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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

by swerve » Thu Aug 09, 2018 10:23 am

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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.

The OA is C.
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Source: — Data Sufficiency |
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by deloitte247 » Sat Aug 18, 2018 11:29 am

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Question : Does point y lie outside the circular area.

Statement 1 : The distance between Point P and Point X is 4 . 5
Since the radius of the circle = 4
Every point that is greater than 4 will be outside the circle. Which means x is outside the circle but information about y was not given in statement 1 .
Hence, statement 1 is NOT SUFFICIENT.

Statement 2 : The distance between point x and point y = 9
We cannot find out the relative position of x and y from this statement alone.
Hence, statement 2 is NOT SUFFICIENT.

Statement 1 and 2 together :
x is 4.5 away from center st point p, since the radius = 4, then x = 4.5 - 4 = 0.5
Distance between x and y is 9
Farthest point from the circle is 0.5 + 8 = 8.5
( that is if we take it to be directly opposite x on the other side of the circle which is the diameter of the circle)
Thus, y is always outside the circle.
Statement 1 ans 2 together is SUFFICIENT.
Option C is CORRECT.
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