15. James wrote a different integer from 1 to 9 in each cell of a table. He then calculated the sum of the integers in each of the rows and in each of the columns of the table. Five of his answers were 12, 13, 15, 16 and 17 , in some order. What was his sixth answer?
A 17
B 16
C 15
D 14
E 13
15. A The total of the sums of the three rows of the table is equal to the sum of all the digits from 1 to 9 , which is 45 . Similarly, the total of the sums of the three columns of the table is also equal to 45 . Hence James' six answers add to $45+45=90$. The sum of the five answers given is $12+13+15+16+17=73$ and hence his sixth answer is $90-73=17$. [It is left as an exercise to find a possible arrangement of the digits 1 to 9 that actually gives these six sums.]