# CAT 2003 LRDI - Retake

Previous year paper questions for CAT 2003 LRDI - Retake

**Choose 1, if the question can be answered by using statement A alone but not by using B alone.**

**Choose 2, if the question can be answered by using statement B alone but not by using A alone.**

**Choose 3, if the question can be answered by using either statement alone.**

**Choose 4, if the question can be answered by using both the statements together but not by either statement.**

**1. CAT 2003 LRDI - Retake | Data Sufficiency**

In a cricket match, the ‘man of the match’ award is given to the player scoring the highest number of runs. In case of a tie, the player (out of those locked in the tie) who has taken the higher number of catches is chosen. Even thereafter if there is a tie, the player (out of those locked in the tie) who has dropped fewer catches is selected. Aakash, Biplab and Chirag who were contenders for the award dropped at least one catch each. Biplab dropped 2 catches more than Aakash did, scored 50, and took 2 catches. Chirag got two chances to catch and dropped both. Who was the ‘man of the match’?

A. Chirag made 15 runs less than both Aakash and Biplab.

B. The catches dropped by Biplab are 1 more than the catches taken by Aakash.

- A.
1

- B.
2

- C.
3

- D.
4

Answer: Option D

**Explanation** :

From Statement A

We get the table as shown above :

∵ We do not know the number of catches taken by Aakash.

∴ Statement A alone is not sufficient.

Statement B does not give any information about the runs scored.

∴ Statement B alone is not sufficient.

After combining both the statements, we get,

Number of catches taken by Aakash = *x* + 1

∴ If *x* = 1 then Aakash is man of the match since he has dropped fewer catches.

If *x* > 1 then Aakash will be the man of the match as he has taken more catches.

Hence, option 4.

Workspace:

**2. CAT 2003 LRDI - Retake | Data Sufficiency**

Four friends, A, B, C and D got the top four ranks in a competitive examination, but A did not get the first, B did not get the second, C did not get the third, and D did not get the fourth rank. Who secured which rank?

A. Neither A nor D were among the first 2.

B. Neither B nor C was third or fourth.

- A.
1

- B.
2

- C.
3

- D.
4

Answer: Option C

**Explanation** :

From statement A,

Neither A nor D were among the first 2 which means that D gets either 3^{rd} or the 4^{th} rank.

∵ D did not get the 4^{th} rank.

∴ D gets the 3^{rd} rank and A gets the 4^{th} rank.

∵ B didn’t get the 2^{nd} rank.

∴ B gets the 1^{st} rank and C gets the 2^{nd} rank.

∴ Statement A alone is sufficient.

From statement B,

B gets either the 1^{st} or the 2^{nd} rank.

We know that B did not get the 2^{nd} rank.

∴ B gets the 1^{st} rank and C gets the 2^{nd} rank.

∵ D didn’t get the 4^{th} rank.

∴ D gets the 3^{rd} rank and A gets 4^{th} rank.

∴ Statement B alone is sufficient.

∴ The question can be answered using either statements alone.

Hence, option 3.

Workspace:

**3. CAT 2003 LRDI - Retake | Data Sufficiency**

The members of a local club contributed equally to pay Rs.600 towards a donation. How much did each one pay?

A. If there had been five fewer members, each one would have paid an additional Rs.10.

B. There were at least 20 members in the club, and each one paid no more than Rs.30.

- A.
1

- B.
2

- C.
3

- D.
4

Answer: Option A

**Explanation** :

From statement A,

Let there are x members in the club.

$\therefore \frac{600}{(x-5)}-\frac{600}{x}=10$

∴ x = 20

∴ Contribution per head = $\frac{600}{20}$ = Rs. 30

∴ Statement A alone is sufficient.

From statement B,

We get there were at least 20 members in the club and each one paid no more than Rs. 30.

The different possibilities for can be :

30 members × 20 rupees = Rs. 600

40 members × 15 rupees = Rs. 600

60 members × 10 rupees = Rs. 600 and so on.

∴ Statement B alone is not sufficient.

Hence, option 1.

Workspace:

**4. CAT 2003 LRDI - Retake | Data Sufficiency**

A family has only one kid. The father says “after ‘n’ years, my age will be 4 times the age of my kid.” The mother says “after ‘n’ years, my age will be 3 times that of my kid.” What will be the combined ages of the parents after ‘n’ years?

A. The age difference between the parents is 10 years.

B. After ‘n’ years, the kid is going to be twice as old as she is now.

- A.
1

- B.
2

- C.
3

- D.
4

Answer: Option A

**Explanation** :

Let the present age of father = *f* years

The present age of mother = *m* years

The present age of the kid = *k* years

∴ *f* + *n* = 4(*k* + *n*) …(i)

∴ *m* + *n* = 3(*k* + *n*) …(ii)

Equation (i) - equation (ii)

∴ *f* − *m* = *k* + *n* …(iii)

Equation (i) + equation (ii)

∴ *f* + *m* + 2*n* = 7*k* + 7*n* = 7(*k* + *n*) …(iv)

From statement A,

*f* − *m* = 10

Substituting in equation (iii), we get,

*k* + *n* = 10

∴ The combined age of the parents after *n* years

= 7(*k* + *n*)

= 7 × 10 = 70 years\

∴ Statement A alone is sufficient.

From statement B,

*k* + *n* = 2*k*

*n* = *k* …(v)

Substituting equation (v) in equation (iii), we get,

*f* − *m* = 2*n*

Substituting equation (v) in equation (iv), we get,

*f* + *m* = 14*n* − 2*n*

*f* + *m* = 12*n*

∵ The value of *n* is not known .

∴ We cannot find the combined age of parents.

∴ Statement B alone is not sufficient.

Hence, option 1.

