Last visit was: 22 Apr 2026, 03:55 It is currently 22 Apr 2026, 03:55
Home
Messages
Tests
Schools
Events
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
 1   2   3   4   
805+ (Hard)|   Probability|      
User avatar
MisterEko
User avatar
Joined: 25 Oct 2010
Last visit: 04 Jan 2011
Posts: 151
Own Kudos:
1,085
 [173]
Given Kudos: 36
Status:Fighting the beast.
Concentration: Accounting
Schools:Pitt, Oregon, LBS...
GPA: 3.8
Posts: 151
Kudos: 1,085
 [173]
A 5 meter long wire is cut into two pieces. If the longer piece is the Updated on: 04 Feb 2020, 10:08
Originally posted by MisterEko on 17 Dec 2010, 09:23.
Last edited by Bunuel on 04 Feb 2020, 10:08, edited 2 times in total.
Renamed the topic and edited the question.
14
Kudos
Add Kudos
158
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

37% (01:54) correct 63% (02:02) wrong based on 1278 sessions

History

Date
Time
Result
Not Attempted Yet
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

Show Spoiler
OA says it is 2/5 because:

The area of the square will be more than 1 if and only if the longer piece of the wire is longer than 4. To produce such a result, the cutting point has to be either on the first meter of the wire or on its last meter. The probability of this is 2/5 .


I have a question. Since area of the square has to be more than 1, its sides have to be more than 1. If its sides are more than 1, its perimeter will be more than 4. In order for this to happen, a piece larger than 4 meters has to be cut. The smallest piece need would be 4 meters and 1 centimeter (or millimeter for that matter). While I agree that the chance of wire being cut on any of the first 1 meters of it is 2/5, don't we need to calculate the probability of it being cut (at least) at 4 meters and 1 centimeter (or mm)? If so, the probability that it will get cut within first 99 cm is 2*99/500, which comes out to 99/250. This is close to 2/5 yes, but isn't this more correct way to look at it?
:musband

Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
GMAT Club Tests Check Our Products Try Free Tests
ShowHide Answer
Official Answer
E
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,740
Own Kudos:
810,535
 [24]
Given Kudos: 105,817
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,740
Kudos: 810,535
 [24]
A 5 meter long wire is cut into two pieces. If the longer piece is the 10 Nov 2013, 03:40
13
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
SravnaTestPrep
Bunuel
MisterEko

Hm, not sure I understood you (or that you understood my question). What I said is that since the piece cut has to be bigger than 4, even marginally bigger, probability will be slightly less than 2/5. Say we can only count in cm. Wire is 500 cm long. In order for square to have area more than 1 meter, perimeter needs to be at least slightly bigger than 400 cm. In that case, the next least place that wire needs to be cut on (and satisfy the area of a square being bigger than 1) would be on 99th cm (down to the 1st cm) or 401st cm (up to 499). Either way, there are 99 positions on the first meter and 99 on the second one that satisfy the length needed. Since the total is 500 cm, probability would be 2*99/500 or 99/250.

Please, forgive me if I am being nuisance, I am kinda intrigued by this. ;)

OK, let me ask you this: what is the probability that the wire will be cut so that we get pieces of exactly 4m and 1m (so at 1m or at 4m)?

What I'm saying is that the probability that the length of a longer piece will be more than 4 OR more than or equal to 4 is the same and equal to 2/5.

I think the answer 2/5 is flawed. Let us take five points 1, 2, 3, 4 and 5. For the longer wire to be more than or equal to 4m, 2 cases are there, it has to be cut at 1m or before OR 4m or after.

Let us take the first case. For example if it is cut at 1m, the longer wire would be 4m. Assume that each 1m is divided into cms. So there are 99 points out of a total of 500 points when the longer wire can be more than 4 m. for example if it is cut at 99th cm the longer wire would be 401 cm or > 4m. and so on. So there are totally 100 points including the exact 1m point out of a total of 500 points. So the probability that the longer wire is equal to or more than 4m is 100/500=1/5. The other case is wire cut at 4m and above. Each case has a probability of 1/5 so that the overall probability is 2/5.

