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 Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

Show Tags

05 Sep 2013, 22:29

5

This post received KUDOS

1

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

35% (medium)

Question Stats:

67% (02:04) correct
33% (01:17) wrong based on 166 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 ?

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

Show Tags

06 Sep 2013, 00:06

3

This post received 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. _________________

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.

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. _________________

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. _________________

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

Answer: C

gmatclubot

Re: A five digit number is to be formed using each of the digits
[#permalink]
30 May 2016, 21:33

Part 2 of the GMAT: How I tackled the GMAT and improved a disappointing score Apologies for the month gap. I went on vacation and had to finish up a...

Cal Newport is a computer science professor at GeorgeTown University, author, blogger and is obsessed with productivity. He writes on this topic in his popular Study Hacks blog. I was...

So the last couple of weeks have seen a flurry of discussion in our MBA class Whatsapp group around Brexit, the referendum and currency exchange. Most of us believed...