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GRE Math Challenge #134-The vertices of an equilateral
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Updated on: 20 Feb 2020, 16:15
Updated on: 20 Feb 2020, 16:15
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Question Stats:
78% (00:49) correct
21% (00:47) wrong based on 97 sessions
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The vertices of an equilateral triangle are on a circle.
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Quantity A |
Quantity B |
The length of a side of the triangle |
The diameter of the circle |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Kudos for the right answer and explanation
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: GRE Math Challenge #134
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17 May 2015, 09:19
17 May 2015, 09:19
sandy wrote:
The vertices of an equilateral triangle are on a circle.
Quantity A: The length of a side of the triangle
Quantity B: The diameter of the circle
Quantity A: The length of a side of the triangle
Quantity B: The diameter of the circle
Something nice happens when we sketch this information and add a center and two radii.
Notice that if we add the lengths of the two radii we get the DIAMETER.
So, we're now comparing the sum of the two radii with one side of the triangle.
Well, there's a nice triangle rule that says: the length of the 3rd side MUST BE less than the sum of the lengths of the other two sides.
So, when we examine the lower triangle (comprised of 2 radii and one side of the equilateral triangle), we know that the length of the side of the equilateral triangle MUST BE LESS than the sum of the two radii (aka the diameter)
Answer: B
Cheers,
Brent
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Re: GRE Math Challenge #134-The vertices of an equilateral
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13 May 2020, 06:42
13 May 2020, 06:42
The height of an eqt. triangle : (Root of 3)/2 * a = 1.732/2 * a < a
The diameter from one edge to the opp. point on the diameter will be greater than a.
Thus B
The diameter from one edge to the opp. point on the diameter will be greater than a.
Thus B