The above is also equivalent to saying that the shorter wire is <= 1m. That is the probability is 2/5 when the longer wire is 4m and the shorter wire is 1m and say when the longer wire is 4.01 m and the shorter wire is 0.99m and so on . But saying equal to or more than 4m is not equivalent to saying less than 1m but only equivalent to saying less than or equal to 1m.


So when we have the shorter wire to be less than 1m, we have to consider only the cases > 4m. When it has to be more than 4m, the probability will be less than the above or less than 2/5.
Show more

The correct answer is E (2/5).

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

To have an area greater than 1, the side of the square must be greater than 1, and thus the perimeter must be greater than 4, which means that the longer piece must be more than 4 meters. Check the diagram shown below:

-----

If the wire is cut anywhere in the red region, then the longer piece will be more than 4 meters long. The probability of the cut being in the red region is \(\frac{2}{5}\), as there are 2 red regions out of 5 total regions. Therefore, the probability that the area of the square will be more than 1 is \(\frac{2}{5}\).

Answer: E.
User avatar
Kurtosis
User avatar
Current Student
Joined: 13 Apr 2015
Last visit: 10 Nov 2021
Posts: 1,384
Own Kudos:
5,234
 [23]
Given Kudos: 1,228
Location: India
Products:
My Reviews
Posts: 1,384
Kudos: 5,234
 [23]
A 5 meter long wire is cut into two pieces. If the longer piece is the 14 Apr 2016, 20:56
15
Kudos
Add Kudos
7
Bookmarks
Bookmark this Post
Alternate solution:

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
General Discussion
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,740
Own Kudos:
810,535
 [10]
Given Kudos: 105,817
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,740
Kudos: 810,535
 [10]
A 5 meter long wire is cut into two pieces. If the longer piece is the 17 Dec 2010, 10:32
7
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
MisterEko
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 says it is 2/5 because:

The area of the square will be more than 1 if and only if the longer piece of the wire is longer than 4. To produce such a result, the cutting point has to be either on the first meter of the wire or on its last meter. The probability of this is 2/5 .


I have a question. Since area of the square has to be more than 1, its sides have to be more than 1. If its sides are more than 1, its perimeter will be more than 4. In order for this to happen, a piece larger than 4 meters has to be cut. The smallest piece need would be 4 meters and 1 centimeter (or millimeter for that matter). While I agree that the chance of wire being cut on any of the first 1 meters of it is 2/5, don't we need to calculate the probability of it being cut (at least) at 4 meters and 1 centimeter (or mm)? If so, the probability that it will get cut within first 99 cm is 2*99/500, which comes out to 99/250. This is close to 2/5 yes, but isn't this more correct way to look at it?
:musband
Show more

Basically you are saying that the probability should be almost 2/5 but not exactly 2/5, because wire can be cut at 1 or 4 meters exactly and in this case probability will be a little less than 2/5. But this is not true, 1 and 4 meters marks are points and point by definition has no length or any other dimension.

It's similar to the followoing example: the probability that a number X picked from the range (0,5) is more than 4 is 1/5 as well as the probability that a number X picked from the range (0,5) is more than or equal to 4 is also 1/5.

Hope it's clear.
User avatar
MisterEko
User avatar
Joined: 25 Oct 2010
Last visit: 04 Jan 2011
Posts: 151
Own Kudos:
1,085
Given Kudos: 36
Status:Fighting the beast.
Concentration: Accounting
Schools:Pitt, Oregon, LBS...
GPA: 3.8
Posts: 151
Kudos: 1,085
A 5 meter long wire is cut into two pieces. If the longer piece is the 17 Dec 2010, 13:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
MisterEko
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 says it is 2/5 because:

The area of the square will be more than 1 if and only if the longer piece of the wire is longer than 4. To produce such a result, the cutting point has to be either on the first meter of the wire or on its last meter. The probability of this is 2/5 .


