Question

If $p$ is prime, then $\sqrt{p}$ is irrational and if $a,b$ are two odd prime numbers, then $a^2-b^2$ is composite. As per the above passage mark the correct answer to the following question.
${119}^2-{111}^2$ is:

• A. a prime number
• B. a composite number
• C. an odd prime number
• D. an odd composite number

Answer 1

The correct option is B a composite number

$a^2-b^2=(a-b)(a+b)$
Now, if a and b are odd then $a-b$ and $a+b$ will be even that makes the resulting value $a^2-b^2$ divisible by 2 . So its a composite number.