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29 Oct 2019, 21:54
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What is the area of the larger of two circular regions, D and E?
(1) The smaller circular region has a circumference one-fourth that of the larger circular region.
(2) The radius of D and E together is equal to 25.
(1) The smaller circular region has a circumference one-fourth that of the larger circular region.
(2) The radius of D and E together is equal to 25.
29 Oct 2019, 23:17
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Let D be the smaller circle with radius "r" .
Let E be the bigger circle with radius "R".
(1) The smaller circular region has a circumference one-fourth that of the larger circular region.
2 * pi * r = (1/4) * (2 * pi * R)
==> r = (1/4) R
or R = 4r
Area of Bigger circle = Pi * R^2 (But R is not known) . Insufficient
(2) The radius of D and E together is equal to 25.
r + R = 25
R = (25 - r)
Area of Bigger Circle = Pi * (25-r)^2 (But r is not known). Insufficient
(1) & (2) gives
(1) R = 4r
(2) R+r = 25
==> 5r = 25 Or r = 5. Therefore R = 20 and Area of Bigger circle is (Pi * 20^2) Sufficient
Ans.C
Let E be the bigger circle with radius "R".
(1) The smaller circular region has a circumference one-fourth that of the larger circular region.
2 * pi * r = (1/4) * (2 * pi * R)
==> r = (1/4) R
or R = 4r
Area of Bigger circle = Pi * R^2 (But R is not known) . Insufficient
(2) The radius of D and E together is equal to 25.
r + R = 25
R = (25 - r)
Area of Bigger Circle = Pi * (25-r)^2 (But r is not known). Insufficient
(1) & (2) gives
(1) R = 4r
(2) R+r = 25
==> 5r = 25 Or r = 5. Therefore R = 20 and Area of Bigger circle is (Pi * 20^2) Sufficient
Ans.C
