by: laborumpossimus
19 mins
by: laborumpossimus
22 mins
Events & Promotions
|
|
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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Sep 1507:00 PM EDT
-09:00 PM EST
Elite scores are possible when you enroll in a powerful GMAT course, taught live online + 6 months access to TTP OnDemand video courses included! Class starts Tues/Thurs Sept. 15, 2026 - Nov. 15, 2027, 7:00pm-9:00pm EST
Sep 2107:00 PM EDT
-10:00 PM EDT
Boost your GMAT score in less than one month in a live online class + 6 months access to TTP OnDemand video courses included! Class starts Mon, Tues, Wed, Thur, Fri Sept. 21, 2026 - Oct. 9, 2027, 7:00pm-10:00pm EST
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
71% (02:05) correct
29%
(02:32)
wrong
based on 135
sessions
History
Date
Time
Result
Not Attempted Yet
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) \(1 : 2\pi\)
(A) \(2 : \sqrt{(2\pi)}\)
(B) \(1 : 2\sqrt{\pi}\)
(C) \(2\sqrt{\pi} : \sqrt{2}\)
(D) \(1 : \sqrt{2}\)
(E) \(1 : 2\pi\)
IMO A
diameter 20,
radius= 10
πr^2 = 100π
area = 100π
side = \(\sqrt{100\pi}\)
diagonal = \(Side * \sqrt{2} = 10\sqrt{(2\pi)}\)
ratio
\(20 : 10\sqrt{(2\pi)}\)
= \(2 : \sqrt{(2\pi)}\)
diameter 20,
radius= 10
πr^2 = 100π
area = 100π
side = \(\sqrt{100\pi}\)
diagonal = \(Side * \sqrt{2} = 10\sqrt{(2\pi)}\)
ratio
\(20 : 10\sqrt{(2\pi)}\)
= \(2 : \sqrt{(2\pi)}\)
zisis
\(area_{circle}=\pi{\frac{diameter^2}{4}}=area_{square}=\frac{diagonal^2}{2}\);
\(\pi{\frac{diameter^2}{4}}=\frac{diagonal^2}{2}\);
\(\frac{diameter^2}{diagonal^2}=\frac{2}{\pi}\);
\(\frac{diameter}{diagonal}=\frac{\sqrt{2}}{\sqrt{\pi}}=\frac{2}{\sqrt{2\pi}}\).
Answer: A.
Pleas format the answers properly.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
zisis
\(\pi r^2 = a^2\)
\(\frac{r}{a} = \frac{1}{\sqrt{\pi}}\)
\(\frac{2r}{\sqrt{2}a} = \frac{2}{\sqrt{2\pi}}\)
Hence A
_________________
Had to copy and paste (pi). Is there a better way?
Posted from my mobile device
Posted from my mobile device
zisis
Mark \pi by [m] button. Also check: https://gmatclub.com/forum/writing-mathe ... 72468.html
hope it helps.
_________________
New to the GMAT Club?
- • Questions: Question Bank | Bunuel's Signature Collection
• Tests: GMAT Club Tests | Forum Quiz
• Guides: Quantitative | Critical Reasoning | Reading Comprehension | Ultimate Quant Guide | All You Need for Quant
• Rules: Quantitative | Verbal
Pansi
Diameter be D and diagonal be y then D/Y = ?
given is area of square = area of circle
=> 1/2*Y^2 = 1/4*pi*D^2
=>D/Y= sqrt(2/pi) = 2/sqrt(2pi)
Ans A it is.
PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
Refer diagram below:
\(\pi r^2 = a^2\)
\(a = \sqrt{\pi}r\)
\(\frac{Diameter of circle}{Diagonal of Square} = \frac{2r}{\sqrt{2} \sqrt{\pi}r}\)
\(Answer = \frac{2}{\sqrt{2 \pi}\) = A
\(\pi r^2 = a^2\)
\(a = \sqrt{\pi}r\)
\(\frac{Diameter of circle}{Diagonal of Square} = \frac{2r}{\sqrt{2} \sqrt{\pi}r}\)
\(Answer = \frac{2}{\sqrt{2 \pi}\) = A
Attachments
pi.png [ 4.75 KiB | Viewed 13822 times ]
PareshGmat
Joined: 27 Dec 2012
Last visit: 10 Jul 2016
Posts: 1,531
Status:The Best Or Nothing
Location: India
Concentration: General Management, Technology
WE:Information Technology (Computer Software)
Posts: 1,531
Answer = A
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 \(= \frac{2}{\sqrt{2*\pi}}\)
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 \(= \frac{2}{\sqrt{2*\pi}}\)
JeffTargetTestPrep
Expert
Target Test Prep Representative
Joined: 04 Mar 2011
Last visit: 05 Jan 2024
Posts: 2,973
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Expert reply
Posts: 2,973
zisis
Let us denote the length of a side of the square by s and the radius of the circle by r.
We can create the equation:
πr^2 = s^2
r√π = s
Since the side of the square s = r√π, the diagonal of the square is r√π x √2 = r√(2π).
The diameter of the circle is 2r. Thus, the ratio of the diameter of the circle to the diagonal of the square is:
2r/[r√(2π)] = 2/√(2π)
Answer: A
_________________
Jeffrey Miller | Head of GMAT Instruction |
[email protected]
See why Target Test Prep is the top rated GMAT course on GMAT Club. Read Our Reviews
Automated notice from GMAT Club BumpBot:
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.
This post was generated automatically.
_________________
Moderator:
Announcements
Tuck at Dartmouth
AI at Dartmouth Tuck: How the School Is Preparing Leaders for the Age of Artificial Intelligence
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Inside the courses, research, and hands-on learning defining wise, decisive leadership in an AI-driven world.
Read More
Top 5 GMAT Debrief Videos
Success stories and strategies from high-scoring candidates.