A certain circular area has its centar at P and as radius 4

Question

A certain circular area has its centar at P and as radius 4 and Points X and Y lie in the same plane as the circular area. Does Y lie outside the circular area? 

1-Distance between point P and Y is 4.5 

2- Distance between X and Y is 9

Please explain!

netskater · Answer

A certain circular area has its centar at P and as radius 4 and Points X and Y lie in the same plane as the circular area. Does Y lie outside the circular area? 

Answer is A.

Consider  

Any point on the circle satisfies the eqn: x^2 + y^2 = 16 (1)
Points outside the circluar area will satisfy: x^2 + y^2 > 16 (2)

In our case, since distance between P and Y is 4.5, this satisfies eqn 2. Hence sufficient.

Consider  
We dont know any reference for X, hence statement is insufficient

eazyb81 · Answer

I think the answer is C.

The circle has a radius of 4, and point x is 4.5 away from the center of the circle (point P). Therefore, it is 0.5 outside the circle. But that doesn't tell you anything about Y, so 1 is insuff.

Statement 2 tells you the distance between x and y is 9, but that doesn't tell you anything about Y's relation to the circle, so 2 is insuff.

When you combine them, you can see that since X is 0.5 outside the circle, and y is 9 from x, there is no possible way that Y could be inside the circle. Even if X was just to the left of the circle, and Y was exactly to the right of X, Y would still be outside of the circle.

Hence, the answer is C.

uvs_mba · Answer

Guys,

This question was discussed sometime back as well. Though GMATPrep said the answer was C, I am not convinced with it. A lot of people believe that this is a mistake with GMATPrep, lol.

Netskater, can you please elaborate a little bit more with that X^2+Y^2 formula? How do you know this? Man, everyday I learn that stupid GMAT has so many tricky questions and I am like crap, I have to study more :cry:

And honestly like this kind of stuff not is available in any prep books man. Anyways, I am going to stop b..... and get back to studying....

And honestly like this kind of stuff not is available in any prep books man. Anyways, I am going to stop b..... and get back to studying....

paddyboy · Answer

This is clearly A. I think the question may not have been correctly replicated, because this question seems to have been discussed before, and it was C that time around... :roll:

diegmat · Answer

A. 

1) Distance between the center of a circle to any point on the circle has to be the radius. 4.5>4 therefore Y is outside the circle. SUFFICIENT

2) Longest distance between any two point on a circle is d â€“ in this case it is 8 â€“ so one of the points is outside the circle but it doesnâ€™t say which â€“ could be X or Y. NOT SUFFICIENT

jd04 · Answer

This one is tricky because of its ridiculous wording. The answer is C because its asks whether POINTS X & Y lie outside the circle. X and Y are not the coordinates (x,y) of some point, but points themselves, with unique sets of coordinates. 

A is NOT SUFF b/c it only addresses point Y
B is NOT SUFF b/c it only addresses the position of point Y relative to point X

C is the correct answer.

If we re-named the points A & B (instead of X & Y) this question would be much easier!!
The GMAT sucks.

eazyb81 · Answer

uva, I think you transcribed the problem incorrectly. I believe the first statement should be the distance between P and X (not Y) is 4.5. This would lead to an OA of C.

A certain circular area has its centar at P and as radius 4

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