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Points a & b

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Points a & b

by grandh01 » Thu Sep 27, 2012 11:07 am
Points A and B lie on the same plane as a circle with center O.
If the radius of circle O is 10, do points A and B both lie within
the area of circle O?
(1) The distance between points A and B is 21.
(2) The distance between points O and B is 11.

OA IS D
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Source: — Data Sufficiency |

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by Ian Stewart » Thu Sep 27, 2012 1:23 pm
grandh01 wrote:Points A and B lie on the same plane as a circle with center O.
If the radius of circle O is 10, do points A and B both lie within
the area of circle O?
(1) The distance between points A and B is 21.
(2) The distance between points O and B is 11.

OA IS D
The diameter of a circle is the maximum distance between 2 points on the circle. So if the diameter is 20, any two points that are both inside the circle must be less than 20 apart. If Statement 1 is true, it is impossible for both points to be within the circle.

If Statement 2 is true, B is not inside the circle at all (only points less than 10 away from the center are within the circle).

So each statement ensures that at least one point is outside the circle, and the answer is D.

Where are all of these questions that you've been posting from? They all ask yes/no questions, and in each of them, you find you have sufficient information to give a 'no' answer. I'm just curious why the question designer is recycling that 'trap' in every question, when it's something that is almost never used in real GMAT questions.
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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