In the chart, the products of the numbers represented by the letters in each of the rows and columns are given. For example, $x y=6$ and $x z=12$. If $x, y, z$, and $w$ are integers, what is the value of $x w$ ?
(A) 150
(B) 300
(C) 31
(D) 75
(E) 30

| $x$ | $y$ | 6 |
| :---: | :---: | :---: |
| $z$ | $w$ | 50 |
| 12 | 25 |  |
Solution

Since $x, y, z$, and $w$ are integers, then $y$ must divide evenly into both 6 and 25 . The only possible value of $y$ is 1 . Thus, $x=6$ and $w=25$. The value of $x w$ is (6)(25) $=150$.ANSWER: