What is the area of a right-angled triangle PQR?

The correct answer to the question "What is the area of a right-angled triangle PQR?" is Option C: Both statements together are sufficient, but neither statement alone is sufficient..

The other options — A) Statement (1) alone is sufficient, but statement (2) alone is not sufficient., B) Statement (2) alone is sufficient, but statement (1) alone is not sufficient., D) Each statement alone is sufficient. — are incorrect for this GMAT Exam Prep question. As explained above: Let the legs be 'a' and 'b', and hypotenuse 'c'. Area = (1/2)ab. (1) a+b+c=30. Insufficient. (2) c=13. a^2+b^2=13^2=169. Insufficient. Combining, a+b+13=30 => a+b=17. We have (a+b)^2 = a^2+b^2+2ab =>…