Bunuel wrote:

Children playing a game roll a circular disc to see who can roll it the farthest. What is the area, in square centimeters, of the disc they are playing with?

(1) One child rolled the disc exactly 540 degrees and it rolled exactly 6π centimeters.

(2) On one roll the disc traveled for 6 complete rotations, which lasted a total of 10 seconds.

Question stem:- Area of disc=?

We require radius of disc.

St1:- One child rolled the disc exactly 540 degrees and it rolled exactly 6π centimeters.

540 degree=360 degree(one complete rotation)+180 degree(Half rotation)=6π

Or, Rolling distance at 540 degree=Rolling distance at one complete rotation+Rolling distance at Half rotation=\(2*\pi*r\)+\(\pi*ri\)=6π

(1 complete rotation is equivalent to a distance of \(2*\pi*r\))

Or, \(3*\pi*r\)=6π Or r=2

Hence area can be determined.

Sufficient.

St2:- On one roll the disc traveled for 6 complete rotations, which lasted a total of 10 seconds.

We need info on distance traveled by the disc in one rotation or 6 rotations in in order to determine radius . Time has no function here.

Insufficient.

Ans. (A)

_________________

Regards,

PKN

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