Question

Four stacks containing an equal number of chips are to be made from 11 orange, 9 white, 13 black and 7 yellow chips. If all of these chips are used and each stack contains at least one chip of each colour, what is the maximum number of white chips in any one stack?

• A. 3
• B. 4
• C. 5
• D. 6

Answer 1

The Correct Option is D

To solve this problem, we need to evenly distribute the chips into four stacks, ensuring each stack has an equal number of each color and all chips are used. Let's denote the number of chips of each color in each stack as follows:

• Orange chips per stack: \(O\)
• White chips per stack: \(W\)
• Black chips per stack: \(B\)
• Yellow chips per stack: \(Y\)

The total chips of each color must sum up to the given number:

• Orange: \(4O=11\)
• White: \(4W=9\)
• Black: \(4B=13\)
• Yellow: \(4Y=7\)

Given the conditions, calculate the values of O, W, B, and Y that satisfy the inequality and equation constraints:

1. Each stack must include at least one chip of each color, so \(O,W,B,Y \geq 1\).
2. The total count of stacks is 4.

We need to focus on maximizing W while adhering to the constraints:

• From \(4O=11\), we have one complete stack of 2 oranges, so \(O=2\) (remaining: 3 oranges).
• From \(4W=9\), same calculation yields \(W=2\) (remaining: 1 white).
• From \(4B=13\), similarly \(B=3\) (remaining: 1 black).
• From \(4Y=7\), hence \(Y=1\) (remaining: 3 yellows).

Now, focus on maximizing \(W\):

• For complete stacks:
  \(O+B+Y=2+3+1=6\) chips needed for 3 complete stacks.
  1 additional stack needs maximizing \(W\).

The remaining white chips from stacks is 1 (initial \(W=2\) for each stack), allowing the remaining chip to be distributed to one stack, making it \(W=6\) in that stack.

Thus, the maximum number of white chips in any one stack is 6.