Workspace:

**5. CAT 2003 LRDI - Retake | LR - Venn Diagram**

70 percent of the employees in a multinational corporation have VCD players, 75 percent have microwave ovens, 80 percent have ACs and 85 percent have washing machines. At least what percentage of employees has all four gadgets?

- A.
15%

- B.
5%

- C.
10%

- D.
Cannot be determined

Answer: Option C

**Explanation** :

70% have VCD Players.

∴ 30% do not have VCD Players.

75% have microwave ovens.

∴ 25% do not have microwave ovens.

80% have ACs.

∴ 20% do not have ACs.

85% have washing machines.

∴ 15% do not have washing machines.

∴ 30 + 25 + 15 + 20 = 90% of employees do not have at least 1 gadget.

∴ Minimum percentage of employees who has all the four gadgets

= 100 – 90 = 10%

Hence, option 3.

Alternatively,

Minimum percentage of employees which possess both VCDs and Microwaves

= 70% + 75% – 100%

= 45%

Minimum percentage of employees which possess both ACs and Washing machines

= 80% + 85% – 100%

= 65%

∴ Minimum percentage of employees which possess all the four gadgets

= 45% + 65% – 100%

= 10%

Hence, option 3.

Workspace:

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

Four families decided to attend the marriage ceremony of one of their colleagues. One family has no kids, while the others have at least one kid each. Each family with kids has at least one kid attending the marriage. Given below is some information about the families, and who reached when to attend the marriage.

The family with 2 kids came just before the family with no kids.

Shanthi who does not have any kids reached just before Sridevi’s family.

Sunil and his wife reached last with their only kid.

Anil is not the husband of Joya.

Anil and Raj are fathers.

Sridevi’s and Anita’s daughters go to the same school.

Joya came before Shanthi and met Anita when she reached the venue.

Raman stays the farthest from the venue.

Raj said his son could not come because of his exams.

**6. CAT 2003 LRDI - Retake | LR - Arrangements**

Which woman arrived third?

- A.
Shanthi

- B.
Sridevi

- C.
Anita

- D.
Joya

Answer: Option A

**Explanation** :

Let’s organize the information given in a tabular form.

Using first two statements, we have,

Anil, Raj and Sunil have kids.

∴ Raman is the husband of Shanthi.

∵ Joya came before Shanthi and met Anita on the Venue.

∴ Anita reached the venue first, Joya reached second, Shanthi reached third and Sridevi reached last.

From the table we can see that Shanthi arrived third.

Hence, option 1.

Workspace:

**7. CAT 2003 LRDI - Retake | LR - Arrangements**

Name the correct pair of husband and wife.

- A.
Raj and Shanthi

- B.
Sunil and Sridevi

- C.
Anil and Sridevi

- D.
Raj and Anita

Answer: Option B

**Explanation** :

Let’s organize the information given in a tabular form.

Using first two statements, we have,

Anil, Raj and Sunil have kids.

∴ Raman is the husband of Shanthi.

∵ Joya came before Shanthi and met Anita on the Venue.

∴ Anita reached the venue first, Joya reached second, Shanthi reached third and Sridevi reached last.

Out of the given choices, Sunil and Sridevi is the correct pair.

Hence, option 2.

Workspace:

**8. CAT 2003 LRDI - Retake | LR - Arrangements**

Of the following pairs, whose daughters go to the same school?

- A.
Anil and Raman

- B.
Sunil and Raman

- C.
Sunil and Anil

- D.
Raj and Anil

Answer: Option C

**Explanation** :

The daughters of Anita and Sridevi go to the same school.

Let’s organize the information given in a tabular form.

Using first two statements, we have,

Anil, Raj and Sunil have kids.

∴ Raman is the husband of Shanthi.

∵ Joya came before Shanthi and met Anita on the Venue.

∴ Anita reached the venue first, Joya reached second, Shanthi reached third and Sridevi reached last.

Anita’s husband is Anil and Sridevi’s husband is Sunil.

∴ Sunil and Anil is the correct answer.

Hence, option 3.

Workspace:

**9. CAT 2003 LRDI - Retake | LR - Arrangements**

Whose family is known to have more than one kid for certain?

- A.
Raman's

- B.
Raj's

- C.
Anil's

- D.
Sunil's

Answer: Option B

**Explanation** :

Raj’s family consists of two kids for certain.

Anil has at least one kid, and hence, could be having exactly one kid also.

Hence, option 2.

Workspace:

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

Recently, the answers of a test held nationwide were leaked to a group of unscrupulous people. The investigative agency has arrested the mastermind and nine other people A, B, C, D, E, F, G, H and I in this matter. Interrogating them, the following facts have been obtained regarding their operation. Initially the mastermind obtains the correct answer-key. All the others create their answer-key from one or two people who already possess the same. These people are called his/her “sources”. If the person has two sources, then he/she compares the answer-keys obtained from both sources. If the key to a question from both sources is identical, it is copied, otherwise it is left blank. If the person has only one source, he/she copies the source’s answers into his/her copy. Finally, each person compulsorily replaces one of the answers (not a blank one) with a wrong answer in his/her answer key.

The paper contained 200 questions; so the investigative agency has ruled out the possibility of two or more of them introducing wrong answers to the same question. The investigative agency has a copy of the correct answer key and has tabulated the following data. These data represent question numbers.

**10. CAT 2003 LRDI - Retake | LR - Puzzles**

Which one among the following must have two sources?

- A.
A

- B.
B

- C.
C

- D.
D

- E.
0

Answer: Option B

**Explanation** :

A, D and G each one has only one wrong answer and no blank answers.

∴ They must have obtained the key from the mastermind directly.

∴ A introduced 46 as the wrong answer, D introduced 17 as the wrong answer and G introduced 25 as the wrong answer.

H and E must have obtained the key from A as they got 46 as the wrong answer.

