# CAT 2004 LRDI | Previous Year CAT Paper

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

Prof. Singh has been tracking the number of visitors to his homepage. His service provider has provided him with the following data on the country of origin of the visitors and the university they belong to:

**1. CAT 2004 LRDI | DI - Tables & Graphs**

University 1 can belong to ______.

- A.
UK

- B.
Canada

- C.
Netherlands

- D.
USA

Answer: Option C

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**Explanation** :

Let us denote University 1 as U_{1}, University 2 as U_{2} and so on.

Consider day 3. 2 students from UK and 1 student from USA visited the homepage. Also, 2 and 1 student from U_{4} and U_{6} respectively visited the homepage.

∴ U_{4} is in UK and U_{6} is in USA. Similarly, considering day 2, U_{3} is in Netherlands and U_{8} is in India.

Canada has 2, 0 and 0 visitors on days 1, 2 and 3 and so have U_{2} and U_{7}. ∴ One of U_{2} and U_{7} is in Canada.

UK has 2, 0 and 2 visitors on days 1, 2 and 3 and we know that U_{4} is in UK. But as U_{4} has 0 visitors on day 1, we can say that either U_{2} or U_{7} is in UK. (If we assume that UK has three of the eight listed universities, U_{4}, U_{1} and U_{5}, then considering the number of visitors on day 1, we do not find appropriate universities for India and Netherlands.)

Similarly, considering India and Netherlands, U_{5} and U_{1} will be in these countries. Thus, we have the following table.

∴ University 1 can belong to Netherlands or India.

Hence, option (c).

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**2. CAT 2004 LRDI | DI - Tables & Graphs**

To which country does University 5 belong?

- A.
India or Netherlands but not USA

- B.
India or USA but not Netherlands

- C.
Netherlands or USA but not India

- D.
India or USA but not UK

Answer: Option A

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**Explanation** :

University 5 can belong to the Netherlands or India.

Hence, option (a).

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**3. CAT 2004 LRDI | DI - Tables & Graphs**

Visitors from how many universities from UK visited Prof. Singh’s homepage in the three days?

- A.
1

- B.
2

- C.
3

- D.
4

Answer: Option B

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**Explanation** :

Students from University 4 and University 2/7 from UK visited Prof. Singh’s homepage in the three days.

Hence, option (b).

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**4. CAT 2004 LRDI | DI - Tables & Graphs**

Which among the listed countries can possibly host three of the eight listed universities?

- A.
None

- B.
Only UK

- C.
Only India

- D.
Both India and UK

Answer: Option A

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**Explanation** :

From the table, none of the countries can host more than two of the listed universities.

Hence, option (a).

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

A study was conducted to ascertain the relative importance that employees in five different countries assigned to five different traits in their Chief Executive Officers. The traits were compassion (C), decisiveness (D), negotiation skills (N), public visibility (P), and vision (V). The level of dissimilarity between two countries is the maximum difference in the ranks allotted by the two countries to any of the five traits. The following table indicates the rank order of the five traits for each country.

**5. CAT 2004 LRDI | LR - Puzzles**

Three of the following four pairs of countries have identical levels of dissimilarity. Which pair is the odd one out?

- A.
Malaysia and China

- B.
China and Thailand

- C.
Thailand and Japan

- D.
Japan and Malaysia

Answer: Option D

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**Explanation** :

Let us consider the options:

1. Malaysia and China: The maximum level of dissimilarity is 4 for ‘V’ or ‘N’.

2. China and Thailand: The maximum level of dissimilarity is 4 for ‘V’.

3. Thailand and Japan: The maximum level of dissimilarity is 4 for ‘D’.

4. Japan and Malaysia: The maximum level of dissimilarity is 3 for ‘V’ or ‘N’.

Hence, option (d).

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**6. CAT 2004 LRDI | LR - Puzzles**

Which amongst the following countries is most dissimilar to India?

- A.
China

- B.
Japan

- C.
Malaysia

- D.
Thailand

Answer: Option B

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**Explanation** :

The table gives levels of dissimilarity between India and the other countries for all traits.

Clearly, Japan is most dissimilar to India (since its level of dissimilarity is 4).

Hence, option (b).

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**7. CAT 2004 LRDI | LR - Puzzles**

Which of the following countries is least dissimilar to India?

