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 1801:30 AM EDT
-02:30 AM EDT
Learn how Kamakshi achieved a GMAT 675 with an impressive 96th %ile in Data Insights. Discover the unique methods and exam strategies that helped her excel in DI along with other sections for a balanced and high score.
Sep 1712:30 AM EDT
-01:30 AM EDT
Thought your job leaves no time for GMAT prep? After multiple GMAT attempts and a demanding consulting job, Kshitij improved to 695 in under 2 months. Learn the mindset shifts, study strategy, and execution changes that made the breakthrough possible.
Sep 1808:00 PM PDT
-09:00 PM PDT
Video explanations + diagnosis of 10 weakest areas + 150+ short videos + study plan!
Sep 1902:30 AM EDT
-03:30 AM EDT
Tejas studied hard but kept repeating the same mistakes. After 3 attempts at 645, a focused 4-week strategy helped him identify and fix what was holding him back—leading to a 695 with just 12–15 hours of study per week.
25 Aug 2021, 08:00
Kudos
Bookmarks
E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
42% (01:56) correct
58%
(02:17)
wrong
based on 137
sessions
History
Date
Time
Result
Not Attempted Yet
An yellow semicircle and its tangent blue quarter-circle are drawn in a square as shown above. If AB is tangent to both yellow semicircle and blue quarter-circle, what is the length of AB ?
A. 10
B. 12
C. 14
D. 16
E. 18
M37-24
|
M37-24
Attachment:
Untitled14.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!
25 Aug 2021, 08:30
Kudos
Bookmarks
Itried to explain in the photo below.
My answer is E
My answer is E
Attachments
20.jpg [ 94.55 KiB | Viewed 4853 times ]
22 Nov 2021, 05:06
Kudos
Bookmarks
Official Solution:
An yellow semicircle and its tangent blue quarter-circle are drawn in a square as shown above. If AB is tangent to both yellow semicircle and blue quarter-circle, what is the length of AB ?
A. \(10\)
B. \(12\)
C. \(14\)
D. \(16\)
E. \(18\)
Join the centers of the circles and the tangency points (recall that the radius of a circle is perpendicular to the tangent line). This would mean that CD is a straight line. Since CD equals to the radius of the semicircle plus the radius of the quarter circle, then \(CD = 6 + 12= 18\)
Draw line segment AE perpendicular to FD.
In a right triangle BGD, \(\angle BDG+\angle GBD =90°\).
In a right triangle CFD, \(\angle BDG+\angle DCF=90°\). So, \(\angle GBD=\angle DCF\).
In a right triangle ABE, \(\angle BAE+\angle GBD=90°\). So, \(\angle BAE=\angle BDG\).
So, two right tringles ABE and DCF are congruent: all angles are equal AND \(AE = DF = side \ of \ the \ square\). Therefore, the hypotenuses of these triangles must be equal: \(AB = CD = 18\)
Answer: E
An yellow semicircle and its tangent blue quarter-circle are drawn in a square as shown above. If AB is tangent to both yellow semicircle and blue quarter-circle, what is the length of AB ?
A. \(10\)
B. \(12\)
C. \(14\)
D. \(16\)
E. \(18\)
Join the centers of the circles and the tangency points (recall that the radius of a circle is perpendicular to the tangent line). This would mean that CD is a straight line. Since CD equals to the radius of the semicircle plus the radius of the quarter circle, then \(CD = 6 + 12= 18\)
Draw line segment AE perpendicular to FD.
In a right triangle BGD, \(\angle BDG+\angle GBD =90°\).
In a right triangle CFD, \(\angle BDG+\angle DCF=90°\). So, \(\angle GBD=\angle DCF\).
In a right triangle ABE, \(\angle BAE+\angle GBD=90°\). So, \(\angle BAE=\angle BDG\).
So, two right tringles ABE and DCF are congruent: all angles are equal AND \(AE = DF = side \ of \ the \ square\). Therefore, the hypotenuses of these triangles must be equal: \(AB = CD = 18\)
Answer: E
