8) Alberto has picked 756 cherries from his grandfather's tree, and he divides them equally among himself and some of his friends. Three of them, however, are not very hungry and return a quarter of the cherries they received to Alberto. With an iron stomach, Alberto, in addition to his own, eats those as well; in the end, he realizes he has eaten no less than 150 cherries. Exactly how many did he eat?
(A) 150
(B) 189
(C) 210
(D) 231
(E) 270
8. The answer is $\mathbf{( B )}$.

Let $x$ be the number of cherries eaten by Alberto, and $N$ be the number of people among whom he divides them (including himself), so $N>3$. Then we have

$$
x=\frac{756}{N}+3 \cdot \frac{756}{4 N}=\frac{7 \cdot 756}{4 N}=\frac{7 \cdot 189}{N}=\frac{3^{3} \cdot 7^{2}}{N} .
$$

Thus, $N$ divides $3^{3} \cdot 7^{2}$, and therefore its prime divisors can only be 3 and 7. If $N$ were not divisible by 7, it would have to be $N=9$ or $N=27$, but both of these values are not admissible because they result in a value of $x$ strictly less than 150. Therefore, $N$ is a multiple of 7, which may have 3 as its only other prime divisor. The only number with these properties for which $x$ is greater than or equal to 150 is $N=7$, yielding $x=27 \cdot 7=189$ [Problem proposed by G. Bresciani]