Question

If $p$ and $n$ are integers such that $p>n>0$ and $p^2-n^2=12$, which of the following can be the value of $pn$?
I. $1$
II. $2$
III. $4$

• A. I only
• B. II only
• C. I and II only
• D. None of these
• E. I, II and III

Answer 1

The correct option is D None of these

Since $p$ are integers so $p+n$ and $p-n$ will also be integers.

$p^2-n^2=(p+n)(p-n)=4\times 3$ On comparing wee get $p+n=4$ and $p-n=3$

On solving these two equation we get $p$ =3.5 and $n$ =0.5

$pn$=3.5x0.5=1.75

So correct answer will be option D