Last visit was: 23 Jul 2024, 05:38 It is currently 23 Jul 2024, 05:38
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.
Close
Request Expert Reply
Confirm Cancel
SORT BY:
Date
Tags:
Difficulty: 555-605 Level,   Geometry,            
Show Tags
Hide Tags
User avatar
Intern
Intern
Joined: 03 Dec 2005
Posts: 3
Own Kudos [?]: 53 [52]
Given Kudos: 0
Send PM
Most Helpful Reply
Math Expert
Joined: 02 Sep 2009
Posts: 94580
Own Kudos [?]: 643207 [11]
Given Kudos: 86728
Send PM
General Discussion
avatar
Intern
Intern
Joined: 16 Jun 2010
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 0
Send PM
avatar
SVP
SVP
Joined: 27 Dec 2012
Status:The Best Or Nothing
Posts: 1558
Own Kudos [?]: 7303 [1]
Given Kudos: 193
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Send PM
Re: If the perimeter of square region S and the perimeter of circular regi [#permalink]
1
Kudos
Please refer diagram below:
Attachments

pi.jpg
pi.jpg [ 34.5 KiB | Viewed 20737 times ]

GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11793 [2]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If the perimeter of square region S and the perimeter of circular regi [#permalink]
1
Kudos
1
Bookmarks
Expert Reply
Hi All,

This question is perfect for TESTing VALUES.

We're told that the PERIMETER of a square is equal to the PERIMETER (meaning the 'circumference') of a circle. We're asked to figure out the approximate ratio of the area of the square to the area of the circle.

Let's TEST VALUES. Since we're dealing with a circle, let's work "pi" into our math right from the beginning....

Perimeter = 4pi

For the Square:
Perimeter = 4pi
Side length = pi
Area = (pi)^2

For the Circle:
Perimeter = 4pi
Radius = 2
Area = 4pi

Area of Square/Area of Circle = (pi)^2/4pi = pi/4 = about 3.14/4 = about 3/4

Final Answer:

GMAT assassins aren't born, they're made,
Rich
avatar
Intern
Intern
Joined: 22 Apr 2015
Posts: 38
Own Kudos [?]: 28 [0]
Given Kudos: 118
Location: United States
GMAT 1: 620 Q46 V27
GPA: 3.86
Send PM
Re: If the perimeter of square region S and the perimeter of the [#permalink]
Bunuel wrote:
chintzzz wrote:
I got an answer of B but the official answer is different. please explain

If the perimeter of square region S and the perimeter of the circular region C are equal, then the ratio of the area of S to area of C is closes to
A.3/2
B.4/3
C.3/4
D.2/3
E.1/2


\(P_{square}=4x=2\pi{r}=P_{circle}\) --> \(x=\frac{\pi{r}}{2}\).

\(\frac{A_{square}}{A_{circle}}=\frac{x^2}{\pi{r^2}}=\frac{\pi^2{r^2}}{4\pi{r^2}}=\frac{\pi}{4}\approx(\frac{3}{4})\).

Answer: C.



Can you explain this portion: Pcircle --> x=πr2.
Math Expert
Joined: 02 Sep 2009
Posts: 94580
Own Kudos [?]: 643207 [0]
Given Kudos: 86728
Send PM
Re: If the perimeter of square region S and the perimeter of the [#permalink]
Expert Reply
xLUCAJx wrote:
Bunuel wrote:
chintzzz wrote:
I got an answer of B but the official answer is different. please explain

If the perimeter of square region S and the perimeter of the circular region C are equal, then the ratio of the area of S to area of C is closes to
A.3/2
B.4/3
C.3/4
D.2/3
E.1/2


\(P_{square}=4x=2\pi{r}=P_{circle}\) --> \(x=\frac{\pi{r}}{2}\).

\(\frac{A_{square}}{A_{circle}}=\frac{x^2}{\pi{r^2}}=\frac{\pi^2{r^2}}{4\pi{r^2}}=\frac{\pi}{4}\approx(\frac{3}{4})\).

Answer: C.



Can you explain this portion: Pcircle --> x=πr2.


Equating the perimeter of square (4x, where x is the length of the side) and the perimeter of the circle (circumference = \(2\pi{r}\)), we get \(4x=2\pi{r}\), which gives \(x=\frac{\pi{r}}{2}\).