∴ H further introduced 92 as the wrong answer and E introduced 90 as the wrong answer.

F must have obtained the key from H and E and found that answers 92 and 90 did not match. He left these blank and introduced 14 as the wrong answer in addition to 46 (which was the same answer though wrong) for H and E.

I must have obtained the key from D and E. Answers 17, 46, 90 didn’t match and he left these as blank. He also introduced 27 as the wrong answer.

C must have obtained the key from I and introduced 56 as the wrong answer.

B must have obtained the key from E and G. Answers 25, 46, 90 didn’t match and he left these blank. He also marked 96 as the wrong answer.

∴ Combining all the above diagrams we get:

From the flowchart, we see that A and D have only 1 source (mastermind).

Even C has only one source.

Only B has 2 sources E and G.

Hence, option 2.

Workspace:

**11. CAT 2003 LRDI - Retake | LR - Puzzles**

How many people (excluding the mastermind) needed to make answer keys before C could make his answer key?

- A.
2

- B.
3

- C.
4

- D.
5

Answer: Option C

**Explanation** :

A, D and G each one has only one wrong answer and no blank answers.

∴ They must have obtained the key from the mastermind directly.

∴ A introduced 46 as the wrong answer, D introduced 17 as the wrong answer and G introduced 25 as the wrong answer.

H and E must have obtained the key from A as they got 46 as the wrong answer.

∴ H further introduced 92 as the wrong answer and E introduced 90 as the wrong answer.

F must have obtained the key from H and E and found that answers 92 and 90 did not match. He left these blank and introduced 14 as the wrong answer in addition to 46 (which was the same answer though wrong) for H and E.

I must have obtained the key from D and E. Answers 17, 46, 90 didn’t match and he left these as blank. He also introduced 27 as the wrong answer.

C must have obtained the key from I and introduced 56 as the wrong answer.

B must have obtained the key from E and G. Answers 25, 46, 90 didn’t match and he left these blank. He also marked 96 as the wrong answer.

∴ Combining all the above diagrams we get:

From the flowchart, we see that C obtained the key from I who obtained it from D and E. E obtained it from A.

∴ Four people were needed: A, D, E and I.

Hence, option 3.

Workspace:

**12. CAT 2003 LRDI - Retake | LR - Puzzles**

Both G and H were sources to:

- A.
F

- B.
B

- C.
I

- D.
None of the nine

Answer: Option D

**Explanation** :

A, D and G each one has only one wrong answer and no blank answers.

∴ They must have obtained the key from the mastermind directly.

∴ A introduced 46 as the wrong answer, D introduced 17 as the wrong answer and G introduced 25 as the wrong answer.

H and E must have obtained the key from A as they got 46 as the wrong answer.

∴ H further introduced 92 as the wrong answer and E introduced 90 as the wrong answer.

F must have obtained the key from H and E and found that answers 92 and 90 did not match. He left these blank and introduced 14 as the wrong answer in addition to 46 (which was the same answer though wrong) for H and E.

I must have obtained the key from D and E. Answers 17, 46, 90 didn’t match and he left these as blank. He also introduced 27 as the wrong answer.

C must have obtained the key from I and introduced 56 as the wrong answer.

B must have obtained the key from E and G. Answers 25, 46, 90 didn’t match and he left these blank. He also marked 96 as the wrong answer.

∴ Combining all the above diagrams we get:

From the flow chart above it is clear that, G and H were not the sources to anyone.

Hence, option 4.

Alternatively,

G got question number 25 wrong and none of the other nine people got the same question number wrong.

Similarly H got question number 92 wrong and none of the other nine people got the same question number wrong.

∴ G and H were sources to none of the nine.

Workspace:

**13. CAT 2003 LRDI - Retake | LR - Puzzles**

Which of the following statements is true?

- A.
C introduced the wrong answer to question 27.

- B.
E introduced the wrong answer to question 46.

- C.
F introduced the wrong answer to question 14

- D.
H introduced the wrong answer to question 46

Answer: Option C

**Explanation** :

A, D and G each one has only one wrong answer and no blank answers.

∴ They must have obtained the key from the mastermind directly.

H and E must have obtained the key from A as they got 46 as the wrong answer.

∴ H further introduced 92 as the wrong answer and E introduced 90 as the wrong answer.

C must have obtained the key from I and introduced 56 as the wrong answer.

∴ Combining all the above diagrams we get:

From the flowchart we get that, statement 3 is the only true statement.

Hence, option 3.

Workspace:

**14. CAT 2003 LRDI - Retake | LR - Puzzles**

Which of the following two groups of people has identical sources?

(I) A, D and G

(II) E and H

- A.
Only (I)

- B.
Only (II)

- C.
Neither (I) nor (II)

- D.
Both (I) and (II)

Answer: Option D

**Explanation** :

A, D and G each one has only one wrong answer and no blank answers.

∴ They must have obtained the key from the mastermind directly.

H and E must have obtained the key from A as they got 46 as the wrong answer.

∴ H further introduced 92 as the wrong answer and E introduced 90 as the wrong answer.

C must have obtained the key from I and introduced 56 as the wrong answer.

∴ Combining all the above diagrams we get:

From the flowchart, we see that

A, D and G had the same source (Mastermind).

E and H had the same source (A).

Hence, option 4.

Workspace:

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

The plan above shows an office block for six officers, A, B, C, D, E and F. Both B and C occupy offices to the right of corridor (as one enters the office block) and A occupies an office to the left of the corridor. E and F occupy offices on opposite sides of the corridor but their offices do not face each other. The offices of C and D face each other. E does not have a corner office. F’s office is further down the corridor than A’s, but on the same side.

**15. CAT 2003 LRDI - Retake | LR - Arrangements**

If E sits in his office and faces the corridor, whose office is to his left?

