# CAT 2005 LRDI | Previous Year CAT Paper

Previous year paper questions for CAT 2005 LRDI

**Answer the following question based on 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. All 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. CAT 2005 LRDI | DI - Tables & Graphs**

From which area did the faculty member retire?

- A.
Finance

- B.
Marketing

- C.
OB

- D.
OM

Answer: Option A

**Explanation** :

Consider this explanation that can be used to answer all the questions of this set.

In any two consecutive years that the number of faculty remains same, the average age of every area increases by 1.

Wherever we find an increase/decrease not equal to 1, we can say that the number of faculty members has changed.

Consider the area of Marketing:

The number of faculty members in Marketing in 2000 = 3

∴ Total age of faculty members in Marketing in 2000 = 3 × 49.33 = 148

In 2001, as the average has decreased, we can say that a faculty member aged 25 has been added to the area.

Thus, the new average = (148 + 3 + 25)/4 = 44

Thereafter the number of faculty remains the same.

Consider the area of OB:

The number of faculty members in 2000 = 4

The number of faculty members remains the same in 2001 and 2002. As it decreases in 2003, we can say that a faculty member has been added.

Thus the new average age = (52.5 × 4 + 4 + 25)/5 = 47.8

Consider the area of Finance:

The number of faculty members in 2000 = 5

The number of faculty members has changed in 2001.

If a new member has been added, the new average would be (50.2 × 5 + 5 + 25)/6 = 46.83, which is not true.

∴ A faculty member aged 60 has retired.

New average = (50.2 × 5 + 5 - 60)/4 = 49

In 2002, there is a change in the number of faculty members again. Here, a new member is added. New average = (49 × 4 + 4 + 25)/5 = 45

The number of faculty members remains the same in 2003.

Consider the area of OM:

Following the above logic, we can say that a faculty member gets added in 2001.

Now, based on the explanation for the four areas, we can say that a member retired from the area of Finance.

Hence, option (a).

Workspace:

**2. CAT 2005 LRDI | DI - Tables & Graphs**

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?

- A.
47

- B.
50

- C.
51

- D.
52

Answer: Option D

**Explanation** :

Consider this explanation that can be used to answer all the questions of this set.

In any two consecutive years that the number of faculty remains same, the average age of every area increases by 1.

Wherever we find an increase/decrease not equal to 1, we can say that the number of faculty members has changed.

Consider the area of Marketing:

The number of faculty members in Marketing in 2000 = 3

∴ Total age of faculty members in Marketing in 2000 = 3 × 49.33 = 148

In 2001, as the average has decreased, we can say that a faculty member aged 25 has been added to the area.

Thus, the new average = (148 + 3 + 25)/4 = 44

Thereafter the number of faculty remains the same.

Consider the area of OB:

The number of faculty members in 2000 = 4

The number of faculty members remains the same in 2001 and 2002. As it decreases in 2003, we can say that a faculty member has been added.

Thus the new average age = (52.5 × 4 + 4 + 25)/5 = 47.8

Consider the area of Finance:

The number of faculty members in 2000 = 5

The number of faculty members has changed in 2001.

If a new member has been added, the new average would be (50.2 × 5 + 5 + 25)/6 = 46.83, which is not true.

∴ A faculty member aged 60 has retired.

New average = (50.2 × 5 + 5 - 60)/4 = 49

In 2002, there is a change in the number of faculty members again. Here, a new member is added. New average = (49 × 4 + 4 + 25)/5 = 45

The number of faculty members remains the same in 2003.

Consider the area of OM:

Following the above logic, we can say that a faculty member gets added in 2001.

As calculated , average age of the three professors in the Marketing area since inception = 49.33

∴ The sum of their ages on April 1 2005 = (49.33 + 5) × 3 = 163

Naresh's age on April 1, 2005 = 57 and Devesh's age on April 1, 2005 = 54

∴ Age of the third professor = 163 – 57 – 54 = 52 years

Hence, option (d).

Workspace:

**3. CAT 2005 LRDI | DI - Tables & Graphs**

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

- A.
2000

- B.
2001

- C.
2002

- D.
2003

Answer: Option C

**Explanation** :

Consider this explanation that can be used to answer all the questions of this set.

In any two consecutive years that the number of faculty remains same, the average age of every area increases by 1.

Wherever we find an increase/decrease not equal to 1, we can say that the number of faculty members has changed.

