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• ### $450 Tuition Credit & Official CAT Packs FREE November 15, 2018 November 15, 2018 10:00 PM MST 11:00 PM MST EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth$100 with the 3 Month Pack ($299) • ### Free GMAT Strategy Webinar November 17, 2018 November 17, 2018 07:00 AM PST 09:00 AM PST Nov. 17, 7 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. # If the perimeter of square region S and the perimeter of circular regi  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics Author Message TAGS: ### Hide Tags Intern Joined: 03 Dec 2005 Posts: 4 If the perimeter of square region S and the perimeter of circular regi [#permalink] ### Show Tags Updated on: 06 Nov 2018, 02:49 4 9 00:00 Difficulty: 45% (medium) Question Stats: 71% (01:28) correct 29% (01:35) wrong based on 519 sessions ### HideShow timer Statistics 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. $$\frac {1}{2}$$ Originally posted by Dumpling on 22 Feb 2006, 12:30. Last edited by Bunuel on 06 Nov 2018, 02:49, edited 2 times in total. Renamed the topic, edited the question, added the OA and moved to PS forum. ##### Most Helpful Expert Reply Math Expert Joined: 02 Sep 2009 Posts: 50580 If the perimeter of square region S and the perimeter of circular regi [#permalink] ### Show Tags 20 Jun 2010, 07:03 4 2 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 Given: $$P_{square}=4x=2\pi{r}=P_{circle}$$ --> $$x=\frac{\pi{r}}{2}$$. $$\frac{A_{square}}{A_{circle}}=\frac{x^2}{\pi{r^2}}=\frac{\pi^2{r^2}}{4\pi{r^2}}=\frac{\pi}{4}\approx(\frac{3}{4})$$. Answer: C. Similar question: https://gmatclub.com/forum/if-the-perim ... 27004.html _________________ ##### General Discussion Intern Joined: 16 Jun 2010 Posts: 1 Re: Ratio [#permalink] ### Show Tags 10 Mar 2011, 09:51 1 If Perimeter of square = Perimeter of Circle, then: 4a = 2$$\pi$$r, where a = side of square and r is radius of the circle a/r = $$\pi$$/2 Area of S/Area of C = $$a^2$$/ $$\pi$$ $$r^2$$ = $$(\pi/2)^2$$ * 1/$$\pi$$ = $$\pi$$/4 = 3.14/4 = $$\approx$$ 3/4 = C SVP Status: The Best Or Nothing Joined: 27 Dec 2012 Posts: 1827 Location: India Concentration: General Management, Technology WE: Information Technology (Computer Software) Re: If the perimeter of square region S and the perimeter of circular regi [#permalink] ### Show Tags 09 Mar 2014, 02:07 1 Please refer diagram below: Attachments pi.jpg [ 34.5 KiB | Viewed 5000 times ] _________________ Kindly press "+1 Kudos" to appreciate EMPOWERgmat Instructor Status: GMAT Assassin/Co-Founder Affiliations: EMPOWERgmat Joined: 19 Dec 2014 Posts: 12853 Location: United States (CA) GMAT 1: 800 Q51 V49 GRE 1: Q170 V170 Re: If the perimeter of square region S and the perimeter of circular regi [#permalink] ### Show Tags 09 Apr 2015, 22:12 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 _________________ 760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com # Rich Cohen Co-Founder & GMAT Assassin Special Offer: Save$75 + GMAT Club Tests Free
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Re: If the perimeter of square region S and the perimeter of the  [#permalink]

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30 Jun 2015, 09:39
Bunuel wrote:
chintzzz wrote:

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

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

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

Can you explain this portion: Pcircle --> x=πr2.
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Posts: 50580
Re: If the perimeter of square region S and the perimeter of the  [#permalink]

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30 Jun 2015, 09:45
xLUCAJx wrote:
Bunuel wrote:
chintzzz wrote:

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

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

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

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.
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If the perimeter of square region S and the perimeter of the  [#permalink]

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28 Sep 2015, 00:24
1
Bunuel wrote:
chintzzz wrote:

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

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

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

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
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Posts: 50580
Re: If the perimeter of square region S and the perimeter of the  [#permalink]

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28 Sep 2015, 02:07
2
DropBear wrote:
Bunuel wrote:
chintzzz wrote:

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

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

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

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.
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Re: If the perimeter of square region S and the perimeter of circular regi  [#permalink]

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07 May 2016, 06:04
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: $$P_{square}=4x=2\pi{r}=P_{circle}$$ --> $$x=\frac{\pi{r}}{2}$$.

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

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Re: If the perimeter of square region S and the perimeter of circular regi  [#permalink]

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07 May 2016, 10:03
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.

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Re: If the perimeter of square region S and the perimeter of circular regi &nbs [#permalink] 07 May 2016, 10:03
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