A circle and a square have the same area. What is the ratio : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 16 Jan 2017, 19:13

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A circle and a square have the same area. What is the ratio

Author Message
TAGS:

### Hide Tags

Manager
Joined: 16 Feb 2010
Posts: 225
Followers: 2

Kudos [?]: 287 [0], given: 16

A circle and a square have the same area. What is the ratio [#permalink]

### Show Tags

15 Sep 2010, 12:36
00:00

Difficulty:

45% (medium)

Question Stats:

63% (02:29) correct 37% (01:48) wrong based on 128 sessions

### HideShow timer Statistics

A circle and a square have the same area. What is the ratio of the diameter of the circle to the diagonal of the square?

(A) $$2 : \sqrt{(2\pi)}$$
(B) $$1 : 2\sqrt{\pi}$$
(C) $$2\sqrt{\pi} : \sqrt{2}$$
(D) $$1 : \sqrt{2}$$
(E) $$1 : 2\pi$$
[Reveal] Spoiler: OA

Last edited by zisis on 16 Sep 2010, 16:03, edited 3 times in total.
Manager
Joined: 16 Feb 2010
Posts: 225
Followers: 2

Kudos [?]: 287 [0], given: 16

Re: MGMAT Challenge Problem Showdown [#permalink]

### Show Tags

15 Sep 2010, 12:41
1
This post was
BOOKMARKED
IMO A

diameter 20,
πr^2 = 100π
area = 100π
side = $$\sqrt{100\pi}$$
diagonal = $$Side * \sqrt{2} = 10\sqrt{(2\pi)}$$

ratio
$$20 : 10\sqrt{(2\pi)}$$
= $$2 : \sqrt{(2\pi)}$$

Last edited by zisis on 16 Sep 2010, 16:05, edited 2 times in total.
Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92925 [2] , given: 10528

A circle and a square have the same area. What is the ratio [#permalink]

### Show Tags

15 Sep 2010, 12:47
2
KUDOS
Expert's post
1
This post was
BOOKMARKED
zisis wrote:
A circle and a square have the same area. What is the ratio of the diameter of the circle to the diagonal of the square?

(A) 2 : √(2)
(B) 1 : 2√
(C) 2√ : √2
(D) 1 : √2
(E) 1 : 2

$$area_{circle}=\pi{\frac{diameter^2}{4}}=area_{square}=\frac{diagonal^2}{2}$$;

$$\pi{\frac{diameter^2}{4}}=\frac{diagonal^2}{2}$$;

$$\frac{diameter^2}{diagonal^2}=\frac{2}{\pi}$$;

$$\frac{diameter}{diagonal}=\frac{\sqrt{2}}{\sqrt{\pi}}=\frac{2}{\sqrt{2\pi}}$$.

_________________
Retired Moderator
Joined: 02 Sep 2010
Posts: 805
Location: London
Followers: 105

Kudos [?]: 956 [0], given: 25

Re: MGMAT Challenge Problem Showdown [#permalink]

### Show Tags

15 Sep 2010, 12:50
zisis wrote:
A circle and a square have the same area. What is the ratio of the diameter of the circle to the diagonal of the square?

(A) 2 : √(2π)
(B) 1 : 2√π
(C) 2√π : √2
(D) 1 : √2
(E) 1 : 2π

$$\pi r^2 = a^2$$

$$\frac{r}{a} = \frac{1}{\sqrt{\pi}}$$

$$\frac{2r}{\sqrt{2}a} = \frac{2}{\sqrt{2\pi}}$$

Hence A
_________________
Manager
Joined: 16 Feb 2010
Posts: 225
Followers: 2

Kudos [?]: 287 [0], given: 16

Re: MGMAT Challenge Problem Showdown [#permalink]

### Show Tags

15 Sep 2010, 13:47
Had to copy and paste (pi). Is there a better way?

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 36520
Followers: 7067

Kudos [?]: 92925 [0], given: 10528

Re: MGMAT Challenge Problem Showdown [#permalink]

### Show Tags

15 Sep 2010, 13:50
zisis wrote:
Had to copy and paste (pi). Is there a better way?

Posted from my mobile device

Mark \pi by [m] button. Also check: writing-mathematical-symbols-in-posts-72468.html

hope it helps.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13419
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: A circle and a square have the same area. What is the ratio [#permalink]

### Show Tags

05 Jan 2015, 22:04
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.
_________________
SVP
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1858
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 47

Kudos [?]: 1928 [0], given: 193

A circle and a square have the same area. What is the ratio [#permalink]

### Show Tags

06 Jan 2015, 21:48

Let the area of circle = area of square = 1

$$\pi r^2 = 1$$

$$r = \frac{1}{\sqrt{\pi}}$$

2r = diameter $$= \frac{2}{\sqrt{\pi}}$$

Side of square = 1

Diagonal $$= \sqrt{2}$$

Ratio $$= \frac{2}{\sqrt{2*\pi}}$$
_________________

Kindly press "+1 Kudos" to appreciate

GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13419
Followers: 575

Kudos [?]: 163 [0], given: 0

Re: A circle and a square have the same area. What is the ratio [#permalink]

### Show Tags

08 Jan 2016, 15:07
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.
_________________
Re: A circle and a square have the same area. What is the ratio   [#permalink] 08 Jan 2016, 15:07
Similar topics Replies Last post
Similar
Topics:
1 If circles x and y have the same area and circle x has a circumference 1 16 Mar 2016, 10:27
12 A circle is inscribed in a square with an area of 121 square 8 12 Jun 2014, 12:52
3 A circle and a square have the same area. What is the ratio 3 08 Nov 2012, 22:56
9 If the two regions above have the same area, what is the 15 11 Oct 2009, 09:03
12 If the area of a square equals the area of a circle, which of the foll 10 11 May 2009, 14:24
Display posts from previous: Sort by