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 4065 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 4065 times ]
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~fluke

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