9. Adam laid 2022 tiles in a long line. Beata removed every sixth tile. Carla then removed every fifth tile. Doris then removed every fourth tile. Lastly, Eric removed all of the remaining tiles.
How many tiles did Eric remove?
A 0
B 337
C 674
D 1011
E 1348
Solution
D

Beata leaves five-sixths of the tiles. Carla leaves four-fifths of the remaining tiles. Doris leaves three-quarters of what's left. Hence the number of tiles which Eric removes is $\frac{5}{6} \times \frac{4}{5} \times \frac{3}{4} \times 2022=\frac{3}{6} \times 2022=\frac{1}{2} \times 2022=1011$.