## Wednesday, 26 October 2011

### Puzzle-13

How many 3 digit numbers have the sum of their digits as an odd number?
(A)540            (B)450             (C)500             (D)125            (E) None of these
Solution follows here:

Solution:

Funda here is --- “For the sum of three numbers to be odd, either all three should be odd or only one number should be odd”

Odd digits: 1,3,5,7,9; Even digits: 0,2,4,6,8

All three odd digits:

First digit – 1/3/5/7/9; Second digit –1/3/5/7/9; Third digit –1/3/5/7/9;

Number of possibilities = 5*5*5 = 125

Only 1st digit odd:

First digit – 1/3/5/7/9; Second digit –0/2/4/6/8; Third digit –0/2/4/6/8;

Number of possibilities = 5*5*5 = 125

Only 2nd digit odd:
First digit – 2/4/6/8; Second digit – 1/3/5/7/9; Third digit –0/2/4/6/8;

Number of possibilities = 4*5*5 = 100

Only 3rd digit odd:

First digit – 2/4/6/8; Second digit – 0/2/4/6/8; Third digit – 1/3/5/7/9;

Number of possibilities = 4*5*5 = 100

Total possible numbers = 125+125+100+100 = 450