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.
Apr 2212:30 AM EDT
-01:30 AM EDT
At one point, she believed GMAT wasn’t for her. After scoring 595, self-doubt crept in and she questioned her potential. But instead of quitting, she made the right strategic changes. The result? A remarkable comeback to 695. Check out how Saakshi did it.
Apr 1612:00 PM EDT
-11:59 PM EDT
You’re first to know: Save $200 on GMAT prep starting tomorrow, 4/13. Get 6 official practice tests and study with real questions. Be ready to save!
Apr 2301:30 AM EDT
-02:30 AM EDT
Struggling with GMAT Verbal as a non-native speaker? Harsh improved his score from 595 to 695 in just 45 days—and scored a 99 %ile in Verbal (V88)! Learn how smart strategy, clarity, and guided prep helped him gain 100 points.
Apr 2308:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Apr 2610:00 AM EDT
-11:00 AM EDT
The Target Test Prep course represents a quantum leap forward in GMAT preparation, a radical reinterpretation of the way that students should study. Try before you buy with a 5-day, full-access trial of the course for FREE!
Apr 2711:00 AM EDT
-12:00 PM EDT
Prefer video-based learning? The Target Test Prep OnDemand course is a one-of-a-kind video masterclass featuring 400 hours of lecture-style teaching by Scott Woodbury-Stewart, founder of Target Test Prep and one of the most accomplished GMAT instructors
Apr 2808:00 AM PDT
-11:00 AM PDT
Whether you are just beginning your MBA journey or fine-tuning your path to a 700+ score, GMAT Day is designed to give you a competitive edge.
18 Aug 2021, 08:00
Kudos
Bookmarks
C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
52% (01:40) correct
48%
(02:01)
wrong
based on 240
sessions
History
Date
Time
Result
Not Attempted Yet
In the image above, two tangent semicircles are drawn in a circle of area 4. If the diameters of the two semicircles are parallel, what is the area of the shaded region?
A. 1
B. 1.5
C. 2
D. 2.5
E. 3
|
M37-37
Attachment:
Untitled4.png
Experience GMAT Club Test Questions
Yes, you've landed on a GMAT Club Tests question
Craving more? Unlock our full suite of GMAT Club Tests here
Want to experience more? Get a taste of our tests with our free trial today
Rise to the challenge with GMAT Club Tests. Happy practicing!
23 Nov 2021, 07:29
Kudos
Bookmarks
Official Solution:
In the image above, two tangent semicircles are drawn in a circle of area 4. If the diameters of the two semicircles are parallel, what is the area of the shaded region?
A. \(1\)
B. \(1.5\)
C. \(2\)
D. \(2.5\)
E. \(3\)
The question has five exact answer choices (no "Cannot be determined" or "None of the above") so one of them must be correct. If one of the answers is correct, the answer must be correct no matter how we draw the diagram (of course we should not violate info that is given).
Re-draw the diagram so that the upper semicircle is infinitely small. In this case the bottom semicircle will occupy half of the circle, and thus the area of the shaded region (which will be just one semicircle now) would be half of the larger circle, so 2.
Answer: C
In the image above, two tangent semicircles are drawn in a circle of area 4. If the diameters of the two semicircles are parallel, what is the area of the shaded region?
A. \(1\)
B. \(1.5\)
C. \(2\)
D. \(2.5\)
E. \(3\)
The question has five exact answer choices (no "Cannot be determined" or "None of the above") so one of them must be correct. If one of the answers is correct, the answer must be correct no matter how we draw the diagram (of course we should not violate info that is given).
Re-draw the diagram so that the upper semicircle is infinitely small. In this case the bottom semicircle will occupy half of the circle, and thus the area of the shaded region (which will be just one semicircle now) would be half of the larger circle, so 2.
Answer: C
General Discussion
18 Aug 2021, 08:42
Kudos
Bookmarks
As the question doesn't say anything about the radius of the internal circles we can suppose that they have the same radius. If so, the tangent point between them is in the center of the bigger circle.
We can picture a right triangle with that center, the center of a semicircle and the point where the semicircle touch the bigger circle.
Let:
R: radius bigger circle
r: radius semicircle
We have:
\(pi*R^2=4\) -> \(R^2=\frac{4}{pi}\)
\(R^2=r^2+r^2=2r^2\) -> \(r^2=\frac{R^2}{2}=\frac{2}{pi}\)
The shaded region is:
\(pi*r^2=pi*\frac{2}{pi}=2\)
IMO C
We can picture a right triangle with that center, the center of a semicircle and the point where the semicircle touch the bigger circle.
Let:
R: radius bigger circle
r: radius semicircle
We have:
\(pi*R^2=4\) -> \(R^2=\frac{4}{pi}\)
\(R^2=r^2+r^2=2r^2\) -> \(r^2=\frac{R^2}{2}=\frac{2}{pi}\)
The shaded region is:
\(pi*r^2=pi*\frac{2}{pi}=2\)
IMO C
