Author 
Message 
TAGS:

Hide Tags

Manager
Status: GMAT in 4 weeks
Joined: 28 Mar 2010
Posts: 147
GPA: 3.89

Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
21 May 2011, 23:51
Question Stats:
22% (02:39) correct 78% (02:21) wrong based on 997 sessions
HideShow timer Statistics
Twenty meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area? (A) 2√2 (B) 2√5 (C) 5 (D) 4√2 (E) none of these **************************** IIM CAT Level Question ****************************
Official Answer and Stats are available only to registered users. Register/ Login.




Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10113
Location: Pune, India

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
24 May 2011, 19:37
You don't need derivatives in CAT either! Anyway, we can solve it either by plugging in numbers or by using this concept: If the sum of given numbers is constant, their product is maximum when they are equal. Given: \(2r + (\frac{Q}{2pi})*2*pi*r = 20\) i.e. \(2r + Qr = 20\) Maximize \((\frac{Q}{2pi})*pi*r^2 = \frac{Qr^2}{2}\) Now \(Qr = 20  2r\) from above. So, Maximize \((202r)r/2 = (10  r)r\) Since \(10  r + r = 10\), to maximize product, \(10  r = r\) i.e. \(r = 5\)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Current Student
Joined: 26 May 2005
Posts: 437

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
22 May 2011, 00:01
hussi9 wrote: Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?
(1) 2√2 (2) 2√5 (3) 5 (4) 4√2 (5) none of these
**************************** IIM CAT Level Question **************************** Requires knowledge of Mensuration and Max/min differenciation which not tested on GMAT. Not sure of any other method Sector of a circle = 2l+r 2r+l = 20 ; l= 20 2r Area = 1/2lr = 1/2*(202r)*r = 10rr^2 Differenciation: dA/dX= 10 2r 102r=0 hence r= 5




Director
Status: Everyone is a leader. Just stop listening to others.
Joined: 22 Mar 2013
Posts: 691
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
21 Aug 2013, 07:16
I know a concept that for a given perimeter equilateral triangle gives maximum area, so this sector must be similar to an equilateral triangle with sides 20/3 = 6.66, it means radius should be less than 6, in answer choices 5 is given so it is the nearest possible sector, other choices are not even around 6.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10113
Location: Pune, India

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
23 Oct 2013, 04:06
SaraLotfy wrote: VeritasPrepKarishma wrote: You don't need derivatives in CAT either! Anyway, we can solve it either by plugging in numbers or by using this concept: If the sum of given numbers is constant, their product is maximum when they are equal.
Given: \(2r + (\frac{Q}{2pi})*2*pi*r = 20\) i.e. \(2r + Qr = 20\)
Maximize \((\frac{Q}{2pi})*pi*r^2 = \frac{Qr^2}{2}\) Now \(Qr = 20  2r\) from above. So, Maximize \((202r)r/2 = (10  r)r\) Since \(10  r + r = 10\), to maximize product, \(10  r = r\) i.e. \(r = 5\) Thanks Karishma for your explanation. I need to clarify one more small point. The length of the arc = 2*pi*r * (Q/360) for which Q is the enclosed central angle between the 2 radii. I noticed that you computed (Q/360) as (Q/2pi). I must be missing something behind this logic, but why do we use Q/2pi here? There are 2 different units in which you can measure angles  degrees and radians. In radians, pi = 180 degrees so 2*pi = 360 degrees. So we can use the formula as 2*pi*r * (Q/360) if Q is in degrees and as 2*pi*r * (Q/2*pi) if Q is in radians. If we don't have the value of Q, we can choose to use either depending on what will make it easier for us. Here, 2*pi makes more sense because pi gets canceled.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Status: GMAT in 4 weeks
Joined: 28 Mar 2010
Posts: 147
GPA: 3.89

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
21 May 2011, 23:54
Area of Sector, A = x/360*pi*r^2
Circumference of the sector = 20 => x/360*2*pi*r +2r= 20 => 2A/r+2r=20 => A= r(10r) = r10r^2
We will now max using derivations
A`=102r
Max value of A will found at A`=0 i.e 102r=0 r=5
=> Choice (3) is the right answer



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10113
Location: Pune, India

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
17 Sep 2013, 04:41
holidevil wrote: VeritasPrepKarishma wrote: You don't need derivatives in CAT either! Anyway, we can solve it either by plugging in numbers or by using this concept: If the sum of given numbers is constant, their product is maximum when they are equal.
Given: \(2r + (\frac{Q}{2pi})*2*pi*r = 20\) i.e. \(2r + Qr = 20\)
Maximize \((\frac{Q}{2pi})*pi*r^2 = \frac{Qr^2}{2}\) Now \(Qr = 20  2r\) from above. So, Maximize \((202r)r/2 = (10  r)r\) Since \(10  r + r = 10\), to maximize product, \(10  r = r\) i.e. \(r = 5\) Can anyone tell me how one obtained this eq. \(2r + (\frac{Q}{2pi})*2*pi*r = 20\)? What is a sector of a circle? It looks like a slice of pizza. Its circumference will be given by Radius + Length of the arc + Radius Length of the arc =\((\frac{Q}{2pi})*2*pi*r\) i.e. it is a fraction of the circumference of the complete circle. Q is the angle the arc makes at the center. Since the rope will be used along the circumference of the sector, the circumference of the sector can be at most equal to the length of the rope i.e. 20 \(r + r + (\frac{Q}{2pi})*2*pi*r = 20\)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



