A certain circular area has its center at point P and has : GMAT Data Sufficiency (DS)
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# A certain circular area has its center at point P and has

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A certain circular area has its center at point P and has [#permalink]

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07 Jun 2009, 16:46
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A certain circular area has its center at point P and has radius 4, and points X and Y lie in the same plane as the circular area. Does point Y lie outside the circular area?

(1) The distance between point P and point X is 4.5.
(2) The distance between point X and point Y is 9.

[Reveal] Spoiler:
1) Not sufficient. The distance between point P and point X is not relevant to determine whether Y is inside or outside of the circular area. It does say that X is a point that is 0.5 away from the circle's edge though.
2) Not sufficient. The distance between point X and point Y gives no relationship to point P so it cannot be determined that point Y is inside/outside of the circle.

C) Sufficient. The point Y lies outside the circular area because X is 4.5 from P (center), therefore X is .5 away from the circle's edge and Y is 9 away that. Given that the circle's diameter is 8, 8 + .5 = 8.5 which is less than 9, therefore it is impossible for Y to be in the circular area.

C is the correct answer. It took me a while to think this through but seems easy now that I've written it out. Can someone please confirm that my logic is correct? Thanks.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-circular-area-has-its-center-at-point-p-and-has-101485.html
[Reveal] Spoiler: OA
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Re: A certain circular area has its center at point P and has [#permalink]

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07 Jun 2009, 17:57
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Re: A certain circular area has its center at point P and has [#permalink]

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08 Jun 2009, 00:45
As the points XY lie in teh same plane as the circle, the given distances are presumed to be perpendicular distance..

and hence the answer shud be C IMO.
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Re: A certain circular area has its center at point P and has [#permalink]

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08 Jun 2009, 01:49
Here, since all the points are in the same plane:.
statement 1, does not give the placement of Y, w.r.t. the circle and X.
statement 2 does not give placement of X and y w.r.t. the circle.
and when taken together, position of Y always lies outside the circle, whether we take it perpendicular to the axis or parallel to it.
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Re: A certain circular area has its center at point P and has [#permalink]

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24 Apr 2011, 07:59
I3igDmsu wrote:
A certain circular area has its center at point P and has radius 4, and points X and Y lie in the same plane as the circular area. Does point Y lie outside the circular area?
1) The distance between point P and point X is 4.5.
2) The distance between point X and point Y is 9.

See attached image "Point_Y_Outside_Circle_C2.PNG"

c2 is the circle with radius 4
Q: Is point "Y" outside circle "c2"?

1. Clearly insufficient as it doesn't say a word about point "Y".

It conveys:
If we draw a circle from point p with radius "4.5"(depicted as circle c3), point "X" will somewhere be on this circle and it is definitely outside the circular area(Area within circle c2) mentioned in the stem.

2.
Insufficient.
Attachment:

Point_X_Outside_Or_Inside_c2.PNG [ 10.62 KiB | Viewed 4607 times ]

Combining both;
We know point "X" lies outside the circle c2(radius=4) and it lies on the circle, c3(radius=4.5 and Diameter=9). And point "Y" is 9 units away from point "X". The closest it can ever get to circle c2 will be when it lies on the circle "c3", diagonally opposite to point "X". Just to reiterate, the point "Y" is 9 units away from "X" and 9 is the length of the diagonal of the bigger circle, c3. Thus, point "Y" will never lie on or inside the circle, c2.

Sufficient.

Ans: "C"

Attachment:

Point_Y_Outside_Circle_C2.PNG [ 10.92 KiB | Viewed 4609 times ]

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Re: A certain circular area has its center at point P and has [#permalink]

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24 Apr 2011, 18:27
(1) is insufficient as there is no information about point Y

(2) is insufficient as we don't know about the location of point X

(1) and (2) combined :

Let us imagine two scenratios the point X is on X-axis at a distance 4.5 from the center, then clearly X lies outside cirlce, so if the point Y lies to the right of X, it's oustide the circle. If the point Y lies to the left of point X, then the point Y is at a distance 4.5 + 4.5, which is greater than the diammeter of circle, hence it lies outside circle.

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Re: A certain circular area has its center at point P and has [#permalink]

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24 Aug 2015, 13:46
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Re: A certain circular area has its center at point P and has [#permalink]

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24 Aug 2015, 22:10
Expert's post
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I3igDmsu wrote:
A certain circular area has its center at point P and has radius 4, and points X and Y lie in the same plane as the circular area. Does point Y lie outside the circular area?

(1) The distance between point P and point X is 4.5.
(2) The distance between point X and point Y is 9.

[Reveal] Spoiler:
1) Not sufficient. The distance between point P and point X is not relevant to determine whether Y is inside or outside of the circular area. It does say that X is a point that is 0.5 away from the circle's edge though.
2) Not sufficient. The distance between point X and point Y gives no relationship to point P so it cannot be determined that point Y is inside/outside of the circle.

C) Sufficient. The point Y lies outside the circular area because X is 4.5 from P (center), therefore X is .5 away from the circle's edge and Y is 9 away that. Given that the circle's diameter is 8, 8 + .5 = 8.5 which is less than 9, therefore it is impossible for Y to be in the circular area.

C is the correct answer. It took me a while to think this through but seems easy now that I've written it out. Can someone please confirm that my logic is correct? Thanks.

A certain circular area has its center at point P and has radius 4, and points X and Y lie in the same plane as the circular area. Does point Y lie outside the circular area?

(1) The distance between point P and point X is 4.5. No info about y. Not sufficient.
(2) The distance between point X and point Y is 9. No relationship between this line segment and circle. Not sufficient.

(1)+(2) From (1) X is outside the circle (as radius is 4). Closest point of this circle to the point X equals to 4.5-4=0.5 and the furthest equals to 0.5+8(diameter)=8.5. As XY=9, then Y must be outside the circle. Sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-certain-circular-area-has-its-center-at-point-p-and-has-101485.html
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Re: A certain circular area has its center at point P and has   [#permalink] 24 Aug 2015, 22:10
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