Consider the area of Marketing:

The number of faculty members in Marketing in 2000 = 3

∴ Total age of faculty members in Marketing in 2000 = 3 × 49.33 = 148

In 2001, as the average has decreased, we can say that a faculty member aged 25 has been added to the area.

Thus, the new average = (148 + 3 + 25)/4 = 44

Thereafter the number of faculty remains the same.

Consider the area of OB:

The number of faculty members in 2000 = 4

The number of faculty members remains the same in 2001 and 2002. As it decreases in 2003, we can say that a faculty member has been added.

Thus the new average age = (52.5 × 4 + 4 + 25)/5 = 47.8

Consider the area of Finance:

The number of faculty members in 2000 = 5

The number of faculty members has changed in 2001.

If a new member has been added, the new average would be (50.2 × 5 + 5 + 25)/6 = 46.83, which is not true.

∴ A faculty member aged 60 has retired.

New average = (50.2 × 5 + 5 - 60)/4 = 49

In 2002, there is a change in the number of faculty members again. Here, a new member is added. New average = (49 × 4 + 4 + 25)/5 = 45

The number of faculty members remains the same in 2003.

Consider the area of OM:

Following the above logic, we can say that a faculty member gets added in 2001.

As per the explanation, one faculty member retired in 2001 and one joined in 2002. The number of members remained same in 2003.

Hence, option (c).

Workspace:

**4. CAT 2005 LRDI | DI - Tables & Graphs**

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

- A.
2000

- B.
2001

- C.
2002

- D.
2003

Answer: Option C

**Explanation** :

Consider this explanation that can be used to answer all the questions of this set.

Consider the area of Marketing:

The number of faculty members in Marketing in 2000 = 3

∴ Total age of faculty members in Marketing in 2000 = 3 × 49.33 = 148

Thus, the new average = (148 + 3 + 25)/4 = 44

Thereafter the number of faculty remains the same.

Consider the area of OB:

The number of faculty members in 2000 = 4

Thus the new average age = (52.5 × 4 + 4 + 25)/5 = 47.8

Consider the area of Finance:

The number of faculty members in 2000 = 5

The number of faculty members has changed in 2001.

∴ A faculty member aged 60 has retired.

New average = (50.2 × 5 + 5 - 60)/4 = 49

The number of faculty members remains the same in 2003.

Consider the area of OM:

Following the above logic, we can say that a faculty member gets added in 2001.

As per the explanation, one faculty member retired in 2001 and one joined in 2002. The number of members remained same in 2003.

Hence, option (c).

Workspace:

**Answer the following question based on the information given below.**

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

**5. CAT 2005 LRDI | DI - Tables & Graphs**

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

- A.
Haryana and Punjab

- B.
Punjab and Andhra Pradesh

- C.
Andhra Pradesh and Haryana

- D.
Uttar Pradesh and Haryana

Answer: Option A

**Explanation** :

The Area, out of the total area (in million hectares), that comes under rice cultivation for different states are -

1) HP : 20% of 6 = 1.2 million hectares

2) Kerala : 60% of 4 = 2.4 million hectares

3) Rajasthan : 20% of 34 = 6.8 million hectares

4) Bihar : 60% of 10 = 6 million hectares

5) Karnataka : 50% of 19 = 9.5 million hectares

6) Haryana : 80% of 4 = 3.2 million hectares

7) West Bengal : 80% of 8 = 7.2 million hectares

8) Gujarat : 60% of 20 = 12 million hectares

9) Punjab : 80% of 5 = 4 million hectares

10) MP : 40% of 31 = 12.4 million hectares

11) TN : 70% of 13 = 9.1 million hectares

12) Maharashtra : 50% of 31 = 15.5 million hectares

13) UP : 70% of 24 = 16.8 million hectares

14) AP : 80% of 28 = 22.4 million hectares

Productivity = Production (in million tons) / Area under rice cultivation (in million hectares)

Using the above formula we get the maximum value of productivity for Punjab and Huryana, which is equal to 6.

Hence, option (a).

Workspace:

**6. CAT 2005 LRDI | DI - Tables & Graphs**

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

- A.
3

- B.
4

- C.
5

- D.
6

Answer: Option B

**Explanation** :

Per capita production of rice for Gujarat = 24/51 = 48/102 ≈ 48%

∴ We shall look for values of production that are close to half or more than half of the population.

