gaps' method. Basically, when we are given 'n' objects to be arranged so that 'a' out of them should NOT be together - we first arrange the remaining 'n-a' objects, and then arrange these 'a' objects in the gaps created by those 'n-a' objects.

I will try to explain by this question.

We have to arrange 1, 2, 3, 4, 5 so that 1 and 2 are not together. So lets first arrange the remaining numbers.
Remaining 3 numbers can be arranged in 3! = 6 ways.

Now, for each of these 6 ways, the arranged numbers create 4 gaps:
...3...4...5...

one gap before 3, another gap between 3 and 4, another gap between 4 and 5, and the last gap after 5.

So for every arrangement of those 3 numbers, we have 4 gaps - and we can now place the numbers '1' and '2' in any two out of these 4 gaps (and thus they will not touch each other). Number of ways of doing that = 4P2 (arranging 4 objects at 2 places) = 12 ways.

Thus total ways = 3! * 4P2 = 6*12 = 72. Hence C answer

PS - this same can be extended to any such question. So if we have 7 people out of which A,B,C have to be separated (no two of them can sit together), we can first arrange remaining 4 people in 4! ways, and now out of the 5 gaps created (4 people in a line will create 5 gaps), we can place A,B,C in any of the 3 gaps out of 5 in 5P3 ways (60). Thus total ways = 4! * 5P3 = 24 * 60 = 1440.

Kudos [?]: 155 [0], given: 268

Director
Joined: 12 Nov 2016
Posts: 794

Kudos [?]: 36 [0], given: 165

Re: A five digit number is to be formed using each of the digits [#permalink]

### Show Tags

23 Sep 2017, 22:57
arakban99 wrote:
A five digit number is to be formed using each of the digits 1, 2, 3, 4 and 5 ONLY ONCE. How many numbers can be formed when 1 and 2 are not together ?

(A) 48
(B) 36
(C) 72
(D) 60
(E) 120

5!- 4!2!

C

Kudos [?]: 36 [0], given: 165

Re: A five digit number is to be formed using each of the digits   [#permalink] 23 Sep 2017, 22:57
Display posts from previous: Sort by