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02 Apr 2012, 03:10
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
45%
(medium)
Question Stats:
65% (01:44) correct
35%
(01:37)
wrong
based on 108
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Is the perimeter of equilateral triangle T equal to the circumference of circle C ?
(1) The sum of the lengths of a side of T and the radius of C is 9.
(2) The length of a side of T is equal to the diameter of C.
(1) The sum of the lengths of a side of T and the radius of C is 9.
(2) The length of a side of T is equal to the diameter of C.
15 Jan 2018, 06:46
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i tried doing the following:
since one side of the triangle is the diameter, the triangle becomes a right triangle inscribed in the circle. Hence is not equilateral and the statement becomes void. M i using the right logic?
since one side of the triangle is the diameter, the triangle becomes a right triangle inscribed in the circle. Hence is not equilateral and the statement becomes void. M i using the right logic?
General Discussion
02 Apr 2012, 20:48
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This is a tricky one
Let's say t = a side of the equilateral triangle T
P = perimeter
C = circumference
Statement I
Sum of the lengths of a side of T and the radius of C is 9.
-> t + r = 9 => r = 9 - t
-> perimeter = 3t
-> circumference = 2(pi) (9-t)
-> 3t = 2(pi)(9-t)
-> 3t = 18pi - 2(pi)t
-> 3t + 2(pi)t = 18pi
Without doing the actual calculation, you should be able to infer that they can equal to each other, which means that perimeter and the circumference can equal to each other. Unfortunately this information is rather useless because it doesn't narrow down your answer. This statement essentially says that (could be) P < C or P = C or P > C
Statement II
The length of a side of T is equal to the diameter of C.
This statement sets up a distinct relationship
-> 3t & t*pi
Since pi is greater than 3, the circumference of the circle C cannot equal to perimeter of the triangle T. 3t cannot be greater than t*pi (because t > 0). Therefore Sufficient
Statement 2 on its own conclusively proves that they cannot equal to each other, but statement 1 doesn't. Therefore, the answer has to be (B)
This is how I see it, but I could be wrong. I think it's way more complicated than it needs to be which always makes me nervous about my answer. Let me know if I'm wrong somewhere.
Let's say t = a side of the equilateral triangle T
P = perimeter
C = circumference
Statement I
Sum of the lengths of a side of T and the radius of C is 9.
-> t + r = 9 => r = 9 - t
-> perimeter = 3t
-> circumference = 2(pi) (9-t)
-> 3t = 2(pi)(9-t)
-> 3t = 18pi - 2(pi)t
-> 3t + 2(pi)t = 18pi
Without doing the actual calculation, you should be able to infer that they can equal to each other, which means that perimeter and the circumference can equal to each other. Unfortunately this information is rather useless because it doesn't narrow down your answer. This statement essentially says that (could be) P < C or P = C or P > C
Statement II
The length of a side of T is equal to the diameter of C.
This statement sets up a distinct relationship
-> 3t & t*pi
Since pi is greater than 3, the circumference of the circle C cannot equal to perimeter of the triangle T. 3t cannot be greater than t*pi (because t > 0). Therefore Sufficient
Statement 2 on its own conclusively proves that they cannot equal to each other, but statement 1 doesn't. Therefore, the answer has to be (B)
This is how I see it, but I could be wrong. I think it's way more complicated than it needs to be which always makes me nervous about my answer. Let me know if I'm wrong somewhere.
