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 .
The correct option is (e).

As $m, n, p$ and $q$ are integers, $7-m, 7-n, 7-p$ and $7-q$ are also integers. Now, $4=1 \times 2 \times 2$ and

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

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

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

thus, $m+n+p+q=28$.