I have a question. Since area of the square has to be more than 1, its sides have to be more than 1. If its sides are more than 1, its perimeter will be more than 4. In order for this to happen, a piece larger than 4 meters has to be cut. The smallest piece need would be 4 meters and 1 centimeter (or millimeter for that matter). While I agree that the chance of wire being cut on any of the first 1 meters of it is 2/5, don't we need to calculate the probability of it being cut (at least) at 4 meters and 1 centimeter (or mm)? If so, the probability that it will get cut within first 99 cm is 2*99/500, which comes out to 99/250. This is close to 2/5 yes, but isn't this more correct way to look at it?
:musband

Basically you are saying that the probability should be almost 2/5 but not exactly 2/5, because wire can be cut at 1 or 4 meters exactly and in this case probability will be a little less than 2/5. But this is not true, 1 and 4 meters marks are points and point by definition has no length or any other dimension.

It's similar to the followoing example: the probability that a number X picked from the range (0,5) is more than 4 is 1/5 as well as the probability that a number X picked from the range (0,5) is more than or equal to 4 is also 1/5.

Hope it's clear.
Show more


Hm, not sure I understood you (or that you understood my question). What I said is that since the piece cut has to be bigger than 4, even marginally bigger, probability will be slightly less than 2/5. Say we can only count in cm. Wire is 500 cm long. In order for square to have area more than 1 meter, perimeter needs to be at least slightly bigger than 400 cm. In that case, the next least place that wire needs to be cut on (and satisfy the area of a square being bigger than 1) would be on 99th cm (down to the 1st cm) or 401st cm (up to 499). Either way, there are 99 positions on the first meter and 99 on the second one that satisfy the length needed. Since the total is 500 cm, probability would be 2*99/500 or 99/250.

Please, forgive me if I am being nuisance, I am kinda intrigued by this. ;)
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,740
Own Kudos:
810,535
 [1]
Given Kudos: 105,817
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,740
Kudos: 810,535
 [1]
A 5 meter long wire is cut into two pieces. If the longer piece is the 17 Dec 2010, 13:51
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
MisterEko

Hm, not sure I understood you (or that you understood my question). What I said is that since the piece cut has to be bigger than 4, even marginally bigger, probability will be slightly less than 2/5. Say we can only count in cm. Wire is 500 cm long. In order for square to have area more than 1 meter, perimeter needs to be at least slightly bigger than 400 cm. In that case, the next least place that wire needs to be cut on (and satisfy the area of a square being bigger than 1) would be on 99th cm (down to the 1st cm) or 401st cm (up to 499). Either way, there are 99 positions on the first meter and 99 on the second one that satisfy the length needed. Since the total is 500 cm, probability would be 2*99/500 or 99/250.

Please, forgive me if I am being nuisance, I am kinda intrigued by this. ;)
Show more

OK, let me ask you this: what is the probability that the wire will be cut so that we get pieces of exactly 4m and 1m (so at 1m or at 4m)?

What I'm saying is that the probability that the length of a longer piece will be more than 4 OR more than or equal to 4 is the same and equal to 2/5.
User avatar
MisterEko
User avatar
Joined: 25 Oct 2010
Last visit: 04 Jan 2011
Posts: 151
Own Kudos:
1,085
Given Kudos: 36
Status:Fighting the beast.
Concentration: Accounting
Schools:Pitt, Oregon, LBS...
GPA: 3.8
Posts: 151
Kudos: 1,085
A 5 meter long wire is cut into two pieces. If the longer piece is the 17 Dec 2010, 14:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
MisterEko

Hm, not sure I understood you (or that you understood my question). What I said is that since the piece cut has to be bigger than 4, even marginally bigger, probability will be slightly less than 2/5. Say we can only count in cm. Wire is 500 cm long. In order for square to have area more than 1 meter, perimeter needs to be at least slightly bigger than 400 cm. In that case, the next least place that wire needs to be cut on (and satisfy the area of a square being bigger than 1) would be on 99th cm (down to the 1st cm) or 401st cm (up to 499). Either way, there are 99 positions on the first meter and 99 on the second one that satisfy the length needed. Since the total is 500 cm, probability would be 2*99/500 or 99/250.

