Three stacks containing equal numbers of chips are to be made from 9 red chips, 7 blue chips, and 5 green chips. If all of these chips are used and each stack contains at least 1 chip of each color, what is the maximum number of red chips in any one stack?

(A) 7
(B) 6
(C) 5
(D) 4
(E) 3


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Three stacks containing equal numbers of chips are to be made from 9 red chips, 7 blue chips, and 5 green chips. If all of these chips are used and each stack contains at least 1 chip of each color, what is the maximum number of red chips in any one stack?

We have 3 stacks. as each stack contains at least 1 chip of each color, we should have at least 1 chip of blue and green in the one stack. We have 9 red chips, thus 9-2 = 7 red chips are the maximum number of red chips.

Answer is 5,

to make it easier, first, you give each chip to each stack. we know that it is 21 chips in total, 7 chips a stack.

now, you observe, since there is 3 kinds of chips, you give each chip to each stack, it means 3 chips must occupied in each stack, leaving you only 4 maximum from each color (only red 6 left or blue 4 left, not enough on green chips because green chips will have 2 left)

here is another crucial point, we know the maximum is 4 is actually incomplete, yes, the maximum addition chips is 4, you need to add those chips that are already in the stack, each chips from each color, right?

thus, Answer is 5, 4 additional + 1 already added by the question = 5.