| View previous topic :: View next topic |
| Author |
Message |
umaa
Really wants to Beat The GMAT!
Joined: 08 Jun 2008
Posts: 117
Thanks given: 2
Thanked 0 times in 0 posts
|
 Posted: Tue Jul 08, 2008 9:32 pm Post subject: permutation, combination |
 |
|
How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0,1,2,3,4,5 (WITHOUT REPETITION)
a. 216
b. 3152
c. 240
d. 600
The answer is 216. |
|
| Back to top |
|
 |
|
|
Ian Stewart
GMAT Instructor
Joined: 02 Jun 2008
Posts: 862
Thanks given: 2
Thanked 166 times in 153 posts
Location: London
GMAT Score: 780
|
| Posted: Wed Jul 09, 2008 4:48 am Post subject: Re: permutation, combination |
|
|
| umaa wrote: | How many 5 digit numbers can be formed which are divisible by 3 using the numerals 0,1,2,3,4,5 (WITHOUT REPETITION)
|
If a number is divisible by 3, the sum of its digits is divisible by 3. We need to choose five digits from {0,1,2,3,4,5} which add to a multiple of 3. We could choose:
{1, 2, 3, 4, 5}
or
{0, 1, 2, 4, 5}
If we use the digits {1, 2, 3, 4, 5}, we have 5 choices for the first digit, 4 for the second, etc- 5! = 120 numbers we can make in total.
If we use the digits {0, 1, 2, 4, 5}, we only have 4 choices for the first digit (because it cannot be zero), 4 choices for the second digit, 3 for the third, etc- 4*4! = 96 numbers we can make in total.
120+96 = 216.
_________________
co-founder, www.gmatix.com
-GMAT blogs, free international directory of GMAT tutors and MBA Admissions Consultants, and more... |
|
| Back to top |
|
|
umaa
Really wants to Beat The GMAT!
Joined: 08 Jun 2008
Posts: 117
Thanks given: 2
Thanked 0 times in 0 posts
|
| Posted: Wed Jul 09, 2008 5:04 am Post subject: |
|
|
Thanks  |
|
| Back to top |
|
|
preetha_85
Rising GMAT Star
Joined: 06 Jul 2008
Posts: 95
Thanks given: 2
Thanked 2 times in 2 posts
Location: INDIA
Test Date: Aug 23
|
| Posted: Wed Jul 09, 2008 5:35 am Post subject: |
|
|
Hi ,
for a no. to be divisible by 3 the nos should add up to a multiple of 3.
Given the digits (0,1,2,3,4,5)
Only the combinations given below will add up to a multiple of 3 :
1. (1,2,3,4,5)
2. (0,1,2,4,5)
Case 1:
these nos can be arranged in 5! ways i.e 120
Case 2:
Since if 0 is the 1st digit it will not form a 5 digit no. they can be arranged in :4*4*3*2*1
hence the total permutations is :120 +96 =216 |
|
| Back to top |
|
|
preetha_85
Rising GMAT Star
Joined: 06 Jul 2008
Posts: 95
Thanks given: 2
Thanked 2 times in 2 posts
Location: INDIA
Test Date: Aug 23
|
| Posted: Wed Jul 09, 2008 5:35 am Post subject: |
|
|
Hi ,
for a no. to be divisible by 3 the nos should add up to a multiple of 3.
Given the digits (0,1,2,3,4,5)
Only the combinations given below will add up to a multiple of 3 :
1. (1,2,3,4,5)
2. (0,1,2,4,5)
Case 1:
these nos can be arranged in 5! ways i.e 120
Case 2:
Since if 0 is the 1st digit it will not form a 5 digit no. they can be arranged in :4*4*3*2*1
hence the total permutations is :120 +96 =216 |
|
| Back to top |
|
|
|
|
evansbd
Rising GMAT Star
Joined: 01 Jul 2008
Posts: 52
Thanks given: 1
Thanked 0 times in 0 posts
Target GMAT Score: 700
|
| Posted: Thu Jul 17, 2008 7:47 am Post subject: Interesting |
|
|
I noticed most people solved this problem exactly the same way.
I did the last part a little different.
Case 1: 5! = 120 - this is the easy part
Case 2:
I kind of understand why people will do 4*4!. However if I were on the exam I probably would not have realized I needed to multiply by four.
Personally, I saw that 0 couldn't be the first number for a 0 1 2 4 5 combination. I could see that I needed to find the number of combinations then subtract the ones that didnt fit the criteria of being divisible by 3. So I said there are 5! combinations of 0 1 2 4 5. However we must subtract the number of combinations where 0 is the first number.
total combinations - 0 first combinations = 5! - 4! = 120 - 24 = 96
Then I added 120 + 96 = 216 |
|
| Back to top |
|
|
|
|
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum
You cannot attach files in this forum
You cannot download files in this forum
|
|
"GMAT" and other GMAC™ trademarks are registered trademarks of the Graduate Management Admission Council™. The Graduate Management Admission Council™ does not endorse, nor is it affiliated in any way with the owner or any content on this website. The opinions expressed here are solely those of the author or those of the members of this website. Copyright © 2008 BTG Test Prep, LLC. Powered by phpBB © 2001, 2005 phpBB Group.
|
|
