CAT 1998 LRDI | Previous Year CAT Paper

Previous year paper questions for CAT 1998 LRDI

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1. CAT 1998 LRDI | LR - Logical Connectives

Direction: In the question below, the main statement is followed by four sentences. Select the pair of sentences that relates logically to the given statement.

Either Sita is sick or she is careless.

A. Sita is not sick.

B. Sita is not careless.

C. Sita is sick.

D. Sita is careless.

A.
AB
B.
AD
C.
BA
D.
DA

2. CAT 1998 LRDI | LR - Logical Connectives

Direction: In the question below, the main statement is followed by four sentences. Select the pair of sentences that relates logically to the given statement.

Ram gets a swollen nose whenever he eats hamburgers.

A. Ram gets a swollen nose.

B. Ram does not eat hamburgers.

C. Ram does not get a swollen nose.

D. Ram eats hamburgers.

A.
AB
B.
DC
C.
AC
D.
CB

3. CAT 1998 LRDI | LR - Logical Connectives

Direction: In the question below, the main statement is followed by four sentences. Select the pair of sentences that relates logically to the given statement.

Either the employees have no confidence in the management or they are hostile by nature.

A. They are not hostile by nature.

B. They are hostile by nature.

C. They have confidence in the management.

D. They have no confidence in the management.

A.
BA
B.
CB
C.
DA
D.
BD

4. CAT 1998 LRDI | LR - Logical Connectives

Direction: In the question below, the main statement is followed by four sentences. Select the pair of sentences that relates logically to the given statement.

Whenever Ram reads late into the night, his father beats him.

A. His father does not beat Ram.

B. Ram reads late into the night.

C. Ram reads early in the morning.

D. Ram's father beats him in the morning.

A.
CD
B.
BD
C.
AB
D.
None of these

5. CAT 1998 LRDI | LR - Logical Connectives

Direction: In the question below, the main statement is followed by four sentences. Select the pair of sentences that relates logically to the given statement.

All irresponsible parents shout if their children do not cavort.

A. All irresponsible parents do not shout.

B. Children cavort.

C. Children do not cavort.

D. All irresponsible parents shout.

A.
AB
B.
BA
C.
CA
D.
All of these

6. CAT 1998 LRDI | LR - Syllogisms

Direction: The question contains four arguments of three sentences each. Choose the set in which the third statement is a logical conclusion of the first two.

A. Some Xs are Ps. Some Ps are Ys. Some Xs are Ys.
B. All Sonas are bright. Some bright are crazy. Some Sonas are crazy.
C. No faith is strong. Only strong have biceps. No faith has biceps.
D. All men are weak. Some weak are strong. Some strong are weak.

A.
A and D
B.
C only
C.
D only
D.
None of these

7. CAT 1998 LRDI | LR - Syllogisms

Direction: The question contains four arguments of three sentences each. Choose the set in which the third statement is a logical conclusion of the first two.

A. Some icicles are cycles. All cycles are men. Some icicles are men.
B. All girls are teeth. No teeth is yellow. No girls are yellow.
C. No hand is foot. Some foot are heads. Some hands are heads.
D. Every man has a wife. All wives are devoted. No devoted has a husband.

A.
A, B and C
B.
A and B
C.
C and B
D.
A, B and C and D

8. CAT 1998 LRDI | LR - Syllogisms

Direction: The question contains four arguments of three sentences each. Choose the set in which the third statement is a logical conclusion of the first two.

A. No sun is not white. All moon is sun. All moon is white.
B. All windows are open. No open space is allocated. All window is closed space.
C. No German can fire. All Americans bombard. Both, Germans and Americans can fight.
D. No X is Z. No Z is Y. No X is Y.

A.
A only
B.
B only
C.
C only
D.
D only

9. CAT 1998 LRDI | LR - Syllogisms

Direction: The question contains four arguments of three sentences each. Choose the set in which the third statement is a logical conclusion of the first two.

A. All Ts are square. All squares are rectangular. All Ts are rectangular.
B. Some fat are elongated. Some elongated things are huge. Some fat are huge.
C. Idiots are bumblers. Bumblers fumble. Idiots fumble.
D. Water is good for health. Health foods are rare. Water is rare.

A.
D only
B.
C only
C.
Both A and C
D.
All of these

Direction: Answer the questions based on the following information.

