SECTION III

Sub-Section III-A

Number of Questions : 10

Note: Questions 1 to 10 carry one mark each.

DIRECTIONS:
Answer questions 1 to 4 on the basis of the information given below.

A management institute was established on January 1, 2000 with 3, 4, 5, and 6 faculty members in the Marketing, Organisational Behaviour (OB), Finance, and Operations Management (OM) areas respectively, to start with. No faculty member retired or joined the institute in the first three months of the year 2000. In the next four years, the institute recruited one faculty member in each of the four areas. AH these new faculty members, who joined the institute subsequently over the years, were 25 years old at the time of their joining the institute. All of them joined the institute on April 1. During these four years, one of the faculty members retired at the age of 60. The following diagram gives the area-wise average age (in terms of number of completed years) of faculty members as on April 1 of 2000, 2001, 2002, and 2003

1. From which area did the faculty member retire?

2. Professors Naresh and Devesh, two faculty members in the Marketing area, who have been with the Institute since its inception, share a birthday, which falls on 20th November. One was born in 1947 and the other one in 1950. On April 1 2005, what was the age of the third faculty member who has been in the same area since inception?

3. In which year did the new faculty member join the Finance area?

4. What was the age of the new faculty member, who joined the OM area, as on April 1, 2003?

DIRECTIONS for Q.5 to Q.7:
The table below reports annual statistics related to rice production in select states of India for a particular year.

5. Which two states account for the highest productivity of rice (tons produced per hectare of rice cultivation)?

6. How many states have a per capita production of rice (defined as total rice production divided by its population) greater than Gujarat?

7. An intensive rice producing state is defined as one whose annual rice production per million of population is at least 400,000 tons. How many states are intensive rice producing states?

DIRECTIONS for Q.8 to Q.10:
The table below reports the gender, designation and age-group of the employees in an organization. It also provides information on their commitment to projects coming up in the months of January (Jan), February (Feb), March (Mar) and April (Apr), as well as their interest in attending workshops on: Business Opportunities (BO), Communication Skills (CS), and E-Governance (EG).

M=Male, F= Female; Exe=Executive, Mgr=Manager, Dir=Director; Y=Young, I=In-between, O=Old For each workshop, exactly four employees are to be sent, of which at least two should be Females and at least one should be Young. No employee can be sent to a workshop in which he/she is not interested in. An employee cannot attend the workshop on

Communication Skills, if he/she is committed to internal projects in the month of January;
Business Opportunities, if he/she is committed to internal projects in the month of February;
E-governance, if he/she is committed to internal projects in the month of March.

8. Assuming that Parul and Hari arc attending the workshop on Communication Skills (CS), then which of the following employees can possibly attend the CS workshop?

9. How many Executives (Exe) cannot attend more than one workshop?

10. Which set of employees cannot attend any of the workshops?

SECTION III

Sub-Section III-B

Number of Questions : 20

Note: Questions 11 to 30 carry two marks each.

DIRECTIONS:
Answer questions 11 to 14 on the basis of the information given below.

In the table below is the listing of players, seeded from highest (#1) to lowest (#32), who are due to play in an Association of Tennis Players (ATP) tournament for women. This tournament has four knockout rounds before the final, i.e., first round, second round, quarterfinals, and semi-finals. In the first round, the highest seeded player plays the lowest seeded player (seed # 32) which is designated match No. 1 of first round; the 2nd seeded player plays the 31st seeded player which is designated match No. 2 of the first round, and so on. Thus, for instance, match No. 16 of first round is to be played between 16lh seeded player and the 17th seeded player. In the second round, the winner of match No. 1 of-first round plays the winner of match No. 16 of first round and is designated match No. I of second round. Similarly, the winner of match No, 2 of first round plays the winner of match No. 15 of first round, and is designated match No. 2 of second round. Thus, for instance, match No. 8 of the second round is to be played between the winner of match No. 8 of first round and the winner of match No. 9 of first round. The same pattern is followed for later rounds as well.

11. If there are no upsets (a lower seeded player beating a higher seeded player) in the first round, and only match Nos. 6, 7, and 8 of the second round result in upsets, then who would meet Lindsay Davenport in quarter finals, in case Davenport reaches quarter finals?

12. If Elena Dementieva and Serena Williams lose in the second round, while Justine Henin and Nadia Petrova make it to the semifinals, then who would play Maria Sharapova in the quarterfinals, in the event Sharapova reaches quarterfinals?