Hope it's clear.
User avatar
Manager
Manager
Joined: 04 May 2015
Posts: 64
Own Kudos [?]: 30 [1]
Given Kudos: 58
Concentration: Strategy, Operations
WE:Operations (Military & Defense)
Send PM
If the perimeter of square region S and the perimeter of the [#permalink]
1
Kudos
Bunuel wrote:
chintzzz wrote:
I got an answer of B but the official answer is different. please explain

If the perimeter of square region S and the perimeter of the circular region C are equal, then the ratio of the area of S to area of C is closes to
A.3/2
B.4/3
C.3/4
D.2/3
E.1/2


\(P_{square}=4x=2\pi{r}=P_{circle}\) --> \(x=\frac{\pi{r}}{2}\).

\(\frac{A_{square}}{A_{circle}}=\frac{x^2}{\pi{r^2}}=\frac{\pi^2{r^2}}{4\pi{r^2}}=\frac{\pi}{4}\approx(\frac{3}{4})\).

Answer: C.


Apologies for what is probably a very simple question, but could someone please explain this step here?

\(\frac{x^2}{\pi{r^2}}=\frac{\pi^2{r^2}}{4\pi{r^2}}\)

Thank you
Math Expert
Joined: 02 Sep 2009
Posts: 94580
Own Kudos [?]: 643207 [2]
Given Kudos: 86728
Send PM
Re: If the perimeter of square region S and the perimeter of the [#permalink]
2
Kudos
Expert Reply
DropBear wrote:
Bunuel wrote:
chintzzz wrote:
I got an answer of B but the official answer is different. please explain

If the perimeter of square region S and the perimeter of the circular region C are equal, then the ratio of the area of S to area of C is closes to
A.3/2
B.4/3
C.3/4
D.2/3
E.1/2


\(P_{square}=4x=2\pi{r}=P_{circle}\) --> \(x=\frac{\pi{r}}{2}\).

\(\frac{A_{square}}{A_{circle}}=\frac{x^2}{\pi{r^2}}=\frac{\pi^2{r^2}}{4\pi{r^2}}=\frac{\pi}{4}\approx(\frac{3}{4})\).

Answer: C.


Apologies for what is probably a very simple question, but could someone please explain this step here?

\(\frac{x^2}{\pi{r^2}}=\frac{\pi^2{r^2}}{4\pi{r^2}}\)

Thank you


\(x=\frac{\pi{r}}{2}\).

\(\frac{A_{square}}{A_{circle}}=\frac{x^2}{\pi{r^2}}=\frac{(\frac{\pi{r}}{2})^2}{\pi{r^2}}=\frac{\frac{\pi^2 r^2}{4}}{\pi{r^2}}=\frac{\pi^2{r^2}}{4\pi{r^2}}=\frac{\pi}{4}\approx(\frac{3}{4})\).

Hope it helps.
Manager
Manager
Joined: 28 Apr 2016
Posts: 70
Own Kudos [?]: 23 [0]
Given Kudos: 79
Send PM
Re: If the perimeter of square region S and the perimeter of circular regi [#permalink]
I reached till (22 * 7)/ 4...Is there a quick way to estimate/ calculate the final answer?


Bunuel wrote:
Stiv wrote:
If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to:

A. \(\frac {3}{2}\)

B. \(\frac {4}{3}\)

C. \(\frac {3}{4}\)

D. \(\frac {2}{3}\)

E. \(\frac {1}{2}\)



Given: \(P_{square}=4x=2\pi{r}=P_{circle}\) --> \(x=\frac{\pi{r}}{2}\).

\(\frac{A_{square}}{A_{sdquare}}=\frac{x^2}{\pi{r^2}}=\frac{\pi^2{r^2}}{4\pi{r^2}}=\frac{\pi}{4}\approx(\frac{3}{4})\).

Answer: C.
GMAT Club Legend
GMAT Club Legend
Joined: 19 Dec 2014
Status:GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Posts: 21835
Own Kudos [?]: 11793 [0]
Given Kudos: 450
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Send PM
Re: If the perimeter of square region S and the perimeter of circular regi [#permalink]
Expert Reply
Hi ameyaprabhu,

The questions that you'll face on the Official GMAT are almost all based on patterns of some type (even if you don't immediately realize that a pattern is there). In the Quant section, TESTing VALUES can often be used to define a pattern, so you might try using that approach in these types of situations. My explanation (2 posts above your post) shows how to approach this prompt in that way.

