5. Four different positive integers are placed on a grid and then covered up. The product of the integers in each row and column is shown in the diagram.
What is the sum of the four integers?
A 10
B 12
C 13
D 14
E 15
Solution
C

Let the four integers in the grid be $p, q, r$ and $s$, as shown here. Since the four integers are different and the product of the integers in the first column is 4 , we have $p$ and $r$ as 1 and 4 in some order. However, we also know that $p \times q=6$ and hence $p$ cannot be 4 . Therefore $p=1$ and hence $q=6, r=4$ and $s=2$.
Therefore the sum of the four integers in the grid is $1+6+4+2=13$ and the completed grid is as shown below.