13. If, in the first round, all even numbered matches (and none of the odd numbered ones) result in upsets, and there are no upsets in the second round, then who could be the lowest seeded player facing Maria Sharapova in semi-finals?

14. If the top eight seeds make it to the quarterfinals, then who, amongst the players listed below, would definitely not play against Maria Sharapova in the final, in case Sharapova reaches the final?

DIRECTIONS:
Answer questions 15 to 18 on the basis of the information given below.

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 arc 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 industry with extraordinarily good results, the returns were twice that of the initially expected returns. For the company belonging to the Steel or the Auto industry, the returns on announcement of extraordinarily good results were only one and a half times that of the initially expected returns. For the remaining two companies, which did not announce extraordinarily good results, the returns realized during the year were the same as initially expected.

15. What is the minimum average return Venkat would have earned during the year?

16. If Venkat earned a 35% return on average during the year, then which of these statements would necessarily be true?
I . Company A belonged either to Auto or to Steel Industry.
II. Company B did not announce extraordinarily good results.
III. Company A announced extraordinarily good results.
IV. Company D did not announce extraordinarily good results.

17. If Venkat earned a 38.75% return on average during the year, then which of these statement(s) would necessarily be true?
I . Company C belonged either to Auto or to Steel Industry.
II. Company D belonged either to Auto or to Steel Industry.
III. Company A announced extraordinarily good results.
IV. Company B did not announce extraordinarily good results.

18. If Company C belonged to the Cement or the IT industry and did announce extraordinarily good results, then which of these statement(s) would necessarily be true?
I . Venkat earned not more than 36.25% return on average.
II. Venkat earned not less than 33.75% return on average.
III. If Venkat earned 33.75% return on average, Company A announced extraordinarily good results.
IV. If Venkat earned 33.75% return on average, Company B belonged either to Auto or to Steel Industry.

DIRECTIONS:
Answer questions 19 to 22 on the basis of the information given below.

The year is 2089. Beijing, London, New York, and Paris are in contention lo 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.
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.
A member is allowed to east 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.)
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.
As long as the member is eligible, (s)he must vote and vote for only one candidate city in any round of voting.

The following incomplete table shows the information on cities that received the maximum and minimum votes in different rounds, the number of votes cast in their favour, and the total votes that were cast in those rounds.

It is also known that All those who voted for London and Paris in round 1, continued to vote for the same cities in subsequent rounds as long as these cities were in contention. 75% of those who voted for Beijing in round 1, voted for Beijing in round 2 as well.
Those who voted for New York in round 1, voted either for Beijing or Paris in round 2.
The difference in votes cast for the two contending cities in the last round was 1.
50% of those who voted for Beijing in round 1, voted for Paris in round 3.

19. What percentage of members from among those who voted for New York in round I, voted for Beijing in round 2?

20. What is the number of votes cast for Paris in round 1?

21. What percentage of members from among those who voted for Beijing in round 2 and were eligible to vote in round 3, voted for London?

22. Which of the following statements must be true?
a. IOC member from New York must have voted for Paris in round 2.
b. IOC member from Beijing voted for London in round 3.

DIRECTIONS for Q.23 to Q.26:
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. arc 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.

23. 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.

24. What can be said regarding the following two statements?
Statement 1: Aggressive Ltd.’s lowest revenues are from MP.
Statement 2: Honest Ltd.’s lowest revenues are from Bihar.

25. What can be said regarding the following two statements?
Statement 1: Honest Ltd. has the highest share in the UP market.
Statement 2: Aggressive Ltd. has the highest share in the Bihar market

26. If Profitable Ltd.’s lowest revenue is from UP, then which of the following is true?

DIRECTIONS for Q.27 to Q.30:
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 one more project.

27. Based on the information given above, the minimum number of volunteers involved in both FR and TR projects, but not in the ER project is:

28. Which of the following additional information would enable to find the exact number of volunteers involved in various projects?

29. After some time, the volunteers who were involved in all the three projects were asked to withdraw from one project. As a result, one of the volunteers opted out of the TR project, and one opted out of the ER project, while the remaining ones involved in all the three projects opted out of the FR project. Which of the following statements, then, necessarily follows?.

30. After the withdrawal of volunteers, as indicated in Question 89, some new volunteers joined the NGO. Each one of them was allotted only one project in a manner such that, the number of volunteers working in one project alone for each of the three projects became identical. At that point, it was also found that the number of volunteers involved in FR and ER projects was the same as the number of volunteers involved in TR and ER projects. Which of the projects now has the highest number of volunteers?