Please, forgive me if I am being nuisance, I am kinda intrigued by this. ;)

OK, let me ask you this: what is the probability that the wire will be cut so that we get pieces of exactly 4m and 1m (so at 1m or at 4m)?

What I'm saying is that the probability that the length of a longer piece will be more than 4 OR more than or equal to 4 is the same and equal to 2/5.
Show more

Now I get it. Thank you... Probabilities will always get ya'...
Cheers!
User avatar
ziko
User avatar
Joined: 28 Feb 2012
Last visit: 29 Jan 2014
Posts: 91
Own Kudos:
223
Given Kudos: 17
Concentration: Strategy, International Business
Schools: INSEAD Jan '13
GPA: 3.9
WE:Marketing (Other)
Schools: INSEAD Jan '13
Posts: 91
Kudos: 223
A 5 meter long wire is cut into two pieces. If the longer piece is the 25 Jun 2012, 21:51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Below is OE with the diagram. Was not it displayed on the test?

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

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 red region then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is 2/5 (2 red pieces out of 5).

Answer: E.
Show more

Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.
User avatar
mydreammba
User avatar
Joined: 28 Jul 2011
Last visit: 06 Dec 2013
Posts: 224
Own Kudos:
1,677
Given Kudos: 16
Location: United States
Concentration: International Business, General Management
GPA: 3.86
WE:Accounting (Commercial Banking)
Posts: 224
Kudos: 1,677
A 5 meter long wire is cut into two pieces. If the longer piece is the 26 Jun 2012, 01:27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
Below is OE with the diagram. Was not it displayed on the test?

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

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 red region then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is 2/5 (2 red pieces out of 5).

Answer: E.
Show more


Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,740
Own Kudos:
810,535
 [2]
Given Kudos: 105,817
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,740
Kudos: 810,535
 [2]
A 5 meter long wire is cut into two pieces. If the longer piece is the 26 Jun 2012, 01:52
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
ziko
Bunuel
Below is OE with the diagram. Was not it displayed on the test?

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

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 red region then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is 2/5 (2 red pieces out of 5).

Answer: E.

Thanks Bunuel, thats very good explanation, but could you clarify onemore thing, isn't 2/5 the probability of getting area of the square which equals to 1. Since cutting on any red sides will leave us longer wire with length 4 which is not more than 1 in area but just equal.
Thanks.
Show more

kotela
Hi Bunnel,

One query...

Seeing the figure how can we say that three(Black dashes) sum to length more than 4?
Show more

I think you both do not understand one thing: each dash is 1 meter long. So, again if we cut anywhere at the red region (from 0 to 1 meter or from 4 to 5 meters) then the rest of the wire (longer piece) will be more than 4 meter long.
avatar
prsnt11
avatar
Joined: 02 Mar 2010
Last visit: 04 Sep 2015
Posts: 15
Own Kudos:
35
 [1]
Given Kudos: 16
Posts: 15
Kudos: 35
 [1]
A 5 meter long wire is cut into two pieces. If the longer piece is the 06 Nov 2013, 17:06
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
MisterEko
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 says it is 2/5 because:

The area of the square will be more than 1 if and only if the longer piece of the wire is longer than 4. To produce such a result, the cutting point has to be either on the first meter of the wire or on its last meter. The probability of this is 2/5 .


