Question

Which of the following is always even.

• A. Sum of three odd numbers
• B. Sum of two odd numbers
• C. Sum of one even and one odd number
• D. None of these

Answer 1

The correct option is B

Sum of two odd numbers

Determine the correct option.

The odd number is represented as $2k+1$ and an even number is represented as $2k$ where $k$ is an integer.

The sum of two odd numbers is always even.

For example:

Three odd number are added as,

$1+3+5=9$

The resultant is an odd number.

Two odd numbers are added as:

$3+5=8$

The resultant is an even number.

An odd number is added to an even number as:

$1+2=3$

The resultant is an odd number.

So, the sum of two odd numbers always gives and even number.

Hence, the correct option is $\left(\mathrm{B}\right)$.