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Circle sector question

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Circle sector question

by gmattesttaker2 » Sat Aug 11, 2012 10:23 pm
Hello,

Can you please explain the solution here:

If O represents the center of a circular clock and the point of the clock hand is on the circumference of the circle, does the shaded sector of the clock represent more than 10 minutes?

1) The clock hand has a length of 10.

2) The area of the sector is more than 16 pi

OA: E

Can you please help?

Regards,
Sri
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Source: — Data Sufficiency |
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by niketdoshi123 » Sat Aug 11, 2012 11:34 pm
gmattesttaker2 wrote:Hello,

Can you please explain the solution here:

If O represents the center of a circular clock and the point of the clock hand is on the circumference of the circle, does the shaded sector of the clock represent more than 10 minutes?

1) The clock hand has a length of 10.

2) The area of the sector is more than 16 pi

OA: E

Can you please help?

Regards,
Sri
Complete area of the circle represents 60 mins
So 1/6 of the area of the circle = 10 mins

Area of the circle = pi*r²

Area of the sector = central angle/360 * pi * r²
=> 1/6 * pi * r² = central angle/360 * pi * r²
=> central angle = 60°
Rephrased question
Is central angle > 60° ?

statement 1:
We can find the area of the circle , but we don't have any information about the central angle.
Hence insufficient

statement 2:
Area of the sector = central angle/360 * pi * r²
central angle/360 * pi * r² > 16pi
=> central angle/360 *r² > 16
We don't know the radius , so we can't say anything about the central angle.
Hence insufficient

Combining both the statements

central angle/ 360 * 100 > 16
=> central angle > 57.6°

Clearly it can be greater than or less than 60°.
Hence insufficient

The correct answer is E
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