Is the radius of circle Q longer than 2?

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AAPL: Moderator; Posts: 2636; Joined: Sun Oct 29, 2017 2:08 pmFollowed by: 2 members

by AAPL » Thu Nov 21, 2019 1:34 am

Economist GMAT

Is the radius of circle Q longer than 2?

1) The circumference of circle Q is longer than 12.
2) AB is a chord of length 5 in circle Q.

OA B

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Source: Beat The GMAT — Data Sufficiency | Thu Nov 21, 2019 1:34 am

deloitte247: Legendary Member; Posts: 2214; Joined: Fri Mar 02, 2018 2:22 pmFollowed by: 5 members

by deloitte247 » Fri Nov 22, 2019 9:21 pm

Statement 1: The circumference of circle Q is longer than 12.
i.e Circumference > 12
$$Circumference\ =2\pi r\ ;\ where\ \pi=\frac{22}{7}$$
$$12=2\cdot\frac{22}{7}\cdot r$$
$$12=6.29r$$
$$r=1.9$$
$$i.e\ radius\ 'r'\ will\ be\ \ge1.91,\ which\ is\ either\ shorter\ than\ 2\ or\ less\ than\ 2.$$
herefore, statement 1 is NOT SUFFICIENT.

Statement 2: AB is a chord of length 5 in circle Q.
Chord = diameter, and diameter = 2r
$$r=\frac{d}{2}=\frac{5}{2}=2.5$$
Therefore, the radius is definetely greater than 2, hence, statement 2 is SUFFICIENT.

Since only statement 2 is SUFFICIENT, the correct option, thus, is OPTION B.

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