CAT 2000 — QA Question 62
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.
O is the centre of two concentric circles. ae is a chord of the outer circle and it intersects the inner circle at point; b and d. c is a point on the chord in between b and d. What is the value of ac/ce?
- bc/cd = 1
- A third circle intersects the inner circle at b and d and the point c is on the line joining the centres of the third circle and the inner circle.
Answer & solution
- A
1
2
- C
3
- D
4
From statement A
bc = cd
If c is the midpoint of bd it would also be midpoint of ae because circles are concentric.
∴ ac = ce
∴ The question can be answered using statement A alone.
From Statement B
If c is the point on the line joining the two centres, it has to bisect the chord bd.
∴ c will also bisect the chord ae as the circles are concentric.
∴ ac = ce
∴ The question can be answered using statement B alone also.
Hence, option (b).