Is the radius of circle P longer than 2

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

by BTGmoderatorDC » Sun Feb 04, 2018 9:39 pm

Is the radius of circle P longer than 2?

(1) AB, the longest chord in circle P, is at least 5.

(2) The diameter of circle P is longer than 5.

Which is the sufficient statement?

OA D

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Source: Beat The GMAT — Data Sufficiency | Sun Feb 04, 2018 9:39 pm

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ErikaPrepScholar: Legendary Member; Posts: 503; Joined: Thu Jul 20, 2017 9:03 amFollowed by: 15 members; Thanked: 86 times; GMAT Score:770

by ErikaPrepScholar » Mon Feb 05, 2018 7:57 am

Statement 1
If we think about all of the chords we can draw in a circle, we should recognize that the longest chord will be one from a point on the circle straight across to the point opposite it on the other side of the circle - in other words, the longest chord in a circle is the diameter of the circle.

So if the longest chord in circle P is at least 5, the diameter of circle P is at least 5. The radius of a circle is half of the diameter. So if the diameter of circle P is at least 5, the radius is at least 2.5. Sufficient.

Statement 2
This directly tells us that the diameter of circle P is at least 5. Using the same logic from the previous statement, we can determine that the radius of circle P is at least 2.5 Sufficient.

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