I have a question. Since area of the square has to be more than 1, its sides have to be more than 1. If its sides are more than 1, its perimeter will be more than 4. In order for this to happen, a piece larger than 4 meters has to be cut. The smallest piece need would be 4 meters and 1 centimeter (or millimeter for that matter). While I agree that the chance of wire being cut on any of the first 1 meters of it is 2/5, don't we need to calculate the probability of it being cut (at least) at 4 meters and 1 centimeter (or mm)? If so, the probability that it will get cut within first 99 cm is 2*99/500, which comes out to 99/250. This is close to 2/5 yes, but isn't this more correct way to look at it?
:musband

Basically you are saying that the probability should be almost 2/5 but not exactly 2/5, because wire can be cut at 1 or 4 meters exactly and in this case probability will be a little less than 2/5. But this is not true, 1 and 4 meters marks are points and point by definition has no length or any other dimension.

It's similar to the followoing example: the probability that a number X picked from the range (0,5) is more than 4 is 1/5 as well as the probability that a number X picked from the range (0,5) is more than or equal to 4 is also 1/5.

Hope it's clear.
Show more

Hey Bunuel,

I'm having hard time understanding your example: "the probability that a number X picked from the range (0,5) is more than 4 is 1/5 as well as the probability that a number X picked from the range (0,5) is more than or equal to 4 is also 1/5."
Basically, I'm getting confused because I think the probability of picking a number from the range (0,5), which I converted to a set {0,1,2,3,4,5}, is 1/6 (6 = total number of terms). So probability of picking a number > 4 is 1/6 (because the only possibility is 5 from the set). But probability of picking up a number >=4 is 2/6 because now two outcomes, 4 and 5, can be considered successful. So, can you kindly let me know where I'm going wrong?
Also, is the probability in the rope = Length of a unit of rope/ Total Length of the rope? Appreciate your help..
Thanks
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,740
Own Kudos:
810,535
Given Kudos: 105,817
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,740
Kudos: 810,535
A 5 meter long wire is cut into two pieces. If the longer piece is the 07 Nov 2013, 05:54
Kudos
Add Kudos
Bookmarks
Bookmark this Post
prsnt11
Bunuel
MisterEko
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 says it is 2/5 because:

The area of the square will be more than 1 if and only if the longer piece of the wire is longer than 4. To produce such a result, the cutting point has to be either on the first meter of the wire or on its last meter. The probability of this is 2/5 .


I have a question. Since area of the square has to be more than 1, its sides have to be more than 1. If its sides are more than 1, its perimeter will be more than 4. In order for this to happen, a piece larger than 4 meters has to be cut. The smallest piece need would be 4 meters and 1 centimeter (or millimeter for that matter). While I agree that the chance of wire being cut on any of the first 1 meters of it is 2/5, don't we need to calculate the probability of it being cut (at least) at 4 meters and 1 centimeter (or mm)? If so, the probability that it will get cut within first 99 cm is 2*99/500, which comes out to 99/250. This is close to 2/5 yes, but isn't this more correct way to look at it?
:musband

Basically you are saying that the probability should be almost 2/5 but not exactly 2/5, because wire can be cut at 1 or 4 meters exactly and in this case probability will be a little less than 2/5. But this is not true, 1 and 4 meters marks are points and point by definition has no length or any other dimension.

It's similar to the followoing example: the probability that a number X picked from the range (0,5) is more than 4 is 1/5 as well as the probability that a number X picked from the range (0,5) is more than or equal to 4 is also 1/5.

Hope it's clear.

