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Source: — Data Sufficiency |

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by Brent@GMATPrepNow » Mon Dec 03, 2012 6:54 am
neeti2711 wrote:If P, Q and R are three distinct points, do line segments PQ and PR have the same length?

(1) P is the midpoint of the segment QR
(2) Q and R lie on the same circle with center P
Target question: Does PQ = PR ?

Statement 1: P is the midpoint of the segment QR
From the definition of midpoint, this statement tells us that PQ must equal PR
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: Q and R lie on the same circle with center P
If P is the center of a circle, then PQ and PR are both radii of that circle.
Since all radii of a circle have the same length, PQ must equal PR
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

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by neeti2711 » Mon Dec 03, 2012 10:31 am
Does "lie on the circle" always mean "on the circumference"? Can't they be somewhere on the chords?
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by Brent@GMATPrepNow » Mon Dec 03, 2012 10:40 am
Good question.

From the Official Guide: A circle is a set of points in a plane that are all located the same distance from a fixed point (the center of the circle).

So, a circle is defined as the points that lie on the circumference.

Later in the OG, we get: A chord of a circle is a line segment that has its endpoints on the circle.

So, if a questions refers to points on a circle, we can read this to mean "on the circumference."

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by bnpetteway » Thu Jan 10, 2013 5:38 pm
@ Brent, Aren't they saying the exact same thing? I got the correct answer as well and just wanted to clarify.
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by Brent@GMATPrepNow » Thu Jan 10, 2013 11:17 pm
bnpetteway wrote:@ Brent, Aren't they saying the exact same thing? I got the correct answer as well and just wanted to clarify.
I wouldn't exactly say that they're same thing.

If Q and R lie on the same circle with center P, then we can't necessarily conclude that P is the midpoint of the segment QR.

However, if P is the midpoint of the segment QR then we can conclude that Q and R lie on the same circle with center P

Nevertheless, the answer is still D.

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