- A.
China

- B.
Japan

- C.
Malaysia

- D.
Thailand

Answer: Option A

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**Explanation** :

From the above table, China is least dissimilar to India (since its level of dissimilarity is only 2).

Hence, option (a).

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**8. CAT 2004 LRDI | LR - Puzzles**

Which of the following pairs of countries are most dissimilar?

- A.
China and Japan

- B.
India and China

- C.
Malaysia and Japan

- D.
Thailand and Japan

Answer: Option D

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**Explanation** :

Consider the levels of dissimilarities for the four options.

China and Japan ≡ 3 (for 'D')

India and China ≡ 2 (for 'N')

Malaysia and Japan ≡ 3 (for 'N' or 'V')

Thailand and Japan ≡ 4 (for 'D')

Hence, option (d).

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

The data points in the figure below represent monthly income and expenditure data of individual members of the Ahuja family , the Bose family , the Coomar family , and the Dubey family . For these questions, savings is defined as

Savings = Income − Expenditure

**9. CAT 2004 LRDI | DI - Tables & Graphs**

Which family has the highest average expenditure?

- A.
Ahuja

- B.
Bose

- C.
Coomar

- D.
Dubey

Answer: Option D

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**Explanation** :

All these questions can be solved by mere observation.

The shaded portion of the graph is the region where Income > Expenditure and the unshaded portion is where Expenditure > Income.

By observation we can see that the average expenditure of the Dubey family is approximately 2000. The average expenditures of the Ahuja family, the Bose family and the Coomar family are definitely lesser than this.

Hence, option (d).

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**10. CAT 2004 LRDI | DI - Tables & Graphs**

Which family has the lowest average income?

- A.
Ahuja

- B.
Bose

- C.
Coomar

- D.
Dubey

Answer: Option C

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**Explanation** :

By observation, the Coomar family has the lowest average income.

Hence, option (c).

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**11. CAT 2004 LRDI | DI - Tables & Graphs**

The highest amount of savings accrues to a member of which family?

- A.
Ahuja

- B.
Bose

- C.
Coomar

- D.
Dubey

Answer: Option A

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**Explanation** :

A member of the Ahuja family has the highest income and lowest expenditure. He/she has the highest amount of savings.

Hence, option (a).

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**12. CAT 2004 LRDI | DI - Tables & Graphs**

Which family has the lowest average savings?

- A.
Ahuja

- B.
Bose

- C.
Coomar

- D.
Dubey

Answer: Option D

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**Explanation** :

Both the members of the Dubey family have Incomes that is almost equal to their Expenditures.

∴ Their average savings are the lowest.

Hence, option (d).

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

The Dean’s office recently scanned student results into the central computer system. When their character reading software cannot read something, it leaves the space blank. The scanner output reads as follows:

In the grading system, A, B, C, D, and F grades fetch 6, 4, 3, 2, and 0 grade points respectively. The Grade Point Average (GPA) is the arithmetic mean of the grade points obtained in the five subjects.

For example Nisha's GPA is $\frac{6+2+4+6+0}{5}=$ 3.6

Some additional facts are also known about the students’ grades. These are:

a. Vipul obtained the same grade in Marketing as Aparna obtained in Finance and Strategy.

b. Fazal obtained the same grade in Strategy as Utkarsh did in Marketing.

c. Tara received the same grade in exactly three courses.

**13. CAT 2004 LRDI | DI - Tables & Graphs**

In Operations, Tara could have received the same grade as ____________.

- A.
Ismet

- B.
Hari

- C.
Jagdeep

- D.
Manab

Answer: Option D

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**Explanation** :

Tara’s total grade points = 2.4 × 5 = 12

She gets B ≡ 4 in Finance. As she gets the same grade in three courses, she would have got B in 3 subjects and F in 2. (Getting a D in 4 subjects would also give the correct GPA. However, this is not possible since it is stated that Tara received the same grade in exactly three courses.)

Thus, she would have got either B or F in Operations, but only B is provided in the options (i.e. Manab's grade).

Hence, option (d).

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**14. CAT 2004 LRDI | DI - Tables & Graphs**

What grade did Preeti obtain in Statistics?

- A.
A

- B.
B

- C.
C

- D.
D

Answer: Option A

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**Explanation** :

Preeti’s total grade points = 3.2 × 5 = 16

Her grade points in Finance, Marketing and Strategy = 0 + 2 + 2 = 4

∴ She scores 12 in Statistics and Operations, which is possible only if she obtains an A in both these subjects.