- A.
A

- B.
B

- C.
C

- D.
D

Answer: Option C

**Explanation** :

From the data given we can figure out that A, F and D have offices on the left side of the corridor and B, E and C have offices on the right side of the corridor.

∵ E cannot occupy the corner office.

∴ E occupies an office in the middle of the right corridor.

∵ F cannot sit opposite E and A has to occupy an office before F.

∴ F occupies an office at far end of the left side of the corridor.

∴ D and C have to be at the beginning of the corridor.

∴ A has to be in the middle of the left corridor and B has to be at the far end of the right corridor.

The arrangement of offices will be as shown in the figure above :

If E sits in his office and faces the corridor. C’s office is to his left.

Hence, option 3.

Workspace:

**16. CAT 2003 LRDI - Retake | LR - Arrangements**

Whose office faces A’s office?

- A.
B

- B.
C

- C.
D

- D.
E

Answer: Option D

**Explanation** :

From the data given we can figure out that A, F and D have offices on the left side of the corridor and B, E and C have offices on the right side of the corridor.

∵ E cannot occupy the corner office.

∴ E occupies an office in the middle of the right corridor.

∵ F cannot sit opposite E and A has to occupy an office before F.

∴ F occupies an office at far end of the left side of the corridor.

∴ D and C have to be at the beginning of the corridor.

∴ A has to be in the middle of the left corridor and B has to be at the far end of the right corridor.

From the arrangement given in the solution of the first question of the set we get that,

E’s office faces A’s office.

Hence, option 4.

Workspace:

**17. CAT 2003 LRDI - Retake | LR - Arrangements**

Who is/are F’s neighbour(s)?

- A.
A only

- B.
A and D

- C.
C only

- D.
B and C

Answer: Option A

**Explanation** :

Only A is F’s neighbour.

Hence, option 1.

Workspace:

**18. CAT 2003 LRDI - Retake | LR - Arrangements**

D was heard telling someone to go further down the corridor to the last office on the right. To whose room was he trying to direct that person?

- A.
A

- B.
B

- C.
C

- D.
F

Answer: Option B

**Explanation** :

D was trying to direct the person to B’s office as B’s office is last on the right side of the corridor.

Hence, option 2.

Workspace:

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

Seven faculty members at a management institute frequent a lounge for strong coffee and stimulating conversation. On being asked about their visit to the lounge last Friday we got the following responses.

JC : I came in first, and the next two persons to enter were SS and SM. When I left the lounge, JP and VR were present in the lounge. DG left with me.

JP : When I entered the lounge with VR, JC was sitting there. There was someone else, but I cannot remember who it was.

SM : I went to the lounge for a short while, and met JC, SS and DG in the lounge on that day.

SS : I left immediately after SM left.

DG : I met JC, SS, SM, JP and VR during my first visit to the lounge. I went back to my office with JC. When I went to the lounge the second time, JP and VR were there.

PK : I had some urgent work, so I did not sit in the lounge that day, but just collected my coffee and left. JP and DG were the only people in the lounge while I was there.

VR : No comments.

**19. CAT 2003 LRDI - Retake | LR - Puzzles**

Based on the responses, which of the two JP or DG, entered the lounge first?

- A.
JP

- B.
DG

- C.
Both entered together

- D.
Cannot be deduced

Answer: Option B

**Explanation** :

The information can be organised in a tabular form as shown above:

JC arrives first in the lounge, followed by SS and SM.

∴ DG must have followed them as SM met him before he left.

SM leaves after DG comes followed by SS.

JP and VR enter to find JC and DG sitting in the lounge.

JC leaves with DG, after meeting JP and VR.

DG comes back on his second visit to the lounge finding JP and VR still sitting in the lounge.

VR leaves the lounge, and only JP and DG are left behind in the lounge.

PK enters the lounge and finds only JP and DG sitting in the lounge.

PK leaves, which means that JP and DG must be the last two faculty members to leave the lounge.

Between JP and DG, DG entered the lounge first.

Hence, option 2.

Workspace:

**20. CAT 2003 LRDI - Retake | LR - Puzzles**

Who was sitting with JC when JP entered the lounge?

- A.
SS

- B.
SM

- C.
DG

- D.
PK

Answer: Option C

**Explanation** :

The information can be organised in a tabular form as shown above:

JC arrives first in the lounge, followed by SS and SM.

∴ DG must have followed them as SM met him before he left.

SM leaves after DG comes followed by SS.

JP and VR enter to find JC and DG sitting in the lounge.

JC leaves with DG, after meeting JP and VR.

DG comes back on his second visit to the lounge finding JP and VR still sitting in the lounge.

VR leaves the lounge, and only JP and DG are left behind in the lounge.

PK enters the lounge and finds only JP and DG sitting in the lounge.

PK leaves, which means that JP and DG must be the last two faculty members to leave the lounge.

DG was sitting with JC when JP entered the lounge.

Hence, option 3.

Workspace:

**21. CAT 2003 LRDI - Retake | LR - Puzzles**

How many of the seven members did VR meet on Friday in the lounge?

- A.
2

- B.
3

- C.
4

- D.
5

Answer: Option B

**Explanation** :

The information can be organised in a tabular form as shown above:

JC arrives first in the lounge, followed by SS and SM.

∴ DG must have followed them as SM met him before he left.

SM leaves after DG comes followed by SS.

JP and VR enter to find JC and DG sitting in the lounge.

JC leaves with DG, after meeting JP and VR.

DG comes back on his second visit to the lounge finding JP and VR still sitting in the lounge.

VR leaves the lounge, and only JP and DG are left behind in the lounge.

PK enters the lounge and finds only JP and DG sitting in the lounge.

PK leaves, which means that JP and DG must be the last two faculty members to leave the lounge.

VR met JC, DG and JP in the lounge on Friday.

Hence, option 2.

