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In the figure shown, triangle ABC is inscribed in the circle

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by BTGmoderatorDC » Sun Mar 31, 2019 4:22 am

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Answers

A

B

C

D

E

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Image

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.

OA E

Source: GMAT Prep
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Source: — Data Sufficiency |

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by Jay@ManhattanReview » Sun Mar 31, 2019 9:43 pm
BTGmoderatorDC wrote:Image

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.

OA E

Source: GMAT Prep
Let's take each statement one by one.

(1) AB is a diameter of the circle.

We do not know the measure of AB, thus, we can't get the value of circumference of the circle. Insufficient.

(2) The ratio of the lengths of BC, AC, and AB, respectively, is 3 : 4 : 5.

Certainly insufficient.

(1) and (2) together

From (1) and (2), we have AB = 5x, where x is a positive integer. However, since the unique value of AB is not known, we can't get the unique value of circumference of the circle. Insufficient.

The correct answer: E

Hope this helps!

-Jay
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