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

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

In the figure shown, if the area of the shaded region is 3 t [#permalink]

Show Tags

11 Nov 2010, 08:09

4

This post received KUDOS

9

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

45% (medium)

Question Stats:

63% (01:07) correct 38% (01:05) wrong based on 376 sessions

HideShow timer Statistics

In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\)

Helpful Geometry formula sheet: http://gmatclub.com/forum/best-geometry-93676.html I hope these will help to understand the basic concepts & strategies. Please Click ON KUDOS Button.

Last edited by Bunuel on 06 Dec 2017, 11:24, edited 2 times in total.

Renamed the topic, edited the question and added the OA.

In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle? A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\)

The area of the shaded region is \(area_{shaded}=\pi{R^2}-\pi{r^2}\) and the area of the smaller circle is \(area_{small}=\pi{r^2}\). Given: \(\pi{R^2}-\pi{r^2}=3\pi{r^2}\) --> \(R^2=4r^2\) --> \(R=2r\);

Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \(\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2\).

Re: In the figure shown, if the area of the shaded region is 3 t [#permalink]

Show Tags

13 Apr 2014, 08:24

Bunuel wrote:

In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle? A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\)

The area of the shaded region is \(area_{shaded}=\pi{R^2}-\pi{r^2}\) and the area of the smaller circle is \(area_{small}=\pi{r^2}\). Given: \(\pi{R^2}-\pi{r^2}=3\pi{r^2}\) --> \(R^2=4r^2\) --> \(R=2r\);

Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \(\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2\).

Answer: C.

HI Bunnel,

Have one doubt on this as you have mentioned here R = 2r. Now we put this in the pi*rsquare then for both circles the are we got is

4pir square = pi r square.

Now area is four times instead of 3 times. So please clarify this

In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle? A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\)

The area of the shaded region is \(area_{shaded}=\pi{R^2}-\pi{r^2}\) and the area of the smaller circle is \(area_{small}=\pi{r^2}\). Given: \(\pi{R^2}-\pi{r^2}=3\pi{r^2}\) --> \(R^2=4r^2\) --> \(R=2r\);

Now, the ratio of the circumference of the larger circle to the that of the smaller circle is \(\frac{C}{c}=\frac{2\pi{R}}{2\pi{r}}=\frac{{2r}}{{r}}=2\).

Answer: C.

HI Bunnel,

Have one doubt on this as you have mentioned here R = 2r. Now we put this in the pi*rsquare then for both circles the are we got is

4pir square = pi r square.

Now area is four times instead of 3 times. So please clarify this

The stem says that the area of the shaded region is 3 times the area of the smaller circular region, not that the area of the larger circular region is 3 times the area of the smaller circular region.

Re: In the figure shown, if the area of the shaded region is 3 t [#permalink]

Show Tags

06 Dec 2017, 11:09

monirjewel wrote:

Attachment:

Untitled2.png

In the figure shown, if the area of the shaded region is 3 times the area of the smaller circular region, then the circumference of the larger circle is how many times the circumference of the smaller circle?

A. \(4\) B. \(3\) C. \(2\) D. \(\sqrt{3}\) E. \(\sqrt{2}\)

The area of the shaded region is areashaded=πR2−πr2areashaded=πR2−πr2 and the area of the smaller circle is areasmall=πr2areasmall=πr2.

I made a mistake here. I write this like: πR^2=3*πr^2 (as is say 3 times)

What mistake have I made?

I think it's addressed above.

The stem says that the area of the shaded region is 3 times the area of the smaller circular region, not that the area of the larger circular region is 3 times the area of the smaller circular region.
_________________