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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. 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.

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.

Re: If X and Y are points in a plane and X lies inside the [#permalink]

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16 Jul 2012, 17:35

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!

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.
_________________

Re: If X and Y are points in a plane and X lies inside the [#permalink]

Show Tags

26 Nov 2013, 10:40

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!

Re: If X and Y are points in a plane and X lies inside the [#permalink]

Show Tags

08 Nov 2015, 02:57

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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.

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 3638 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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If X and Y are points in a plane and X lies inside the
[#permalink]
09 Nov 2015, 00:10

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