• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• 5-Day Free Trial
5-day free, full-access trial TTP Quant

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to $200 Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

# If A and C are points in a plane, C is the center of circle

00:00

A

B

C

D

E

## Global Stats

Difficult

If A and C are points in a plane, C is the center of circle O, and the length of line segment AC is x, does point A lie outside circle O ?

(1) The circumference of circle O is xπ.
(2) The area of circle O is xπ.

OA A

Source: Princeton Review

### GMAT/MBA Expert

GMAT Instructor
Joined
22 Aug 2016
Posted:
1394 messages
Followed by:
26 members
470
BTGmoderatorDC wrote:
If A and C are points in a plane, C is the center of circle O, and the length of line segment AC is x, does point A lie outside circle O ?

(1) The circumference of circle O is xπ.
(2) The area of circle O is xπ.

OA A

Source: Princeton Review
Given C is the center of the circle, point A is outside of the circle if AC = x > radius of the circle (r)

Let's take each statement one by one.

(1) The circumference of circle O is xπ.

Circumference of circle O = 2πr
=> 2πr = xπ

x = 2r

x > r. Sufficient.

(2) The area of circle O is xπ.

=> πr^2 = xπ

x = r^2

Case 1: Say r = 1/2, then r^2 = 1/4. We see that x < r. The answer is no.
Case 2: Say r = 2, then r^2 = 4. We see that x > r. The answer is yes.

Insufficient.

Hope this helps!

-Jay
_________________
Manhattan Review GRE Prep

Locations: GRE Classes Miami | GRE Prep Course Munich | GRE Prep Denver | LSAT Prep Course Orlando | and many more...

### GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
528 messages
Followed by:
25 members
59
Quote:
If A and C are points in a plane, C is the center of circle O, and the length of line segment AC is x, does point A lie outside circle O ?

(1) The circumference of circle O is xπ.
(2) The NUMERICAL VALUE of the area of circle O is equal to the NUMERICAL VALUE of xπ.
Obs.: xπ is measured in unit of length, while areas are measured in unit of length squared. That´s why we modified statement (2) accordingly.
${\text{dist}}\left( {A,C} \right)\,\,\, = \,\,x\,\,\,\,\mathop > \limits^? \,\,\,r$
$\left( 1 \right)\,\,\,\,2\pi r = \pi x\,\,\,\,\mathop \Rightarrow \limits^{:\,\,\pi \,} \,\,\,\,\,x = 2r\,\,\mathop > \limits^{r\,\, > \,0} r\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle$
$\left( 2 \right)\,\,\,\pi {r^2} = x\pi \,\,\,\,\mathop \Rightarrow \limits^{:\,\,\pi \,} \,\,\,\,\,x = {r^2}\,\,\,\left\{ \begin{gathered} \,{\text{Take}}\,\,r = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 4 > 2\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\ \,{\text{Take}}\,\,r = 0.5\,\,\,\,\, \Rightarrow \,\,\,\,\,x = 0.25 < 0.5\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{N}}{\text{O}}} \right\rangle \hfill \\ \end{gathered} \right.$

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

Regards,
Fabio.

_________________
Fabio Skilnik :: www.GMATH.net (Math for the GMAT)
Course release PROMO : finish our test drive till 30/Sep with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 70% discount!

### Top First Responders*

1 Jay@ManhattanReview 83 first replies
2 Brent@GMATPrepNow 68 first replies
3 fskilnik 55 first replies
4 GMATGuruNY 36 first replies
5 ceilidh.erickson 13 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

### Most Active Experts

1 fskilnik

GMAT Teacher

199 posts
2 Brent@GMATPrepNow

GMAT Prep Now Teacher

160 posts
3 Scott@TargetTestPrep

Target Test Prep

109 posts
4 Jay@ManhattanReview

Manhattan Review

95 posts
5 GMATGuruNY

The Princeton Review Teacher

90 posts
See More Top Beat The GMAT Experts