SVP
Status: Nothing comes easy: neither do I want.
Joined: 12 Oct 2009
Posts: 2461
Location: Malaysia
Concentration: Technology, Entrepreneurship
GMAT 1: 670 Q49 V31 GMAT 2: 710 Q50 V35

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
22 May 2011, 00:24
max , min can be tested. But the gmat wont expect you to use calculus. So by simple methods you should be able to get the max value. eg A = 10rr^2 = 2.5.r  r^2  25 + 25 = 25  (r5)^2 => max only when r = 5
_________________
Fight for your dreams : For all those who fear from Verbal lets give it a fightMoney Saved is the Money Earned Jo Bole So Nihaal , Sat Shri Akaal Support GMAT Club by putting a GMAT Club badge on your blog/Facebook GMAT Club Premium Membership  big benefits and savingsGmat test review : http://gmatclub.com/forum/670to710alongjourneywithoutdestinationstillhappy141642.html



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10113
Location: Pune, India

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
22 Oct 2013, 20:42
SaraLotfy wrote: VeritasPrepKarishma wrote: You don't need derivatives in CAT either! Anyway, we can solve it either by plugging in numbers or by using this concept: If the sum of given numbers is constant, their product is maximum when they are equal.
Given: \(2r + (\frac{Q}{2pi})*2*pi*r = 20\) i.e. \(2r + Qr = 20\)
Maximize \((\frac{Q}{2pi})*pi*r^2 = \frac{Qr^2}{2}\) Now \(Qr = 20  2r\) from above. So, Maximize \((202r)r/2 = (10  r)r\) Since \(10  r + r = 10\), to maximize product, \(10  r = r\) i.e. \(r = 5\) Hello Karishma Can I assume that the max surface area will be reached in a 90 degree sector? since the biggest sector that can be reached is a right angle, if it exceeds 90, would it still be called a sector? Yes, it is still a sector even if the angle exceeds 90. The angle could even go up to almost 360 though we usually deal with minor sectors i.e. when the angle is less than 180. So we cannot assume that the maximum surface area will be reached in a 90 degree sector.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Joined: 24 Apr 2013
Posts: 50
Location: United States

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
23 Oct 2013, 00:47
VeritasPrepKarishma wrote: You don't need derivatives in CAT either! Anyway, we can solve it either by plugging in numbers or by using this concept: If the sum of given numbers is constant, their product is maximum when they are equal.
Given: \(2r + (\frac{Q}{2pi})*2*pi*r = 20\) i.e. \(2r + Qr = 20\)
Maximize \((\frac{Q}{2pi})*pi*r^2 = \frac{Qr^2}{2}\) Now \(Qr = 20  2r\) from above. So, Maximize \((202r)r/2 = (10  r)r\) Since \(10  r + r = 10\), to maximize product, \(10  r = r\) i.e. \(r = 5\) Thanks Karishma for your explanation. I need to clarify one more small point. The length of the arc = 2*pi*r * (Q/360) for which Q is the enclosed central angle between the 2 radii. I noticed that you computed (Q/360) as (Q/2pi). I must be missing something behind this logic, but why do we use Q/2pi here?



Math Expert
Joined: 02 Sep 2009
Posts: 61396

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
02 Dec 2013, 00:45
catalysis wrote: Will the GMAT actually test for area of sector of a circle? Are we supposed to have this formula memorized? Yes, you should know how it's derived. Check here: mathcircles87957.htmlHope this helps.
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10113
Location: Pune, India

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
08 Dec 2013, 20:36
cumulonimbus wrote: Hi Karishma, In a question where one of the options is "None of the above" can we still test options?
Also with r=5, Q=360/pi = 2 deg, is it correct? quite unintuitive.
My initial thought was > for a given parameter equilateral triangle has the largest area. Wouldn't the area of triangle + sector largest when the triangle on which sector is formed is equilateral??
As the original poster said, this is not a GMAT question. GMAT questions do not have 'None of the above' as an option. So you can test options in GMAT if the question permits. \(2*\pi\) radians = 360 degrees (just like 1 km = 1000 m) (Recall that \(\pi = 3.1416\) approx) So about 6.28 radians = 360 degrees As for our question: Qr = 20  2r (where Q is in radians since we used \(Q/2\pi\) in the formula) Put r = 5 here, you get Q = 2 radians (not degrees) 2 radians = \(360/\pi\) degrees = 114.6 degrees Also why would you assume that it must be equilateral? What is the logic behind that? It is a sector we are talking about, not a triangle.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 10113
Location: Pune, India

