Logical Reasoning previous years questions (CAT)  Set 0005

Previous years`s CAT questions: Logical Reasoning
Post your solutions as reply to respective questions below.

Question 1
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 tiebreaking rules so that exactly four teams from each group advance to the next stage.
1) What is the total number of matches played in the tournament?
a. 28 b. 55 c. 63 d. 35
2) The minimum number of wins needed for a team in the first stage to guarantee its advancement to the next stage is:
a. 5 b. 6 c. 7 d. 4
3) What is the highest number of wins for a team in the first stage in spite of which it would be eliminated at the end of first stage?
a. 1 b. 2 c. 3 d. 4
4) What is the number of rounds in the second stage of the tournament?
a. 1 b. 2 c. 3 d. 4
5) Which of the following statements is true?
a. The winner will have more wins than any other team in the tournament.
b. At the end of the first stage, no team eliminated from the tournament will have more wins than any of the teams qualifying for the second stage.
c. It is possible that the winner will have the same number of wins in the entire tournament as a team eliminated at the end of the first stage.
d. The number of teams with exactly one win in the 2^{nd} stage of the tournament is 4.
(CAT 2000)

Question 2
Four students (Ashish, Dhanraj, Felix and Sameer) sat for the Common Entrance Exam for Management (CEEM). One student got admission offers from three National Institutes of Management (NIM), another in two NIMs, the third in one NIM, while the fourth got none. Below are some of the facts about who got admission offers from how many NlMs and what is their educational background.
 The one who is an engineer didn’t get as many admissions as Ashish.
 The one who got offer for admissions in two NIMs isn’t Dhanraj nor is he a chartered accountant.
 Sameer is an economist.
 Dhanraj isn’t an engineer and received more admission offers than Ashish.
 The medical doctor got the most number of admission offers.
Which one of the following statements is necessarily true?
a. Ashish is a chartered accountant and got offer for admission in three NIMs.
b. Dhanraj is a medical doctor and got admission offer in one NIM.
c. Sameer is an economist who got admission offers in two NIMs.
d. Felix who is not an engineer did not get any offer for admission. (CAT 2002)

Question 3
Five boys went to a store to buy sweets. One boy had Rs. 40. Another boy had Rs. 30. Two other boys had Rs. 20 each. The remaining boy had Rs. 10. Below are some more facts about the initial and final cash positions.
 Alam started with more than Jugraj.
 Sandeep spent Rs. 1.50 more than Daljeet.
 Ganesh started with more money than just only one other person.
 Daijeet started with 2/3 of what Sandeep started with.
 Alam spent the most, but did not end with the least.
 Jugraj spent the least and ended with more than Alam or Daljeet.
 Alam spent 10 times more than what Ganesh did.
 Ganesh spent Rs 3.50
In the choices given below, all statements except one are false. Which one of the following statements can be true?
a. Alam started with Rs.40 and ended with Rs.9.50.
b. Sandeep started with Rs.30 and ended with Rs. 1 .00.
c. Ganesh started with Rs.20 and ended with Rs.4.00.
d. Jugraj started with Rs.10 and ended with Rs.7.00. (CAT 2002)

Question 4
In a hospital there were 200 Diabetes, 150 Hyperglycaemia and 150 Gastroenteritis patients. Of these, 80 patients were treated for both Diabetic and Hyperglycaemia. Sixty patients were treated for Gastroenteritis and Hyperglycaemia, while 70 were treated for Diabetes and Gastroenteritis. Some of these patients have all the three diseases. Doctor Dennis treats patients with only Diabetes. Doctor Hormis treats patients with only Hyperglycaemia and Doctor Gerard treats patients with only Gastroenteritis. Doctor Paul is a generalist. Therefore, he can treat patients with multiple diseases. Patients always prefer a specialist for their disease. If Dr. Dennis had 80 patients the other three doctors can be arranged in terms of the number of patients treated as:
a. Paul > Gerard > Hormis
b. Paul > Hormis > Gerard
c. Gerard > Paul > Hormis
d. none of these (CAT 2002)

Question 5
Three children won the prizes in the Bournvita Quiz contest. They are from the schools; Loyola, Convent, Little Flowers, which are located at different cities. Below are some of the facts about the schools, the children the city they are from:
 One of the children is Bipin.
 Loyola School’s contestant did not come first.
 Little Flower’s contestant was named Riaz.
 Convent School is not in Hyderabad.
 The contestant from Pune took third place.
 The contestant from Pune is not from Loyola School.
 The contestant from Bangalore did not come first.
 Convent School’s contestant’s name is not Balbir.
Which of the following statements is true?
a. 1st prize: Riaz (Little Flowers), 2nd prize: Bipin (Convent), 3rd prize: Balbir (Loyola).
b. 1st prize: Bipin (Convent), 2nd prize: Riaz (Little Flowers), 3rd prize: Balbir (Loyola)
c. 1st prize: Riaz (Little Flowers), 2nd prize: Balbir(Loyola), 3rd prize: Bipin (Convent).
d. 1st prize: Bipin (Convent), 2nd prize: Balbir (Loyola), 3rd prize: Riaz(Little Flowers)
(CAT 2002)