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die comes to rest

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die comes to rest

by sanju09 » Thu Jul 29, 2010 4:42 am
A die is rolled randomly on to a circular board with a triangle inscribed in the circle. (All three vertices of the triangle are on the circumference of the circle.) What is the probability that the die comes to rest outside the triangular region?

1. The hypotenuse of the triangle is a diameter of the circle.
2. The radius of the circle is 2 units, and the area of the triangle is 4 square units.

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by kvcpk » Thu Jul 29, 2010 5:55 am
sanju09 wrote:A die is rolled randomly on to a circular board with a triangle inscribed in the circle. (All three vertices of the triangle are on the circumference of the circle.) What is the probability that the die comes to rest outside the triangular region?

1. The hypotenuse of the triangle is a diameter of the circle.
2. The radius of the circle is 2 units, and the area of the triangle is 4 square units.

[spoiler]Source: majortests.com[/spoiler]
From statement1, we know that the the triangle is right angled. But e have no info about the area of triangle.
INSUFF

From Statement 2, we know areas of both triangle and circle.
Hence we can calculate the difference.
SUFF

pick B
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by aleph777 » Thu Jul 29, 2010 6:32 am
I like this problem.

The question doesn't really give us much to go by, except that all three vertices of the triangle touch the edges of the circular board. So to solve the question, we need to know the areas of both the circle and the triangle.

1) One side of the triangle = the diameter of the circle.
INSUF because we don't have any idea what the radius of the circle is, the length of a side of the triangle, an angle, etc., and therefore can't solve for either area.

2) Radius of circle = 2 and Area of triangle = 4
SUF because we are given the area of the triangle outright and we can solve for the area of the circle with a = pi * r^2.

Answer: B
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