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# Three stacks containing equal numbers of chips are to be made from 9

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Re: Three stacks containing equal numbers of chips are to be made from 9 [#permalink]
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IMO 5

its a question of min max -
Step 1 GIVE 1 OF EACH TO EACH STACK- Fulfill the min requirement.

Step 2 -Now as we know each stack can have only 7 chips that means to max the num of red chips in stack 1 minimize the number of blue and green chips ( i.e put them in other stacks ) S1 will have only 1 blue and 1 green chip but since we have to maintain an equal of 7 that means you have to give 5 more chips to stack 1
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Re: Three stacks containing equal numbers of chips are to be made from 9 [#permalink]

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?

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Re: Three stacks containing equal numbers of chips are to be made from 9 [#permalink]
HKD1710 wrote:
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

My approach is a bit different, 9RC + 7BC + 5GC, total chips can be 315, LCM of all 3 color chips

Now they will be in 3 stacks of equal number of chips, 315/3 = 105 chips/ stack

You can get this from C

9 * 5 + 7 *5 + 5 * 5 = 105
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Re: Three stacks containing equal numbers of chips are to be made from 9 [#permalink]
HKD1710 wrote:
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

­Just visualize to make stacks
the lowest we have is 5 chips and all stacks must have at least one chip of every colour
so 5 stacks is the highest we can make­
Re: Three stacks containing equal numbers of chips are to be made from 9 [#permalink]
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