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21 May 2016, 03:50
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D
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Difficulty:
55%
(hard)
Question Stats:
58% (02:03) correct
42%
(01:56)
wrong
based on 149
sessions
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Is the area of circle C greater than the area of square S?
(1) The diameter of C is equal to the diagonal of square S.
(2) The perimeter of S is less than the circumference of C.
(1) The diameter of C is equal to the diagonal of square S.
(2) The perimeter of S is less than the circumference of C.
21 May 2016, 05:13
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Bunuel
Hi,
Area of a circle is dependent on radius, r, and That of square on side, say a..
so if we know the ratio between radius and the side we can answer the Q..
(1) The diameter of C is equal to the diagonal of square S.
This tells us that \(2r=\sqrt{2}a\)..
Suff..
(2) The perimeter of S is less than the circumference of C.
since we are dealing with inequality sign, always better to check for the values..
\(4a<2*pi*r................. a<pi*\frac{r}{2}\).....................
since both sides are +ive, square both sides...
\(a^2<(pi*\frac{r}{2})^2.........................a^2<pi*r^2*\frac{pi}{4}\).......................
since pi/4 <1, we can safely say \(a^2<pi*r^2\) OR area of square < area of circle
Suff
D
TheMechanic
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27 Sep 2017, 19:37
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We need to find if Area(C) >Area(S)
Let the side of the square is 'a' and radius of the circle be 'r'.
Stmt1: diameter (d)=\(\sqrt{2}a\)
on solving this we get, radius r = \(\sqrt{2}a/2\)
Using this relation we can deduce a relationship between the areas, hence we don't need to solve any further. This statement is sufficient.
Stmt2: \(4a<2 * pi * r\)
=> \(2a<pi*r\)
On squaring both sides...
=> \(a^2 < (pi^2 * r^2)/4\)
Again a clear relationship between a and r can be found here.. Hence this statement is sufficient.
The answer is D.
Let the side of the square is 'a' and radius of the circle be 'r'.
Stmt1: diameter (d)=\(\sqrt{2}a\)
on solving this we get, radius r = \(\sqrt{2}a/2\)
Using this relation we can deduce a relationship between the areas, hence we don't need to solve any further. This statement is sufficient.
Stmt2: \(4a<2 * pi * r\)
=> \(2a<pi*r\)
On squaring both sides...
=> \(a^2 < (pi^2 * r^2)/4\)
Again a clear relationship between a and r can be found here.. Hence this statement is sufficient.
The answer is D.
