CAT 2000 — QA Question 58
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.
How many people are watching TV programme P?
- Number of people watching TV programme Q is 1000 and number of people watching both the programmes, P and Q, is 100.
- Number of people watching either P or Q or both is 1500.
Answer & solution
- A
1
- B
2
3
- D
4
From Statement A
Q = 1000
P ∩ Q = 100
This doesn’t gives any information regarding how many people are watching TV programme P
From Statement B
P ∪ Q = 1500
This statement alone is not sufficient.
Let’s combine the information in both the statements.
∴ P ∪ Q = P + Q − P ∩ Q
∴ 1500 = P + 1000 – 100
∴ P = 600
Hence, option (c).
Alternatively
By combining both the statements together we can arrive at the above Venn diagram which gives the number of people watching programme P.
Hence, option (c).