We can see that only Haryana, Punjab, Maharashtra, and Andhra Pradesh satisfy this criterion.

Hence, option (b).

Workspace:

**7. CAT 2005 LRDI | DI - Tables & Graphs**

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?

- A.
5

- B.
6

- C.
7

- D.
8

Answer: Option D

**Explanation** :

We are looking for states with

Production in million tons × 106/population in millions > 4 × 105

i.e. production in million tons × 10 > 4 × population in millions

Haryana, Gujarat, Punjab, Madhya Pradesh, Tamil Nadu, Maharashtra, Uttar Pradesh, and Andhra Pradesh are such states.

Hence, option (d).

Workspace:

**Answer the following question based on the information given below.**

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 or she is not interested in. An employee cannot attend the workshop on

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

**8. CAT 2005 LRDI | LR - Selection & Distribution**

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

- A.
Rahul and Yamini

- B.
Dinesh and Lavanya

- C.
Anshul and Yamini

- D.
Fatima and Zeena

Answer: Option A

**Explanation** :

Apart from Parul and Hari, at least one female should attend the CS workshop. Also, the two selected for the CS workshop should not be committed to internal projects in January.

Consider the options.

In options 2, 3 and 4, Dinesh, Anshul, Fatima, and Zeena are committed to internal projects in January.

Employees in option 1 i.e. Rahul and Yamini can attend the CS workshop.

Hence, option (a).

Workspace:

**9. CAT 2005 LRDI | LR - Selection & Distribution**

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

- A.
2

- B.
3

- C.
15

- D.
16

Answer: Option B

**Explanation** :

Dinesh, Gayatri, Kalindi, Parul, Urvashi, and Zeena are executives. Out of these, Dinesh, Kalindi, and Parul can attend two workshops each. The rest attend less than two, i.e. not more than one workshop.

Hence, option (b).

Workspace:

**10. CAT 2005 LRDI | LR - Selection & Distribution**

Which set of employees cannot attend any of the workshops?

- A.
Anshul, Charu, Eashwaran, and Lavanya

- B.
Anshul, Bushkant, Gayatri, and Urvashi

- C.
Charu, Urvashi, Bushkant, and Mandeep

- D.
Anshul, Gayatri, Eashwaran, and Mandeep

Answer: Option B

**Explanation** :

Consider the options.

Option 1: Lavanya can attend 2 workshops.

Option 3 and 4: Mandeep can attend 1 workshop.

All the employees in option 2 are unable to attend any workshop.

Hence, option (b).

Workspace:

**Answer the following question based on 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 16th 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. 1 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. CAT 2005 LRDI | DI - Games & Tournaments**

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?

- A.
Justine Henin

- B.
Nadia Petrova

- C.
Patty Schnyder

- D.
Venus Williams

Answer: Option D

**Explanation** :

The table shows the match nos. and the seed numbers of players playing those matches in Round 1 and 2.

As there are no upsets in the first round, players seeded 1 to 16 reach round 2.

There are upsets only in matches 6, 7 and 8 in round 2. So, seed numbers 1, 2, 3, 4, 5, 11, 10 and 9 reach the quarter finals. Then Davenport who is seed no. 2 plays seed no. 10, who is Venus Williams.

Hence, option (d).

Workspace:

**12. CAT 2005 LRDI | DI - Games & Tournaments**

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?

- A.
Dinara Safina

- B.
Justine Henin

- C.
Nadia Petrova

- D.
Patty Schnyder

Answer: Option C

**Explanation** :

Seed numbers 6 and 8 lose in the second round and seed numbers 7 and 9 reach the semi-finals.

Seed number 9 plays matches 9, 8 and 1 in rounds 1, 2 and the quarterfinals.

Sharapova, who is seed number 1, plays match no. 1 in every round. Thus, Sharapova plays seed number 9, Nadia Petrova, in the quarterfinals.

Hence, option (c).

Workspace:

**13. CAT 2005 LRDI | DI - Games & Tournaments**

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?

- A.
Anastasia Myskina

- B.
Flavia Pennetta

- C.
Nadia Petrova

- D.
Svetlana Kuznetsova

Answer: Option A

**Explanation** :

The matches in rounds 1 and 2, quarterfinals and semi-finals are as shown in the table.

Sharapova is seeded 1. The lowest seed that could face her in the semi-finals could be seed no. 13, which is Anastasia Myskina.

