NEW HERE? LEARN MORE
closeclose
Last visit was: 08 May 2024, 18:48 It is currently 08 May 2024, 18:48
Decision Tracker
My Rewards
New posts
New comers' posts

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

Two strings have equal length. One of the strings is shaped, with no

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 93096
Own Kudos [?]: 622261 [8]
Given Kudos: 81800
Send PM
CAT Tests Forum Quiz Mode
Two strings have equal length. One of the strings is shaped, with no [#permalink] New post   22 May 2020, 11:17
8
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

80% (02:01) correct 20% (02:08) wrong based on 336 sessions
Hide Show timer Statistics
Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?


A. \(1:2\)

B. \(\pi:2\)

C. \(1:1\)

D. \(4:\pi\)

E. The ratio depends on the length of the two strings.


PS20405
ShowHide Answer
Official Answer
D
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1878
Own Kudos [?]: 6331 [0]
Given Kudos: 704
Location: India
Send PM
Two strings have equal length. One of the strings is shaped, with no [#permalink] New post   22 May 2020, 12:16
Suppose the length of the strings = \(4\pi\)

Perimeter of the square = \(4\pi\)
Length of the side of square = \(\pi\)
Area of square= \({\pi}^2\)

Perimeter of the square =\( 4\pi\)
Radius of the side of square = [\(\frac{4\pi}{2\pi} =2\)
Area of square= \({\pi}*2^2\) = \(4\pi\)

ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square = \(4\pi\) : \({\pi}^2\) = \(4:\pi\)

Bunuel wrote:
Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?


A. \(1:2\)

B. \(\pi:2\)

C. \(1:1\)

D. \(4:\pi\)

E. The ratio depends on the length of the two strings.


PS20405
User avatar
B
Enchanting
Intern
Intern
Joined: 07 Apr 2020
Posts: 44
Own Kudos [?]: 85 [1]
Given Kudos: 2
Send PM
Re: Two strings have equal length. One of the strings is shaped, with no [#permalink] New post   22 May 2020, 12:28
1
Bookmarks
Bunuel wrote:
Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?


A. \(1:2\)

B. \(\pi:2\)

C. \(1:1\)

D. \(4:\pi\)

E. The ratio depends on the length of the two strings.
PS20405

Solution:
    Length of the two strings are equal, say l.
      Circumference of circle = l
      2*π*r=l, where r is the radius of circle.
      \(r=\frac{l}{2π}\)
        Area= \(π*r^2=π*\frac{l^2}{(4π^2 )}=\frac{l^2}{4π}\)
    Perimeter of square = l
    Side of the square = \(\frac{l}{4}\)
      Area = \((\frac{l}{4})^2=\frac{l^2}{16}\)
    Required ratio = \(\frac{\frac{l^2}{4π}}{\frac{l^2}{16}}=\frac{4}{π}\)
Answer: Option D.
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8026
Own Kudos [?]: 4117 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User
Re: Two strings have equal length. One of the strings is shaped, with no [#permalink] New post   22 May 2020, 19:53
let strings be 12 each
so for circle ; 2 pi r= 12 ; r = 6/pi
and for square ; 4s = 12 ;s =3
area of circle ; 36/pi
and area of square = 9
ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square
36/pi * 1/9 = 4:pi
OPTION D

Bunuel wrote:
Two strings have equal length. One of the strings is shaped, with no overlap, into a circle. The other string is shaped, with no overlap, into a square. What is the ratio of the area of the region enclosed by the circle to the area of the region enclosed by the square?


A. \(1:2\)

B. \(\pi:2\)

C. \(1:1\)

D. \(4:\pi\)

E. The ratio depends on the length of the two strings.


PS20405
User avatar
G
NitishJain
IESE School Moderator
Joined: 11 Feb 2019
Posts: 271
Own Kudos [?]: 171 [0]
Given Kudos: 53
Send PM
Re: Two strings have equal length. One of the strings is shaped, with no [#permalink] New post   23 May 2020, 17:57
D?

Let the total length = l
Side of square = a
radius of circle = r

length of the string should be equal to the perimeter of the square
l = 4a
or a = l/4

Similarly, length of the string should be equal to the perimeter of the circle
l = 2(pie)r
r = l/2(pie)

Area of circle : Area os Square = (pie) r^2 : a^2

Substituting values of 'r' and 'a' in terms of 'l':
Area of circle : Area os Square = 4: (pie)
avatar
koam7
Intern
Intern
Joined: 18 Apr 2020
Posts: 1
Own Kudos [?]: 0 [0]
Given Kudos: 0
Send PM
Re: Two strings have equal length. One of the strings is shaped, with no [#permalink] New post   23 May 2020, 18:49
Let the length of the string be x.

The length of each side of the square will be x/4, so the area of the square will be x^2/16

The circumference of the circle will be x, so 2(pi)R = x, or R = x / 2(pi). So, the area of the circle will be pi * x^2/4(pi^2), or x^2/4pi

The ratio of the area of the circle to the square will be

x^2/4pi : x^2/16

eliminate the x^2

1/4pi : 1/16

Simplified, this gives 4 : pi

So, the answer is D
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 963
Own Kudos [?]: 224 [0]
Given Kudos: 434
Location: United States
Send PM
Re: Two strings have equal length. One of the strings is shaped, with no [#permalink] New post   28 Nov 2020, 12:59
Let \(x = length of each string\)

\frac{x}{4} = side of a square

\(\frac{x}{4}^2 = \frac{x^2}{16}\)

\(x = circumference\)

\(x = 2πr\)

\(\frac{x}{2π} = r\)

\(\frac{x^2}{4π^2} = r^2\)

\(\frac{x^2}{4π} = πr^2\)

\(\frac{area of circle}{area of square} = \frac{16}{4π} = \frac{4}{π}\)

Answer is D.
User avatar
B
tarunrathi999
Intern
Intern
Joined: 04 Mar 2014
Posts: 18
Own Kudos [?]: 2 [0]
Given Kudos: 102
Send PM
GMAT ToolKit User
Two strings have equal length. One of the strings is shaped, with no [#permalink] New post   09 Sep 2022, 20:36
[Ac][/As] = [π*r*r][/a*a]
eq 1

2πr = 4a
r/a = 4/2π

eq 2

Substitute and you'll get 4: π
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32853
Own Kudos [?]: 828 [0]
Given Kudos: 0
Send PM
Re: Two strings have equal length. One of the strings is shaped, with no [#permalink] New post   09 Jan 2024, 16:34
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: Two strings have equal length. One of the strings is shaped, with no [#permalink]
09 Jan 2024, 16:34
Moderators:
Bunuel
Math Expert
93096 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions