sum digits = 5

Forum Index GMAT Math Problem Solving

New MBA Student Life Forum: Ask your questions to current MBA students from Harvard, Stanford, Wharton, Kellogg and Haas

Post new topic   Reply to topic

atulkumar79
Just gettin' started!



Joined: 17 Mar 2009
Posts: 15

Thanks given: 0
Thanked 0 times in 0 posts
Topic: sum digits = 5
PostThu Jul 02, 2009 8:57 pm Reply with quote
How many positive integers less than 10,000 are there in which the sum of the digits equals 5?

(A) 31
(B) 51
(C) 56
(D) 62
(E) 93


OA C
Back to top
View user's profile Send private message
Robinmrtha
Rising GMAT Star



Joined: 01 Apr 2009
Posts: 91

Thanks given: 6
Thanked 9 times in 9 posts
PostThu Jul 02, 2009 9:47 pm Reply with quote
the sum of the digits can be five
in the following cases
when the digits of the number are from the following sets
1. (0,0,0,5)
2.(1,0,0,4)
3.(1,2,2,0)
4.(3,2,0,0)
5.(3,1,1,0)
6.(2,1,1,1)

from set one the no. of digits with sum 5 = 4!/3!=4
from set two the no. of digits with sum 5 = 4!/2!=12
from set three the no. of digits with sum 5 = 4!/2!=12
from set four the no. of digits with sum 5 = 4!/2!=12
from set five the no. of digits with sum 5 = 4!/2!=12
from set six the no. of digits with sum 5 = 4!/3!=4

Therefore, the answer is 4 +12+12+12+12+4=56

OA C
Back to top
View user's profile Send private message
Thanked by: abhinav_mgm
getso
Rising GMAT Star



Joined: 28 Feb 2009
Posts: 44

Thanks given: 7
Thanked 1 times in 1 posts
PostThu Jul 02, 2009 10:30 pm Reply with quote
Hi,

Could you please explain permutation part. I could not understand.

Thanks,
Shobha
Back to top
View user's profile Send private message
Robinmrtha
Rising GMAT Star



Joined: 01 Apr 2009
Posts: 91

Thanks given: 6
Thanked 9 times in 9 posts
PostThu Jul 02, 2009 11:29 pm Reply with quote
lets take an example...
in how many ways the alphabets of the word apple be arranged to form new words(may not have meaning)

apple has 5 alphabets
where there are 2 ps...
so even if we interchange p the word will remain same...
so before we take this into consideration the permutation will be 5!
But since p is repeated...we got to divide 5! by 2!
i.e. 5!/2!

I have done the same in above explanation...
in set one total digits is 4 but there are 3 zeros....
so i have divided 4!/3!
hope this helps....
Back to top
View user's profile Send private message
Display posts from previous:   

Post new topic   Reply to topic All times are GMT - 8 Hours
Page 1 of 1