by: EnergyAlpha
32 mins
by: Theeldertwin
41 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:
(N/A)
Question Stats:
0% (00:00) correct
0%
(00:00)
wrong
based on 0
sessions
History
Date
Time
Result
Not Attempted Yet
If the inside circles are all of the same size and each center is a corner of the interiour square, and the interiour circles lie on the circumference of the outside circle, what is the area of the of the highlighted green area?
(1) The circumference of the outside circle is \(5\Pi\).
(2) The ratio of the outside circle's diameter to the radius of one of the interiour circles is \(2+\sqrt{2}:1\).
(1) The circumference of the outside circle is \(5\Pi\).
(2) The ratio of the outside circle's diameter to the radius of one of the interiour circles is \(2+\sqrt{2}:1\).
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Posts: 1,012
Hades
A.
(1) The circumference of the outside circle is \(5\Pi\).
large circle:
C = 2 PI R = 5 PI
R = 5/2
D = ac = ab+bf+cf = 5
Small & large circles:
redius of smal circles = ab = bd = de = cf.
If ab = x, bd = de = cf = x. Also be = ef = 2x
bf = sqrt(be^2 + ef^2)
bf = sqrt(4x^2 + 4x^2)
bf = sqrt(8x^2)
bf = 2x sqrt(2)
D = ab+bf+cf
5 = x + 2x sqrt(2) + x
5 = 2x + 2x sqrt(2)
5 = 2x [1+sqrt(2)]
x = 5/[2{1+sqrt(2)}]
Since we know diameters and redii of small and large circles and sides of the square, it is sufficient to find the area of the green colored space.
(2) The ratio doesnot help. Need absolute value. So insuff...
Attachments
diagram%201.jpg [ 19.61 KiB | Viewed 2098 times ]
GMAT TIGER
Excellent work GMAT Tiger!
I think we can do faster without calculation. Let's look at the figure. We have only one option how to build this system inside a circle (square cannot be lesser or larger, so too small circles). It means that all ratio between linear sizes are constant. So, if we know any linear size in the system, we can find other size and area.
1) suff. we know one linear size.
2) insuff. we don't know any linear size in the system.
1) suff. we know one linear size.
2) insuff. we don't know any linear size in the system.
Yes that is the best way to approach it as well.
I would look at it and deduce that everything is locked into ratio-- there is only 1 way to to construct the shape. Hence we just need to know the length of something so we can scale it, and then thus answer question about it. Even rotating the circles inside the big circle doesn't change anything. (1) provides us with this
2 - Again it's a ratio, and doesn't give us a fixed value. Furthermore, since everything is locked into scale already, we can figure out any ratio from the shape. Hence insufficient
A
I would look at it and deduce that everything is locked into ratio-- there is only 1 way to to construct the shape. Hence we just need to know the length of something so we can scale it, and then thus answer question about it. Even rotating the circles inside the big circle doesn't change anything. (1) provides us with this
2 - Again it's a ratio, and doesn't give us a fixed value. Furthermore, since everything is locked into scale already, we can figure out any ratio from the shape. Hence insufficient
A
Posts: 78
Agree with A
Draw two perpendicular line which divide the 4 small circles into 4 equal parts and a line links the center of the the large and any small circle, we can see R = r + r sqrt 2.
From that we can calculate the green area = area of large circle - area of total 4 circles - (area of the square - area of a small circles)
Draw two perpendicular line which divide the 4 small circles into 4 equal parts and a line links the center of the the large and any small circle, we can see R = r + r sqrt 2.
From that we can calculate the green area = area of large circle - area of total 4 circles - (area of the square - area of a small circles)
Posts: 16
The correct answer is A. If (2) would involve an absolute value rather than a ratio it would be solvable and the answer would be D.
Pretty much everyone knows that you have to use an absolute value as input to get an absolute value as output (which is what they are asking for), thus even the 300-400 scorers will have a 50-50 chance on this one.
Pretty much everyone knows that you have to use an absolute value as input to get an absolute value as output (which is what they are asking for), thus even the 300-400 scorers will have a 50-50 chance on this one.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
Announcements
How to Tell If Your GMAT Prep Resources Are Actually Helping You
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
Subscribe to GMAT Club for New Podcast Episodes, Debriefs, & Insightful Sessions on GMAT Preparation
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.