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

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Bunuel
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If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  02 Jul 2012, 02:36
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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.
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Bunuel
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  02 Jul 2012, 02:36
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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
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  02 Jul 2012, 03:11
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Hi,

Difficulty level: 600

With reference to below figure (one of the possible cases):
Attachment:
xy.jpg
xy.jpg [ 3.64 KiB | Viewed 35125 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),

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venmic
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  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
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cyberjadugar
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  03 Jul 2012, 01:22
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venmic wrote:
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,
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Bunuel
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  06 Jul 2012, 03:58
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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
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  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!
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Bunuel
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  17 Jul 2012, 02:28
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dygoo wrote:
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.
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  17 Jul 2012, 07:07
Thanks, Bunuel!!!
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  26 Nov 2013, 11:40
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dygoo wrote:
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... ;)
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  09 Nov 2015, 01:10
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Bunuel wrote:
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 26626 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
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Re: If X and Y are points in a plane and X lies inside the circle C with [#permalink] New post  17 Jun 2018, 19:58
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Bunuel wrote:
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
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