GMAT assassins aren't born, they're made,
Rich
Director
Director
Joined: 04 Dec 2015
Posts: 620
Own Kudos [?]: 1618 [0]
Given Kudos: 276
Location: India
Concentration: Technology, Strategy
WE:Information Technology (Consulting)
Send PM
Re: If the perimeter of square region S and the perimeter of circular regi [#permalink]
Dumpling wrote:
If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to:


A. \(\frac {3}{2}\)

B. \(\frac {4}{3}\)

C. \(\frac {3}{4}\)

D. \(\frac {2}{3}\)

E. \(\frac {1}{2}\)


Let Perimeter of Square \(= 4a\) and Area of Square \(= a^2\)

Let Perimeter of Circle = \(2\)\(\pi\)\(r\) and Area of Circle \(= \pi\)\(r^2\)

Perimeter of Square and Circle are equal.

\(4a =\) \(2\)\(\pi\)\(r\) \(=> a = \frac{r\pi}{2}\)

Ratio of Area of Square to Area of Circle \(= \frac{a^2}{r^2\pi}\)

Substituting value of \("a"\) in above expression we get;

\(\frac{(r\pi/2)^2}{r^2\pi}\) \(= \frac{(r^2\pi^2/4)}{r^2\pi}\) \(= \frac{r^2\pi^2}{4r^2\pi}\)

Hence Ratio of Area of Square to Area of Circle = \(\frac{\pi}{4}\)

\(\pi\) is approx \(= 3\)

Hence required ratio \(= \frac{3}{4}\)

Answer C
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3710
Own Kudos [?]: 17353 [0]
Given Kudos: 165
Send PM
Re: If the perimeter of square region S and the perimeter of circular regi [#permalink]
Expert Reply

Solution



Given:
    • The perimeter of square region S and the perimeter of circular region C are equal.

To find:
    • The ratio of the area of S to the area of C is closest to which option among the given ones.

Approach and Working:

    • Let side of square region S is a and radius of circular region C is r.
      o Perimeter of square = Perimeter of circle
      o 4a= 2*pi*r
      o 2a= pi*r
      o \(a= \frac{{pi * r}}{2}\)

    • Area of S : Area of C = \(a^2 :pi * r^2\)
      o = \(\frac{{pi^2 * r^2}}{4} : pi * r^2\)
      o = \(\frac{pi}{4}\)= ¾

Hence, the correct answer is option C.

Answer: C
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6047
Own Kudos [?]: 4767 [0]
Given Kudos: 463
Location: India
GPA: 3.5
WE:Business Development (Commercial Banking)
Send PM
Re: If the perimeter of square region S and the perimeter of circular regi [#permalink]
Dumpling wrote:
If the perimeter of square region S and the perimeter of circular region C are equal, then the ratio of the area of S to the area of C is closest to:


A. \(\frac {3}{2}\)

B. \(\frac {4}{3}\)

C. \(\frac {3}{4}\)

D. \(\frac {2}{3}\)

E. \(\frac {1}{2}\)


\(S = C\)

\(4a = 2πr\)

\(2a = πr\)

\(2a = \frac{22r}{7}\)

\(a = \frac{11r}{7}\)

If \(r = 7\) , \(a = 11\)

So, Area of \(S = 7*7\) ; Area of \(C = 2*\frac{22}{7}*7\)

Or, Area S = 49 & Area C = 44

Area S / Area C = \(\frac{49}{44} = 1.11xxxx\)

Now, Check the options Denominator > Numerator ( Reject options C, D & E)

Option (A) can be rejected as 3/2 = 1.5 , left with option (B) , Our ANswer
User avatar
Non-Human User
Joined: 09 Sep 2013
Posts: 34048
Own Kudos [?]: 853 [0]
Given Kudos: 0
Send PM
Re: If the perimeter of square region S and the perimeter of circular regi [#permalink]
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
Re: If the perimeter of square region S and the perimeter of circular regi [#permalink]
Moderator:
Math Expert
94580 posts