Last visit was: 14 Sep 2024, 08:23 It is currently 14 Sep 2024, 08:23
Decision Tracker
My Rewards
Unanswered
Active Topics
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

If X and Y are points in a plane and X lies inside the circle C with

SORT BY:
Date
Kudos
Tags:
Difficulty: Sub 505 Level,   Geometry,                        
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95505
Own Kudos [?]: 658509 [21]
Given Kudos: 87257
Send PM
CAT Tests Forum Quiz Mode
If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   02 Jul 2012, 02:36
4
Kudos
17
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

5% (low)

Question Stats:

86% (01:10) correct 14% (01:15) wrong based on 1975 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?

(1) The length of line segment XY is 3.
(2) The length of line segment OY is 1.5.
ShowHide Answer
Official Answer
B
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95505
Own Kudos [?]: 658509 [1]
Given Kudos: 87257
Send PM
CAT Tests Forum Quiz Mode
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   02 Jul 2012, 02:36
1
Bookmarks
Expert Reply
SOLUTION

If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?

(1) The length of line segment XY is 3. The maximum distance between two points on a circle is equal to the diameter, so in our case to 4, which means that the line segment XY could be entirely in the circle. But Y could also be outside the circle as well, for example consider the case when X coincides with center O. Not sufficient.

(2) The length of line segment OY is 1.5. Since OY<radius, then point Y must lie within the circle. Sufficient.

Answer: B.

Similar question to practice: if-point-x-is-inside-a-circle-with-center-o-and-radius-2-is-102751.html
User avatar
B
cyberjadugar
Senior Manager
Senior Manager
Joined: 29 Mar 2012
Posts: 266
Own Kudos [?]: 1541 [3]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Send PM
GMAT ToolKit User
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   02 Jul 2012, 03:11
2
Kudos
1
Bookmarks
Hi,

Difficulty level: 600

With reference to below figure (one of the possible cases):
Attachment:
xy.jpg
xy.jpg [ 3.64 KiB | Viewed 36581 times ]

Using (1),
XY = 3, Y can be anywhere in the plane. Insufficient.

Using (2),
OY = 1.5, radius of the circle is 2. Thus OY is less than the radius of the circle. Thus, Y lies inside the circle. Sufficient.

Answer is (B),

Regards,
User avatar
B
venmic
Manager
Manager
Joined: 02 Nov 2009
Posts: 74
Own Kudos [?]: 677 [0]
Given Kudos: 180
Send PM
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   03 Jul 2012, 00:38
Ok B is defintely sufficent but vvhy cant A be sufficient

this is hovv I vvorked it

since X is inside the circle - the value of X 0 .... 1.9 since radius is 2

novv


(1) The length of line segment XY is 3.
implies

Y-x =3
if X =0 minimal Y is 3 so it lies outside

case 2 is maximum
(1) The length of line segment XY is 3.
Y-X =3
Y-1.9 =3
Y=4.9
Y still lies outside

so VVhy cant A be proven or sufficent
User avatar
B
cyberjadugar
Senior Manager
Senior Manager
Joined: 29 Mar 2012
Posts: 266
Own Kudos [?]: 1541 [1]
Given Kudos: 23
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Send PM
GMAT ToolKit User
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   03 Jul 2012, 01:22
1
Kudos
venmic
Ok B is defintely sufficent but vvhy cant A be sufficient

this is hovv I vvorked it

since X is inside the circle - the value of X 0 .... 1.9 since radius is 2

novv


(1) The length of line segment XY is 3.
implies

Y-x =3
if X =0 minimal Y is 3 so it lies outside

case 2 is maximum
(1) The length of line segment XY is 3.
Y-X =3
Y-1.9 =3
Y=4.9
Y still lies outside

so VVhy cant A be proven or sufficent
Hi,

I will discuss one possibility for (1):
The diameter of circle is 4,
If X & Y can lie within circle on the diameter, both can lie inside the circle.

Otherwise, as stated previously Y can lie outside.
Thus, statement (1) is insufficient.

Regards,
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95505
Own Kudos [?]: 658509 [2]
Given Kudos: 87257
Send PM
CAT Tests Forum Quiz Mode
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   06 Jul 2012, 03:58
2
Kudos
Expert Reply
SOLUTION

If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?

(1) The length of line segment XY is 3. The maximum distance between two points on a circle is equal to the diameter, so in our case to 4, which means that the line segment XY could be entirely in the circle. But Y could also be outside the circle as well, for example consider the case when X coincides with center O. Not sufficient.

(2) The length of line segment OY is 1.5. Since OY<radius, then point Y must lie within the circle. Sufficient.