Hence, option (a).

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**15. CAT 2004 LRDI | DI - Tables & Graphs**

What grade did Utkarsh obtain in Finance?

- A.
B

- B.
C

- C.
D

- D.
F

Answer: Option C

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**Explanation** :

Utkarsh’s grade in Marketing = Fazal’s grade in Strategy

= (2.4 × 5 – 2 – 0 – 4 – 2) = 4 ≡ B

∴ Utkarsh’s grade in Finance = (3 × 5 – 6 – 3 – 0 – 4) = 2 ≡ D

Hence, option (c).

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**16. CAT 2004 LRDI | DI - Tables & Graphs**

In Strategy, Gowri’s grade point was higher than that obtained by _________.

- A.
Fazal

- B.
Hari

- C.
Nisha

- D.
Rahul

Answer: Option B

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**Explanation** :

Gowri’s grade points in Strategy = (3.8 × 5 – 3 – 3 – 6 – 4) = 3 ≡ C

Fazal’s grade points in Strategy = 4 ≡ B (from the previous answer)

Hari’s grade points in Strategy and Finance = (2.8 × 5 – 4 – 6 – 2) = 2, i.e. he got grades F and D in Strategy and Finance, in some order.

Nisha’s grade points in Strategy = 6 ≡ A

Rahul’s grade points in Strategy = 4.2 × 5 – 6 – 3 – 6 – 0 = 6 ≡ A

∴ Gowri’s grade point in Strategy is higher than Hari’s.

Hence, option (b).

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

Purana and Naya are two brands of kitchen mixer-grinders available in the local market. Purana is an old brand that was introduced in 1990, while Naya was introduced in 1997. For both these brands, 20% of the mixer-grinders bought in a particular year are disposed off as junk exactly two years later. It is known that 10 Purana mixer-grinders were disposed off in 1997. The following figures show the number of Purana and Naya mixer-grinders in operation from 1995 to 2000, as at the end of the year.

**17. CAT 2004 LRDI | DI - Tables & Graphs**

How many Naya mixer-grinders were disposed of by the end of 2000?

- A.
10

- B.
16

- C.
22

- D.
Cannot be determined from the data

Answer: Option B

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**Explanation** :

The number of mixer-grinders in operation in any year can be divided into four categories: Newly purchased, one year old, two year old and older.

Consider Naya mixer-grinders.

As 30 mixer-grinders were in operation in 1997 and the brand itself was introduced in that year, all 30 were newly purchased.

In 1998, 80 were in operation, out of which 30 were one-year old.

∴ 50 were newly purchased.

In 1999, 124 were in operation, out of which 50 were one-year old.

Out of the 30 purchased in 1997, 20% or 6 were disposed of in 1999.

∴ 30 × 0.8 = 24 out of the 124 were two-year old.

Similarly in 2000, 134 were in operation, out of which 50 were one year old, 40 were two years old and 24 were older than two years.

Thus we have the following:

Consider Purana Mixer-grinders. As 10 of these were disposed of in 1997,

$\frac{10}{0.2}$ = 50 were bought in 1995.

∴ 70 mixer-grinders in operation in 1995 were old. The break-up of these however cannot be found.

Out of the 162 in operation in 1996, 50 were one year old. The break-up of the rest cannot be found as we do not have data of years before 1995 and we have not been given the number of mixer-grinders purchased in 1996.

In 1997, 182 were in operation and 10 were disposed of. Thus 182 + 10 = 192 mixer-grinders were either newly purchased or old.

Out of these 192, 162 existed in 1996 too.

∴ 192 – 162 = 30 were newly purchased in 1997.

As the number of newly purchased mixer-grinders in 1996 is not known, the number that were disposed of in 1998 cannot be found. Consequently, the number that were newly purchased also cannot be found.

Continuing this process for the years 1999 and 2000, the entire data can be presented as follows:

∴ 10 + 6 = 16 Naya mixer-grinders were disposed of by the end of 2000.

Hence, option (b).

Workspace:

**18. CAT 2004 LRDI | DI - Tables & Graphs**

How many Naya mixer-grinders were purchased in 1999?

- A.
44

- B.
50

- C.
55

- D.
64

Answer: Option B

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**Explanation** :

50 Naya mixer-grinders were purchased in 1999.

Hence, option (b).

