1. For integers $a, b, c$ and $d$, it is given that the difference between $a$ and $b$ is 2, the difference between $b$ and $c$ is 3, and the difference between $c$ and $d$ is 4.

Which of the following values cannot be the difference between $a$ and $d$?
A) 1
B) 3
C) 5
D) 7
E) 9
A1. D) 7

From the data in the problem, we deduce that $a-b= \pm 2, b-c= \pm 3$ and $c-d= \pm 4$.

We then get

$$
a-d=(a-b)+(b-c)+(c-d)= \pm 2 \pm 3 \pm 4
$$

We can now go through all eight possibilities for the plus and minus signs:

$$
\begin{array}{rrrr}
2+3+4=9, & 2+3-4=1, & 2-3+4=3, & 2-3-4=-5, \\
-2-3-4=-9, & -2-3+4=-1, & -2+3-4=-3, & -2+3+4=5 .
\end{array}
$$

The only value that does not occur (neither with a plus sign nor with a minus sign) is 7.