Bunuel wrote:
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 \(16\pi\).
Kudos for a correct solution.Attachment:
2015-06-24_1004.png
Total angle at the centre of the clock = 360
Total parts in which the angle 360 is divided equally = 12
Angle between any two adjacent numbers in clock (i.e. 1 gap) = 360/12 = 30 degree
Angular measurement of 10 minutes in a clock = Angle between two gaps = 30*2 = 60 degrees
Question REDEFINED : Does the shaded sector of the clock represent more than 60 degrees?Statement 1: The clock hand has a length of 10With Radius of the sector, we can't find the angle made by sector
Hence,
NOT SUFFICIENTStatement 2: The area of the sector is more than \(16\pi\)Area of Sector > (Angle/360)*\((/pi)r^2\)
But Radius of the sector is unknown, therefore, we can't find the angle made by sector
Hence,
NOT SUFFICIENTCombining the two statementsRadius = 10
Area of Sector > \(16\pi\)
Area of Sector = (Angle/360)*\((/pi)r^2\)
i.e. (Angle/360)*\((/pi)r^2\) > \(16\pi\)
i.e. (Angle) > \(16*360 / 10^2\)
i.e. (Angle) > \(57.6\)
i.e. Angle may or may not be Greater than 60 degrees
Hence,
NOT SUFFICIENTAnswer: Option
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