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Is the radius of circle Q longer than 2?

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Source: — Data Sufficiency |
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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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