The problem states that the average length of the 5 pieces of wood is 124. Remember this about averages:
Whenever you're given an average, figure out the sum.
The sum of the lengths of the 5 pieces is 5 * 124 = 620.
Since the median of the 5 pieces has to be 140, the middle piece likely will be 140 centimeters.
Let's call the 5 pieces, from shortest to longest: shortest, x, 140, y, z.
The question asks for the maximum possible length of the shortest piece of wood.
Whenever a PS question asks for a specific amount, consider trying out the answers in order to determine which is correct.
Since we want the shortest piece to be as long as it can be, we should start with 140, the biggest answer choice:'
Using 140 for the shortest piece, the 5 pieces will be 140, x, 140, y, z.
This means x = 140, so the 5 pieces will be 140, 140, 140, y, z.
This means the sum of the 3 shortest pieces will be 140+140+140 = 420, so the sum of y and z will have to be 620 - 420 = 200.
This doesn't work because y and z each have to be at least 140, and 140 + 140 = 280.
Darn!
The next largest answer choice is 100. Let's try it:
Using 100 for the shortest piece, the 5 pieces will be 100, x, 140, y, z.
If we make y and z each 140 (the shortest each can be), the 5 pieces will be 100, x, 140, 140, 140.
This means the sum of the 4 known pieces will be 100 + 140 + 140 + 140 = 520, making x = 620-520 = 100
So the 5 pieces will be 100, 100, 140, 140, 140.
This works! The sum is 100+100+140+140+140 = 620, and the median piece is 140.
No reason to try the other answer choices because they're smaller than answer choice D, and we need the biggest answer that will work.
The correct answer is D.
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