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

It is currently 18 Jun 2019, 02:01

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

How many different 6-digit positive integers are there, where 3 of the

  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: 55664
How many different 6-digit positive integers are there, where 3 of the  [#permalink]

Show Tags

New post 16 May 2019, 00:00
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

44% (02:51) correct 56% (02:45) wrong based on 16 sessions

HideShow timer Statistics

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 55664
Re: How many different 6-digit positive integers are there, where 3 of the  [#permalink]

Show Tags

New post 16 May 2019, 00:02
Senior Manager
Senior Manager
avatar
P
Joined: 19 Oct 2018
Posts: 480
Location: India
Re: How many different 6-digit positive integers are there, where 3 of the  [#permalink]

Show Tags

New post 16 May 2019, 00:48
1. When there are 2 same digits and 1 different are selected from 5 and 7, and 3 different digits are selected from 1,4,6 and 8
Total numbers possible= 2*4*6!/2!=2880
2. When there are 2 same digits and 1 different selected from 5 and 7, and 2 same and 1 different are selected from 1,4,6 and 8
Total numbers possible= 2*6*2*6!/2!2!=4320
3. When there are 2 same digits and 1 different selected from 5 and 7, and 3 same digits selected from 1,4,6 and 8
Total numbers possible= 2*4*6!/2!3!=480
4. When there are 3 same digits from 5 and 7, and 3 different digits selected from 1,4,6 and 8
Total numbers possible= 2*4*6!/3!=960
5. When there are 3 same digits selected from 5 and 7, and 2 same and 1 different are selected from 1,4,6 and 8
Total numbers possible= 2*6*2*6!/3!2!=1440
6. When there are 3 same digits selected from 5 and 7, and 3 same digits selected from 1,4,6 and 8
Total numbers possible= 2*4*6!/3!3!=160

different 6-digit positive integers possible under given constraints= 2880+4320+480+960+1440+160=10240
CEO
CEO
User avatar
P
Joined: 18 Aug 2017
Posts: 3868
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member CAT Tests
Re: How many different 6-digit positive integers are there, where 3 of the  [#permalink]

Show Tags

New post 16 May 2019, 10:45
Bunuel wrote:
How many different 6-digit positive integers are there, where 3 of the digits are each one of the digits 5 or 7, and the other 3 digits are each of one of the digits 1, 4, 6, or 8 ?


A. 5,760

B. 7,290

C. 7,680

D. 8,640

E. 10,240


GMATinsight ; sir for this particular question , i tired solving the same but i am ended up getting many possible cases since the placement of 5 & 7 is not fixed ...
is there any easy way to solve this question <120 sec :(
_________________
If you liked my solution then please give Kudos. Kudos encourage active discussions.
Target Test Prep Representative
User avatar
D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6563
Location: United States (CA)
Re: How many different 6-digit positive integers are there, where 3 of the  [#permalink]

Show Tags

New post 19 May 2019, 20:09
Bunuel wrote:
How many different 6-digit positive integers are there, where 3 of the digits are each one of the digits 5 or 7, and the other 3 digits are each of one of the digits 1, 4, 6, or 8 ?


A. 5,760

B. 7,290

C. 7,680

D. 8,640

E. 10,240


The number of ways to create the 6-digit number, if the first 3 digits are either 5 or 7 and the last 3 are 1, 4, 6, or 8 is 2 x 2 x 2 x 4 x 4 x 4 = 8 x 64 = 512. However, since there are 6!/(3!3!) = 720/36 = 20 ways to arrange the digits, there are a total 512 x 20 = 10,240 such numbers.

Answer: E
_________________

Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9328
Location: Pune, India
Re: How many different 6-digit positive integers are there, where 3 of the  [#permalink]

Show Tags

New post 19 May 2019, 21:16
1
Bunuel wrote:
How many different 6-digit positive integers are there, where 3 of the digits are each one of the digits 5 or 7, and the other 3 digits are each of one of the digits 1, 4, 6, or 8 ?


A. 5,760

B. 7,290

C. 7,680

D. 8,640

E. 10,240


3 digits, say DDD, need to be selected from 5 and 7. You can do this in 2*2*2 ways. You get all combinations eg 555, 557, 577, 575 etc
3 digits, say EEE, need to be selected from 1, 4, 6 and 8. You can do this in 4*4*4 ways. You get all combinations e.g. 111, 141... etc
(A digit can be repeated)

Now you just need to mix up these two DDD and EEE to get a 6 digit number. You do need to arrange the Ds and Es among themselves since you have already accounted for their arrangements.

Total number of ways = 2*2*2*4*4*4 * 6!/3!*3! = 8*64*20 = 10,240

Answer (E)
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
GMAT Club Bot
Re: How many different 6-digit positive integers are there, where 3 of the   [#permalink] 19 May 2019, 21:16
Display posts from previous: Sort by

How many different 6-digit positive integers are there, where 3 of the

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


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