Bunuel wrote:

Is the area of the top of a rectangular pool larger than 1000 square feet?

(1) The pool's top measures 50 feet diagonally.

(2) One side of the pool's top measures 25 feet.

Kudos for a correct solution.

Is l*b > 1000 ft^2?

Per statement 1, diag = 50 feet ---> the sides of the rectangle can be 30, 40 feet resp. Thus area = 30*40 = 1200 ft^2 . "Yes"

But if , \(b=10\) ---> \(l = 20\sqrt{6}\) ---->\(l*b = 10*20\sqrt{6}\) = \(200 \sqrt{6}\) < 1000. Thus "No". This statement is not sufficient.

Per statement 2, b =25. Without l, we can not find the area. Thus this statement is not sufficient.

COmbining, we get diag = 50, b =25 ---> \(l = \sqrt{1875}\).

You do not have to calculate the area but only need to know that you will get 1 unique value for the area that will either be a "yes" for >1000 or a definite "no" for >1000.

Either way, both statements are sufficient when combined and hence C is the correct answer.