GRE Prep 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.
In the figure above, the radius of the larger circle is twice the rad
[#permalink]
18 Feb 2025, 00:53
18 Feb 2025, 00:53
Expert Reply
00:00
Question Stats:
91% (01:12) correct
8% (00:39) wrong based on 12 sessions
Hide Show timer Statistics
Attachment:
GRE crcle shaded area.png [ 63.03 KiB | Viewed 619 times ]
In the figure above, the radius of the larger circle is twice the radius of the smaller circle. How many times is the area of the shaded region more than the area of the unshaded region?
A. 1
B. 2
C. 3
D. 4
E. 5
- Part of the project: GRE Quant & Verbal ADVANCED Daily Challenge 2025 NEW Edition - Gain 20 Kudos & Get FREE Access to GRE Prep Club TESTS
- Also replying to the unanswered questions
Manager
Joined: 11 Nov 2023
Posts: 228
Given Kudos: 78
WE:Business Development (Advertising and PR)
Re: In the figure above, the radius of the larger circle is twice the rad
[#permalink]
18 Feb 2025, 15:49
18 Feb 2025, 15:49
1
Let x = the radius of the smaller circle
The area of the smaller circle is πx^2; this is also the area of the unshaded region.
Given that the radius of the larger circle is twice the radius of the smaller circle, the larger circle's radius = 2x
The area of the larger circle is π(2x)^2 = 4πx^2
The area of the shaded region is the area of the larger circle minus the area of the smaller circle
= 4πx^2 - πx^2
= 3πx^2
Since the ratio of the area shaded region to the area of the unshaded region is 3πx^2 : πx^2, the area of the shaded region is 3 times more than the area of the unshaded region.
The area of the smaller circle is πx^2; this is also the area of the unshaded region.
Given that the radius of the larger circle is twice the radius of the smaller circle, the larger circle's radius = 2x
The area of the larger circle is π(2x)^2 = 4πx^2
The area of the shaded region is the area of the larger circle minus the area of the smaller circle
= 4πx^2 - πx^2
= 3πx^2
Since the ratio of the area shaded region to the area of the unshaded region is 3πx^2 : πx^2, the area of the shaded region is 3 times more than the area of the unshaded region.
Re: In the figure above, the radius of the larger circle is twice the rad
[#permalink]
12 May 2025, 01:03
12 May 2025, 01:03
1
The area of bigger circle is pi*r^2
The area of the shaded region is pi*r^2 - pi*(r/2)^2
Now, we need to find how many time the area of smaller circle is equal to the shaded region.
Hence, this area is equal to x*pi*(r/2)^2
Equating both will be x=3
hence, C
The area of the shaded region is pi*r^2 - pi*(r/2)^2
Now, we need to find how many time the area of smaller circle is equal to the shaded region.
Hence, this area is equal to x*pi*(r/2)^2
Equating both will be x=3
hence, C
