I was wondering how the answer is D? Why can’t you draw a line in the middle to get a right triangle and therefore solve for the line in the middle and then use Pythagorean theorem to solve for QR? Is that violating rules or assuming too much?

The line you drop will make an angle of 90 but the angle of other two sides are unknown and the only info we have about them is that they sum to 90(Hence, can’t apply Pythagoras Theorem )

You can use Triangle Inequality Theorem to prove that the length of QR will be less than or equal to length of (QP + RP), hence the ans is D

But we know it is a right angle so can’t we use Pythagorean theorem then? And then do 5^2-4^2 to get the length of the middle line? And then solve QR? Or can we not assume that the length would be 4 since 8/2?

QR can be any value in-between 3>QR>13, your assumption just provides one of its value and as it’s a QC question ,hence, you’ve to make sure that you’ve checked for all the cases !

Clever trap layed by GRE peeps