It is currently 23 Jan 2018, 12:07

Close

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
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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many different arrangements of the digits 1, 2, 3, 4, and 5 are po

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 43381
How many different arrangements of the digits 1, 2, 3, 4, and 5 are po [#permalink]

Show Tags

New post 25 Dec 2017, 00:51
Expert's post
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

44% (00:50) correct 56% (02:16) wrong based on 16 sessions

HideShow timer Statistics

How many different arrangements of the digits 1, 2, 3, 4, and 5 are possible where no two consecutive digits are adjacent?

A. 42
B. 21
C. 14
D. 10
E. 6
[Reveal] Spoiler: OA

_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Expert Post
examPAL Representative
User avatar
B
Joined: 07 Dec 2017
Posts: 122
Re: How many different arrangements of the digits 1, 2, 3, 4, and 5 are po [#permalink]

Show Tags

New post 25 Dec 2017, 02:26
Bunuel wrote:
How many different arrangements of the digits 1, 2, 3, 4, and 5 are possible where no two consecutive digits are adjacent?

A. 42
B. 21
C. 14
D. 10
E. 6


As it is hard to calculate this directly, we'll start by writing down numbers and see how it goes.
This is an Alternative approach.

If we start with a 1 then the next number must be 3,4 or 5.
Starting with 1-3 means that 5 must come next (as 2 and 4 are adjacent to 3) then 2 then 4.
Similarly, 1-4-2-5-3 must follow from 1-4.
However, if we try to continue 1-5-3 we become stuck as both 4 and 2 are impossible.
So, there are 2 numbers starting with 1.
Let's start with 2:
2 can be followed by 4 or 5. Building these gives
2-4-1-3-5 and 2-4-1-5-3
2-5-1- impossible! and 2-5-3-1-4
We have a 3 numbers starting with 2.
Moving on to 3, which can be followed by 1 or 5:
3-1-4-2-5 and 3-1-5-2-4
3-5-2-4-1 and 3-5-1-4-2
4 more options.
Finally, we can list another 3 numbers for 4 and 2 for 5.
In total, we have 2+3+4+3+2=14 options.
(C) is our answer.

** Note: as 1,2,3,4,5 is a symmetrical sequence (5 and 1 are 'end numbers' and 2 and 4 are 'inbetween numbers') then we know that 1 and 5 have the same number of sequences without listing them. Similarly, 2 and 4 have the same number of sequences.
_________________

David
Senior tutor at examPAL
Signup for a free GMAT course
Image
Image

Expert Post
e-GMAT Representative
User avatar
S
Joined: 04 Jan 2015
Posts: 786
Re: How many different arrangements of the digits 1, 2, 3, 4, and 5 are po [#permalink]

Show Tags

New post 25 Dec 2017, 05:43
Bunuel wrote:
How many different arrangements of the digits 1, 2, 3, 4, and 5 are possible where no two consecutive digits are adjacent?

A. 42
B. 21
C. 14
D. 10
E. 6


I had to list down all the cases, keeping the following conditions in mind.

    • 1 can be grouped with 3,4 and 5
    • 2 can be grouped with 4 and 5
    • 3 can be grouped with 1 and 5
    • 4 can be grouped with 1 and 2
    • 5 can be grouped with 1,2 and 3

I started of with 1 as the starting digit and found all the possible cases, then moved on to numbers starting with 2, 3, 4 and 5.

After writing down the cases, one can clearly see that the numbers formed with starting digits as 1,2 or 3, the number of cases are roughly 2 or 3 or 4 and thus, the answer would be somewhere between 10 and 16.

One may mark the answer as 14 and move on to the next question, if solving the question takes more than 2.5-3 minutes. :)

Total cases :

    • 1 3 5 2 4
    • 1 4 2 5 3
    • 2 4 1 3 5
    • 2 4 1 5 3
    • 2 5 3 1 4
    • 3 1 4 2 5
    • 3 1 5 2 4
    • 3 5 1 4 2
    • 3 5 2 4 1
    • 4 2 5 3 1
    • 4 2 5 1 3
    • 4 1 3 5 2
    • 5 2 4 1 3
    • 5 3 1 4 2

Thus, the correct answer is Option C.


Thanks,
Saquib
Quant Expert
e-GMAT
_________________












| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: How many different arrangements of the digits 1, 2, 3, 4, and 5 are po   [#permalink] 25 Dec 2017, 05:43
Display posts from previous: Sort by

How many different arrangements of the digits 1, 2, 3, 4, and 5 are po

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.