Last visit was: 14 Sep 2024, 08:23 It is currently 14 Sep 2024, 08:23
Toolkit
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.

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

SORT BY:
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 95505
Own Kudos [?]: 658509 [21]
Given Kudos: 87257
Math Expert
Joined: 02 Sep 2009
Posts: 95505
Own Kudos [?]: 658509 [1]
Given Kudos: 87257
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
Manager
Joined: 02 Nov 2009
Posts: 74
Own Kudos [?]: 677 [0]
Given Kudos: 180
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
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
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
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
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,
Math Expert
Joined: 02 Sep 2009
Posts: 95505
Own Kudos [?]: 658509 [2]
Given Kudos: 87257
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
2
Kudos
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.

Intern
Joined: 16 Jul 2012
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 1
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
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!
Math Expert
Joined: 02 Sep 2009
Posts: 95505
Own Kudos [?]: 658509 [0]
Given Kudos: 87257
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
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.
Intern
Joined: 16 Jul 2012
Posts: 2
Own Kudos [?]: [0]
Given Kudos: 1
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
Thanks, Bunuel!!!
Intern
Joined: 26 Nov 2013
Posts: 1
Own Kudos [?]: 1 [1]
Given Kudos: 0
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
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...
Tutor
Joined: 20 Aug 2015
Posts: 348
Own Kudos [?]: 1427 [3]
Given Kudos: 10
Location: India
GMAT 1: 760 Q50 V44
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
1
Kudos
2
Bookmarks
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 [ 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
Target Test Prep Representative
Joined: 04 Mar 2011
Affiliations: Target Test Prep
Posts: 3036
Own Kudos [?]: 6833 [2]
Given Kudos: 1646
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
1
Kudos
1
Bookmarks
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.

Non-Human User
Joined: 09 Sep 2013
Posts: 34832
Own Kudos [?]: 878 [0]
Given Kudos: 0
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
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.
Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink]
Moderator:
Math Expert
95503 posts