Hence, option (a).

Workspace:

**14. CAT 2005 LRDI | DI - Games & Tournaments**

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?

- A.
Amelie Mauresmo

- B.
Elena Dementieva

- C.
Kim Clijsters

- D.
Lindsay Davenport

Answer: Option C

**Explanation** :

The top 8 seeds make it to the quarterfinals. Thus matches 1 to 4 in quarter finals are between 1 and 8, 2 and 7, 3 and 6, and 4 and 5.

Sharapova is seeded 1. If she reaches the finals, she definitely beats seed number 8 in the quaterfinals and one of seed numbers 4 or 5 in the semi-finals. So, she can play seed numbers 2, 3, 6, or 7 in the finals. Kim Clijsters is seeded 4. Thus, she will definitely not play against Sharapova in the final.

Hence, option (c).

Workspace:

**Answer the following question based on 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 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 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. CAT 2005 LRDI | LR - Mathematical Reasoning**

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

- A.
30%

- B.
31.25%

- C.
32.5%

- D.
Cannot be determined

Answer: Option A

**Explanation** :

At the time of investment, the total price of the four stocks was Rs. 400

Total expected returns = (20 + 10 + 30 + 40) = Rs. 100

Venkat would earn the minimum average return when the companies with the two lowest expected returns would give 2 times and 1.5 times their expected returns.

Thus, minimum expected returns = 20 × 1.5 + 10 × 2 + 30 + 40 = Rs.120 = 30% of initial investment

Hence, option (a).

Workspace:

**16. CAT 2005 LRDI | LR - Mathematical Reasoning**

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.

- A.
I and II only

- B.
II and III only

- C.
I and IV only

- D.
II and IV only

Answer: Option B

**Explanation** :

Venkat earned 35% average return i.e. Rs. 140.

∴ He earned Rs. 40 more than expected.

∴ 40 = x + 0.5y,

where x and y correspond to expected returns on stocks that gave extraordinarily good results.

∴ 0.5y = 40 − x

But x and y can be 20, 10, 30 or 40.

If x = 20, y = 40, which is possible

If x = 10, y = 60, which is not possible

If x = 30, y = 20, which is possible

If x = 40, y = 0, which is not possible

Thus, Company A with x = 20 necessarily announced extraordinarily good results along with company C or D. B did not announce extraordinarily good results.

Hence, option (b).

Workspace:

**17. CAT 2005 LRDI | LR - Mathematical Reasoning**

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.

- A.
I and II only

- B.
II and III only

- C.
I and IV only

- D.
II and IV only

Answer: Option C

**Explanation** :

Venkat earned a return of 38.75% = Rs. 155

∴ He earned Rs. 55 more than expected.

∴ 55 = x + 0.5y

where x and y correspond to expected returns on stocks that gave extraordinarily good results.

But x and y can be 20, 10, 30 or 40.

If x = 20, y = 70, which is not possible.

If x = 10, y = 90, which is not possible.

If x = 30, y = 50, which is not possible.

If x = 40, y = 30, which is possible.

Thus company C and company D announced returns that were respectively one and a half and two times the initially expected returns.

∴ Company C belonged to either Auto or Steel Industry and Company A and B did not announce extraordinarily good results.

Statements I and IV are true.

Hence, option (c).

Workspace:

**18. CAT 2005 LRDI | LR - Mathematical Reasoning**

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.

- A.
I and II only

- B.
II and IV only

- C.
II and III only

- D.
III and IV only

Answer: Option B

**Explanation** :

Company C gave a return of Rs. 60.

∴ Total returns will be the minimum possible when B gives 1.5 times the initially expected returns.

∴ Total returns would be 20 + 15 + 60 + 40 = Rs.135 = 33.75% of the initial investment.

Statement II is true.

Also, when returns are 33.75%, company B belongs to Auto or Steel Industry. Statement IV is true and Statement III is false.

Total returns will be the maximum possible when D gives 1.5 times the initially expected returns.

∴ Total returns would be 20 + 10 + 60 + 60 = Rs.150 = 37.5% of the initial investment.

Statement I is false.

Hence, option (b).

Workspace:

**Answer the following question based on the information given below.**

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.

- 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 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).
- 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. CAT 2005 LRDI | LR - Puzzles**

What percentage of members from among those who voted for New York in round 1, voted for Beijing in round 2?

