Logic

(CAT 2006) In a Class X Board examination, ten papers are distributed over five Groups - PCB, Mathematics, Social Science, Vernacular and English. Each of the ten papers is evaluated out of 100. The final score of a student is calculated in the following manner. First, the Group Scores are obtained by averaging marks in the papers within the Group. The final score is the simple average of the Group Scores. The data for the top ten students are presented below. (Dipan's score in English Paper II has been intentionally removed in the table.) Note: B or G against the name of a student respectively indicates whether the student is a boy or a girl. 1. How much did Dipan get in English Paper II? a. 94 b. 96.5 c. 97 d. 98 e. 99 2. Among the top ten students, how many boys scored at least 95 in at least one paper from each of the groups? a. 1 b. 2 c. 3 d. 4 e. 5 3. Had Joseph, Agni, Pritam and Tirna each obtained Group Score of 100 in the Soc...

(CAT 2006) K, L, M, N, P, Q, R, S, U and W are the only ten members in a department. There is a proposal to form a team from within the members of the department, subject to the following conditions: 1. A team must include exactly one among P, R, and S. 2. A team must include either M or Q, but not both. 3. If a team includes K, then it must also include L, and vice versa. 4. If a team includes one among S, U, and W, then it must also include the other two. 5. L and N cannot be members of the same team. 6. L and U cannot be members of the same team. The size of a team is defined as the number of members in the team. 1. Who cannot be a member of a team of size 3? a. L b. M c. N d. P e. Q 2. Who can be a member of a team of size 5? a. K b. L c. M d. P e. R 3. What would be the size of the largest possible team? a. 8 b. 7 c. 6 d. 5 e. Cannot be determined 4. What could be the size of a team that includes K? a. 2 or 3 b...

Faculty’sAge 1. c 2. d 3. c 4. c RiceProduction 1. a 2. b 3. d Workshopfor Employees 1. a 2. b 3. b ATPtournament for women 1. d 2. c 3. a 4. c Venkat,the stockbroker 1. a 2. b 3. c 4. b Voting in IOC 1. d 2. d 3. d 4. a Honest,Aggressive, Truthful and Profitable Ltd. 1. b 2. c 3. c 4. c NGO Help Distress 1. c 2. a 3. b 4. d

(CAT 2005) Help Distress (HD) is an NGO involved in providing assistance to people suffering from natural disasters. Currently, it has 37 volunteers. They are involved in three projects: Tsunami Relief (TR) in Tamil Nadu, Flood Relief (FR in Maharashtra, and Earthquake Relief (ER) in Gujarat. Each volunteer working with Help Distress has to be involved in at least one relief work project. A maximum number of volunteers are involved in the FR project. Among them, the number of volunteers involved in FR project alone is equal to the volunteers having additional involvement in the ER project. • The number of volunteers involved in the ER project alone is double the number of volunteers involved in all the three projects. • 17 volunteers are involved in the TR project. • The number of volunteers involved in the TR project alone is one less than the number of volunteers involved in ER project alone. • Ten volunteers involved in the TR project are also involved in at least on...

(CAT 2005) The table below presents the revenue (in million rupees) of four firms in three states. These firms, Honest Ltd., Aggressive Ltd., Truthful Ltd. and Profitable Ltd. are disguised in the table as A, B, C and D, in no particular order. Further, it is known that: • In the state of MP, Truthful Ltd. has the highest market share. • Aggressive Ltd.’s aggregate revenue differs from Honest Ltd.’s by Rs. 5 million. 1. What can be said regarding the following two statements? Statement 1: Profitable Ltd. has the lowest share in MP market. Statement 2: Honest Ltd.’s total revenue is more than Profitable Ltd. a. If Statement 1 is true then Statement 2 is necessarily true. b. If Statement 1 is true then Statement 2 is necessarily false. c. Both Statement 1 and Statement 2 are true. d. Neither Statement 1 nor Statement 2 is true. 2. What can be said regarding the following two statements? Statement 1: Aggressive Ltd.’s lowest revenues are from MP. ...

(CAT 2005) The year is 2089. Beijing, London, New York, and Paris are in contention to host the 2096 Olympics. The eventual winner is determined through several rounds of voting by members of the IOC with each member representing a different city. All the four cities in contention are also represented in IOC. (a) In any round of voting, the city receiving the lowest number of votes in that round gets eliminated. The survivor after the last round of voting gets to host the event. (b) A member is allowed to cast votes for at most two different cities in all rounds of voting combined. (Hence, a member becomes ineligible to cast a vote in a given round if both the cities (s)he voted for in earlier rounds are out of contention in that round of voting.) (c) A member is also ineligible to cast a vote in a round if the city (s)he represents is in contention in that round of voting. (d) As long as the member is eligible, (s)he must vote and vote for only one candidate city in any ...

(CAT 2005) Venkat, a stockbroker, invested a part of his money in the stock of four companies — A, B, C and D. Each of these companies belonged to different industries, viz., Cement, Information Technology (IT), Auto, and Steel, in no particular order. At the time of investment, the price of each stock was Rs. 100. Venkat purchased only one stock of each of these companies. He was expecting returns of 20%, 10%, 30% and 40% from the stock of companies A, B, C and D, respectively. Returns are defined as the change in the value of the stock after one year, expressed as a percentage of the initial value. During the year, two of these companies announced extraordinarily good results. One of these two companies belonged to the Cement or the IT industry, while the other one belonged to either the Steel or the Auto industry. As a result, the returns on the stocks of these two companies were higher than the initially expected returns. For the company belonging to the Cement or the IT in...