Workspace:

**19. CAT 2004 LRDI | DI - Tables & Graphs**

How many Purana mixer-grinders were purchased in 1999?

- A.
20

- B.
23

- C.
50

- D.
Cannot be determined from the data

Answer: Option A

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**Explanation** :

20 Purana mixer-grinders were purchased in 1999.

Hence, option (a).

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**20. CAT 2004 LRDI | DI - Tables & Graphs**

How many Purana mixer-grinders were disposed of in 2000?

- A.
0

- B.
5

- C.
6

- D.
Cannot be determined from the data

Answer: Option D

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**Explanation** :

As the number of Purana mixer-grinders purchased in 1996 is not known, the ones purchased and disposed of in 1998 and 2000 cannot be determined.

Hence, option (d).

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

Coach John sat with the score cards of Indian players from the 3 games in a one-day cricket tournament where the same set of players played for India and all the major batsmen got out. John summarized the batting performance through three diagrams, one for each game. In each diagram, the three outer triangles communicate the number of runs scored by the three top scorers from India, where K, R, S, V, and Y represent Kaif, Rahul, Saurav, Virender, and Yuvraj respectively. The middle triangle in each diagram denotes the percentage of total score that was scored by the top three Indian scorers in that game. No two players score the same number of runs in the same game. John also calculated two batting indices for each player based on his scores in the tournament; the R-index of a batsman is the difference between his highest and lowest scores in the 3 games while the M-index is the middle number, if his scores are arranged in a non-increasing order

**21. CAT 2004 LRDI | LR - Mathematical Reasoning**

Which of the players had the best M-index from the tournament?

- A.
Rahul

- B.
Saurav

- C.
Virender

- D.
Yuvraj

Answer: Option B

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**Explanation** :

Consider the game against Pakistan (G_{1}).

Runs scored by Y, V and K = 40 + 130 + 28 = 198

Total runs scored = 198/0.9 = 220

∴ Runs scored by R (*r*_{1}) and S (*s*_{1}), *r*_{1}, *s*_{1} < 28 and *r*_{1} + *s*_{1} ≤ 22

Consider the game against South Africa (G_{2}).

Runs scored by K, R and S = 51 + 49 + 75 = 175

Total runs scored = 175/0.7 = 250

∴ Runs scored by Y (*y*_{2}) and V (*v*_{2}), *y*_{2}, *v*_{2} < 49 and *y*_{2} + *v*_{2} ≤ 75

Consider the game against Australia (G_{3}).

Runs scored by R, Y and S = 87 + 55 + 50 = 192

Total runs scored = 192/0.8 = 240

∴ Runs scored by V (*v*_{3}) and K (*k*_{3}), *v*_{3}, *k*_{3} < 50, *v*_{3} + *k*_{3} ≤ 48

R’s M-index = 49

S’s M-index = 50

V’s M-index ≤ 49

Y’s M-index is either 40 or between 41 and 49.

∴ S had the best M-index.

Hence, option (b).

Workspace:

**22. CAT 2004 LRDI | LR - Mathematical Reasoning**

Among the players mentioned, who can have the lowest R-index from the tournament?

- A.
Only Kaif, Rahul or Yuvraj

- B.
Only Kaif or Rahul

- C.
Only Kaif or Yuvraj

- D.
Only Kaif

Answer: Option A

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**Explanation** :

If *y*_{2 }< 40, then Y’s R-index = 87 − *y*_{2} > 47; i.e. 47 < Y’s R-index ≤ 87

If *y*_{2} > 40, then Y’s R-index = 87 – 40 = 47

∴ 47 ≤ Y’s R-index ≤ 87

Similarly,

23 ≤ K’s R-index ≤ 51

33 ≤ R’s R-index ≤ 55 (∵ *r*_{1}, *s*_{1} < 28 and *r*_{1} + *s*_{1} ≤ 22)

53 ≤ S’s R-index ≤ 75 (∵ *r*_{1}, *s*_{1} < 28 and *r*_{1} + *s*_{1} ≤ 22)

82 ≤ V’s R-index ≤ 130 (∵ *v*_{3}, *k*_{3} < 50, *v*_{3} + *k*_{3} ≤ 48)

∴ Any one of Y, K or R could have the lowest R-index.

Hence, option (a).

Workspace:

**23. CAT 2004 LRDI | LR - Mathematical Reasoning**

For how many Indian players is it possible to calculate the exact M-index?

