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by GMATGuruNY » Thu Nov 10, 2011 1:09 pm
MBA.Aspirant wrote:How many positive integers less than 10,000 are there in which the sum of digits equals 5?

A)31
B)51
C)56
D)62
E)93
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by neelgandham » Thu Nov 10, 2011 1:10 pm
No of one digit numbers whose digits sum to 5 = 1 (Just the number 5)

No of two digit numbers whose digits sum to 5 = 5 (23,32,41,14,50)

No of three digit numbers whose digits sum to 5 = 15 (500,401,104,410,140,302,203,320,230,311,113,131,221,212,122

No of four digit numbers whose digits sum to 5 = 35
The possible sets are
(1,2,2,0) - 9 different numbers
(1,1,1,2) - 4 different numbers
(1,3,1,0) - 9 different numbers
(3,2,0,0) - 6 different numbers
(4,1,0,0) - 6 different numbers
(5,0,0,0) - 1 number

Total number of positive integers less than 10000 with the sum of digits equal to 5 = 35+15+5+1 = 56

IMO C
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