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26 Apr 2019, 07:42
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D
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90% (01:16) correct
10%
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wrong
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The heart-shaped decoration shown in the figure above consists of a square and two semicircles. What is the radius of each semicircle?
(1) The diagonal of the square is \(10\sqrt{2}\) centimeters long.
(2) The area of the square region minus the sum of the areas of the semicircular regions is 100 − 25π square centimeters.
DS18502.01
Quantitative Review 2020 NEW QUESTION
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26 Apr 2019, 11:22
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From S1:
Diagonal of a square = \(a\sqrt{2}\) = \(10\sqrt{2}\)
Side, a = 10
diameter of the semicircle = side of the square.
Radius = 10/2 = 5
Sufficient.
From S2:
\(a^2-π*r^2\) = 100-25π
\(a^2 = 100\)
\(π*r^2 = 25π\)
Radius = 5
Sufficient.
D is the answer.
Diagonal of a square = \(a\sqrt{2}\) = \(10\sqrt{2}\)
Side, a = 10
diameter of the semicircle = side of the square.
Radius = 10/2 = 5
Sufficient.
From S2:
\(a^2-π*r^2\) = 100-25π
\(a^2 = 100\)
\(π*r^2 = 25π\)
Radius = 5
Sufficient.
D is the answer.
27 Apr 2019, 04:50
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Please note that the solution presented above by Chethan92 is wrong, as it relates to statement (2) as an equation with two variables, but relates to it as having only one solution.
The Logical approach to this question will be based on the fact that in both squares and circles one measurement, any measurement (side, diagonal, radius, perimeter, etc.) is enough on order to find all other measurements.
Statement (1) is enough, since the diagonal of the square can give us its side (since it creates a 45-45-90 triangle, all we need is to divide the diagonal by √2). And since the radius is half the length of this side (which is also the diameter of the semicircle), that's enough information.
Statement (2) provides one equation with one variable, and thus has only one possible solution. We only need one variable since we can use 2r as the side of the square. Also, since in Geometry there are no negative measurements, we can expect just one, positive value of r.
Since each of the statements is sufficient on its own, the correct answer is (D).
Posted from my mobile device
The Logical approach to this question will be based on the fact that in both squares and circles one measurement, any measurement (side, diagonal, radius, perimeter, etc.) is enough on order to find all other measurements.
Statement (1) is enough, since the diagonal of the square can give us its side (since it creates a 45-45-90 triangle, all we need is to divide the diagonal by √2). And since the radius is half the length of this side (which is also the diameter of the semicircle), that's enough information.
Statement (2) provides one equation with one variable, and thus has only one possible solution. We only need one variable since we can use 2r as the side of the square. Also, since in Geometry there are no negative measurements, we can expect just one, positive value of r.
Since each of the statements is sufficient on its own, the correct answer is (D).
Posted from my mobile device
