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.
A is the center of the circle above.
[#permalink]
07 Feb 2023, 02:31
07 Feb 2023, 02:31
Expert Reply
00:00
Question Stats:
57% (01:36) correct
42% (02:06) wrong based on 28 sessions
Hide Show timer Statistics
Attachment:
GRE A is the center of the circle above..jpg [ 11.74 KiB | Viewed 1630 times ]
A is the center of the circle above.
Quantity A |
Quantity B |
The perimeter of triangle ABC |
The perimeter of the shaded region |
A) Quantity A is greater.
B) Quantity B is greater.
C) The two quantities are equal.
D) The relationship cannot be determined from the information given.
Re: A is the center of the circle above.
[#permalink]
20 Feb 2023, 07:43
20 Feb 2023, 07:43
1
Expert Reply
OE
The two perimeters share the line BC, therefore, you can recast this question:
A. The combined length of two radii (AB and AC)
B. The length of arc BDC
The easiest thing to do in this situation is use numbers. Assume the radius of the circle is 2. If the radius is 2, then you can rewrite Quantity A is 4
Now you need to figure out the length of arc BDC if the radius is 2. You can set up a proportion, because the ratio of central angle to 360° will be the same as the ratio of the arc length to the circumference:
120/360=1/3
Circumference is \(2 \pi r\)
\(C=2 \pi (2) = 4 \pi\)
Arc length is 1/3 so it is \(\frac{4 \pi}{3}\)
So B >A
The two perimeters share the line BC, therefore, you can recast this question:
A. The combined length of two radii (AB and AC)
B. The length of arc BDC
The easiest thing to do in this situation is use numbers. Assume the radius of the circle is 2. If the radius is 2, then you can rewrite Quantity A is 4
Now you need to figure out the length of arc BDC if the radius is 2. You can set up a proportion, because the ratio of central angle to 360° will be the same as the ratio of the arc length to the circumference:
120/360=1/3
Circumference is \(2 \pi r\)
\(C=2 \pi (2) = 4 \pi\)
Arc length is 1/3 so it is \(\frac{4 \pi}{3}\)
So B >A
gmatclubot
Re: A is the center of the circle above. [#permalink]
20 Feb 2023, 07:43
Moderators:
