The symbol $\odot$ represents a special operation with numbers; some examples are $2 \odot 4=10,3 \odot 8=27,4 \odot 27=112$ and $5 \odot 1=10$. What is the value of $4 \odot(8 \odot 7)$?
(a) 19
(b) 39
(c) 120
(d) 240
(e) 260
$ A correct option is (e).

We need to figure out what the rule of this operation is. Note that

$$
2 \odot 4=10=2 \times 4+2,3 \odot 8=27=3 \times 8+3,4 \odot 27=112=4 \times 27+4
$$

and $5 \odot 1=10=5 \times 1+5$.

A plausible hypothesis is that the rule defining the operation $\odot$ is $a \odot b=a \times b+a$. According to this rule, we have

$$
4 \odot(8 \odot 7)=4 \odot(8 \times 7+8)=4 \odot 64=4 \times 64+4=260
$$