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M14-17

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lastshot wrote:
Bunuel wrote:
Official Solution:

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. $$\frac{1}{6}$$
B. $$\frac{1}{5}$$
C. $$\frac{3}{10}$$
D. $$\frac{1}{3}$$
E. $$\frac{2}{5}$$

In order the area of a square to be more than 1, its side must be more than 1, or the perimeter must be more than 4. Which means that the longer piece must be more than 4. Look at the diagram below:

If the wire will be cut anywhere at the bolded region, then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is $$\frac{2}{5}$$ (2 red pieces out of 5).

Bunnel,

I am confused in your explanation as , I got to the logic that in order for area of square to be greater than 1, its perimeter must be greater than 4.

Now, Point of confusion is , That there are n ( no. of points ) in between point 4-5 of rope,

How you came up with the idea of region ?

Also in case of there are more similar question & you have link, pls share ...

Regards
LS

Don't understand what you mean by the red part above. There are infinite number of points from 4 and 5...

Consider a number line: {total} is line segment of 5 units (from 0 to 5) and {favorable} is a line segment of 2 units (from 0 to 1 and 4 to 5), thus P = {favorable}/{total} = 2/5.

Check Probability and Geometry Questions to practice from our Special Questions Directory.

Hope it helps.
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Maybe this can simplify the question:

Main concept: Probability = (desired outcomes)/(possible outcomes)

Possible outcomes for the longer out of the 2 wires = 5-2.5 = 2.5
Desired outcomes for the longer wire to be greater than 4 = 5-4=1

Therefore the probability will be = 1/2.5 = 2/5.
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I think this is a high-quality question and I agree with explanation. nice question.. its tricky
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Excellent question!
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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?

Since the question says longer piece is used to form a perimeter of a square:
We have Perimeter between 2.5 meter and 5 meter
It implies: side of a square will be between 2.5/4 equals 5/8 and 5/4, On a number line it will be represented as : 5/8__________1__favourable___5/4

Probability= favourable/Total
Favourable= 5/4-1=1/4
Total= 5/4-5/8= 5/8

Probability= 1/4 divided by 5/8 which equals to 2/5 Ans.
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I think this is a high-quality question and I agree with explanation.
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I think this is a high-quality question and I agree with explanation.
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Was trying to explain this question to someone on the YouTube community section. When I realised this

Think of this situation as if you were playing darts with this wire and the wire is cut at where ever the dart lands ( the question stem says the wire is cut at an arbitrary point )

L ————————————-———— R
|1cm|_______|3cm|_________|1cm|

As long as the dart lands on either of the 1cm lengths we get our required result

So now we have 2cm of the total 5cm where making a cut will yield the required result

Hence 2/5 (e)

Posted from my mobile device
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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I'm still confused because, there was no "integer" clue.
So I thought the longer piece could be 4≤x<5(like 4.2, 4,4..).

Thanks.­
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Chloee wrote:
I'm still confused because, there was no "integer" clue.
So I thought the longer piece could be 4≤x<5(like 4.2, 4,4..).

Thanks.­

Consider a number line: 'total' is a line segment of 5 units (from 0 to 5), and 'favorable' is a line segment of 2 units (from 0 to 1 and 4 to 5). Thus, P = favorable/total = 2/5.

You can check other solutions here:

https://gmatclub.com/forum/a-5-meter-lo ... 06448.html

Hope this helps.