A circular well is constructed within a circular garden. The circumfer

Question

A circular well is constructed within a circular garden. The circumference of the well is 1/5 that of the garden. What is the area of the mouth of the well?

(1) The area of the garden is  25\pi  square meters.

(2) The edging around the garden is  10\pi  meters long.

Archit3110 · Answer

#1
radius = 5 sufficient
#2
again 2* pi * r = 10 pi
r= 5
sufficient
IMO D

Kinshook · Answer

Given:  A circular well is constructed within a circular garden. The circumference of the well is 1/5 that of the garden.

Asked:  What is the area of the mouth of the well?

The circumference of the well is 1/5 that of the garden. 
The radius of the well is 1/5 that of the garden (Circumference =  2\pi radius)
Area of the well is 1/25 that of the garden (Area =  \pi * radius^2 )

(1) The area of the garden is  25\pi  square meters.
Area of the well is  1/25*25 \pi= \pi square meters. (if area of mouth of well = area of the well)
SUFFICIENT

(2) The edging around the garden is  10\pi  meters long.
 2\pi * radius of garden = 10 \pi 
radius of garden = 5 meters
radius of well = 1/5 * 5 = 1 meter
Area of well  = \pi * 1^2 = \pi  square meters
SUFFICIENT

IMO D

QuantMadeEasy · Answer

Let radius of well be r and that of garden by R

Given: circumference of the well is 1/5 that of the garden OR 
r = R /5 ---- (i)

To find: area of well OR we need to find radius of the well ie. r

(1) pi x R^2 = 25 pi, from this we can determine r by using equation (i). We actually dont need to find the values. Sufficient.

(2) 2 x pi x R = 10 pi. Again same reasoning. Sufficient.

D is correct.

Bunuel · Answer

Official Explanation

We have two circles, and we need to find the radius of the smaller one. The circumference, area, or radius of either the larger or smaller circle will be sufficient to do so. On to the statements, separately first.

Statement (1) tells us that the radius of the garden is 5. The radius of the well is 1/5 that of the garden, so the radius of the well is 1, and the area of the mouth of the well is  \pi . We have answered the question definitively, so Statement (1) is sufficient.

Statement (2) gives us the circumference of the larger circle. From it, we know that the circumference of the smaller circle is  2\pi . Therefore, the radius of the smaller circle is 1 and the area is . We have answered the question definitively, so Statement (2) is sufficient. The correct answer is (D). Since various facts about a circle gives us its radius and the radius gives us all of those things in turn, Data Sufficiency questions involving circles tend toward sufficiency.

Again, the correct answer is (D).

Bunuel · Answer

Video Explanation

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A circular well is constructed within a circular garden. The circumfer

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