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# Children playing a game roll a circular disc to see who can roll it th

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Math Expert
Joined: 02 Sep 2009
Posts: 58464
Children playing a game roll a circular disc to see who can roll it th  [#permalink]

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29 Aug 2018, 03:49
00:00

Difficulty:

25% (medium)

Question Stats:

81% (01:24) correct 19% (01:05) wrong based on 39 sessions

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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.

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Joined: 07 Oct 2017
Posts: 252
Re: Children playing a game roll a circular disc to see who can roll it th  [#permalink]

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29 Aug 2018, 05:57
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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.

St1) We know one rotation covers 2*pi*r distance and we know the number of rotations. So we can equate that distance by 6pi

Sufficient

St2) only thing we can know is velocity that is of no use to find radius.
Insufficient

Thank you = Kudos
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Thank you =Kudos
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Children playing a game roll a circular disc to see who can roll it th  [#permalink]

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29 Aug 2018, 06:43
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=?

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)
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Children playing a game roll a circular disc to see who can roll it th   [#permalink] 29 Aug 2018, 06:43
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