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

Question

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

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

styleashish20 · Accepted Answer

Answer = 5 (C)

Total chips = 9 + 7 + 5 = 21
So each stack will have 21/3 = 7 chips (stacks containing equal numbers of chips)

Each stack must contain  at least 1 chip of each color

If we keep  1 blue chip ,  1 green chip  and  5 red chips :

1B   1G   5R  => total = 7 chips

5 red chips is the maximum number which can be kept in a stack, as it is impossible to insert more than 5 red chips in one stack because the rule will be broken "each stack contains at least 1 chip of each color".

kookies · Answer

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

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.

NCRanjan · Answer

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

HIkerDRT · Answer

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.

KanishkM · Answer

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

ADisHere · Answer

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

bumpbot · Answer

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

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