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

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Manager
Joined: 19 Aug 2007
Posts: 169
A certain circular area has its center at point P and has [#permalink]

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26 Dec 2007, 20:17
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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
Director
Joined: 12 Jul 2007
Posts: 858

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26 Dec 2007, 20:53
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Answer is C. Point Y is outside the circular area.

1. X is just outside the circle at 4.5 away from P. Tells us nothing of Y
2. X and Y are 9 apart. On it's own this tells us nothing.

Now taken together...

X is just .5 outside of the circle that has a radius of 4. If Y is 9 away from P, there's no way in can be inside the circle. The circle has a diameter of 8, so if you're starting from .5 outside the circle and have to go 9 away, the best you can do is .5 outside the circle on the opposite side.

I know I'm doing a terrible job of explaining it, but imagine two circles. One with a radius of 4 and starting at point P. The other starts at point X and has a radius of 9. The smaller circle is completely inside the larger circle. Since they don't overlap at any point there is no way for Y to be within the circle.
CEO
Joined: 29 Mar 2007
Posts: 2559

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27 Dec 2007, 18:03
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jimjohn 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

C

1: tells us about the d for X, but nothing about y. Insuff.

2: D btwn x and y is 9. could be in or out of the circle.

Together suff: y is outside the circle by .5.

Also we cant have the line go way outside the circle (essentially the opposite way). Its not possible under these constraints
CEO
Joined: 21 Jan 2007
Posts: 2739
Location: New York City

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12 Mar 2008, 03:51
eschn3am wrote:
Answer is C. Point Y is outside the circular area.

1. X is just outside the circle at 4.5 away from P. Tells us nothing of Y
2. X and Y are 9 apart. On it's own this tells us nothing.

Now taken together...

X is just .5 outside of the circle that has a radius of 4. If Y is 9 away from P, there's no way in can be inside the circle. The circle has a diameter of 8, so if you're starting from .5 outside the circle and have to go 9 away, the best you can do is .5 outside the circle on the opposite side.

if y is 9 away from X....
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You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Re:   [#permalink] 12 Mar 2008, 03:51
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