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a circular tree orchard

by sanju09 » Mon Oct 17, 2011 1:27 am
Trees are to be planted inside a circular tree orchard so that there are 5 trees per square meter. The circumference of the tree orchard is 30 meters. If trees are available only in allotments of packages of 6, how many allotments will the caretaker need to purchase?
(A) 58
(B) 59
(C) 60
(D) 117
(E) 118
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by shankar.ashwin » Mon Oct 17, 2011 1:35 am
Area = Pi(15/Pi)^2 = 71.6

No of trees = 71.6*5 = 358

Therefore No of allotments = 358/6 = 60(approx) C IMO
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by neelgandham » Mon Oct 17, 2011 1:45 am
sanju09 wrote:Trees are to be planted inside a circular tree orchard so that there are 5 trees per square meter. The circumference of the tree orchard is 30 meters. If trees are available only in allotments of packages of 6, how many allotments will the caretaker need to purchase?
(A) 58
(B) 59
(C) 60
(D) 117
(E) 118
Step 1 Circumference of circle, 2*pi*r = 30, Implies, r = 15/pi - (1)

Step 2 Area of circle = pi*r*r = pi * 15/pi * 15/pi (from 1) = 225/pi square meters

Step 3 1 square meter should contain 5 trees, so 225/pi square meters should contain 225*5/pi.

Step 46 trees make a bundle, 225*5/pi trees make 225*5/(pi*6) =~ 59.7 and the next nearest integer is 60. Hence, option C
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by GmatKiss » Mon Oct 17, 2011 3:19 am
IMO: C
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