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Luke has a bag of 100 colored marbles. The bag has an equal number of green and blue marbles and an equal number of red and yellow marbles. If Luke arranged all of the green marbles in groups of 8 and all of the blue marbles in groups of 6, how many yellow marbles are in the bag?

A22
B24
C26
D28

Verified Answer :

Since the number of green and blue marbles is the same, and the number of green marbles is divisible by 8, and the blue marbles by 6, the number of green marbles (and of the blue marbles) must be a multiple of both 6 and 8. The least common multiple of 6 and 8 is 24. So there can be either 24 blue and 24 green marbles, leaving 52 for red and yellow, or 48 blue and 48 green marbles, leaving 2 for red and yellow.

Since red and yellow are the same number, there could be either 26 yellow, or 1 yellow. Since 1 isn't given as an option, it has to be C) 26.

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