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probability - A 5 meter long wire is cut

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probability - A 5 meter long wire is cut

by fiza gupta » Tue Jan 03, 2017 12:18 am
A 5 meter long wire is cut into two pieces. If the longer piece is then used to form a perimeter of a square, what is the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point?

A) 1/6
B) 1/5
C) 3/10
D) 1/3
E) 2/5

OA:[spoiler]E
[/spoiler]
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by Anaira Mitch » Tue Jan 03, 2017 1:40 am
Length of wire = 5m

If the markings are such that each metre has 10 subdivisions then a longer piece of wire can be obtained at 2.6, 2.7, 2.8, .... 5.0 --> 25 ways

Area of square > 1 when Perimeter > 4.

Perimeter > 4 when the wire is cut at points > 4.0 m --> 4.1, 4.2, .... 5.0 --> 10 ways

Probability = 10/25 = 2/5

Answer: E
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by [email protected] » Tue Jan 03, 2017 10:44 am
Hi fiza gupta,

This question is vaguely worded in spots, but I've offered an explanation that matches the 'intent' of the question. There's an aspect to this question that many Test Takers would miss: regardless of where on the wire the 'cut' is made, the 'longer' piece is the one that's used to make the square. Thus, unless you cut the wire exactly in the middle, there are will always be two versions of each measure.

For example...
if you cut the wire at the 1m "mark", you'll have a 1m piece and a 4m piece
if you cut the wire at the 4m "mark", you'll also have a 1m piece and a 4m piece

Since area of a square is (side)^2, for the area to be GREATER than 1 m^2, the side lengths have to be GREATER than 1. By extension, this means that the perimeter would have to be GREATER than 4. Thus, any cut that produces a longer piece that is greater than 4m will satisfy what this question is asking for...

Cutting LESS than 1m will do it.
Cutting MORE than 4m will also do it.

That's approximately 2m of a 5m wire... 2/5

Final Answer: E

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