Question

If you add any two odd numbers together, the answer is 

(a) Always even

(b) Always odd

(c) Something Even

(d) 1

Answer 1

Hint: In order to solve this problem, we need to understand the definition of odd numbers. so, there are two types of numbers, even numbers, and odd numbers.  numbers which are alternate starting from 0 are all called even numbers and all the alternate numbers starting from 1 are classified as odd numbers. Therefore, we can write even numbers like 0, 2, 4, 6, 8,10, ……… and odd numbers can be written as 1, 3, 5, 7, 9…. and so on. Now, we can solve this question and use the trial and error to calculate the summation of any two odd numbers.

Complete step-by-step solution:

We are asked to find the summation of two odd numbers.

We need to understand what we mean by odd numbers.

There are two types of numbers even and odd numbers based on the divisibility of the 2.

The numbers which are divisible by two are even numbers whereas numbers which are not divisible by 2 are odd numbers.

There is an exception in this, number 0 is considered an even number.

We can also say that numbers, which are alternate starting from 0 are all called even numbers and all the alternate numbers starting from 1 are classified as odd numbers.

Therefore, we can write even numbers like $0, 2, 4, 6, 8,10, ………$ and odd numbers can be written as $1, 3, 5, 7, 9…..$ and so on.

Now we are asked to find the summation of any two odd numbers.

Let's take any two odd numbers 1 and 3.

Adding these numbers, we get,

$1 + 3 = 4$.

The sum of 1 and 3 is 4.

Let's consider another pair of 5 and 7.

Adding these numbers, we get,

$5 + 7 = 12$.

The sum of 5 and 7 is 12.

So, we can say that the sum of any two odd numbers is always an even number.

Hence, the correct option is (a).

Note: We can solve this problem with another approach to this problem, we know that 2q+1 also gives an odd number so let’s add two odd numbers represented by $2p+1$ & $2q+1$. By adding the numbers, we get as follows,

$2p+1 + 2q+1 = 2(p+q)+2 = 2m+2 = 2(m+1)$.

We can also write it as $2(m+1)$. As we can see that the term is the multiple of 2, so any term multiple of 2 is an even number. So, we can say that the sum of two odd numbers is an even number.