Identify the right option for the product obtained by multiplying two odd numbers.

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An odd number

An even number

A prime number

None of the above

answer is A.

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Detailed Solution

The given data is two odd numbers.
We are required to find out the product obtained by multiplying two odd numbers.
We solve the problem in the following way.
Let us assume that the two odd numbers are

2 n + 1, 2 n + 3 where n=0,1,2, …

We perform the product of these odd numbers in the following way.

⇒ 2 n + 1 × 2 n + 3 ⇒ 2 n × 2 n + 3 + 1 × 2 n + 3 ⇒ 4 n 2 + 6 n + 2 n + 3 ⇒ 4 n 2 + 8 n + 3

We observe the following.

⇒ 4 n 2 + 8 n + 3 n = 0 = 3 n = 0 ⇒ 4 n 2 + 8 n + 3 n = 1 = 15 n = 1 ⇒ 4 n 2 + 8 n + 3 n = 2 = 35 n = 2

So, we find that the resultant expression

4 n 2 + 8 n + 3

is an odd number.
Therefore, the required correct option is 1.

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