If $x$ and $y$ are positive integers and $x+y=5$, then a possible value for $2 x-y$ is
(A) 3
(B) -3
(C) 2
(D) -2
(E) 0
Solution 1

Since $x$ and $y$ have to be positive integers and add up to 5, it is easy to make a chart of the possibilities:

Of the choices, only -2 is a possibility.

| $x$ | $y$ | $2 x-y$ |
| :---: | :---: | :---: |
| 1 | 4 | -2 |
| 2 | 3 | 1 |
| 3 | 2 | 4 |
| 4 | 1 | 7 |

## Solution 2

We can rewrite $2 x-y=3 x-x-y=3 x-(x+y)=3 x-5$.

Of the five possibilities, the only one that is 5 less than a multiple of 3 is -2 .

ANSWER: (D)