Question

If p, q, r are three consecutive natural numbers, then what must be true for M if $M=(q+r-p)(p+r-q)(p+q-r)$?

• A. Positive
• B. Negative
• C. Either positive or zero
• D. Zero

Answer 1

The correct option is C Either positive or zero

As $p,q,r$ are consecutive natural numbers, we can write them as

$p=n-1$

$q=n$

$r=n+1$

According to question,

$M=(q+r-p)(p+r-q)(p+q-r)=(n+n+1-n+1)(n-1+n+1-n)(n-1+n-n-1)$

$=(n+2)\left(n\right)(n-2)$

Minimum possible value of $n-1=1$

$\Rightarrow n\ge 2$

$\therefore M$ is either positive or zero$(n=2)$