It is currently 28 Nov 2023, 04:58
Register
GMAT Club Tests
GMAT Club Tests
Decision Tracker
My Rewards
New posts
New comers' posts

Close

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
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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

P is a point (not shown in the figure) in the plane containing O, R, a

7 posts Go to First Unread Post
Print view
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
SORT BY:
Date
Kudos
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 90078
CAT Tests Forum Quiz Mode
P is a point (not shown in the figure) in the plane containing O, R, a [#permalink] New post  23 May 2020, 06:20
27
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

35% (medium)

Question Stats:

72% (02:01) correct 28% (02:07) wrong based on 477 sessions

Hide Show timer Statistics


P is a point (not shown in the figure) in the plane containing O, R, and Q where O is the center of the circle and R and Q are points on the circle. If r is the radius of the circle, is P inside the circle?

(1) PR > PO
(2) PR + PQ = 5r



DS21262


Show Spoiler
Attachment:
1.png
1.png [ 10.36 KiB | Viewed 7980 times ]
ShowHide Answer
Official Answer
Official Answer and Stats are available only to registered users. Register/Login.

_________________
New to the GMAT CLUB Forum?

My Signature Questions' Collection:


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
User avatar
L
nick1816
Retired Moderator
Joined: 19 Oct 2018
Posts: 1886
Location: India
Re: P is a point (not shown in the figure) in the plane containing O, R, a [#permalink] New post  23 May 2020, 13:04
4
Kudos
Statement 1-
Attachment:
Untitled.png
Untitled.png [ 10.99 KiB | Viewed 7715 times ]


Insufficient

Statement 2-
Attachment:
Untitled.png
Untitled.png [ 9.99 KiB | Viewed 7651 times ]

If P lies inside the circle, Maximum value of PR and PQ is always less than 4r.

Sufficient
User avatar
B
Kali123
Intern
Intern
Joined: 24 Jun 2017
Posts: 27
Re: P is a point (not shown in the figure) in the plane containing O, R, a [#permalink] New post  06 Jun 2020, 23:25
VeritasKarishma.. Could you provide a better solution?
User avatar
G
TestPrepUnlimited
Tutor
Joined: 16 Sep 2014
Posts: 1255
Location: United States
GMAT 1: 780 Q51 V45
GRE 1: Q170 V167
Re: P is a point (not shown in the figure) in the plane containing O, R, a [#permalink] New post  07 Jun 2020, 12:11
Expert Reply
Bunuel wrote:

P is a point (not shown in the figure) in the plane containing O, R, and Q where O is the center of the circle and R and Q are points on the circle. If r is the radius of the circle, is P inside the circle?

(1) PR > PO
(2) PR + PQ = 5r



DS21262


Show Spoiler
Attachment:
The attachment 1.png is no longer available



Statement 1:
P must be further away from R than O, we can have the two cases showed in the attachment. Insufficient.

Statement 2:
While keeping P within the circle, PR is at most 2r. PQ is also at most 2r. Considering that, even if we add the maximums directly we cannot hit 5r. While keeping P inside the circle, the maximum of PR + PQ involves an optimization problem and it is certainly less than 4r. Therefore P must be outside the circle. Sufficient.

Ans: B
Attachments

File comment: For statement 1
Circle1.png
Circle1.png [ 25.13 KiB | Viewed 7282 times ]


_________________
Source: We are an NYC based, in-person and online GMAT tutoring and prep company. We are the only GMAT provider in the world to guarantee specific GMAT scores with our flat-fee tutoring packages, or to publish student score increase rates. Our typical new-to-GMAT student score increase rate is 3-9 points per tutoring hour, the fastest in the world. !
Signature Read More
User avatar
L
KarishmaB
Tutor
Joined: 16 Oct 2010
Posts: 14348
Location: Pune, India
Re: P is a point (not shown in the figure) in the plane containing O, R, a [#permalink] New post  09 Jun 2020, 02:07
2
Kudos
1
Bookmarks
Expert Reply
Bunuel wrote:

P is a point (not shown in the figure) in the plane containing O, R, and Q where O is the center of the circle and R and Q are points on the circle. If r is the radius of the circle, is P inside the circle?

(1) PR > PO
(2) PR + PQ = 5r



DS21262


Show Spoiler
Attachment:
1.png


(1) PR > PO

Consider point P in the top half of the circle somewhere. PR > PO.
Now move the point P vertically up outside the circle. Still PR > PO.
So P may be inside or outside the circle - not sufficient

(2) PR + PQ = 5r

If two points are inside or at the circle, maximum distance between them will be 2r (the diameter). For any points Q and R on the circle, the maximum sum of distance of P from Q and R will be 2 * 2r = 4r.
If the sum of the distances is 5r, P MUST be outside the circle.
Sufficient

Answer (B)
_________________
Karishma Bansal - ANA PREP

Join my next LIVE ONLINE CLASS for FREE by registering at ANA PREP
(Includes FREE trial access to Study Modules, Conceptual Videos and Practice Questions)

YouTube Channel @karishma.anaprep
youtube.com/channel/UCVxczpVAbQSQGEUyt72G2Eg/
Signature Read More
User avatar
G
Basshead
Director
Director
Joined: 09 Jan 2020
Posts: 996
Location: United States
Re: P is a point (not shown in the figure) in the plane containing O, R, a [#permalink] New post  26 Nov 2020, 18:38
Bunuel wrote:

P is a point (not shown in the figure) in the plane containing O, R, and Q where O is the center of the circle and R and Q are points on the circle. If r is the radius of the circle, is P inside the circle?

(1) PR > PO
(2) PR + PQ = 5r



DS21262


Show Spoiler
Attachment:
1.png


(1) One way to visualize this statement is that Point P is closer to Point O than Point R. This could certainly be possible inside the circle and outside the circle. INSUFFICIENT.

(2) \(PR + PQ = 5r\)

Given the radius = r
diameter = 2r

Since we're told PR + PQ = 5r, we can conclude with certainty that P is NOT in the circle because the diameter is 2r. SUFFICIENT.

Answer is B.
_________________
Help me get better -- please critique my responses!
Signature Read More
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 30689
Re: P is a point (not shown in the figure) in the plane containing O, R, a [#permalink] New post  29 Jun 2023, 22:46
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
Signature Read More
GMAT Club Bot
gmatclubot
Re: P is a point (not shown in the figure) in the plane containing O, R, a [#permalink]
29 Jun 2023, 22:46
NEW TOPIC
POST REPLY
Downloads
My Bookmarks
Reviews
Moderator:
Bunuel
Math Expert
90078 posts

cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions