Problem:
All of Marcy's marbles are blue, red, green, or yellow. One third of her marbles are blue, one fourth of them are red, and six of them are green. What is the smallest number of yellow marbles that Marcy could have?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The total number of Marcy's marbles must be divisible by both and thus it must be a multiple of . If she has just marbles, then are blue and are red, leaving just other marbles, so she could not have green marbles. If she has marbles, then are blue and are red, leaving other marbles, so she could have green marbles and yellow marbles. The smallest number of yellow marbles that Marcy would have is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions