surajgarg wrote:Five pieces of wood have an average (arithmetic mean) length of 124 centimeters and a median length of 140 centimeters. What is the maximum possible length in centimeters of the shortest piece of wood?
A. 90
B. 100
C. 110
D. 130
E. 140
Solution approach pls.
Whenever you're given an average, figure out the sum.
Sum = (number of things) * (average) = 5 * 124 = 620.
Median = 140 centimeters.
Let's call the 5 pieces, from shortest to longest: w, x, 140, y, z.
Let's plug in the answers for w (the shortest piece of wood). Since we want to maximize w, we should start with the biggest answer choice:
If w =140, 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.
140+140+140 = 420, so y+z = 620 - 420 = 200.
This doesn't work because y and z each have to be at least 140, and 140+140 = 280.
The next largest answer choice is 100. Let's try it:
If w=100, then 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.
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.
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