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 2__

^{nd}

__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 3__

^{rd}

__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

**Answer (B)**

This can be solved in a simpler way by just getting all the numbers that are 3 digit (900), half of them will add to even and half odd. so and is 450 :)

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