• 7 CATs FREE!
    If you earn 100 Forum Points

    Engage in the Beat The GMAT forums to earn
    100 points for $49 worth of Veritas practice GMATs FREE

    Veritas Prep
    VERITAS PRACTICE GMAT EXAMS
    Earn 10 Points Per Post
    Earn 10 Points Per Thanks
    Earn 10 Points Per Upvote
    REDEEM NOW

In the figure above, acr QRO is a semicircle. What is the

This topic has 2 expert replies and 0 member replies

In the figure above, acr QRO is a semicircle. What is the

Post

Timer

00:00

Your Answer

A

B

C

D

E

Global Stats

Difficult



Princeton Review



In the figure above, acr QRO is a semicircle. What is the area of the circle with center O?

1) The area of the triangle PQO is 30.
2) The length of QRO is 2.5π.

OA C.

  • +1 Upvote Post
  • Quote
  • Flag
Post
AAPL wrote:
Princeton Review



In the figure above, acr QRO is a semicircle. What is the area of the circle with center O?

1) The area of the triangle PQO is 30.
2) The length of QRO is 2.5π.

OA C.
We have to get the area of the circle with center O.

Let's take each statement one by one.

1) The area of the triangle PQO is 30.

1/2 * OP * OQ = 30 => R*2r = 60 => R*r = 30, wether OP = R = radius of the bigger circle and r = radius of the smaller circle

We know that the area of the bigger circle = πR^2, but we can't get the unique value of R. Insufficient.

2) The length of QRO is 2.5π.

=> 2πr/2 = 2.5π => r = 2.5. We can't get the unique value of R. Insufficient.

(1) and (2) together

From (1), we have R*r = 30 and from (2), we have r = 2.5, thus, R = 30/2.5 = 6.

Thus, the area of the bigger circle = πR^2 = π*6^2 = 36π. Sufficient.

The correct answer: C

Hope this helps!

-Jay
_________________
Manhattan Review GMAT Prep

Locations: Manhattan Review New Delhi | Hyderabad | GRE Prep Chennai | Madhapur GRE Coaching | and many more...

Schedule your free consultation with an experienced GMAT Prep Advisor! Click here.

  • +1 Upvote Post
  • Quote
  • Flag
Post
AAPL wrote:
Princeton Review



In the figure above, arc QRO is a semicircle. What is the area of the circle with center O?

1) The area of the triangle PQO is 30.
2) The length of QRO is 2.5π.
$$? = {S_{{\text{big}}\,\, \odot }}\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\boxed{\,? = OP\,}\,$$



$$\left( {1 + 2} \right)\,\,\,\,\left\{ \matrix{
\,\left( 2 \right)\,\,\, \Rightarrow \,\,\,OQ = 5 \hfill \cr
\,\left( 1 \right)\,\,\, \Rightarrow \,\,\,30 = {{OP \cdot OQ} \over 2} \hfill \cr} \right.\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,?\,\, = \,\,\,OP\,\,{\rm{unique}}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\left( {\rm{C}} \right)$$


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: https://GMATH.net (Math for the GMAT) or https://GMATH.com.br (Portuguese version)
Course release PROMO : finish our test drive till 30/Dec with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount!

  • +1 Upvote Post
  • Quote
  • Flag
  • Target Test Prep
    5-Day Free Trial
    5-day free, full-access trial TTP Quant

    Available with Beat the GMAT members only code

    MORE DETAILS
    Target Test Prep
  • Magoosh
    Magoosh
    Study with Magoosh GMAT prep

    Available with Beat the GMAT members only code

    MORE DETAILS
    Magoosh
  • Economist Test Prep
    Free Trial & Practice Exam
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    Economist Test Prep
  • Varsity Tutors
    Award-winning private GMAT tutoring
    Register now and save up to $200

    Available with Beat the GMAT members only code

    MORE DETAILS
    Varsity Tutors
  • Kaplan Test Prep
    Free Practice Test & Review
    How would you score if you took the GMAT

    Available with Beat the GMAT members only code

    MORE DETAILS
    Kaplan Test Prep
  • EMPOWERgmat Slider
    1 Hour Free
    BEAT THE GMAT EXCLUSIVE

    Available with Beat the GMAT members only code

    MORE DETAILS
    EMPOWERgmat Slider
  • The Princeton Review
    FREE GMAT Exam
    Know how you'd score today for $0

    Available with Beat the GMAT members only code

    MORE DETAILS
    The Princeton Review
  • e-gmat Exclusive Offer
    Get 300+ Practice Questions
    25 Video lessons and 6 Webinars for FREE

    Available with Beat the GMAT members only code

    MORE DETAILS
    e-gmat Exclusive Offer
  • PrepScholar GMAT
    5 Day FREE Trial
    Study Smarter, Not Harder

    Available with Beat the GMAT members only code

    MORE DETAILS
    PrepScholar GMAT
  • Veritas Prep
    Free Veritas GMAT Class
    Experience Lesson 1 Live Free

    Available with Beat the GMAT members only code

    MORE DETAILS
    Veritas Prep

Top First Responders*

1 fskilnik@GMATH 62 first replies
2 Brent@GMATPrepNow 62 first replies
3 Jay@ManhattanReview 50 first replies
4 GMATGuruNY 35 first replies
5 Rich.C@EMPOWERgma... 25 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 image description fskilnik@GMATH

GMATH Teacher

126 posts
2 image description Brent@GMATPrepNow

GMAT Prep Now Teacher

99 posts
3 image description Max@Math Revolution

Math Revolution

90 posts
4 image description Jay@ManhattanReview

Manhattan Review

84 posts
5 image description Rich.C@EMPOWERgma...

EMPOWERgmat

63 posts
See More Top Beat The GMAT Experts