Workspace:

**22. CAT 2003 LRDI - Retake | LR - Puzzles**

Who were the last two faculty members to leave the lounge?

- A.
JC and DG

- B.
PK and DG

- C.
JP and PK

- D.
JP and DG

Answer: Option D

**Explanation** :

The information can be organised in a tabular form as shown above:

JC arrives first in the lounge, followed by SS and SM.

∴ DG must have followed them as SM met him before he left.

SM leaves after DG comes followed by SS.

JP and VR enter to find JC and DG sitting in the lounge.

JC leaves with DG, after meeting JP and VR.

DG comes back on his second visit to the lounge finding JP and VR still sitting in the lounge.

VR leaves the lounge, and only JP and DG are left behind in the lounge.

PK enters the lounge and finds only JP and DG sitting in the lounge.

PK leaves, which means that JP and DG must be the last two faculty members to leave the lounge.

JP and DG were the last two faculty members to leave the lounge.

Hence, option 4.

Workspace:

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

Shown below is a layout of major streets in a city.

Two days (Thursday and Friday) are left for campaigning before a major election, and the city administration has received requests from five political parties for taking out their processions along the following routes.

Congress: A-C-D-E

BJP: A-B-D-E

SP: A-B-C-E

BSP: B-C-E

CPM: A-C-D

Street B-D cannot be used for a political procession on Thursday due to a religious procession. The district administration has a policy of not allowing more than one procession to pass along the same street on the same day. However, the administration must allow all parties to take out their procession during these two days.

**23. CAT 2003 LRDI - Retake | DI - Routes & Networks**

Congress procession can be allowed:

- A.
Only on Thursday.

- B.
Only on Friday.

- C.
On either day.

- D.
Only if the religious procession is cancelled.

Answer: Option A

**Explanation** :

∵ Route BD cannot be used on Thursday.

∴ BJP has to take out its procession on Friday.

∵ Route DE is common to BJP and Congress.

∴ Congress should take out its procession on Thursday.

∵ Route AB is common to SP and BJP.

∴ SP should take out its procession on Thursday.

∴ BSP and CPM have to take out their processions on Friday.

∴ Congress procession can be allowed only on Thursday.

Hence, option 1.

Workspace:

**24. CAT 2003 LRDI - Retake | DI - Routes & Networks**

Which of the following is not true?

- A.
Congress and SP can take out their processions on the same day.

- B.
The CPM procession cannot be allowed on Thursday.

- C.
The BJP procession can only take place on Friday.

- D.
Congress and BSP can take out their processions on the same day.

Answer: Option D

**Explanation** :

∵ Route BD cannot be used on Thursday.

∴ BJP has to take out its procession on Friday.

∵ Route DE is common to BJP and Congress.

∴ Congress should take out its procession on Thursday.

∵ Route AB is common to SP and BJP.

∴ SP should take out its procession on Thursday.

∴ BSP and CPM have to take out their processions on Friday.

From the explanation we get that,

Congress takes out a procession on Thursday and BSP on Friday.

∴ Only option 4 is not true.

Hence, option 4.

Workspace:

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

Below is a table that lists countries region-wise. Each region-wise list is sorted, first by birth rate and then alphabetically by the name of the country. We now wish to merge the region-wise list into one consolidated list and provide overall rankings to each country based first on birth rate and then on death rate. Thus, if some countries have the same birth rate, then the country with a lower death rate will be ranked higher. Further, countries having identical birth and death rates will get the same rank. For example, if two countries are tied for the third position, then both will be given rank 3, while the next country (in the ordered list) will be ranked 5.

**25. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

In the consolidated list, what would be the overall rank of the Philippines?

- A.
32

- B.
33

- C.
34

- D.
35

Answer: Option B

**Explanation** :

Number of countries with birth rate less than 34 = 32 (as birth rate of Philippines is 34)

Number of countries with birth rate equals to 34 = 4 (Including Philippines)

Amongst these 4 countries, there are 3 countries with equal death rates (equal to10).

Those 3 countries are Thailand, Philippines and Colombia.

This means that all these 3 countries get the same rank of 33.

Hence, option 2.

Workspace:

**26. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

In the consolidated list, how many countries would rank below Spain and above Taiwan?

- A.
9

- B.
8

- C.
7

- D.
6

Answer: Option A

**Explanation** :

Spain has a birth rate of 18 and a death rate of 8.

Other countries with a birth rate of 18 and a death rate more than 8 = 2 …(i)

Taiwan has a birth rate of 26 and a death rate of 5.

Other countries with birth rate of 26 and death rate less than 5 = 0 …(ii)

Countries with birth rate more than 18 and less than 26 = 7 …(iii)

∴ Countries ranking below Spain and above Taiwan

= equation (i) + equation (ii) + equation (iii)

= 9

Hence, option 1.

Workspace:

**27. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

In the consolidated list, which country ranks 37th?

- A.
South Africa

- B.
Brazil

- C.
Turkey

- D.
Venezuela

Answer: Option D

**Explanation** :

Philippines ranks 33 (calculated earlier). There are 3 countries at rank 33.

Turkey with birth rate of 34 and death rate of 12 has a rank of 36.

Among countries with a birth rate of 36, Venezuela has the lowest death rate and hence ranks 37th.

Hence, option 4.

Workspace:

**28. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

In the consolidated list, how many countries in Asia will rank lower than every country in South America, but higher than at least one country in Africa?

- A.
8

- B.
7

- C.
6

- D.
5

Answer: Option A

**Explanation** :

Countries in Asia must be ranked above at least Upper Volta in Africa.

∴ Afghanistan is excluded.

Countries must also be ranked below Ecuador.

∴ Countries from Japan to Burma are also excluded.

Only 8 countries, from Iran to Iraq in the list, meet the requirement.

