Suppose that $N=3 x+4 y+5 z$, where $x$ equals 1 or -1 , and $y$ equals 1 or -1 , and $z$ equals 1 or -1 . How many of the following statements are true?

- $N$ can equal 0 .
- $N$ is always odd.
- $N$ cannot equal 4.
- $N$ is always even.
(A) 0
(B) 1
(C) 2
(D) 3
(E) 4
When $N=3 x+4 y+5 z$ with each of $x, y$ and $z$ equal to either 1 or -1 , there are 8 possible combinations of values for $x, y$ and $z$ :

| $x$ | $y$ | $z$ | $N$ |
| :---: | :---: | :---: | :---: |
| 1 | 1 | 1 | 12 |
| 1 | 1 | -1 | 2 |
| 1 | -1 | 1 | 4 |
| 1 | -1 | -1 | -6 |
| -1 | 1 | 1 | 6 |
| -1 | 1 | -1 | -4 |
| -1 | -1 | 1 | -2 |
| -1 | -1 | -1 | -12 |

From this information, $N$ cannot equal $0, N$ is never odd, $N$ can equal 4 , and $N$ is always even. Therefore, exactly one of the four given statements is true.

ANSwER: (B)