Hi Sri,
With a right triangle, and no restrictions, there would be limitless possibilities to consider. However, the prompt tells us that ALL SIDES are INTEGERS. There aren't that many possibilities for the Pythagorean Theorem in which all 3 numbers are integers. The two Facts deal with relatively small numbers, so I'm going to list out the simple possibilities for easy reference:
3/4/5 and the multiples
6/8/10
9/12/15
12/16/20
etc.
5/12/13 and the multiples
10/24/26
etc.
The prompt asks us for the area of the triangle, so we'll need the base and the height. We're told that all sides are integers.
Fact 1: PQ + QR = 21
We need a right triangle, with all integer sides, AND the two short sides add up to 21.
There's ONLY ONE possibility: 9/12/15
Fact 1 is SUFFICIENT
Fact 2: PR = 15
We need a triangle with a hypotenuse of 15 and the other 2 sides are also integers.
There's ONLY ONE possibility: 9/12/15
Fact 2 is SUFFICIENT
Final Answer: D
GMAT assassins aren't born, they're made,
Rich