Hence, option 1.

Workspace:

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

Answer the questions on the basis of the following charts.

(Note: Availability is defined as production less export.)

**29. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

In which year during the period 1996-1999 was Chaidesh’s export of tea, as a proportion of tea produced, the highest?

- A.
1996

- B.
1997

- C.
1998

- D.
1999

Answer: Option B

**Explanation** :

Required proportions are:

For 1996 = $\frac{189}{561}$ = 0.337

For 1997 = $\frac{209}{587}$ = 0.356

For 1998 = $\frac{215}{645}$ = 0.333

For 1999 = $\frac{220}{660}$ = 0.333

∴ Chaidesh’s export of tea as a proportion of tea produced during the period 1996-1999 was highest in the year 1997.

Hence, option 2.

Workspace:

**30. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

In which of the following years was the population of Chaidesh the lowest?

- A.
1995

- B.
1996

- C.
1997

- D.
1999

Answer: Option A

**Explanation** :

Availability of Tea = Production − Export

∴ Per Capita availability = $\frac{Production-Export}{Totalpopulation}$

∴ Total population = $\frac{Production-Export}{percapitaavailability}$

Population in 1995 = $\frac{421-207}{487}=\frac{214}{487}$ = 0.44

Population in 1996 = $\frac{561-189}{464}=\frac{372}{464}$ = 0.8

Population in 1997 = $\frac{587-209}{510}=\frac{378}{510}$ = 0.74

Population in 1999 = $\frac{660-220}{556}=\frac{440}{556}$ = 0.79

Hence, option 1.

Workspace:

**31. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

The area under tea cultivation continuously decreased in all four years from 1996 to 1999, by 10%, 7%, 4% and 1% respectively. In which year was tea productivity (production per unit of area) the highest?

- A.
1999

- B.
1998

- C.
1997

- D.
1996

Answer: Option A

**Explanation** :

Tea production is constantly increasing and the area under cultivation is decreasing.

Tea productivity = $\frac{ProductionofTea}{Areaundercultivation}$

∵ Production of tea is maximum in the year 1999, also the area under cultivation is the least in 1999.

∴ Tea productivity is the maximum for the year 1999.

Hence, option 1.

Workspace:

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

The profitability of a company is defined as the ratio of its operating profit to its operating income, typically expressed in percentage. The following two charts show the operating income as well as the profitability of six companies in the Financial Years (F.Y.s) 2001-02 and 2002-03.

The operating profits of four of these companies are plotted against their respective operating income figures for the F.Y. 2002-03, in the third chart given below.

**32. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

What is the approximate average operating profit, in F.Y. 2001-2002, of the two companies excluded from the third chart?

- A.
-7.5 crore

- B.
3.5 crore

- C.
25 crore

- D.
Cannot be determined

Answer: Option A

**Explanation** :

The two companies that are excluded from the graph 3 are B and D.

∴ Operating Profit of B = $\left(\frac{-4.2}{100}\times 240\right)$ = -10.08

∴ Operating Profit of D = $\left(\frac{-2.1}{100}\times 250\right)$ = -5.25

Average operating profit of B and D in F.Y. 2001-2002

$=\frac{-10.08-5.25}{2}$ = -7.6 crore

Hence, option 1.

**Alternatively,**

The two companies that are excluded from the third chart are B and D. These companies had a negative profitability in the year 2001-02.

∴ Only answer possible is option 1.

Hence, option 1.

Workspace:

**33. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Which company recorded the highest operating profit in F.Y. 2002-03?

- A.
A

- B.
C

- C.
E

- D.
F

Answer: Option C

**Explanation** :

Operating Profit = $\frac{Profitability}{100}$ × Operating Income

Operating Profit for A = $\left(\frac{7.5}{100}\times 190\right)$ = 14.25

Operating Profit for C = $\left(\frac{15}{100}\times 200\right)$ = 30

Operating Profit for E = $\left(\frac{17.5}{100}\times 200\right)$ = 35

Operating Profit for F = $\left(\frac{9}{100}\times 220\right)$ = 19.8

Hence, option 3.

**Alternatively,**

Among the given choices, the operating profit is almost same for all but the profitability is the highest for E.

∴ E should have the highest operating profit in 2002-03.

Hence, option 3.

Workspace:

**34. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Which of the following statements is NOT true?

- A.
The company with the third lowest profitability in F.Y. 2001-02 has the lowest operating income in F.Y. 2002-03.

- B.
The company with the highest operating income in the two financial years combined has the lowest operating profit in F.Y. 2002-03.

- C.
Companies with a higher operating income in F.Y. 2001-02 than in F.Y. 2002-03 have higher profitability in F.Y. 2002-03 than in F.Y. 2001-02.

- D.
Companies with profitability between 10% and 20% in F.Y. 2001-02 also have operating incomes between 150 crore and 200 crore in F.Y. 2002-03.

Answer: Option D

**Explanation** :

Let us analyse each of the given statement.

Consider option 1:

The company with the third-lowest profitability in 2001-02 is A and the company showing the lowest operating income in 2002-03 is also A.

∴ Option 1 is true.

Consider option 2:

From graph 1 we can conclude that the combined operating income both the years is highest for D.

Approximate operating profit for D(2002 - 03) = $\left(\frac{1.20}{100}\times 275\right)$ = 2.75

From the 3^{rd} graph, the operating profits for companies are above 15. These four companies are A, C, E and F.

∴ We have to compare operating profits for D and B.

∴ (Operating Profit)_{B} = $\left(\frac{2.5}{100}\times 225\right)>$ ((Operating Profit)_{D}

∴ D shows the lowest operating profit.

∴ Option 2 is also true

Consider option 3:

Company with higher operating income in 2001-02 than in 2002-03 is just one which is B.

B shows higher profitability in 2002-03 than in 2001-02.

