Nice problem!!.

This problem has 2 steps.
1. find the angle subtended by arc PQ at the center of the circle.
2. using the circle ratios find length of arc PQ.

Step1:
Since PQ || OR, length of arc OP = length of arc QR.
Now arc OP subtends a 35 degree angle at the circumferance.
Hence, arc OP subtends a 70 degree angle at the center of circle.

Similarly arc QR subtends a 70 degree angle at center of circle.
Together, both arcs subtends a 140 degree angle at center.
Total angle in the semicircle is 180.
So arc PQ subtends 180 - 140 = 40 degree angle at center.


Step 2.
We can use this ratio.

circumferance of circle / 360 = length of arc PQ / 40

= pi*18 / 360 = arc PQ/40
Solving arc PQ = 2*PI.


HT helps.

Sher1 wrote:Real GMAT questions.

Kindly do not post any real questions here. I guess this is a GMATPREP qtn that may have occured in real exam. I would request to edit areas where you mentioned about real qtn. you may want to instead just mention the qtn as GMATPrep