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Statistics Problem 2 - Median

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by surajgarg » Thu Jul 22, 2010 2:43 am
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.
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by selango » Thu Jul 22, 2010 2:56 am
Sum/5=124

Sum=620

Median=140

A B 140 D E

To get the maximum short value,minimize all other values.

A B 140 140 140

A+B+420=620

A+B=200

A=100,B=100

Maximum short value=100

Hope this clarify
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by surajgarg » Thu Jul 22, 2010 3:07 am
selango wrote:Sum/5=124

Sum=620

Median=140

A B 140 D E

To get the maximum short value,minimize all other values.

A B 140 140 140

A+B+420=620

A+B=200

A=100,B=100

Maximum short value=100

Hope this clarify
Thanks, nicely explained.
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by BastiG » Thu Jul 22, 2010 3:13 am
Okay. I understand. Good explanation!
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by surajgarg » Thu Jul 22, 2010 3:16 am
BastiG wrote:And why isn't A= 90 and B= 110? The median would still be 140 and the average 124.
Cos the question asks maximum possible length of the shortest piece of wood
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by VS2013 » Thu Jul 22, 2010 2:52 pm
surajgarg wrote:
BastiG wrote:And why isn't A= 90 and B= 110? The median would still be 140 and the average 124.
Cos the question asks maximum possible length of the shortest piece of wood
Is there another approach to this? Thank you.
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by GMATGuruNY » Thu Jul 22, 2010 3:07 pm
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.

The correct answer is D.
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