Answer: B.

Similar question to practice: if-point-x-is-inside-a-circle-with-center-o-and-radius-2-is-102751.html
avatar
dygoo
Intern
Intern
Joined: 16 Jul 2012
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 1
Send PM
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   16 Jul 2012, 18:35
Hello, Guys!
I think there may be information missing, since for the 2nd statement to solve the question I'd have to assume also that the points X, Y and O are in the same plane, but I believe this is not writen nor implyed in the question.

The plane in which lie the points X and Y is not necessarily the same plane of the whole circle, even though a few points of the circle may be on the plane.

What do you think? Hope I'm not bothering you with nonsense.
Best regards!
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 95505
Own Kudos [?]: 658509 [0]
Given Kudos: 87257
Send PM
CAT Tests Forum Quiz Mode
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   17 Jul 2012, 02:28
Expert Reply
dygoo
Hello, Guys!
I think there may be information missing, since for the 2nd statement to solve the question I'd have to assume also that the points X, Y and O are in the same plane, but I believe this is not writen nor implyed in the question.

The plane in which lie the points X and Y is not necessarily the same plane of the whole circle, even though a few points of the circle may be on the plane.

What do you think? Hope I'm not bothering you with nonsense.
Best regards!

This is the case when you can safely infer from the stem that all points are in the same plane. Anyway, on the GMAT you won't have a question with some points in one plane and some other points in some other plane.
avatar
dygoo
Intern
Intern
Joined: 16 Jul 2012
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 1
Send PM
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   17 Jul 2012, 07:07
Thanks, Bunuel!!!
avatar
mo_anger
Intern
Intern
Joined: 26 Nov 2013
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 0
Send PM
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   26 Nov 2013, 11:40
1
Kudos
dygoo
Hello, Guys!
I think there may be information missing, since for the 2nd statement to solve the question I'd have to assume also that the points X, Y and O are in the same plane, but I believe this is not writen nor implyed in the question.

The plane in which lie the points X and Y is not necessarily the same plane of the whole circle, even though a few points of the circle may be on the plane.

What do you think? Hope I'm not bothering you with nonsense.
Best regards!

Quoting - Page 24 GMAT 13th Edition Review last sentence - :

"All figures lie in a plane UNLESS OTHERWISE INDICATED"

I thought really long about this question until I looked it up here and afterwards found this sentence. Clarifies a lot... ;)
User avatar
TeamGMATIFY
Tutor
Joined: 20 Aug 2015
Posts: 348
Own Kudos [?]: 1427 [3]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Send PM
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   09 Nov 2015, 01:10
1
Kudos
2
Bookmarks
Expert Reply
Bunuel
If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?

(1) The length of line segment XY is 3.
(2) The length of line segment OY is 1.5.


Given: X and Y lie in a plane, X lies inside the circle with Center O and radius 2
Required: Does Y lie inside the Circle?

Statement 1: The length of line segment XY is 3.
The radius of the circle is given as 2, hence the longest line in the circle will be the diameter, with length = 4

The line XY may be fully in the circle or may be partially contained.

Attachment:
Question1.JPG
Question1.JPG [ 13.49 KiB | Viewed 27920 times ]

Hence INSUFFICIENT

Statement 2: The length of line segment OY is 1.5.
This means that the distance OY < radius of the circle
Hence Y will be inside the circle.

SUFFICIENT
User avatar
P
JeffTargetTestPrep
Target Test Prep Representative
Joined: 04 Mar 2011
Status:Head GMAT Instructor
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6833 [2]
Given Kudos: 1646
Send PM
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   17 Jun 2018, 19:58
1
Kudos
1
Bookmarks
Expert Reply
Bunuel
If X and Y are points in a plane and X lies inside the circle C with center O and radius 2, does Y lie inside circle C?

(1) The length of line segment XY is 3.
(2) The length of line segment OY is 1.5.

The length of line segment XY is 3.

We don’t have enough information to determine whether Y lies inside circle C. For example, if X is a point near the circumference of the circle, Y could be either inside or outside of the circle and be 3 units away from X. Statement one alone is not sufficient.

Statement Two Alone:

The length of line segment OY is 1.5.

Since the radius of the circle is 2 and O is the center, we see that OY is less than 2, so Y must be inside circle C. Statement two alone is sufficient.

Answer: B
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 34832
Own Kudos [?]: 878 [0]
Given Kudos: 0
Send PM
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] If X and Y are points in a plane and X lies inside the circle C with   20 May 2023, 16:49
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 Club Bot
gmatclubot
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
20 May 2023, 16:49
Moderator:
Bunuel
Math Expert
95503 posts