2024 AMC 8

Solution 1

Since she has half as many red marbles as green, we can call the number of red marbles , and the number of green marbles . Since she has half as many green marbles as blue, we can call the number of blue marbles . Adding them up, we have: marbles. The number of marbles therefore must be a multiple of , as represents an integer, so the only possible answer is

Solution 2

Suppose Maria has green marbles and total marbles. She then has red marbles and blue marbles. Altogether, Maria has

marbles, so so must be a multiple of . The only multiple of in the answer choices is