Hey Bunuel,

I'm having hard time understanding your example: "the probability that a number X picked from the range (0,5) is more than 4 is 1/5 as well as the probability that a number X picked from the range (0,5) is more than or equal to 4 is also 1/5."
Basically, I'm getting confused because I think the probability of picking a number from the range (0,5), which I converted to a set {0,1,2,3,4,5}, is 1/6 (6 = total number of terms). So probability of picking a number > 4 is 1/6 (because the only possibility is 5 from the set). But probability of picking up a number >=4 is 2/6 because now two outcomes, 4 and 5, can be considered successful. So, can you kindly let me know where I'm going wrong?
Also, is the probability in the rope = Length of a unit of rope/ Total Length of the rope? Appreciate your help..
Thanks
Show more

Why do you consider only integers? The numbers from 0 to 5 consists of ALL numbers from 0 to 5, not only of integers.
avatar
prsnt11
avatar
Joined: 02 Mar 2010
Last visit: 04 Sep 2015
Posts: 15
Own Kudos:
35
Given Kudos: 16
Posts: 15
Kudos: 35
A 5 meter long wire is cut into two pieces. If the longer piece is the 07 Nov 2013, 11:14
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hey Bunuel,

I'm having hard time understanding your example: "the probability that a number X picked from the range (0,5) is more than 4 is 1/5 as well as the probability that a number X picked from the range (0,5) is more than or equal to 4 is also 1/5."
Basically, I'm getting confused because I think the probability of picking a number from the range (0,5), which I converted to a set {0,1,2,3,4,5}, is 1/6 (6 = total number of terms). So probability of picking a number > 4 is 1/6 (because the only possibility is 5 from the set). But probability of picking up a number >=4 is 2/6 because now two outcomes, 4 and 5, can be considered successful. So, can you kindly let me know where I'm going wrong?
Also, is the probability in the rope = Length of a unit of rope/ Total Length of the rope? Appreciate your help..
Thanks[/quote]

Why do you consider only integers? The numbers from 0 to 5 consists of ALL numbers from 0 to 5, not only of integers.[/quote]

Thanks for your prompt help. But I'm still confused Bunuel! :( There are infinite real numbers between 0 & 5, so how did we get 1/5 as the probability? I'm unable to visualize this problem. Can you kindly explain it to me in terms of successful outcomes/total outcomes? Thanks for your help...
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,740
Own Kudos:
810,535
 [2]
Given Kudos: 105,817
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,740
Kudos: 810,535
 [2]
A 5 meter long wire is cut into two pieces. If the longer piece is the 07 Nov 2013, 11:41
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
prsnt11

Thanks for your prompt help. But I'm still confused Bunuel! :( There are infinite real numbers between 0 & 5, so how did we get 1/5 as the probability? I'm unable to visualize this problem. Can you kindly explain it to me in terms of successful outcomes/total outcomes? Thanks for your help...
Show more

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

Hope it's clear.
User avatar
SVaidyaraman
User avatar
Joined: 17 Dec 2012
Last visit: 11 Jul 2025
Posts: 566
Own Kudos:
1,833
 [1]
Given Kudos: 20
Location: India
Expert
Expert reply
Posts: 566
Kudos: 1,833
 [1]
A 5 meter long wire is cut into two pieces. If the longer piece is the 09 Nov 2013, 22:07
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
MisterEko

Hm, not sure I understood you (or that you understood my question). What I said is that since the piece cut has to be bigger than 4, even marginally bigger, probability will be slightly less than 2/5. Say we can only count in cm. Wire is 500 cm long. In order for square to have area more than 1 meter, perimeter needs to be at least slightly bigger than 400 cm. In that case, the next least place that wire needs to be cut on (and satisfy the area of a square being bigger than 1) would be on 99th cm (down to the 1st cm) or 401st cm (up to 499). Either way, there are 99 positions on the first meter and 99 on the second one that satisfy the length needed. Since the total is 500 cm, probability would be 2*99/500 or 99/250.

Please, forgive me if I am being nuisance, I am kinda intrigued by this. ;)

OK, let me ask you this: what is the probability that the wire will be cut so that we get pieces of exactly 4m and 1m (so at 1m or at 4m)?

