In each row of the table, the sum of the first two numbers equals the third number. Also, in each column of the table, the sum of the first two numbers equals the third number. What is the sum of the nine numbers in the

| $m$ | 4 | $m+4$ |
| :---: | :---: | :---: |
| 8 | $n$ | $8+n$ |
| $m+8$ | $4+n$ | 6 |

table?
(A) 18
(B) 42
(C) -18
(D) -6
(E) 24
Solution 1

Looking at the third row of the table, $(m+8)+(4+n)=6$ or $m+n+12=6$ or $m+n=-6$. The sum of the nine numbers in the table is

$m+4+m+4+8+n+8+n+m+8+4+n+6=3(m+n)+42=3(-6)+42=24$

## Solution 2

Try setting $m=0$.

Then the table becomes

| 0 | 4 | 4 |
| :---: | :---: | :---: |
| 8 | $n$ | $8+n$ |
| 8 | $4+n$ | 6 |.

From the third row, $8+(4+n)=6$ or $n+12=6$ or $n=-6$.

The table thus becomes

| 0 | 4 | 4 |
| :---: | :---: | :---: |
| 8 | -6 | 2 |
| 8 | -2 | 6 |.

The sum of the nine numbers in the table is $0+4+4+8+(-6)+2+8+(-2)+6=24$.

ANSWER: (E)