- A.
33.33

- B.
50

- C.
66.67

- D.
75

Answer: Option D

**Explanation** :

Let there be x members in the IOC.

As a member cannot vote if his or her city is in contention, the number of voters in Round 1 (R1) = x – 4

The number of voters in Round 2 (R2) = x – 3 and

The number of voters in Round 3 (R3) = x – 2 – n

Where n is the number of voters who have voted for New York (NY) in R1 and Beijing (B) in R2.

Since x – 3 = 83, we get x – 4 = 82 and x – 2 – n = 75 or n = 9

21 members voted for B in R2. Out of these, 9 voted for NY in R1.

The remaining 12 who voted for B comprised 75% of those who voted for B in R1.

Thus 12/0.75 = 16 members voted for B in R1.

∴ Paris (P) got 82 – 16 – 30 – 12 = 24 votes in R1.

All those who voted for London (L) and P in R1 continued to vote for the same cities in subsequent rounds. Thus, 24 voters of P in R2 had voted for P in R1 too. Also from the given information, 3 voters who had voted for NY in R1 voted for Paris in R2.

Out of the remaining 5 that voted for P in R2, 4 had voted for Beijing in R1 and 1 vote came from the member who represented NY.

In R3, the difference in the votes cast for L and P was 1, i.e. L and P got 37 and 38 votes in some order.

The composition of 75 voters of R3 was as follows:

12 members who had voted for B in R1 and R2 were eligible for voting in R3.

30 and 24 members who voted for L and P in R1 continued to do so in R3.

4 voters of R3, voted for B in R1 and P in R2.

3 voters of R3, voted for NY in R1 and P in R2.

1 member represented NY and 1 represented B.

From given information, 50% of voters of B in R1 i.e. 8 voted for P in R3. So, 8 out of the 12 who voted for B in R1 and R2, voted for London in R3.

The information can be summarised as shown in the table:

Required percentage = $\frac{9}{12}$ × 100 = 75%

Hence, option (d).

Workspace:

**20. CAT 2005 LRDI | LR - Puzzles**

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

- A.
16

- B.
18

- C.
22

- D.
24

Answer: Option D

**Explanation** :

Let there be x members in the IOC.

As a member cannot vote if his or her city is in contention, the number of voters in Round 1 (R1) = x – 4

The number of voters in Round 2 (R2) = x – 3 and

The number of voters in Round 3 (R3) = x – 2 – n

Where n is the number of voters who have voted for New York (NY) in R1 and Beijing (B) in R2.

Since x – 3 = 83, we get x – 4 = 82 and x – 2 – n = 75 or n = 9

21 members voted for B in R2. Out of these, 9 voted for NY in R1.

The remaining 12 who voted for B comprised 75% of those who voted for B in R1.

Thus 12/0.75 = 16 members voted for B in R1.

∴ Paris (P) got 82 – 16 – 30 – 12 = 24 votes in R1.

All those who voted for London (L) and P in R1 continued to vote for the same cities in subsequent rounds. Thus, 24 voters of P in R2 had voted for P in R1 too. Also from the given information, 3 voters who had voted for NY in R1 voted for Paris in R2.

Out of the remaining 5 that voted for P in R2, 4 had voted for Beijing in R1 and 1 vote came from the member who represented NY.

In R3, the difference in the votes cast for L and P was 1, i.e. L and P got 37 and 38 votes in some order.

The composition of 75 voters of R3 was as follows:

12 members who had voted for B in R1 and R2 were eligible for voting in R3.

30 and 24 members who voted for L and P in R1 continued to do so in R3.

4 voters of R3, voted for B in R1 and P in R2.

3 voters of R3, voted for NY in R1 and P in R2.

1 member represented NY and 1 represented B.

From given information, 50% of voters of B in R1 i.e. 8 voted for P in R3. So, 8 out of the 12 who voted for B in R1 and R2, voted for London in R3.

The information can be summarised as shown in the table:

As can be seen from the formulated table, 24 votes were cast for Paris in R1.

Hence, option (d).

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**21. CAT 2005 LRDI | LR - Puzzles**

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?

- A.
33.33

- B.
38.10

- C.
50

- D.
66.67

Answer: Option D

**Explanation** :

Let there be x members in the IOC.

