CAT 2000 — QA Question 59
Choose 1; if the question can be answered by using one of the statements alone, but cannot be answered using the other statement alone.
Choose 2; if the question can be answered by using either statement alone.
Choose 3; if the question can be answered by using both statements together, but cannot be answered using either statement alone.
Choose 4; if the question cannot be answered even by using both statements together.
Triangle PQR has angle PRQ equal to 90 degrees. What is the value of PR + RQ?
- Diameter of the inscribed circle of the triangle PQR is equal to 10 cm.
- Diameter of the circumscribed circle of the triangle PQR is equal to 26 cm.
Answer & solution
Correct answer: 3
- A
1
- B
2
3
- D
4
From statement A
PF = PR – FR = PR – OD = PR – 5
QD = QR – DR = QR – OF = QR – 5
âµ PE = PF and QE = QD
∴ PE = PR – 5 and QE = QR – 5
∴ PQ = PE + QE = PR – 5 + QR – 5
∴ PR + QR = PQ + 10
This statement alone is not sufficient to find PR + RQ.
From Statement B
Diameter of the circumscribing circle = hypotenuse of the triangle
∴ PQ = 26
âµ PR2 + RQ2 = PQ2
But this does not give the value of PR + RQ.
∴ This statement alone is not sufficient.
Let’s combine both the statements.
∴ PR + QR = PQ + 10 = 26 + 10 = 36
Hence, option (c).