Max has a box of 200 colored blocks. The box has an equal number of green and blue blocks and an equal number of red and yellow blocks. If Max arranged all of the green blocks in stacks of 12 and all of the blue blocks in stacks of 7, how many red blocks are in the box?

A) 16

B) 32

C) 48

D) 64

Clearly, if there are x stacks of green & blue, and y of red & yellow, then

20x+14y = 300

10x+7y = 150

y = (150-10x) / 7

y = 10 (15-x) / 7

Since there must be an integer number of blocks, and 7 does not divide 10, it must divide 15-x

So, 15-x = 7 or 14

and y = 10 or 20

So, there may be 70 yellow and red, and 80 green & blue

or 140 yellow and red, and 10 green & blue