As a member cannot vote if his or her city is in contention, the number of voters in Round 1 (R1) = x – 4

The number of voters in Round 2 (R2) = x – 3 and

The number of voters in Round 3 (R3) = x – 2 – n

Where n is the number of voters who have voted for New York (NY) in R1 and Beijing (B) in R2.

Since x – 3 = 83, we get x – 4 = 82 and x – 2 – n = 75 or n = 9

21 members voted for B in R2. Out of these, 9 voted for NY in R1.

The remaining 12 who voted for B comprised 75% of those who voted for B in R1.

Thus 12/0.75 = 16 members voted for B in R1.

∴ Paris (P) got 82 – 16 – 30 – 12 = 24 votes in R1.

All those who voted for London (L) and P in R1 continued to vote for the same cities in subsequent rounds. Thus, 24 voters of P in R2 had voted for P in R1 too. Also from the given information, 3 voters who had voted for NY in R1 voted for Paris in R2.

Out of the remaining 5 that voted for P in R2, 4 had voted for Beijing in R1 and 1 vote came from the member who represented NY.

In R3, the difference in the votes cast for L and P was 1, i.e. L and P got 37 and 38 votes in some order.

The composition of 75 voters of R3 was as follows:

12 members who had voted for B in R1 and R2 were eligible for voting in R3.

30 and 24 members who voted for L and P in R1 continued to do so in R3.

4 voters of R3, voted for B in R1 and P in R2.

3 voters of R3, voted for NY in R1 and P in R2.

1 member represented NY and 1 represented B.

From given information, 50% of voters of B in R1 i.e. 8 voted for P in R3. So, 8 out of the 12 who voted for B in R1 and R2, voted for London in R3.

The information can be summarised as shown in the table:

required percentage = 8 × 100/12 = 66.67%

Hence, option (d).

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**22. CAT 2005 LRDI | LR - Puzzles**

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.

- A.
Only a

- B.
Only b

- C.
Both a and b

- D.
Neither a nor b

Answer: Option A

**Explanation** :

Let there be x members in the IOC.

The number of voters in Round 2 (R2) = x – 3 and

The number of voters in Round 3 (R3) = x – 2 – n

Where n is the number of voters who have voted for New York (NY) in R1 and Beijing (B) in R2.

Since x – 3 = 83, we get x – 4 = 82 and x – 2 – n = 75 or n = 9

21 members voted for B in R2. Out of these, 9 voted for NY in R1.

The remaining 12 who voted for B comprised 75% of those who voted for B in R1.

Thus 12/0.75 = 16 members voted for B in R1.

∴ Paris (P) got 82 – 16 – 30 – 12 = 24 votes in R1.

The composition of 75 voters of R3 was as follows:

12 members who had voted for B in R1 and R2 were eligible for voting in R3.

30 and 24 members who voted for L and P in R1 continued to do so in R3.

4 voters of R3, voted for B in R1 and P in R2.

3 voters of R3, voted for NY in R1 and P in R2.

1 member represented NY and 1 represented B.

The information can be summarised as shown in the table:

It can be clearly seen, that only statement a is true.

Hence, option (a).

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**Answer the following question based on the information given below.**

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.

**23. CAT 2005 LRDI | DI - Tables & Graphs**

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.

Answer: Option B

**Explanation** :

Truthful Ltd. has the highest market share in MP.

Thus Truthful Ltd. could be Firm A or Firm C.

Aggregate revenues of Firms A, B, C and D are 190, 217, 222 and 185 (in million rupees) respectively.

Thus, Aggressive Ltd. and Honest Ltd. could be A and D or B and C in some order.

Case 1: Truthful Ltd. = A

Aggressive Ltd. and Honest Ltd. = B and C

Profitable Ltd. = D

Case 2: Truthful Ltd. = C

Aggressive Ltd. and Honest Ltd. = A and D

Profitable Ltd. = B

If statement 1 is true, then Firm B is profitable Ltd., which means that Honest Ltd. is Firm A or D.

But, the total revenue of Firms A and D each is lesser than that of firm B.

Thus, if statement 1 is true, statement 2 is necessarily false.

Hence, option (b).

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**24. CAT 2005 LRDI | DI - Tables & Graphs**

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.

- A.
If Statement 2 is true then Statement 1 is necessarily false.

- B.
If Statement 1 is false then Statement 2 is necessarily true.

- C.
If Statement 1 is true then Statement 2 is necessarily true.

- D.
None of the above.