Mr Bankatlal acted as a judge for the beauty contest. There were four participants, viz. Ms Andhra Pradesh, Ms Uttar Pradesh, Ms West Bengal and Ms Maharashtra. Mrs Bankatlal, who was very anxious about the result, asked him about it as soon as he was back home. Mr Bankatlal just told that the one who was wearing the yellow saree won the contest. When Mrs Bankatlal pressed for further details, he elaborated as follows:

All of them were sitting in a row.
All of them wore sarees of different colours, viz. green, yellow, white, red.
There was only one runner-up and she was sitting beside Ms. Maharashtra.
The runner-up was wearing the green saree.
Ms West Bengal was not sitting at the ends and was not the runner up.
The winner and the runner-up are not sitting adjacent to each other.
Ms Maharashtra was wearing white saree.
Ms Andhra Pradesh was not wearing the green saree.
Participants wearing yellow saree and white saree were at the ends.

10. CAT 1998 LRDI | LR - Arrangements

Who wore the red saree?

A.
Ms Andhra Pradesh
B.
Ms West Bengal
C.
Ms Uttar Pradesh
D.
Ms Maharashtra

11. CAT 1998 LRDI | LR - Arrangements

Ms. West Bengal was sitting adjacent to

A.
Ms Andhra Pradesh and Ms Maharashtra
B.
Ms Uttar Pradesh and Ms Maharashtra
C.
Ms Andhra Pradesh and Ms Uttar Pradesh
D.
Ms Uttar Pradesh

12. CAT 1998 LRDI | LR - Arrangements

Which saree was worn by Ms Andhra Pradesh?

A.
Yellow
B.
Red
C.
Green
D.
White

13. CAT 1998 LRDI | LR - Arrangements

Who was the runner-up?

A.
Ms Andhra Pradesh
B.
Ms West Bengal
C.
Ms Uttar Pradesh
D.
Ms Maharashtra

Direction: The following table gives the quantity of apples (in tonnes) arriving at
New Delhi market from various states in a particular year. The month in which demand was more than supply, the additional demand was met by the stock from cold storage.

14. CAT 1998 LRDI | DI - Tables & Graphs

What was the maximum percentage of apples supplied by any state in any of the months?

A.
99%
B.
95%
C.
88%
D.
100%

15. CAT 1998 LRDI | DI - Tables & Graphs

Which state supplied the maximum number of apples?

A.
UP
B.
HP
C.
J&K
D.
Cold Storage

16. CAT 1998 LRDI | DI - Tables & Graphs

Which state supplied the highest percentage of apples from the total apples supplied?

A.
HP
B.
UP
C.
J&K
D.
Cannot be determined

17. CAT 1998 LRDI | DI - Tables & Graphs

In which of the following periods was the supply greater than the demand?

A.
August-March
B.
June-October
C.
May-September
D.
Cannot be determined

18. CAT 1998 LRDI | DI - Tables & Graphs

If the yield per tree was 40 kg, then from how many trees were the apples supplied to New Delhi (in millions) during the year?

A.
11.5
B.
12.5
C.
13.5
D.
Cannot be determined

Answer: Option B

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Explanation :

Total quantity of apples supplied to Delhi during the year was (231028 + 258 + 262735) = 494021 tonnes = 494021000 kg
If one tree yields 40 kg of apple, then the number of trees required to yield 49,40,21,000 kg

$= \frac{494021000}{40}$ = 1,23,50,525 trees

= 12.5 million trees (approximately)

19. CAT 1998 LRDI | DI - Tables & Graphs

Using the data in previous question, if there were 250 trees per hectare, then how many hectares of land was used?

A.
9,400 hectares
B.
49,900 hectares
C.
50,000 hectares
D.
49,450 hectares

Answer: Option D

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Explanation :

If there are 250 trees per hectare, then area required to have 12350525 $= \frac{12350525}{250}$ = 49402 = 49450 (approximately)

Direction: Answer the questions based on the following information.

The following bar chart gives the growth percentage in the number of households in middle, upper-middle and high income categories in the four regions for the period between 1987-88 and 1994-95.

20. CAT 1998 LRDI | DI - Tables & Graphs

Which region showed the highest growth in number of households in all the income categories for the period?

A.
North
B.
South
C.
West
D.
None of these

21. CAT 1998 LRDI | DI - Tables & Graphs

What was the total household income in northern region for upper-middle class?

A.
Rs. 50 lakh
B.
Rs. 500 million
C.
Rs. 300 million
D.
Cannot be determined

22. CAT 1998 LRDI | DI - Tables & Graphs

What is the percentage increase in total number of households for the northern region (upper-middle) over the given period?

A.
100%
B.
200%
C.
240%
D.
Cannot be determined

23. CAT 1998 LRDI | DI - Tables & Graphs

What was the average income of the high-income group in 1987-88?

A.
Rs. 75,000
B.
Rs. 25,000
C.
Rs. 2,25,000
D.
Cannot be determined

Direction: Answer the questions based on the following information.

The following bar chart gives the growth percentage in the number of households in middle, upper-middle and high income categories in the four regions for the period between 1987-88 and 1994-95.

