Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

 It is currently 16 Jul 2019, 13:36 ### 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

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

Track

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.  # The radius of circle A is r, and the radius of circle B is 3/4*r

Author Message
TAGS:

### Hide Tags

Math Expert V
Joined: 02 Sep 2009
Posts: 56244

### Show Tags 00:00

Difficulty:   15% (low)

Question Stats: 83% (00:47) correct 18% (01:44) wrong based on 49 sessions

### HideShow timer Statistics The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

_________________
Retired Moderator D
Joined: 30 Jan 2015
Posts: 805
Location: India
Concentration: Operations, Marketing
GPA: 3.5
Re: The radius of circle A is r, and the radius of circle B is 3/4*r  [#permalink]

### Show Tags

Area of Circle A = π*r^2
Area of Circle B = π*(3/4*r)^2 = (π*r^2)*9/16

Ratio = Area of Circle A / Area of Circle B
= π*r^2 / (π*r^2)*9/16 ( Cancelling, π*r^2 from numerator and denominator)
= 1/(9/16)
= 16/9

Hence, E.
_________________
The few, the fearless !

Thanks VP  D
Joined: 31 Oct 2013
Posts: 1392
Concentration: Accounting, Finance
GPA: 3.68
WE: Analyst (Accounting)
Re: The radius of circle A is r, and the radius of circle B is 3/4*r  [#permalink]

### Show Tags

Bunuel wrote:
The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

Area of a circle = π $$r^2$$

Area of circle A = π$$r^2$$

Area of Circle B = π $$(3/4r)^2$$

Ratio = π $$r^2$$ / π $$(3/4r)^2$$

= r^2 / (9/16) $$r^2$$

= 1 / (9/16)

= 16 : 9

Thus the best answer is E.
Board of Directors P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4512
Location: India
GPA: 3.5
Re: The radius of circle A is r, and the radius of circle B is 3/4*r  [#permalink]

### Show Tags

Bunuel wrote:
The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

Ratio of the Area of Circles is actually the ratio of their Radii as $$πR^2 : πr^2 = R^2 : r^2$$

Thus, ratio of the Area of the circles is $$r^2 : (\frac{3}{4r})^2 = 16 : 9$$, Answer must be (E)
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Senior SC Moderator V
Joined: 22 May 2016
Posts: 3063

### Show Tags

Bunuel wrote:
The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

Let radius of $$A = 4$$
Radius of $$B =\frac{3}{4}A=(\frac{3}{4}*4)=3$$

Area of A: $$\pi r^2=\pi 4^2=16\pi$$
Area of B: $$\pi r^2=\pi 3^2=9\pi$$

Ratio of the area of circle A to the area of circle B:
$$\frac{A}{B}=\frac{16 \pi}{9 \pi}=\frac{16}{9}=(16 : 9)$$

_________________
SC Butler has resumed!
Get two SC questions to practice, whose links you can find by date, here.

Tell me, what is it you plan to do with your one wild and precious life? -- Mary Oliver
Target Test Prep Representative D
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 6923
Location: United States (CA)
Re: The radius of circle A is r, and the radius of circle B is 3/4*r  [#permalink]

### Show Tags

Bunuel wrote:
The radius of circle A is r, and the radius of circle B is $$\frac{3}{4}r$$. What is the ratio of the area of circle A to the area of circle B ?

A. 1 to 4
B. 3 to 4
C. 4 to 3
D. 9 to 16
E. 16 to 9

Area of circle A = πr^2

Area of circle B = π(¾ r)^2 = π(9/16)r^2

So the ratio of the area of circle A to the area of circle B is

πr^2/[π(9/16)r^2] = 1/(9/16) = 16/9

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: The radius of circle A is r, and the radius of circle B is 3/4*r   [#permalink] 19 Jul 2018, 12:36
Display posts from previous: Sort by

# The radius of circle A is r, and the radius of circle B is 3/4*r  