A teacher has 237 candies to give to her 31 students. What is the minimum number of additional candies she needs to ensure that all her students receive the same number of candies, with none left over?
(a) 11
(b) 20
(c) 21
(d) 31
(e) 41
The correct option is (a).

Dividing 237 by 37, we get $237=7 \times 31+20$. Therefore, 237 is not divisible by 31. This means the teacher really needs to buy more candies so that all the students can receive the same number of candies. We need to add to the expression $7 \times 31+20$ the smallest positive integer $x$ such that $7 \times 31+20+x$ is a multiple of 31. Since $20+11=31$, the teacher only needs to buy 11 additional candies.