Answer: Option C

**Explanation** :

If statement 1 is true, then Firm B is Aggressive Ltd. This implies that Firm C is Honest Ltd.

Firm C’s lowest revenues are from Bihar. Thus, statement 2 is necessarily true.

Hence, option (c).

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**25. CAT 2005 LRDI | DI - Tables & Graphs**

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.

- A.
Both statements could be true.

- B.
At least one of the statements must be true.

- C.
At most one of the statements is true.

- D.
None of the above

Answer: Option C

**Explanation** :

The two statements talk about two firms having the highest shares in the UP and Bihar Markets. Thus, both the statements refer to Firm B. From the explanation given in the first question, only one of the two statements can be true at a time.

Hence, option (c).

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**26. CAT 2005 LRDI | DI - Tables & Graphs**

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

- A.
Truthful Ltd.’s lowest revenues are from MP.

- B.
Truthful Ltd.’s lowest revenues are from Bihar.

- C.
Truthful Ltd.’s lowest revenues are from UP.

- D.
No definite conclusion is possible.

Answer: Option C

**Explanation** :

Profitable Ltd. is firm D (Case 1 from the explanation given earlier).

∴ Truthful Ltd. is firm A.

Thus, Truthful Ltd.’s lowest revenues are from UP.

Hence, option (c).

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**Answer the following question based on the information given below.**

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, FloodRelief (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. CAT 2005 LRDI | LR - Venn Diagram**

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:

- A.
1

- B.
3

- C.
4

- D.
5

Answer: Option C

**Explanation** :

17 volunteers are involved in the TR project and 10 in TR are also involved in other projects. Thus, 7 volunteers are involved only in TR.

∴ 8 volunteers are involved in ER alone.

∴ 4 volunteers are involved in all the three projects.

Let x people be involved in FR alone.

∴ Number of people involved in FR and ER but not TR = x – 4

Now, a + b + 4 = 10

∴ a + b = 6

Also, 7 + a + b + 4 + x + x – 4 + 8 = 37

∴ 2x = 16 or x = 8

Number of Volunteers involved in FR > Number of Volunteers involved in TR

And Number of Volunteers involved in FR > Number of Volunteers involved in ER

∴ 16 + a > 17 and 16 + a > 16 + b or a > b

∴ a and b can be (6, 0), (5, 1), (4, 2)

The minimum number of volunteers involved in both FR and TR projects, but not in the ER Project = minimum value of a = 4

Hence, option (c).

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**28. CAT 2005 LRDI | LR - Venn Diagram**

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

- A.
Twenty volunteers are involved in FR.

- B.
Four volunteers are involved in all the three projects.

- C.
Twenty three volunteers are involved in exactly one project.

- D.
No need for any additional information.

Answer: Option A

**Explanation** :

We can obtain the information in options 2 and 3 from the initial data.

Based on the information given in the explanation to the first question, the information in option 1 will give us the value of a, which in turn will give us the value of b. Thus, option 1 would enable us to find the exact number of volunteers involved in various projects.

Hence, option (a).

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**29. CAT 2005 LRDI | LR - Venn Diagram**

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?

- A.
The lowest number of volunteers is now in TR project.

- B.
More volunteers are now in FR project as compared to ER project.

- C.
More volunteers are now in TR project as compared to ER project.

- D.
None of the above

Answer: Option B

**Explanation** :

After the volunteers withdraw as mentioned, the number of volunteers working on different projects is as shown.

∴ Number of volunteers working on TR = 7 + 6 + 3 = 16

Number of volunteers working on FR = 14 + a

Number of volunteers working on ER = 15 + b

Considering the possible values of a and b, 14 + a > 15 + b

∴ More volunteers are now in FR than in ER

Hence, option (b).

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**30. CAT 2005 LRDI | LR - Venn Diagram**

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?

- A.
ER

- B.
FR

- C.
TR

- D.
Cannot be determined

Answer: Option A

**Explanation** :

Let m volunteers be added to TR project and n be added to each of FR and ER projects.

Then, 7 + m = 8 + n

∴ m = n + 1

Also, b + 2 = 5

∴ b = 3 and a = 3

Number of volunteers working on TR = 7 + n + 1 + 4 + 5 = 17 + n

Number of volunteers working on FR = 17 + n

Number of volunteers working on ER = 18 + n

Thus, ER has the highest number of volunteers.

Hence, option (a).

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