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
27 Jan 2016, 01:23
manohar0265 wrote: A for me .Hello guys, I don't know whether my answer is correct. For a sector to have greater area and circumference,sector should have greater central angle.In options given A gives higher (305). The correct answer is (C). Maximising the central angle may not give you the greatest surface area because surface area depends on radius too. Check the solutions given on the previous page.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Manager
Status: GMAT in 4 weeks
Joined: 28 Mar 2010
Posts: 147
GPA: 3.89

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
22 May 2011, 00:12
sudhir18n wrote: hussi9 wrote: Twenty metres of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle in meters be, if we wish to have a flower bed with the greatest possible surface area?
(1) 2√2 (2) 2√5 (3) 5 (4) 4√2 (5) none of these
**************************** IIM CAT Level Question **************************** Requires knowledge of Mensuration and Max/min differenciation which not tested on GMAT. Not sure of any other method Sector of a circle = 2l+r 2r+l = 20 ; l= 20 2r Area = 1/2lr = 1/2*(202r)*r = 10rr^2 Differenciation: dA/dX= 10 2r 102r=0 hence r= 5 Are you sure Max/min is never tested on GMAT?



Director
Status: There is always something new !!
Affiliations: PMI,QAI Global,eXampleCG
Joined: 08 May 2009
Posts: 773

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
24 May 2011, 01:49
interesting question indeed.



Intern
Joined: 21 Mar 2011
Posts: 29

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
24 May 2011, 08:35
I'm wondering why we can't go this route. It's obviously wrong because I got the wrong answer but:
We know the circumference is 20. So we should be able to find the Diameter/radius
C = Pi * D
20 = pi* D
D = 20/Pi
D = ~ 6.37
So I picked E



Intern
Joined: 22 Feb 2010
Posts: 32

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
16 Sep 2013, 18:33
VeritasPrepKarishma wrote: You don't need derivatives in CAT either! Anyway, we can solve it either by plugging in numbers or by using this concept: If the sum of given numbers is constant, their product is maximum when they are equal.
Given: \(2r + (\frac{Q}{2pi})*2*pi*r = 20\) i.e. \(2r + Qr = 20\)
Maximize \((\frac{Q}{2pi})*pi*r^2 = \frac{Qr^2}{2}\) Now \(Qr = 20  2r\) from above. So, Maximize \((202r)r/2 = (10  r)r\) Since \(10  r + r = 10\), to maximize product, \(10  r = r\) i.e. \(r = 5\) Can anyone tell me how one obtained this eq. \(2r + (\frac{Q}{2pi})*2*pi*r = 20\)?



Manager
Joined: 24 Apr 2013
Posts: 50
Location: United States

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
21 Oct 2013, 12:32
VeritasPrepKarishma wrote: You don't need derivatives in CAT either! Anyway, we can solve it either by plugging in numbers or by using this concept: If the sum of given numbers is constant, their product is maximum when they are equal.
Given: \(2r + (\frac{Q}{2pi})*2*pi*r = 20\) i.e. \(2r + Qr = 20\)
Maximize \((\frac{Q}{2pi})*pi*r^2 = \frac{Qr^2}{2}\) Now \(Qr = 20  2r\) from above. So, Maximize \((202r)r/2 = (10  r)r\) Since \(10  r + r = 10\), to maximize product, \(10  r = r\) i.e. \(r = 5\) Hello Karishma Can I assume that the max surface area will be reached in a 90 degree sector? since the biggest sector that can be reached is a right angle, if it exceeds 90, would it still be called a sector?



Intern
Joined: 26 May 2012
Posts: 42
Concentration: Marketing, Statistics

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
01 Dec 2013, 23:11
Will the GMAT actually test for area of sector of a circle? Are we supposed to have this formula memorized?



Manager
Joined: 14 Nov 2011
Posts: 114
Location: United States
Concentration: General Management, Entrepreneurship
GPA: 3.61
WE: Consulting (Manufacturing)

Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
Show Tags
07 Dec 2013, 03:24
VeritasPrepKarishma wrote: You don't need derivatives in CAT either! Anyway, we can solve it either by plugging in numbers or by using this concept: If the sum of given numbers is constant, their product is maximum when they are equal.
Given: \(2r + (\frac{Q}{2pi})*2*pi*r = 20\) i.e. \(2r + Qr = 20\)
Maximize \((\frac{Q}{2pi})*pi*r^2 = \frac{Qr^2}{2}\) Now \(Qr = 20  2r\) from above. So, Maximize \((202r)r/2 = (10  r)r\) Since \(10  r + r = 10\), to maximize product, \(10  r = r\) i.e. \(r = 5\) Hi Karishma, In a question where one of the options is "None of the above" can we still test options? Also with r=5, Q=360/pi = 2 deg, is it correct? quite unintuitive. My initial thought was > for a given parameter equilateral triangle has the largest area. Wouldn't the area of triangle + sector largest when the triangle on which sector is formed is equilateral??




Re: Twenty meters of wire is available to fence off a flower bed in the
[#permalink]
07 Dec 2013, 03:24



Go to page
1 2
Next
[ 33 posts ]



