If four distinct positive integers $m, n, p$ and $q$ satisfy the equation

$$
(7-m)(7-n)(7-p)(7-q)=4
$$

then the sum $m+n+p+q$ is equal to:
(a) 10
(b) 21
(c) 24
(d) 26
(e) 28
As $m, n, p$ and $q$ are integers, then $7-m$, $7-n$, $7-p$ and $7-q$ are also integers. Now,

$$
4=(-1) \times(-2) \times 1 \times 2
$$

is the only decomposition of 4 into a product of distinct integers. It follows that

$$
(7-m)+(7-n)+(7-p)+(7-q)=(-1)+(-2)+1+2
$$

and from this we obtain $m+n+p+q=28$. The correct option is (e).