GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 12 Nov 2018, 14:49

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 in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • Essential GMAT Time-Management Hacks

     November 14, 2018

     November 14, 2018

     08:00 PM MST

     09:00 PM MST

    Join the webinar and learn time-management tactics that will guarantee you answer all questions, in all sections, on time. Save your spot today! Nov. 14th at 7 PM PST
  • $450 Tuition Credit & Official CAT Packs FREE

     November 15, 2018

     November 15, 2018

     10:00 PM MST

     11:00 PM MST

    EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299)

How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50544
How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d  [#permalink]

Show Tags

New post 21 Mar 2018, 22:01
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

59% (01:41) correct 41% (01:49) wrong based on 75 sessions

HideShow timer Statistics

How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-digit number so that the two occurrences of the digit 3 are separated by at least one other digit?

(A) 48
(B) 36
(C) 24
(D) 18
(E) 12

_________________

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

Intern
Intern
avatar
Joined: 14 Mar 2018
Posts: 10
Re: How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d  [#permalink]

Show Tags

New post 21 Mar 2018, 22:09
Bunuel wrote:
How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-digit number so that the two occurrences of the digit 3 are separated by at least one other digit?

(A) 48
(B) 36
(C) 24
(D) 18
(E) 12


5!/2! - 4! = 120/2 - 24 = 36
B
Intern
Intern
User avatar
B
Joined: 03 Aug 2016
Posts: 40
Re: How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d  [#permalink]

Show Tags

New post 21 Mar 2018, 22:27
Option B - 36



Arrangement without restriction = 5!/2!

Arrangement with the restriction where both the I's are together = 4! 2! /2!= 4!

(Method: subtracting what's not allowed from total)

Total = 5!/2! - 4! = 36

Posted from my mobile device

Posted from my mobile device
_________________

Please press +1 Kudos if you find my post/reply helpful :-)

Intern
Intern
avatar
B
Joined: 25 Mar 2017
Posts: 1
GMAT ToolKit User
How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d  [#permalink]

Show Tags

New post 23 Mar 2018, 07:25
2
With gaps of one:
1. ( 3 _ 3 _ _ )
2. ( _ 3 _ 3 _ )
3. ( _ _ 3 _ 3 )

With gaps of two:
4. ( 3 _ _ 3 _ )
5. ( _ 3 _ _ 3 )

With gaps of three:
6. (3 _ _ _ 3 )

Total- 6 ways
Remaining numbers: 4, 5, 6- arranged in 3! ways
Therefore 6*3! = 36, Option B
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d  [#permalink]

Show Tags

New post 23 Mar 2018, 11:44
Bunuel wrote:
How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-digit number so that the two occurrences of the digit 3 are separated by at least one other digit?

(A) 48
(B) 36
(C) 24
(D) 18
(E) 12



The only way that the two digits are separated by at least one other digit is if they are NOT next to each other. We can use the formula:

(Total number of ways to create the numbers) - (number of ways with the 3’s together) = number of ways to create the numbers with 3’s separated by at least one digit

Using the indistinguishable permutations formula, we note that the two 3’s are indistinguishable. Thus, the total number of ways to create the 5-digit numbers is 5!/2! = 60 ways.

Total number of ways to create the numbers with the 3’s together is 4! = 24 ways.

So, the number of ways to create the numbers with the 3’s separated by at least one digit is 60 - 24 = 36.

Answer: B
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3108
Location: Canada
Re: How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d  [#permalink]

Show Tags

New post 25 Mar 2018, 15:16
Top Contributor
Bunuel wrote:
How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-digit number so that the two occurrences of the digit 3 are separated by at least one other digit?

(A) 48
(B) 36
(C) 24
(D) 18
(E) 12


Here's another approach:

Take the task of arranging the 5 digits and break it into stages.

Stage 1: Arrange the 4, 5 and 6
We can arrange n unique objects in n! ways
So, we can arrange these 3 digits in 3! ways (6 ways)
So, we can complete stage 1 in 6 ways

TRICKY PART: We'll now add some spaces where the 3's can be placed.
So, for example, if in stage 1, we arranged three digits as 645, then we'll add spaces before and after each digit.
So, we'd get: _6_4_5_
We will place the two 3's in two of the 4 possible spaces.
This will ENSURE that the 3's are not together.

Stage 2: Select two spaces in which to place the 3's
Since the order in which we select the spaces does not matter, we can use combinations.
We can select 2 spaces from 4 spaces in 4C2 ways (6 ways)
So, we can complete stage 2 in 6 ways

By the Fundamental Counting Principle (FCP), we can complete the two stages (and thus arrange all 5 digits) in (6)(6) ways (= 36 ways)

Answer: B

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

RELATED VIDEOS





_________________

Brent Hanneson – GMATPrepNow.com
Image

GMAT Club Bot
Re: How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d &nbs [#permalink] 25 Mar 2018, 15:16
Display posts from previous: Sort by

How many ways can the five digits 3, 3, 4, 5, 6 be arranged into a 5-d

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| 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®.