December 13, 2018 December 13, 2018 08:00 AM PST 09:00 AM PST What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL. December 14, 2018 December 14, 2018 09:00 AM PST 10:00 AM PST 10 Questions will be posted on the forum and we will post a reply in this Topic with a link to each question. There are prizes for the winners.
Author 
Message 
TAGS:

Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
25 Sep 2016, 01:55



Senior Manager
Joined: 09 Feb 2015
Posts: 358
Location: India
Concentration: Social Entrepreneurship, General Management
GMAT 1: 690 Q49 V34 GMAT 2: 720 Q49 V39
GPA: 2.8

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
18 May 2017, 23:58
Bunuel wrote: SravnaTestPrep wrote: Bunuel wrote: 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. 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.



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
19 May 2017, 00:15



Senior Manager
Joined: 03 Apr 2013
Posts: 275
Location: India
Concentration: Marketing, Finance
GPA: 3

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
06 Jul 2017, 01:01
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? Got the answer as 2/5. What I'm wondering is that is it a GMAT question? Bunuel please answer
_________________
Spread some love..Like = +1 Kudos



Math Expert
Joined: 02 Sep 2009
Posts: 51121

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
06 Jul 2017, 01:05
ShashankDave 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? Got the answer as 2/5. What I'm wondering is that is it a GMAT question? Bunuel please answer ________________ I don't see why not.
_________________
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



Director
Joined: 13 Mar 2017
Posts: 664
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
06 Jul 2017, 01:17
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? Area of the square > 1. so, Side >1. so, perimeter > 4. Now we need to think of cutting the wire such that the larger piece of wire has a length > 1. So, lets put a wire of 5 m length and measure it from left. Required condition is possible only if it is cut before 1 m mark or after 4 m mark. It should not be cut between 1 m mark to 4 m mark It can be represented as below. ______1______2______3______4 _______5So, required probability = 2/5. Answer E.
_________________
CAT 2017 99th percentiler : VA 97.27  DILR 96.84  QA 98.04  OA 98.95 UPSC Aspirants : Get my app UPSC Important News Reader from Play store.
MBA Social Network : WebMaggu
Appreciate by Clicking +1 Kudos ( Lets be more generous friends.) What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".



Intern
Joined: 09 Jun 2016
Posts: 22

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
05 Dec 2017, 21:49
Senthil1981 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
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 If the side is x/4, the area will be (\(x^2\))/16 and not (\(x^2\))/4
_________________
.................................................................................................................. microlevel speed, macrolevel patience  KUDOS for the post ,shall be appreciated the most



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13064
Location: United States (CA)

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
22 Jan 2018, 15:26
Hi All, This question is vaguely worded in spots, but I've offered an explanation that matches the 'intent' of the question. There's an aspect to this question that many Test Takers would miss: regardless of where on the wire the 'cut' is made, the 'longer' piece is the one that's used to make the square. Thus, unless you cut the wire exactly in the middle, there are will always be two versions of each measure. For example... if you cut the wire at the 1m "mark", you'll have a 1m piece and a 4m piece if you cut the wire at the 4m "mark", you'll also have a 1m piece and a 4m piece Since area of a square is (side)^2, for the area to be GREATER than 1 m^2, the side lengths have to be GREATER than 1. By extension, this means that the perimeter would have to be GREATER than 4. Thus, any cut that produces a longer piece that is greater than 4m will satisfy what this question is asking for... Cutting LESS than 1m will do it. Cutting MORE than 4m will also do it. That's approximately 2m of a 5m wire... 2/5 Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****



Director
Joined: 31 Jul 2017
Posts: 504
Location: Malaysia
GPA: 3.95
WE: Consulting (Energy and Utilities)

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
22 Jan 2018, 19:04
[quote="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 Good Question. Let the two parts cut be a & b. Now, \(a + b =5.\) Given, square is formed with greater side (Suppose a). So,\(a = 4s\) (S is the side of each square). The question is asking for \(S^2 > 1\) or \(a^2/16 > 1\) which means \(4<a<5\). Now, this wire can be cut from 1 to 2 or from 4 to 5, hence two possibilities.. i.e. \(2/5\)
_________________
If my Post helps you in Gaining Knowledge, Help me with KUDOS.. !!



Intern
Joined: 09 Jun 2016
Posts: 10
GMAT 1: 710 Q48 V39 GMAT 2: 730 Q49 V39

A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
12 Sep 2018, 11:10
I guess there is a lot of confusion about this question. My 2 cents of the solution ( hope it helps)
If area > 1 means, each side of a square > 1 which means that perimeter has to be greater than 4.
Now coming to the 2 lengths of the wire to be cut. Let us count the possibilities first.
Lengths of wires greater than 4 meters can be cut from either end 1 or end 2 = 2 ways point 1 or The wire can be cut from midpoint i.e 2.5 meters each = 1 way or Wire length could be between 2.5 m to 4 mts from either end 1 or end 2 = 2 ways
So effectively, the total number of ways to cut the wire = 5 ways point 2
So the probability of having lengths greater than 4 mts = 2 / 5. from points 1 and 2.



Manager
Joined: 06 Sep 2018
Posts: 172
Location: Pakistan
Concentration: Finance, Operations
GPA: 2.87
WE: Engineering (Other)

Re: A 5 meter long wire is cut into two pieces. If the longer
[#permalink]
Show Tags
08 Oct 2018, 21:20
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? :musband highlighted part is not clear as there is no unit mentioned with 1. it could be 1cm^2 or 1m^2
_________________
Hitting Kudos is the best way of appreciation.
Eric Thomas, "When you want to succeed as bad as you want to breathe, then you'll be successful."




Re: A 5 meter long wire is cut into two pieces. If the longer &nbs
[#permalink]
08 Oct 2018, 21:20



Go to page
Previous
1 2
[ 31 posts ]



