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11 May 2011, 23:45
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
85%
(hard)
Question Stats:
51% (02:27) correct
49%
(02:34)
wrong
based on 245
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Not Attempted Yet
Attachment:
circles.png [ 7.66 KiB | Viewed 18553 times ]
(1) R=r+3k
(2) kR/(kr-6)=-1
03 Mar 2012, 08:24
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rohitgoel15
Spidy001
In the figure, small circel with radius r intersects larger circle with radius R (R>r). If k>0, what is the difference in the areas of the non overlapping parts of two circles?
(1) R=r+3k
(2) kR/(kr-6)=-1
Let x be the overlapping area.
we were asked find difference in non overlapping areas = \((pi*R^2-x)-(pi*r^2-x)\)
= pi*(R^2-r^2) = pi*(R+r)*(R-r)
1. Not sufficient.
we only know R-r ,not R+r.
2. Not sufficient
\(kR/(kr-6) = -1\)
=> R+r = 6/k. but we dont know R-r
Together, its sufficient.
= pi*(R+r)(R-r) = pi*(6/k)(3k) = 18pi.
Answer is C.
(1) R=r+3k
(2) kR/(kr-6)=-1
Let x be the overlapping area.
we were asked find difference in non overlapping areas = \((pi*R^2-x)-(pi*r^2-x)\)
= pi*(R^2-r^2) = pi*(R+r)*(R-r)
1. Not sufficient.
we only know R-r ,not R+r.
2. Not sufficient
\(kR/(kr-6) = -1\)
=> R+r = 6/k. but we dont know R-r
Together, its sufficient.
= pi*(R+r)(R-r) = pi*(6/k)(3k) = 18pi.
Answer is C.
I have one question in the above explanation.
Shouldnt x be deducted only once in the equation ?? ..
(pi*R^2-x)-(pi*r^2-x) --> (pi*R^2)-(pi*r^2) - x
Look at the diagram:
Attachment:
Circles.JPG [ 13.02 KiB | Viewed 17580 times ]
Difference between the areas will be: {Green}-{Yellow} = ({Big circle} - {Red}) - ({Small circle} - {Red}) = {Big circle} - {Small circle}.
Hope it's clear.
12 May 2011, 04:59
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Area 1 = OVerlap + ( pi*r^2 - Overlap)
Area 2 = OVerlap + ( pi*R^2 - Overlap)
So ( pi*R^2 - Overlap) - ( pi*r^2 - Overlap) = ?
= pi(R-r)(r+R)
(1)
R-r = 3k
Insufficient
(2)
kR = -kr +6
=> r+R = 6/k
Insufficient
(1) + (2)
So difference = pi* 3k * 6/k = 18pi
Answer - C
What is the OA ?
Area 2 = OVerlap + ( pi*R^2 - Overlap)
So ( pi*R^2 - Overlap) - ( pi*r^2 - Overlap) = ?
= pi(R-r)(r+R)
(1)
R-r = 3k
Insufficient
(2)
kR = -kr +6
=> r+R = 6/k
Insufficient
(1) + (2)
So difference = pi* 3k * 6/k = 18pi
Answer - C
What is the OA ?