- A.
0

- B.
1

- C.
2

- D.
More than 2

Answer: Option C

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**Explanation** :

Consider the game against Pakistan (G_{1}).

Runs scored by Y, V and K = 40 + 130 + 28 = 198

Total runs scored = 198/0.9 = 220

∴ Runs scored by R (*r*_{1}) and S (*s*_{1}), *r*_{1}, *s*_{1} < 28 and *r*_{1} + *s*_{1} ≤ 22

Consider the game against South Africa (G_{2}).

Runs scored by K, R and S = 51 + 49 + 75 = 175

Total runs scored = 175/0.7 = 250

∴ Runs scored by Y (*y*_{2}) and V (*v*_{2}), *y*_{2}, *v*_{2} < 49 and *y*_{2} + *v*_{2} ≤ 75

Consider the game against Australia (G_{3}).

Runs scored by R, Y and S = 87 + 55 + 50 = 192

Total runs scored = 192/0.8 = 240

∴ Runs scored by V (*v*_{3}) and K (*k*_{3}), *v*_{3}, *k*_{3} < 50, *v*_{3} + *k*_{3} ≤ 48

R’s M-index = 49

S’s M-index = 50

V’s M-index ≤ 49

Y’s M-index is either 40 or between 41 and 49.

The M-index of only R and S can be exactly calculated.

Hence, option (c).

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**24. CAT 2004 LRDI | LR - Mathematical Reasoning**

How many players among those listed definitely scored less than Yuvraj in the tournament?

- A.
0

- B.
1

- C.
2

- D.
More than 2

Answer: Option B

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**Explanation** :

Y scored 127 in G_{1} and G_{3}. V scored 130 in G1 itself.

K’s max score could be 28 + 51 + 48 = 127

R’s max score could be 49 + 55 + 22 = 126

S’s max score could be 75 + 50 + 22 = 147

∴ Only R definitely scored less than Y.

Hence, option (b).

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

Twenty one participants from four continents (Africa, Americas, Australasia, and Europe) attended a United Nations conference. Each participant was an expert in one of four fields, labour, health, population studies, and refugee relocation. The following five facts about the participants are given.

a. The number of labour experts in the camp was exactly half the number of experts in each of the three other categories.

b. Africa did not send any labour expert. Otherwise, every continent, including Africa, sent at least one expert for each category.

c. None of the continents sent more than three experts in any category.

d. If there had been one less Australasian expert, then the Americas would have had twice as many experts as each of the other continents.

e. Mike and Alfanso are leading experts of population studies who attended the conference. They are from Australasia.

**25. CAT 2004 LRDI | DI - Tables & Graphs**

Which of the following numbers cannot be determined from the information given?

- A.
Number of labour experts from the Americas.

- B.
Number of health experts from Europe.

- C.
Number of health experts from Australasia.

- D.
Number of experts in refugee relocation from Africa.

Answer: Option D

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**Explanation** :

Let there be x labour experts. Then, the number of health, population and refugee relocation experts will be 2x each.

Hence, x + 2x + 2x + 2x = 7x = 21

∴ x = 3

That is, the number of Labour, Health, Population and Refugee Relocation experts are 3, 6, 6 and 6 respectively.

Let Australasia have (y + 1) experts. Then the Americas have 2y experts and Africa and Europe have y experts each.

∴ y + 1 + 2y + y + y = 21

∴ y = 4

That is, Australasia, Americas, Africa and Europe have 5, 8, 4 and 4 experts respectively.

As Australasia has sent at least 2 experts on population studies, it has sent 1 expert each for the other three fields.

∴ The Americas and Europe have sent 1 expert each on labour.

∴ Europe has sent 1 expert each on Health, Population Studies and Refugee Relocation.

Number of experts in Refugee Relocation from Africa cannot be found.

Hence, option (d).

Workspace:

**26. CAT 2004 LRDI | DI - Tables & Graphs**

Which of the following combinations is NOT possible?

- A.
2 experts in population studies from the Americas and 2 health experts from Africa attended the conference.

- B.
2 experts in population studies from the Americas and 1 health expert from Africa attended the conference.

- C.
3 experts in refugee relocation from the Americas and 1 health expert from Africa attended the conference.

- D.
Africa and America each had 1 expert in population studies attending the conference.

