Which of the following is always even
options
(a) Sum of three odd numbers
(b) Sum of two odd numbers
(c) Sum of one even and one odd numbers
(d) none of these
Answers
The sum of two odd numbers is always even.
- Odd numbers are those numbers which can not be divided by two. For example - 3, 7, 17 , 21 etc.
- Thus, the sum of two odd numbers will always be even.
- For example- 3 + 5 = 8 or 11 + 17 = 28
- Whereas, if two or more odd numbers are multiplied, there product is always odd and also the sum of an even number of odd numbers is even.
Given : Few statement about odd even numbers
To Find : Which of the following is always even options
(a) Sum of three odd numbers
(b) Sum of two odd numbers
(c) Sum of one even and one odd numbers
(d) none of these
Solution:
Even number = 2k
Odd number = 2k + 1
where k belongs to integer
a) Sum of three odd numbers
2a + 1 + 2b + 1 + 2c + 1
= 2(a + b + c) + 3
= 2(a + b + c) + 2 + 1
= 2(a + b + c + 1) + 1
= 2k + 1
= odd
(b) Sum of two odd numbers
= 2a + 1 + 2b + 1
= 2a + 2b + 2
= 2(a + b + 1)
= 2k
= EVEN
(c) Sum of one even and one odd numbers
= 2a + 2b + 1
= 2(a + b) + 1
= 2k + 1
= odd
Sum of two odd numbers is always EVEN
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