Additional direction: The numbers of households in each category were equally distributed in all the regions.

24. CAT 1998 LRDI | DI - Tables & Graphs

The ratio of total income for the high-income category to the upper-middle class increased by how much percentage in the given period?

A.
20%
B.
36%
C.
25%
D.
Cannot be determined

Answer: Option B

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Explanation :

The total income of high income category in 1987-88 is Rs. (5000 × 75000).
The total income of upper-middle class category in 1987-88 is Rs. (10000 × 50000).
Hence, the current ratio of their total incomes = 3 : 4 = 0.75
Since the number of households in each category were equally distributed in all regions, we can have the following table for high income category.

The average household income for high-income category increased by 90%. Hence, average household income for this category in 1994-95 = (75000 × 1.9) = Rs. 1,42,500
Hence, the total income for high-income category in 1994-95 = (17375 × 142500) = Rs. 2,476 million The same table can be drawn for upper-middle class category as follows:

The average household income for upper-middle class category increased by 60%. Hence, the average
household income for this category in 1994-95 = (50000 ×1.6) = Rs. 80,000
Hence, the total income for high-income category in 1994-95 = (30125 × 80000) = Rs. 2,410 million Hence, the ratio of total income for these two categories in 1994-95 = $\frac{2476}{2410} = 1.02 .$

Hence, percentage increase in ratio $= \frac{(1.02 - 0.75)}{0.75} = 36 %$

25. CAT 1998 LRDI | DI - Tables & Graphs

The average income for the northern region in 1987-88 was

A.
Rs. 37,727
B.
Rs. 37,277
C.
Rs. 35,000
D.
Cannot be determined

Answer: Option A

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Explanation :

For northern region, we can draw the following table for 1987-88.

Hence, the average income for northern region

$= \frac{518.75}{13750} \times 10^{6}$ = Rs. 37,727

Direction: Answer the questions based on the following information.

Krishna distributed 10-acre land to Gopal and Ram who paid him the total amount in the ratio 2 : 3. Gopal invested a further Rs. 2 lakh in the land and planted coconut and lemon trees in the ratio 5 : 1 on equal areas of land. There were a total of 100 lemon trees. The cost of one coconut was Rs. 5. The crop took 7 years to mature and when the crop was reaped in 1997, the total revenue generated was 25% of the total amount put in by Gopal and Ram together. The revenue generated from the coconut and lemon trees was in the ratio 3 : 2 and it was shared equally by Gopal and Ram as the initial amount spent by them were equal.

26. CAT 1998 LRDI | DI - Tables & Graphs

What was the total output of coconuts?

A.
24,000
B.
36,000
C.
18,000
D.
48,000

Answer: Option B

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Explanation :

It is said that Gopal and Ram invested equal amounts initially. Let the amount paid by both of them to Krishna
be 2x and 3x respectively. Gopal further invested Rs. 2 lakh. Hence, we can say (2x + 2) = 3x or x = 2 lakh. Hence, the initial amounts paid by Gopal and Ram to Krishna is 4 lakh and 6 lakh. So Gopal and Ram together put in (6 + 6) = 12 lakh initially (note that this includes Rs. 2 lakh put in by Gopal later). The total revenue generated is 25% of 12 lakh = 3 lakh.
The revenue from coconut and lemon trees are in the ratio 3 : 2. Hence, 3 lakh when divided in the ratio 3 : 2 gives Rs. 1,80,000 from coconut and Rs. 1,20,000 from lemons. And since each coconut costs Rs. 5, the total output of coconut would be $(\frac{180000}{5})$ = 36000

27. CAT 1998 LRDI | DI - Tables & Graphs

What was the value of output per acre of lemon trees planted?

A.
0.24 lakh per acre
B.
2.4 lakh per acre
C.
24 lakh per acre
D.
Cannot be determined

Answer: Option A

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Explanation :

Lemon and coconut trees were planted on equal areas of land, viz. 5 acres each. The value of lemon output per acre of land = $(\frac{120000}{5})$ = 0.24 lakh per acre

28. CAT 1998 LRDI | DI - Tables & Graphs

What was the amount received by Gopal in 1997?

A.
Rs. 1.5 lakh
B.
Rs. 3 lakh
C.
Rs. 6 lakh
D.
None of these

Answer: Option A

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Explanation :

The total revenue of Rs. 3,00,000 was divided equally by Gopal and Ram. Hence, the amount received by Gopal in 1997 = $\frac{1}{2}$ × 300000 = Rs. 1.5 lakh

29. CAT 1998 LRDI | DI - Tables & Graphs

What was the value of output per tree for coconuts?

