How
many 3 digit numbers have the sum of their digits as an odd number?
Answer (B)
(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
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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