Walkabout wrote:

Attachment:

Circle.png

What is the circumference of the circle above with center O?

(1) The perimeter of triangle OXZ is \(20 + 10\sqrt{2}\).

(2) The length of arc XYZ is \(5\pi\).

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 independent equations ensures a solution.

By Variable Approach method, we can identify a circle with just 1 varable, which is a radius. Thus D is the answer most likely.

Let \(r\) be the radius of the above circle.

Condition 1)

\(2 \cdot r + r\sqrt{2} = r \cdot (2 + \sqrt{2} ) = 20 + 10\sqrt{2}\)

Thus \(r = 10\).

This condition is sufficient.

Condition 2)

The arc XYZ is \(\frac{1}{4} \cdot 2 \pi r = 5 \pi\).

Thus \(r = 10\).

This condition is also sufficient.

Therefore D is the answer as expected.

-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.

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