Find all School-related info fast with the new School-Specific MBA Forum

It is currently 19 Sep 2014, 02:13

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

How many 5 digit numbers are there , whose digits add up to

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
avatar
Joined: 21 Jun 2006
Posts: 289
Followers: 1

Kudos [?]: 17 [0], given: 0

GMAT Tests User
How many 5 digit numbers are there , whose digits add up to [#permalink] New post 07 Aug 2006, 17:18
How many 5 digit numbers are there , whose digits add up to an odd number?
VP
VP
User avatar
Joined: 02 Jun 2006
Posts: 1270
Followers: 2

Kudos [?]: 37 [0], given: 0

GMAT Tests User
 [#permalink] New post 07 Aug 2006, 17:27
Edited: :wall A correct solution is below by ps_dahiya...

Knowing odd+even =odd and odd+odd=even

Odd = {1,3,5,7,9}
Even= {2,4,6,8,0}

We have the following cases for odd sum of digits:

Case 1: 1 Odd & 5 Even
# of ways of picking 1 of 5 odd = 5
# of ways of picking 4 of 5 even = 5
Total = 25 numbers

Case 2: 3 Odd & 2 Even
# of ways of picking 3 of 5 odd = 5x4x3/3x2 = 10 ways
# of ways of picking 2 of 4 even = 4x3/2 = 6

Total number of numbers = 10x6 = 60.

Case 3: 5 Odd
# of ways of picking 5 of 5 =1

Adding all three cases= 5+1+60 = 66

Last edited by haas_mba07 on 08 Aug 2006, 04:17, edited 2 times in total.
Manager
Manager
avatar
Joined: 30 Jun 2006
Posts: 89
Followers: 0

Kudos [?]: 4 [0], given: 0

 [#permalink] New post 07 Aug 2006, 22:10
Haas_mba07,

A good way to solve the problem but did'nt you miss the numbers with 0's and numbers with repetition of digits.

Also,

Case 3: 5 Odd
# of ways of picking 5 of 5 =1


I have 5 odd digits. Then the numbers of 5 digit numbers formed by those numbers is not 1 but it should be 5! = 120. (and this is also the ones without repetition. What about numbers like 55555 or 33333 etc etc etc )

There are many other combinations which needs to be considered apart from the ones mentioned by you.
CEO
CEO
User avatar
Joined: 20 Nov 2005
Posts: 2922
Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
Followers: 15

Kudos [?]: 80 [0], given: 0

GMAT Tests User
 [#permalink] New post 07 Aug 2006, 23:00
No need of hefty calculations.
Total 5 digit numbers = 99999-9999 = 90000
Half of these digits have odd sum of digits and half them have even sum of digits.
Answer = 90000/2 = 45000
_________________

SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
Senior Manager
avatar
Joined: 19 Jul 2006
Posts: 361
Followers: 1

Kudos [?]: 2 [0], given: 0

GMAT Tests User
 [#permalink] New post 07 Aug 2006, 23:14
Total no. of 5 digits no. = 9*10*10*10*10= 90000

No. of 5-digit positive integers whose sum digits are even = No. of 5-digit positive integers whose sum digits are odd


so its 90000/2 = 45000
VP
VP
User avatar
Joined: 02 Jun 2006
Posts: 1270
Followers: 2

Kudos [?]: 37 [0], given: 0

GMAT Tests User
 [#permalink] New post 08 Aug 2006, 04:15
:beat ... should've thought of that!

Thanks ps/


ps_dahiya wrote:
No need of hefty calculations.
Total 5 digit numbers = 99999-9999 = 90000
Half of these digits have odd sum of digits and half them have even sum of digits.
Answer = 90000/2 = 45000
  [#permalink] 08 Aug 2006, 04:15
    Similar topics Author Replies Last post
Similar
Topics:
Experts publish their posts in the topic The three digits of a number add up to 11. The number is div Asifpirlo 3 21 Aug 2013, 00:36
How many 5-digit numbers can be formed from the digits Ravshonbek 5 11 Nov 2007, 03:53
With the five numbers 1-5 how many such 5-digit numbers are studentnow 10 15 Sep 2007, 15:58
How many 5-digit positive integers exist the sum of whose apollo168 5 05 Aug 2006, 05:19
How many 5 digit numbers can be created if the following chet719 12 16 Sep 2005, 16:44
Display posts from previous: Sort by

How many 5 digit numbers are there , whose digits add up to

  Question banks Downloads My Bookmarks Reviews Important topics  


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

Powered by phpBB © phpBB Group and phpBB SEO

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®.