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

Question

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.

Bunuel · Answer

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

cyberjadugar · Answer

Hi,

Difficulty level: 600

With reference to below figure (one of the possible cases):

Attachment:

xy.jpg [ 3.64 KiB | Viewed 37862 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,

venmic · Answer

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

cyberjadugar · Answer

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,

Bunuel · Answer

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

dygoo · Answer

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!

Bunuel · Answer

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.

dygoo · Answer

Thanks, Bunuel!!!

mo_anger · Answer

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...

TeamGMATIFY · Answer

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. Question1.JPG 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

JeffTargetTestPrep · Answer

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

bumpbot · Answer

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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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