What I'm saying is that the probability that the length of a longer piece will be more than 4 OR more than or equal to 4 is the same and equal to 2/5.
Show more

I think the answer 2/5 is flawed. Let us take five points 1, 2, 3, 4 and 5. For the longer wire to be more than or equal to 4m, 2 cases are there, it has to be cut at 1m or before OR 4m or after.

Let us take the first case. For example if it is cut at 1m, the longer wire would be 4m. Assume that each 1m is divided into cms. So there are 99 points out of a total of 500 points when the longer wire can be more than 4 m. for example if it is cut at 99th cm the longer wire would be 401 cm or > 4m. and so on. So there are totally 100 points including the exact 1m point out of a total of 500 points. So the probability that the longer wire is equal to or more than 4m is 100/500=1/5. The other case is wire cut at 4m and above. Each case has a probability of 1/5 so that the overall probability is 2/5.

The above is also equivalent to saying that the shorter wire is <= 1m. That is the probability is 2/5 when the longer wire is 4m and the shorter wire is 1m and say when the longer wire is 4.01 m and the shorter wire is 0.99m and so on . But saying equal to or more than 4m is not equivalent to saying less than 1m but only equivalent to saying less than or equal to 1m.


So when we have the shorter wire to be less than 1m, we have to consider only the cases > 4m. When it has to be more than 4m, the probability will be less than the above or less than 2/5.
User avatar
phammanhhiep
User avatar
Joined: 06 May 2013
Last visit: 02 Apr 2014
Posts: 9
Own Kudos:
36
Given Kudos: 2
Location: United States
GMAT 1: 700 Q49 V36
GMAT 1: 700 Q49 V36
Posts: 9
Kudos: 36
A 5 meter long wire is cut into two pieces. If the longer piece is the 26 Nov 2013, 19:03
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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:
Show Spoiler
E

That the area of the square is more than 1 square meter means that the perimeter of the square is more than 4 meter. Imagine the wire is divided into 5 pieces:
0__1__2__3__4__5

I see that if we cut the wire at any point from 0 to 1 or any point from 4 to 5, we will have a long wire whose perimeter is more than 4 meter.
If we cut the wire at any point from 1 to 4, we get a long wire whose perimeter is less than 4 meter.

Undoubtedly, we have 3 choices if we cut the wire: from 0 to 1, from 1 to 4, and from 4 to 5. Following this reasoning, I think the probability that the area of the square will be more than 1 if the original wire was cut at an arbitrary point should be 2/3.

Please explain what is wrong with my explanation?
User avatar
WillEconomistGMAT
User avatar
Economist GMAT Tutor Instructor
Joined: 01 Oct 2013
Last visit: 19 Dec 2013
Posts: 58
Own Kudos:
193
 [1]
Given Kudos: 7
Expert
Expert reply
Posts: 58
Kudos: 193
 [1]
A 5 meter long wire is cut into two pieces. If the longer piece is the 26 Nov 2013, 21:57
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Your explanation is close, but take another look at your suggested cuts.

If we divide the potential cuts into 0 to 1, 1 to 4, and 4 to 5, we have a 1:3:1 ratio where either end will give us the square with area >1.

Add up the parts to get 5, 2 of which are successful outcomes, and you get a probability of 2/5.
User avatar
yezz
User avatar
Retired Moderator
Joined: 05 Jul 2006
Last visit: 26 Apr 2022
Posts: 830
Own Kudos:
1,686
 [1]
Given Kudos: 49
Posts: 830
Kudos: 1,686
 [1]
A 5 meter long wire is cut into two pieces. If the longer piece is the 25 Sep 2016, 01:13
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
I would very much appreciate if someone can point out the flaw in my logic

the line is cut into 2 pieces ....x , 5-x

assuming x is the larger piece then x>2.5....... ( the larger piece)

side of square = x/4 , area of square = x^2/16 , question is to test x^2/16>1

we get ............-4................4.............. the inequality is true in the ranges x<-4 and x>4 but we have a restriction that x>2.5 thus x>4

