Hi All,

We're asked if the point Q is on the circle with center C. This is a YES/NO question and can be approached with some logic (and a few examples/drawings might help).

(1) R is a point on the circle and the distance from Q to R is equal to the distance from Q to C.

Since C is the CENTER of the circle, and R is on the circumference, we know that CR is a RADIUS of the circle. With the information in Fact 1, point Q can be ANY point that is equidistance from R and C.

IF....

-we have an equilateral triangle, with R and Q on the circumference, then the answer to the question is YES.

-we have point Q in the exact middle of the radius CR, then the answer to the question is NO.

Fact 1 is INSUFFICIENT

(2) S is a point on the circle and the distance from Q to S is equal to the distance from S to C.

Since C is the CENTER of the circle, and S is on the circumference, we know that CS is a RADIUS of the circle. With the information in Fact 2, we know that the length of QS is the SAME length as the RADIUS.

IF....

-we have an equilateral triangle, with S and Q on the circumference, then the answer to the question is YES.

-we have point Q in any other position that is exactly one radius in length from point S, then the answer to the question is NO.

Fact 2 is INSUFFICIENT

Combined, we know...

R is a point on the circle and the distance from Q to R is equal to the distance from Q to C.

S is a point on the circle and the distance from Q to S is equal to the distance from S to C.

With both Facts, we can create two different examples:

-we have two equilateral triangles, with Q on the circumference and R and S on opposite sides of Q, then the answer to the question is YES.

-we have an isosceles triangle, with Q OUTSIDE of the circle and CR as the non-equal side, then the answer to the question is NO.

Combined, INSUFFICIENT

Final Answer:

GMAT assassins aren't born, they're made,

Rich

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Contact Rich at: Rich.C@empowergmat.comThe Course Used By GMAT Club Moderators To Earn 750+ souvik101990 Score: 760 Q50 V42 ★★★★★ ENGRTOMBA2018 Score: 750 Q49 V44 ★★★★★