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In the figure shown, triangle ABC is inscribed in the circle. What is the circumference of the circle?
(1) AB is a diameter of the circle.
(2) The ratio of the lengths of BC, AC, and AB, respectively, is 3 : 4 : 5.
Attachment:
geometry.png [ 5.88 KiB | Viewed 38834 times ]
02 Sep 2015, 04:37
Kudos
Bookmarks
Hi shakticnb,
The problem can be solved without even writing a single line.
We have been asked the circumference of the circle, but none of the statements give us anything in terms of absolute values, hence we do not have sufficient information to find the answer. Option E
To dive deep:
Given: Triangle is inscribed in the Circle
Required: Circumference of the circle
Statement 1:
AB is the diameter of the circle. This tells us that the Circumference will be 2*pi*(AB/2)
But we do not have the value of AB.
INSUFFICIENT
Statement 2:
This statement tells us the ratio of the sides, but nothing about the actual measurements.
The sides can be 3,4,5 or 6,8,10 or 9,14,15 and so on ...
INSUFFICIENT
Statements 1 and 2 combined:
Still we do not have a value for any of the sides.
INSUFFICIENT
The problem can be solved without even writing a single line.
We have been asked the circumference of the circle, but none of the statements give us anything in terms of absolute values, hence we do not have sufficient information to find the answer. Option E
To dive deep:
Given: Triangle is inscribed in the Circle
Required: Circumference of the circle
Statement 1:
AB is the diameter of the circle. This tells us that the Circumference will be 2*pi*(AB/2)
But we do not have the value of AB.
INSUFFICIENT
Statement 2:
This statement tells us the ratio of the sides, but nothing about the actual measurements.
The sides can be 3,4,5 or 6,8,10 or 9,14,15 and so on ...
INSUFFICIENT
Statements 1 and 2 combined:
Still we do not have a value for any of the sides.
INSUFFICIENT
03 Sep 2015, 04:37
Kudos
Bookmarks
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and equations ensures a solution.
In the figure shown, triangle ABC is inscribed in the circle. What is the circumference of the circle?
(1) AB is a diameter of the circle.
(2) The ratio of the lengths of BC, AC, and AB, respectively, is 3 : 4 : 5.
In the original condition, the triangle has 3 variables and the circle has another variable therefore there are overall 4 variables. In order to match the number of variables and equations,we need 4 equations and since there is only 1 each in 1) and 2), E is likely the answer. Using 1) & 2) together, if the AB is the diameter C is 90 degrees, and side the ratio of the length is 3:4:5, AB = 5, 10,15...thus the answer is not unique. Therefore it is not sufficient.
The answer is E.
In the figure shown, triangle ABC is inscribed in the circle. What is the circumference of the circle?
(1) AB is a diameter of the circle.
(2) The ratio of the lengths of BC, AC, and AB, respectively, is 3 : 4 : 5.
In the original condition, the triangle has 3 variables and the circle has another variable therefore there are overall 4 variables. In order to match the number of variables and equations,we need 4 equations and since there is only 1 each in 1) and 2), E is likely the answer. Using 1) & 2) together, if the AB is the diameter C is 90 degrees, and side the ratio of the length is 3:4:5, AB = 5, 10,15...thus the answer is not unique. Therefore it is not sufficient.
The answer is E.
and side the ratio of the length is 3:4:5, AB = 5, 10,15...thus the answer is not unique. Therefore it is not sufficient.