∴ Option 3 is also true.

Consider option 4:

Companies with profitability between 10% and 20% in 2001-02 are A, C and E.

Operating income of C is more than 200 crores in 2002-03.

∴ Option 4 is not true.

Hence, option 4.

Workspace:

**35. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

The average operating profit in F.Y. 2002-03, of companies with profitability exceeding 10% in F.Y. 2002-03, is approximately

- A.
17.5 crore

- B.
25 crore

- C.
27.5 crore

- D.
32.5 crore

Answer: Option D

**Explanation** :

Companies with profitability exceeding 10% in F.Y.2002-03 are C and E.

The operating profits of C and E are 30 and 35 respectively from the earlier question

∴ Average operating profit = $\frac{30+35}{2}$ = 32.5 crore

Hence, option 4.

Workspace:

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

Answer the questions on the basis of the data presented in the figure below.

**36. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Which of the following statements is correct?

- A.
November rainfall exceeds 100 cm in each location.

- B.
September rainfall exceeds 50 cm in each location.

- C.
March rainfall is lower than September rainfall in each location.

- D.
None of the above.

Answer: Option C

**Explanation** :

The first statement is incorrect as November rainfall is below 100 cm in location 7.

The second statement is incorrect as the September rainfall does not exceed 50 cm in location 1.

The third statement is correct as March rainfall is lower than September rainfall in each location.

Hence, option 3.

Workspace:

**37. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Locations 6 and 7 differ from all the rest because only in these two locations,

- A.
April rainfall exceeds March rainfall.

- B.
Peak rainfall occurs in April.

- C.
November rainfall is lower than March rainfall.

- D.
April rainfall is less than 200 cm.

Answer: Option B

**Explanation** :

The first statement is incorrect as April rainfall exceeds March rainfall in all the locations.

The third statement is incorrect as November rainfall is lower than March rainfall in location 7 only and not in location 6.

The fourth statement is incorrect as April rainfall is less than 200 cm in locations 1, 2 and 3 as well.

The second statement is the only one that is correct as peak rainfall occurs in April only in locations 6 and 7.

Hence, option 2.

Workspace:

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

In a Decathlon, the events are 100m, 400m, 100m hurdles, 1500m, High jump, Pole vault, Long jump, Discus, Shot put and Javelin. The performance in the first four of these events is consolidated into Score 1, the next three into Score 2, and the last three into Score 3. Each such consolidation is obtained by giving appropriate positive weights to individual events. The final score is simply the total of these three scores. The athletes with the highest, second highest and the third highest final scores receive the gold, silver and bronze medals, respectively. The table given below gives the scores and performance of nineteen top athletes in this event.

**38. CAT 2003 LRDI - Retake | LR - Mathematical Reasoning**

The athletes from FRG and USA decided to run a 4 × 100 m relay race for their respective countries with the country having three athletes borrowing the athlete from CZE. Assume that all the athletes ran their stretch of the relay race at the same speed as in Decathlon event. How much more time did the FRG relay team take as compared to the USA team?

- A.
0.18

- B.
0.28

- C.
0.78

- D.
0.00

Answer: Option A

**Explanation** :

Total time taken by the FRG team = 10.58 + 10.85 + 10.95 + 10.63 = 43.01

∵ 10.63 is the time taken by Tomas (CZE) who joins the FRG team.

Total time taken by the USA team = 10.78 + 10.75 + 10.94 + 10.36 = 42.83

Extra time taken by FRG team

= 43.01 − 42.83

= 0.18

Hence, option 1.

Workspace:

**39. CAT 2003 LRDI - Retake | LR - Mathematical Reasoning**

What is the least that Daley Thompson must get in Score 2 that ensures him a bronze medal?

- A.
5309

- B.
5296

- C.
5271

- D.
5270

Answer: Option B

**Explanation** :

Score of First rank holder = 8905

Score of second-highest rank holder = 8897

To get the bronze, Daley has to score one more than that scored by Torsten who scores 8880.

Required Score 2

= 8881 − (3003 + 582)

= 8881 − 3585

= 5296

Hence, option 2.

Workspace:

**40. CAT 2003 LRDI - Retake | LR - Mathematical Reasoning**

At least how many competitors (excluding Daley Thompson) must Michael Smith have out-jumped in the long jump event?

- A.
1

- B.
2

- C.
3

- D.
4

Answer: Option D

**Explanation** :

Score 2 includes high jump, pole vault and long jump.

Score 2 of Michael Smith = 5274 (7th rank)

Michael’s score in High Jump is 1.97 and in Pole Vault is 4.9

Scores of six competitors less than 5274 are tabulated as shown above.

Michael may or may not have out jumped Tomas, as Michael’s score in pole vault and high jump are higher than those of Tomas.

Michael must have out jumped Torsten as his score in pole vault and high jump are lower than that of Torsten and also Michael scores higher than Torsten.

By similar logic, Michael must have out jumped Jurgen, Grigory and Steve as Michael’s corresponding scores in pole vault and high jump are lower than those of Grigory and Steve.

∴ These are at least 4 competitors whom Michael Smith must have out jumped.

Hence, option 4.

Workspace:

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

The following is the Wholesale Price Index (WPI) of a select list of items with the base year of 1993-94. In other words, all the item prices are made 100 in that year (1993-94). Price in all other years for an item are measured with respect to its price in the base year. For instance, the price of cement went up by 1% in 1994-95 as compared to 1993-94. Similarly, the price of power went up by 3% in 1996–97 as compared to 1993-94.

