January 19, 2019 January 19, 2019 07:00 AM PST 09:00 AM PST Aiming to score 760+? Attend this FREE session to learn how to Define your GMAT Strategy, Create your Study Plan and Master the Core Skills to excel on the GMAT. January 20, 2019 January 20, 2019 07:00 AM PST 07:00 AM PST Get personalized insights on how to achieve your Target Quant Score.
Author 
Message 
TAGS:

Hide Tags

Manager
Status: Fighting the beast.
Joined: 25 Oct 2010
Posts: 166
Schools: Pitt, Oregon, LBS...

A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
Updated on: 14 Apr 2016, 19:41
Question Stats:
39% (01:12) correct 61% (01:35) wrong based on 454 sessions
HideShow timer Statistics
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?
Official Answer and Stats are available only to registered users. Register/ Login.
_________________
[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight] http://gmatclub.com/forum/massivecollectionofverbalquestionsscrcandcr106195.html#p832142
[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001dsquestionsfile106193.html#p832133
Originally posted by MisterEko on 17 Dec 2010, 08:23.
Last edited by Vyshak on 14 Apr 2016, 19:41, edited 1 time in total.
OA and OE are now hidden




Math Expert
Joined: 02 Sep 2009
Posts: 52285

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
10 Nov 2013, 02:40
SravnaTestPrep wrote: Bunuel wrote: MisterEko wrote: 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. 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Math Expert
Joined: 02 Sep 2009
Posts: 52285

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
17 Dec 2010, 09:32
MisterEko wrote: 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? 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Status: Fighting the beast.
Joined: 25 Oct 2010
Posts: 166
Schools: Pitt, Oregon, LBS...

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
17 Dec 2010, 12:43
Bunuel wrote: MisterEko wrote: 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? 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. 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.
_________________
[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight] http://gmatclub.com/forum/massivecollectionofverbalquestionsscrcandcr106195.html#p832142
[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001dsquestionsfile106193.html#p832133



Math Expert
Joined: 02 Sep 2009
Posts: 52285

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
17 Dec 2010, 12:51
MisterEko wrote: 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.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Status: Fighting the beast.
Joined: 25 Oct 2010
Posts: 166
Schools: Pitt, Oregon, LBS...

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
17 Dec 2010, 13:03
Bunuel wrote: MisterEko wrote: 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. Now I get it. Thank you... Probabilities will always get ya'... Cheers!
_________________
[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight] http://gmatclub.com/forum/massivecollectionofverbalquestionsscrcandcr106195.html#p832142
[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight] http://gmatclub.com/forum/1001dsquestionsfile106193.html#p832133



Intern
Joined: 02 Mar 2010
Posts: 19

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
06 Nov 2013, 16:06
Bunuel wrote: MisterEko wrote: 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? 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



Math Expert
Joined: 02 Sep 2009
Posts: 52285

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
07 Nov 2013, 04:54
prsnt11 wrote: Bunuel wrote: MisterEko wrote: 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? 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 Why do you consider only integers? The numbers from 0 to 5 consists of ALL numbers from 0 to 5, not only of integers.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 02 Mar 2010
Posts: 19

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
07 Nov 2013, 10:14
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...



Math Expert
Joined: 02 Sep 2009
Posts: 52285

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
07 Nov 2013, 10:41



Intern
Joined: 26 Feb 2012
Posts: 14
Concentration: Strategy, International Business

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
09 Nov 2013, 12:54
Bunuel wrote: prsnt11 wrote: 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... 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. Hi, Two comments: 1 Can sbdy please edit the question so that OA is not spoiled? 2 I don't agree with OA = 2/5, since question says that we use the longer side to create the square. Therefore no distinction is made between the "two" sides of the rope. Only the longer side is considered for our purpose. What I am saying is that I would pick 1/5 as the answer.



Director
Joined: 17 Dec 2012
Posts: 625
Location: India

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
09 Nov 2013, 21:07
Bunuel wrote: MisterEko wrote: 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.
_________________
Srinivasan Vaidyaraman Sravna Holistic Solutions http://www.sravnatestprep.com
Holistic and Systematic Approach



Intern
Joined: 06 May 2013
Posts: 13
Location: United States

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
26 Nov 2013, 18:03
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: 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?



Economist GMAT Tutor Instructor
Joined: 01 Oct 2013
Posts: 68

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
26 Nov 2013, 20:57
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.
_________________
Economist GMAT Tutor http://econgm.at/econgmat (866) 2920660



Math Expert
Joined: 02 Sep 2009
Posts: 52285

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
27 Nov 2013, 00:50
phammanhhiep wrote: 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: 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? Merging similar topics. Please search before posting.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 26 Mar 2013
Posts: 20
Location: India
Concentration: Finance, Strategy

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
17 Jan 2015, 12:00
2/5
Need > 4 meter
and cutting the 5 m wire from 01m & 45 m gives us the lengthy wire to be >4m
p = (1m+1m)/5m = 2/5



Intern
Joined: 26 Mar 2013
Posts: 20
Location: India
Concentration: Finance, Strategy

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
17 Jan 2015, 12:02
Good question...initially didnt consider the other side of thread so got 1/5....but soon realized the missing part



SC Moderator
Joined: 13 Apr 2015
Posts: 1687
Location: India
Concentration: Strategy, General Management
GPA: 4
WE: Analyst (Retail)

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
14 Apr 2016, 19:56
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



Senior Manager
Joined: 23 Apr 2015
Posts: 302
Location: United States
Concentration: General Management, International Business
WE: Engineering (Consulting)

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
24 Aug 2016, 21:58
MisterEko wrote: 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
Let the place where the rope is cut be \(x\) and it's used to form a square with \(x\) as perimeter and hence side is \(\frac{x}{4}\) and Area =\(\frac{x^2}{4}\) The area should be more than 1 so \(x^2/4 > 1\) , so \(x^2 > 4\) giving \(x > 2\). Out the places where it can be cut, 1,2,3,4 , 3 and 4 are above 2, so \(\frac{2}{5}\) Answer is E



Retired Moderator
Joined: 05 Jul 2006
Posts: 1722

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
25 Sep 2016, 00:13
I would very much appreciate if someone can point out the flaw in my logic
the line is cut into 2 pieces ....x , 5x
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 = (54)/5 = 1/5 ............Bunuel where am i going wrong if you plz.




Re: A 5 meter long wire is cut into two pieces. If the longer &nbs
[#permalink]
25 Sep 2016, 00:13



Go to page
1 2
Next
[ 31 posts ]



