TheCATExam
Sign in

CAT 2000 — QA Question 59

CirclesEasy
Passage / Data

Answer the following question based on the information given below.

Sixteen teams have been invited to participate in the ABC Gold Cup cricket tournament. The tournament is conducted in two stages. In the first stage, the teams are divided into two groups. Each group consists of eight teams, with each team playing every other team in its group exactly once. At the end of the first stage, the top four teams from each group advance to the second stage while the rest are eliminated. The second stage comprises of several rounds. A round involves one match for each team. The winner of a match in a round advances to the next round, while the loser is eliminated. The team that remains undefeated in the second stage is declared the winner and claims the Gold Cup.

The tournament rules are such that each match results in a winner and a loser with no possibility of a tie. In the first stage, a team earns one point for each win and no points for a loss. At the end of the first stage teams in each group are ranked on the basis of total points to determine the qualifiers advancing to the next stage. Ties are resolved by a series of complex tie-breaking rules so that exactly four teams from each group advance to the next stage.

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?

  1. Diameter of the inscribed circle of the triangle PQR is equal to 10 cm.
  2. Diameter of the circumscribed circle of the triangle PQR is equal to 26 cm.
     

Answer & solution

  • A

    1

  • B

    2

  • 3

  • D

    4

Solution

From statement A

PF = PR – FR = PR – OD = PR – 5

QD = QR – DR = QR – OF = QR – 5

∵ 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

∵ 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).

CAT 2000 QA Q59: Choose 1 ; if the question can be answered by using one of the statements alone, but cannot be answered using — Solution | TheCATExam