Question

Several students are seated at a large circular table. They pass around a bag containing $100$ pieces of candy. Each person receives the bag, takes one piece of candy, and then passes the bag to the next person. If Chris takes the first and the last piece of candy, then the number of students at the table could be

$10$

$11$

$19$

$20$

$25$

Solution:

Chris takes the first piece, and then the bag goes around until Chris takes the last ( $100$ th) piece. So the $99$ pieces after Chris's first must be exactly a whole number of trips around the table back to Chris.

This means the number of students divides $99$ . Among the choices, only $11$ divides $99$ .

Thus, the correct answer is B .

1990 AMC 8 Problem 22

Solution:

Problem 22 in Other Years