thus 4<x<5 , thus probability = (5-4)/5 = 1/5 ............Bunuel where am i going wrong if you plz.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 22 Apr 2026
Posts: 109,740
Own Kudos:
810,535
Given Kudos: 105,817
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 109,740
Kudos: 810,535
A 5 meter long wire is cut into two pieces. If the longer piece is the 25 Sep 2016, 02:55
Kudos
Add Kudos
Bookmarks
Bookmark this Post
yezz
I would very much appreciate if someone can point out the flaw in my logic

the line is cut into 2 pieces ....x , 5-x

assuming x is the larger piece then x>2.5....... ( the larger piece)

side of square = x/4 , area of square = x^2/16 , question is to test x^2/16>1

we get ............-4................4.............. the inequality is true in the ranges x<-4 and x>4 but we have a restriction that x>2.5 thus x>4

thus 4<x<5 , thus probability = (5-4)/5 = 1/5 ............Bunuel where am i going wrong if you plz.
Show more

What if 5-x is larger piece and not x. In this case you'd have (5 - x)^2/16 > 1 giving x < 1.
User avatar
goforgmat
User avatar
Joined: 09 Feb 2015
Last visit: 02 Nov 2019
Posts: 235
Own Kudos:
108
 [1]
Given Kudos: 232
Location: India
Concentration: Social Entrepreneurship, General Management
Schools: Booth '21 (D) Cambridge "21 (D) LBS '22 (D)
GMAT 1: 690 Q49 V34
GMAT 2: 720 Q49 V39
GPA: 2.8
Products:
My Reviews
Schools: Booth '21 (D) Cambridge "21 (D) LBS '22 (D)
GMAT 2: 720 Q49 V39
Posts: 235
Kudos: 108
 [1]
A 5 meter long wire is cut into two pieces. If the longer piece is the 19 May 2017, 00:58
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
SravnaTestPrep
Bunuel


OK, let me ask you this: what is the probability that the wire will be cut so that we get pieces of exactly 4m and 1m (so at 1m or at 4m)?

What I'm saying is that the probability that the length of a longer piece will be more than 4 OR more than or equal to 4 is the same and equal to 2/5.

I think the answer 2/5 is flawed. Let us take five points 1, 2, 3, 4 and 5. For the longer wire to be more than or equal to 4m, 2 cases are there, it has to be cut at 1m or before OR 4m or after.

Let us take the first case. For example if it is cut at 1m, the longer wire would be 4m. Assume that each 1m is divided into cms. So there are 99 points out of a total of 500 points when the longer wire can be more than 4 m. for example if it is cut at 99th cm the longer wire would be 401 cm or > 4m. and so on. So there are totally 100 points including the exact 1m point out of a total of 500 points. So the probability that the longer wire is equal to or more than 4m is 100/500=1/5. The other case is wire cut at 4m and above. Each case has a probability of 1/5 so that the overall probability is 2/5.

The above is also equivalent to saying that the shorter wire is <= 1m. That is the probability is 2/5 when the longer wire is 4m and the shorter wire is 1m and say when the longer wire is 4.01 m and the shorter wire is 0.99m and so on . But saying equal to or more than 4m is not equivalent to saying less than 1m but only equivalent to saying less than or equal to 1m.


So when we have the shorter wire to be less than 1m, we have to consider only the cases > 4m. When it has to be more than 4m, the probability will be less than the above or less than 2/5.

The correct answer is E (2/5).

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

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 red region then the rest of the wire (longer piece) will be more than 4 meter long. The probability of that is 2/5 (2 red pieces out of 5).

Answer: E.
Show more

Why do we consider the 1st and 2d red region as two separate instances. the rope doesn't have two distinct ends right? Cut at region 1 or region 2 it gives the same result.
 1   2   3   4   
Moderators:
Bunuel
Math Expert
109740 posts
Krunaal
Tuck School Moderator
853 posts