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avigutman
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Tutor
Joined: 17 Jul 2019
Last visit: 30 Sep 2025
Posts: 1,285
Given Kudos: 66
Location: Canada
Schools: NYU Stern (WA)
GMAT 1: 780 Q51 V45
GMAT 2: 780 Q50 V47
GMAT 3: 770 Q50 V45
Expert reply
21 Oct 2021, 04:38
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kskumar
kskumar the square will have an area greater than 1 if its perimeter is greater than 4, so rephrase the question:
What's the probability that the longer piece (which by definition is longer than 2.5 and shorter than 5) is longer than 4.
So, analogous question:
If 2.5﹤x﹤5, what's the probability that x﹥4?
*Note: the length of the range between 2.5 and 5 does NOT depend on whether the range is inclusive or exclusive. See page 29 of my book for more on that.
Well, the total range that we'd be happy with is length 1 (between 4 and 5), out of a total possible range of 2.5 (between 2.5 and 5), so the correct answer is 1/2.5. Expand by a factor of 2 and get 2/5.
14 Apr 2022, 05:52
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Hi,
this question really is not that hard.
Given that x is the length of the rope, and we always take the longer piece, we can infer that 2.5<= x < 5.
Now, we have to form the perimeter of a square with x. Perimeter is given by 4a=P with a being one side's length of the sqaure. We know in total:
4a=x
a=x/4
-> 2.5/4 <= x < 5/4
0.625 <= x < 1.25
For A=a^2>1 -> a>1. Our range is approximately 0.6, and less than 0.25 values fulfill our requirement -> approximately 40%
this question really is not that hard.
Given that x is the length of the rope, and we always take the longer piece, we can infer that 2.5<= x < 5.
Now, we have to form the perimeter of a square with x. Perimeter is given by 4a=P with a being one side's length of the sqaure. We know in total:
4a=x
a=x/4
-> 2.5/4 <= x < 5/4
0.625 <= x < 1.25
For A=a^2>1 -> a>1. Our range is approximately 0.6, and less than 0.25 values fulfill our requirement -> approximately 40%
06 Dec 2022, 05:53
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Bookmarks
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
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