Answer: Option D

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**Explanation** :

If Africa and Americas, each have 1 expert in population studies, the total number of experts in this field = 5, which is not possible as we know that the number is 6.

∴ Option 4 is not possible.

Hence, option (d).

Workspace:

**27. CAT 2004 LRDI | DI - Tables & Graphs**

If Ramos is the lone American expert in population studies, which of the following is NOT true about the numbers of experts in the conference from the four continents?

- A.
There is one expert in health from Africa.

- B.
There is one expert in refugee relocation from Africa.

- C.
There are two experts in health from the Americas.

- D.
There are three experts in refugee relocation from the Americas.

Answer: Option C

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**Explanation** :

If Americas have 1 expert in population studies, we have the following.

∴ Option 3 is not true.

Hence, option (c).

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**28. CAT 2004 LRDI | DI - Tables & Graphs**

Alex, an American expert in refugee relocation, was the first keynote speaker in the conference. What can be inferred about the number of American experts in refugee relocation in the conference, excluding Alex?

i. At least one

ii. At most two

- A.
Only i and not ii

- B.
Only ii and not i

- C.
Both i and ii

- D.
Neither i nor ii

Answer: Option C

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**Explanation** :

Since Africa has 4 experts in total and none of them are from labour, the number of experts from the other 3 fields should be 4.

Hence, Africa’s Refugee Relocation experts ≤ 2

The total number of Refugee Relocation experts in the conference was 6. Of these, 1 is from Europe and 1 is from Australasia.

Hence, Refugee Relocation experts from Africa and Americas = 4

Hence, Total number of Refugee Relocation experts from Americas = 2 or 3

∴ Apart from Alex, there is at least one more and at most 2 more American experts in refugee relocation.

Hence, option (c).

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

The year was 2006. All six teams in Pool A of World Cup hockey, play each other exactly once. Each win earns a team three points, a draw earns one point and a loss earns zero points. The two teams with the highest points qualify for the semi-finals. In case of a tie, the team with the highest goal difference (Goal For – Goals Against) qualifies.

In the opening match, Spain lost to Germany. After the second round (after each team played two matches), the pool table looked as shown below.

In the third round, Spain played Pakistan, Argentina played Germany, and New Zealand played South Africa. All the third round matches were drawn. The following are some results from the fourth and fifth round matches.

a. Spain won both the fourth and fifth round matches.

b. Both Argentina and Germany won their fifth round matches by 3 goals to 0.

c. Pakistan won both the fourth and fifth round matches by 1 goal to 0.

**29. CAT 2004 LRDI | DI - Games & Tournaments**

Which one of the following statements is true about matches played in the first two rounds?

- A.
Pakistan beat South Africa by 2 goals to 1.

- B.
Argentina beat Pakistan by 1 goal to 0.

- C.
Germany beat Pakistan by 2 goals to 1.

- D.
Germany beat Spain by 2 goals to 1.

Answer: Option B

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**Explanation** :

Since Pakistan’s ‘Goals For’ (GF) and ‘Goals Against’ (GA) is 2 and 1 respectively, and it won 1 game and lost the other, the only possible combination of scores for Pakistan in its two matches will be 2:0 and 0:1.

Similarly, Germany’s scores in its two matches will be 2:1 and 1:0; while Argentina’s scores in its two matches will be 1:0 and 1:0.

Hence, we have the following table:

(G stands for Germany, A for Argentina, S for Spain, P for Pakistan, NZ for New Zealand and SA for South Africa)

Since Spain lost to Germany in the opening round, one of Spain’s score could be either 0:1 or 1:2. Since Spain’s total GF = 5 and GA = 2 for the first 2 rounds, we have the following possible scores for Spain:

Since the GF for both South Africa and New Zealand is 1, for each of these teams the GF for one match will be 1 while the GF of the second match will be 0. Hence, the different possibilities are as follows:

Combining the above possibilities for Spain, SA and NZ with the table showing the scores of Germany, Argentina and Pakistan, we see that the 1st possibility for SA is not possible since no possibility for any other team has the score 3:1. Similarly, the 2nd and 3rd possibility for NZ can also be eliminated. Hence, we have,

Looking at the GF and GA values, we can guess which teams played against others, for certain cases. (For example, SA has a score of 1:2 and Germany is the only team to have 2:1.) These are filled in the first column of the above table.

