In a magic square, all rows, columns, and diagonals have the same sum. The magic square shown uses each of the integers from -6 to +2 . What is the value of $Y$ ?
(A) -1
(B) 0
(C) -6
(D) +2
(E) -2

| +1 |  | $Y$ |
| :---: | :---: | :---: |
| -4 |  |  |
| -3 |  | -5 |
First we must find the magic constant, that is, the sum of each row, column and diagonal. From column one, we find that the magic constant is $(+1)+(-4)+(-3)=-6$.

In the diagonal extending from the top left corner to the bottom right corner, the two existing numbers +1 and -5 have a sum of -4 .

Thus, to obtain the magic constant of -6 in this diagonal, -2 must occupy the centre square. In the diagonal extending from the bottom left corner to the top right corner, the two numbers -3 and -2 , have a sum of -5 .

Thus, to obtain the magic constant of -6 in this diagonal, $Y$ must equal -1 .

The completed magic square is shown below.

| +1 | -6 | -1 |
| :---: | :---: | :---: |
| -4 | -2 | 0 |
| -3 | +2 | -5 |

ANSWER: (A)