Last visit was: 23 May 2024, 05:58 It is currently 23 May 2024, 05:58
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Math Expert
Joined: 02 Sep 2009
Posts: 93417
Own Kudos [?]: 626030 [41]
Given Kudos: 81940
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 93417
Own Kudos [?]: 626030 [14]
Given Kudos: 81940
Send PM
General Discussion
avatar
Manager
Manager
Joined: 28 Aug 2013
Posts: 59
Own Kudos [?]: 80 [2]
Given Kudos: 23
Location: India
Concentration: Operations, Marketing
GMAT Date: 08-28-2014
GPA: 3.86
WE:Supply Chain Management (Manufacturing)
Send PM
Math Expert
Joined: 02 Sep 2009
Posts: 93417
Own Kudos [?]: 626030 [4]
Given Kudos: 81940
Send PM
Re: M14-17 [#permalink]
2
Kudos
2
Bookmarks
Expert Reply
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).


Answer: E


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.
avatar
Intern
Intern
Joined: 20 Sep 2015
Posts: 2
Own Kudos [?]: 8 [2]
Given Kudos: 28
Send PM
Re: M14-17 [#permalink]
2
Bookmarks
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.
Intern
Intern
Joined: 11 Jun 2014
Status:CFA Charterholder
Posts: 15
Own Kudos [?]: 10 [0]
Given Kudos: 9
Location: Turkey
GMAT 1: 720 Q50 V37
WE:Research (Investment Banking)
Send PM
Re: M14-17 [#permalink]
I think this is a high-quality question and I agree with explanation. nice question.. its tricky
Manager
Manager
Joined: 16 Jan 2013
Posts: 66
Own Kudos [?]: 21 [0]
Given Kudos: 1323
Location: Bangladesh
GMAT 1: 490 Q41 V18
GMAT 2: 610 Q45 V28
GPA: 2.75
Send PM
Re: M14-17 [#permalink]
Excellent question!
Current Student
Joined: 01 Aug 2017
Posts: 6
Own Kudos [?]: 5 [0]
Given Kudos: 87
Location: India
Schools: ISB '23 (A)
GMAT 1: 700 Q49 V35
GPA: 3.7
Send PM
Re: M14-17 [#permalink]
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.
Intern
Intern
Joined: 28 Mar 2017
Posts: 4
Own Kudos [?]: 0 [0]
Given Kudos: 45
Send PM
Re: M14-17 [#permalink]
I think this is a high-quality question and I agree with explanation.
Manager
Manager
Joined: 09 Nov 2018
Posts: 68
Own Kudos [?]: 46 [0]
Given Kudos: 222
Schools: ISB '21 (A)
Send PM
Re: M14-17 [#permalink]
I think this is a high-quality question and I agree with explanation.
Intern
Intern
Joined: 18 Jul 2022
Posts: 6
Own Kudos [?]: 3 [2]
Given Kudos: 129
Location: India
Send PM
Re: M14-17 [#permalink]
2
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
Math Expert
Joined: 02 Sep 2009
Posts: 93417
Own Kudos [?]: 626030 [0]
Given Kudos: 81940
Send PM
Re: M14-17 [#permalink]
Expert Reply
I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
User avatar
Intern
Intern
Joined: 25 Apr 2024
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 4
Location: Korea,Republic of
Send PM
M14-17 [#permalink]
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..).

Can anyone answer my question?

Thanks.­
Math Expert
Joined: 02 Sep 2009
Posts: 93417
Own Kudos [?]: 626030 [1]
Given Kudos: 81940
Send PM
Re: M14-17 [#permalink]
1
Kudos
Expert Reply
 
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..).

Can anyone answer my question?

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.
GMAT Club Bot
Re: M14-17 [#permalink]
Moderator:
Math Expert
93417 posts