**41. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Let us suppose that one bag of cement (50 kgs) consumes 100 kgs of limestones and 10 units of power. The only other cost item in producing cement is in the form of wages. During 1993-94, limestone, power and wages contribute, respectively, 20%, 25%, and 15% to the cement price per bag. The average operating profit (% of price per cement bag) earned by a cement manufacturer during 2002-03 is closest to

- A.
40%

- B.
39.5%

- C.
38.5%

- D.
37.5%

Answer: Option C

**Explanation** :

WPI of cement in 2002-03 = 104

Operating cost of cement can be calculated as below:

∴ Operating Profit per bag of cement

$=\frac{104-63.795}{104}$× 100 = 38.7%

Hence, option 3.

Workspace:

**42. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Steel manufacturing requires the use of iron ore, power and manpower. The cost of iron ore has followed the All Item index. During 1993-94 power accounted for 30% of the selling price of steel, iron ore for 25%, and wages for 10% of the selling price of steel. Assuming the cost and price data for cement as given in the previous question, the operating profit (% of selling price) of an average steel manufacture in 2002-03

- A.
is more than that of a cement manufacturer

- B.
is less than that of a cement manufacturer

- C.
is the same as that of a cement manufacturer

- D.
cannot be determined

Answer: Option B

**Explanation** :

WPI of steel in 2002-03 = 105.5

∴ Operating Profit per bag of steel in 2002-03

$=\frac{105.5-69.43}{105.5}$ × 100 = 34.2%

∴ Profit percentage of a steel manufacturer in 2002-03 is less than the profit percentage of a cement manufacturer in 2002-03.

Hence, option 2.

Workspace:

**43. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Which item experienced continuous price rise during the ten-year period?

- A.
Power

- B.
Cement

- C.
Wages

- D.
Limestone

Answer: Option A

**Explanation** :

Power experiences a continuous price rise.

Cement shows a decline from 1996-97 to 1997-97 and 1998-99 to 1999-00.

Wages show a decline from 1998-99 to 1999-2000.

Limestone shows a decline from 1996-97 to 1997-98.

Hence, option 1.

Workspace:

**44. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Which item(s) experienced only one decline in price during the ten-year period?

- A.
Steel and Limestone

- B.
Steel and Cement

- C.
Timber

- D.
Timber and Wages

Answer: Option D

**Explanation** :

Cement and limestone declined twice each.

Timer and wages declined once each.

Hence, option 4.

Workspace:

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

Sex Ratio (Number of females per 1,000 males) of Selected States in India : 1901-2001

**45. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Each of the following statements pertains to the number of states with females outnumbering males in a given census year. Which of these statements is NOT correct?

- A.
This number never exceeded 5 in any census year.

- B.
This number registered its sharpest decline in the year 1971

- C.
The number of consecutive censuses in which this number remained unchanged never exceeded 3

- D.
Prior to the 1971 census, this number was never less than 4.

Answer: Option C

**Explanation** :

Option 1 is true because from 1901 to 2001 the number of states where females outnumber males are either five or less than that.

Option 2 is true because from 1961 to 1971 this number changes from 4 to 1.

Option 4 is true because there are at least four states that have more females than males for all the censuses prior to 1971.

For four years from 1971 to 2001 this number remains 1.

∴ Option 3 is false.

Hence, option 3.

Workspace:

**46. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

The two states which achieved the largest increases in sex ratio over the period 1901-2001 are

- A.
Punjab and HP

- B.
HP and Kerala

- C.
Assam and J & K

- D.
Kerala and J & K

Answer: Option B

**Explanation** :

Increase in the sex ratio in Punjab = 874 – 832 = 42

Increase in the sex ratio in HP = 970 – 884 = 86

Increase in the sex ratio in Assam = 932 – 919 = 13

Increase in the sex ratio in J&K = 900 – 882 = 18

Increase in the sex ratio in Kerala = 1058 – 1004 = 54

Hence, option 2.

Workspace:

**47. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

Among the states which have a sex ratio exceeding 1000 in 1901, the sharpest decline over the period 1901-2001 was registered in the state of

- A.
Goa

- B.
TN

- C.
Bihar

- D.
Orissa

Answer: Option C

**Explanation** :

Decline in sex ratio in Bihar = 1061 – 921 = 140

Decline in sex ratio in Goa = 1091 – 960 =131

Decline in sex ratio in TN = 1044 – 986 = 58

Decline in sex ratio in Orissa = 1037 – 972 = 65

∴ The sharpest decline in the sex ratio over the period 1901-2001 was registered in Bihar.

Hence, option 3

Workspace:

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

Answer the questions on the basis of the data presented in the figure below.

**48. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

During 1996-2002, the number of commodities that exhibited a net overall increase and a net overall decrease, respectively, were

- A.
3 and 3

- B.
2 and 4

- C.
4 and 2

- D.
5 and 1

Answer: Option C

**Explanation** :

By observing the graph, we can conclude that Rice, Onion. Egg and Chillies have shown increase from 1996

to 2002 whereas Edible Oil and Dal have shown decrease in their respective prices.

∴ The required answers are 4 and 2.

Hence, option 3.

Workspace:

**49. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

The number of commodities that experienced a price decline for two or more consecutive years is

- A.
2

- B.
3

- C.
4

- D.
5

Answer: Option D

**Explanation** :

Onion in 1997-99, Chillies in 1998-00, Egg in 2000-02, Dal in 1998-00 and Rice in 1999-01 have shown a decline in two or more consecutive years.

Hence, option 4.

Workspace:

**50. CAT 2003 LRDI - Retake | DI - Tables & Graphs**

For which commodities did a price increase immediately follow a price decline only once in this period?

- A.
Rice, Edible oil, and Dal

- B.
Egg and Dal

- C.
Onion only

- D.
Egg and Onion

Answer: Option D

**Explanation** :

Onion in 1998-00 and Egg in 1997-99 have shown a price increase immediately after a price decline. Even Edible Oil, Dal, Rice and Chillies have shown this property, but more than once.

Hence, option 4.

Workspace:

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