Also, since Germany beats SA with a score of 2:1, it beats Spain with a score of 1:0. This eliminates the 2nd possibility for Spain. This implies that Spain beats NZ with 5:1, eliminating NZ’s 1st possibility. Hence, we have,

Compiling the above information, we have the following:

Argentina beat Pakistan by 1 goal to 0.

Hence, option (b).

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**30. CAT 2004 LRDI | DI - Games & Tournaments**

Which one of the following statements is true about matches played in the first two rounds?

- A.
Germany beat New Zealand by 1 goal to 0.

- B.
Spain beat New Zealand by 4 goals to 0.

- C.
Spain beat South Africa by 2 goals to 0.

- D.
Germany beat South Africa by 2 goals to 1.

Answer: Option D

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**Explanation** :

Germany beat SA by 2 goals to 1.

Hence, option (d).

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**31. CAT 2004 LRDI | DI - Games & Tournaments**

If Pakistan qualified as one of the two teams from Pool A, which was the other team that qualified?

- A.
Argentina

- B.
Germany

- C.
Spain

- D.
Cannot be determined

Answer: Option D

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**Explanation** :

The following table gives the distribution of games within each round:

(Note: There is an inconsistency in the question. In Round 4, only 4 teams have played while in Round 5, two teams (NZ and SA) have played 2 matches. This, as we will see later, causes an inconsistency in the question as well.)

The points table will be as follows:

Since, 4 teams are tied with the same number of points, the qualifying teams will be chosen based on their Goal Difference (GD).

The GFs and GAs for the first two rounds is already given. In the third round, the match of Germany versus Argentina was drawn. Hence, both their GFs and GAs will be equal (say, X). In the fourth round, Spain won the match against Argentina. Hence, if Spain’s score is (say) A:B, where A > B, then Argentina’s will be B:A.

Following along similar lines, we have the following table:

Hence,

GD for Pakistan = (2 + Y + 1 + 1) – (1 + Y + 0 + 0) = 3

GD for Germany = (3 + X + 0 + 3) – (1 + X + 1 + 0) = 4

GD for Argentina = (2 + X + B + 3) – (0 + X + A + 0) = 5 + (B – A)

Since B < A, hence (B – A) < 0

∴ GD for Argentina < 5

GD for Spain = (5 + Y + A + C) – (2 + Y + B + D) = 3 + (A – B) + (C – D)

Since A > B and C > D, hence (A − B) ≥ 1 and (C – D) ≥ 1

∴ GD for Spain ≥ 5

Hence, Pakistan cannot qualify for the finals! The closest option that can be marked is 'Cannot be determined'.

Hence, option (d).

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**32. CAT 2004 LRDI | DI - Games & Tournaments**

Which team finished at the top of the pool after five rounds of matches?

- A.
Argentina

- B.
Germany

- C.
Spain

- D.
Cannot be determined

Answer: Option C

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**Explanation** :

The following table gives the distribution of games within each round:

(Note: There is an inconsistency in the question. In Round 4, only 4 teams have played while in Round 5, two teams (NZ and SA) have played 2 matches. This, as we will see later, causes an inconsistency in the question as well.)

The points table will be as follows:

Since, 4 teams are tied with the same number of points, the qualifying teams will be chosen based on their Goal Difference (GD).

The GFs and GAs for the first two rounds is already given. In the third round, the match of Germany versus Argentina was drawn. Hence, both their GFs and GAs will be equal (say, X). In the fourth round, Spain won the match against Argentina. Hence, if Spain’s score is (say) A:B, where A > B, then Argentina’s will be B:A.

Following along similar lines, we have the following table:

Hence,

GD for Pakistan = (2 + Y + 1 + 1) – (1 + Y + 0 + 0) = 3

GD for Germany = (3 + X + 0 + 3) – (1 + X + 1 + 0) = 4

GD for Argentina = (2 + X + B + 3) – (0 + X + A + 0) = 5 + (B – A)

Since B < A, hence (B – A) < 0

∴ GD for Argentina < 5

GD for Spain = (5 + Y + A + C) – (2 + Y + B + D) = 3 + (A – B) + (C – D)

Since A > B and C > D, hence (A − B) ≥ 1 and (C – D) ≥ 1

∴ GD for Spain ≥ 5

it is clear that Germany, Argentina, Spain and Pakistan are tied after 5 rounds, but only Spain’s GD ≥ 5.

Hence, option (c).

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