8. William has four cards with different integers written on them. Three of these integers are 2,3 and 4 . He puts one card in each cell of the $2 \times 2$ grid shown.
The sum of the two integers in the second row is 6 . The sum of the two integers in the second column is 10 . Which number is on the card he places in the top left cell?
A 2
B 3
C 4
D 6
E Can't be sure
8. B Let the integers on the cards placed in each cell be as shown.
The sum of the two integers in the second row is 6 and the sum of the two integers in the second column is 10 . Since no pair of the integers 2,3 and 4 add to 10 , we can conclude that the unknown integer is written in the second column. Therefore the integer $a$ is one of 2,3 or 4 . Consider each possibility in turn.
If $a=2$, then $b=4$ (since $a+b=6$ ), $c=6$ (since $c+b=10)$ and hence $d=3$.
If $a=3$, then $b=3$, which is impossible since $a$ and $b$ are different.
If $a=4$, then $b=2, c=8$ and hence $d=3$.
Therefore the number William writes in the top left cell is 3 .