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23 Feb 2015, 03:31
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C
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Difficulty:
25%
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Question Stats:
73% (01:32) correct
27%
(01:37)
wrong
based on 331
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In the diagram above, what is the circumference of the circle?
(1) The area of triangle is \(16*\sqrt{3}\)
(2) ∠B = 60°
Kudos for a correct solution.
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23 Feb 2015, 04:32
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Let us say that the radius of the circle is 'r'
If we can find that out, we will be able to find out the circumference of the circle as well.
From statement 1: We get the area of the triangle.
Let us say that the perpendicular sides are a & b
Then, the area is ab/2 = 16*sqrt(3)
=> ab = 32sqrt(3)
From this, we cannot determine the value of 'r'
=> Statement 1 is not sufficient.
From statement 2: We get that the triangle is a 30-60-90 triangle
=> Ratio of the sides is 1:sqrt(3):2
=> We cannot find out the radius from this information
=> Statement 1 is not sufficient.
Using both the statements together, we can say that the biggest side of the triangle is 2r
=> The smaller sides are r and r*sqrt(3)
=> We can form an equation in r and the given area in statement 1
From that, we will be able to find out the value of the radius and the value of the circumference.
We can solve the question using both the statements together.
Correct Answer: C
If we can find that out, we will be able to find out the circumference of the circle as well.
From statement 1: We get the area of the triangle.
Let us say that the perpendicular sides are a & b
Then, the area is ab/2 = 16*sqrt(3)
=> ab = 32sqrt(3)
From this, we cannot determine the value of 'r'
=> Statement 1 is not sufficient.
From statement 2: We get that the triangle is a 30-60-90 triangle
=> Ratio of the sides is 1:sqrt(3):2
=> We cannot find out the radius from this information
=> Statement 1 is not sufficient.
Using both the statements together, we can say that the biggest side of the triangle is 2r
=> The smaller sides are r and r*sqrt(3)
=> We can form an equation in r and the given area in statement 1
From that, we will be able to find out the value of the radius and the value of the circumference.
We can solve the question using both the statements together.
Correct Answer: C
02 Mar 2015, 06:56
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Bunuel
MAGOOSH OFFICIAL SOLUTION:
From the diagram, we know that BC is a diameter — the special case of a triangle in a semicircle. If we can find BC, we can find the circumference.
Statement #1: this gives us the area of the triangle, but the angles could be anything, and so the sides could have an array of different values. Statement #1, alone and by itself, is insufficient.
Statement #2: this statement would allow us to figure out all three angles of triangle ABC, but you need a length to find a length. Without any length given, we can’t find the length of BC or the circumference. Statement #2, alone and by itself, is insufficient.
Statements #1 & #2 combined: Now, with both statements, we know ABC is a 30-60-90 triangle, and we know its area, so we could figure out the side lengths, which would allow us to figure out the diameter & circumference. Combined, the statements are sufficient.
Answer = C.
