circular area and points X & Y

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LevelOne: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Fri Jun 19, 2009 11:46 am; Location: London; Thanked: 1 times

by LevelOne » Fri Jul 03, 2009 5:54 am

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.

Can someone explain, pls? thanks

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Source: Beat The GMAT — Data Sufficiency | Fri Jul 03, 2009 5:54 am

ssmiles08: Master | Next Rank: 500 Posts; Posts: 472; Joined: Sun Mar 29, 2009 6:54 pm; Thanked: 56 times

Re: circular area and points X & Y

by ssmiles08 » Fri Jul 03, 2009 6:12 am

LevelOne 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.

Can someone explain, pls? thanks

IMO C.

1) insufficient b/c it gives us no information on point Y.
2) insufficient b/c it gives us no information on whether any of the two points are located inside or outside the circle.

together:

we know point x is outside the circle, (distance of 0.5 away from the point ON the circle).

xy = 9

the diameter of the circle is 8, which means the largest distance covered and the point y can still be covered inside the circle is 8.

4.5 + 4 = 8.5 (can be the maximum distance allowed for xy for y to still be a part inside the circle).

Therefore point y will lie outside the circle.

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LevelOne: Senior | Next Rank: 100 Posts; Posts: 69; Joined: Fri Jun 19, 2009 11:46 am; Location: London; Thanked: 1 times

by LevelOne » Fri Jul 03, 2009 6:18 am

OA is C, thanks

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