A.
Rs. 36
B.
Rs. 360
C.
Rs. 3,600
D.
Rs. 240

Answer: Option B

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Explanation :

The ratio of the number of trees of coconut and lemon was 5 : 1. Since the number of lemon trees is 100, the number of coconut trees is 500. So they totally obtained a revenue of Rs. 1,80,000 from 500 coconut trees.
Hence, the value per tree = $(\frac{180000}{500})$ = Rs. 360.

30. CAT 1998 LRDI | DI - Tables & Graphs

What was the ratio of yields per acre of land for coconuts and lemons (in terms of number of lemons and coconuts)?

A.
3 : 2
B.
2 : 3
C.
1 : 1
D.
Cannot be determined

Direction: Answer the questions based on the following information.

Ghosh Babu has a manufacturing unit. The following graph gives the cost for various number of units. Given: Profit = Revenue – Variable cost – Fixed cost. The fixed cost remains constant up to 34 units after which additional investment is to be done in fixed assets. In any case, production cannot exceed 50 units.

31. CAT 1998 LRDI | DI - Tables & Graphs

What is the minimum number of units that need to be produced to make sure that there was no loss?

A.
5
B.
10
C.
20
D.
Indeterminate

32. CAT 1998 LRDI | DI - Tables & Graphs

How many units should be manufactured such that the profit was at least Rs. 50?

A.
20
B.
34
C.
45
D.
30

33. CAT 1998 LRDI | DI - Tables & Graphs

If at the most 40 units can be manufactured, then what is the number of units that can be manufactured to maximise profit per unit?

A.
40
B.
34
C.
35
D.
25

34. CAT 1998 LRDI | DI - Tables & Graphs

If the production cannot exceed 45 units, then what is the number of units that can maximise profit per unit?

A.
40
B.
34
C.
45
D.
35

35. CAT 1998 LRDI | DI - Tables & Graphs

If the fixed cost of production goes up by Rs. 40, then what is the minimum number of units that need to be manufactured to make sure that there is no loss?

A.
10
B.
19
C.
15
D.
20

Direction: Answer the questions based on the following information.

In the following chart, the price of logs shown is per cubic metre that of plywood and saw timber is per tonne.

36. CAT 1998 LRDI | DI - Tables & Graphs

What is the maximum percentage increase in price per cubic metre or per tonne over the previous year?

A.
33.33%
B.
85%
C.
50%
D.
Cannot be determined

37. CAT 1998 LRDI | DI - Tables & Graphs

Which product shows the maximum percentage increase in price over the period?

A.
Saw timber
B.
plywood
C.
Logs
D.
Cannot be determined

38. CAT 1998 LRDI | DI - Tables & Graphs

If 1 m³ = 750 kg for saw timber, find in which year was the difference in prices of saw timber and logs the least?

A.
1989
B.
1990
C.
1991
D.
1992

Answer: Option B

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Explanation :

Since the price of saw timber is given in rupees per tonne and that of log is given in rupees per cubic metre, we cannot compare the two. Hence, using the given conversion, let us convert the price of saw timber in per cubic metre. The table will be as follows:

(Note: 1 tonne = $\frac{4}{3}$ = 1.33 cubic m)

Thus, we see that the difference is least in the year 1990.

39. CAT 1998 LRDI | DI - Tables & Graphs

If one cubic metre = 700 kg for plywood and 800 kg for saw timber, find in which year was the difference in the prices of plywood and saw timber (per cubic metre) the maximum?

A.
1989
B.
1990
C.
1991
D.
1992

Answer: Option D

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Explanation :

(Note: 1 tonne = $\frac{4}{3}$ = 1.33 cubic m)

As in the above table, we can draw a similar table for saw timber and logs.

(Note: One tonne of plywood = $\frac{10}{7}$ cubic m = 1.43 cubic m and one tonne of saw timber = $\frac{5}{4}$ cubic m = 1.25 cubic m.)

Hence, it can be seen that the difference is maximum for 1992.

40. CAT 1998 LRDI | DI - Tables & Graphs

If the volume sales of plywood, saw timber and logs were 40%, 30% and 30% respectively, then what was the average realisation in 1993 per cubic metre of sales? (Weight of one cubic metre of saw dust and plywood both = 800 kg)

A.
18
B.
15
C.
16
D.
13

Answer: Option D

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Explanation :

Note that one tonne = $\frac{4}{3}$ m³ = 1.33 m³, for both plywood and saw timber.
In 1993, price of logs = Rs. 20 per cubic metre.

Price of plywood = $(\frac{7}{1.33})$ = Rs. 5.26 per cubic metre.

And price of saw timber = $(\frac{19}{1.33})$ = 14.28 per cubic metre.
Now the sales volume of plywood, saw timber and logs are in the ratio 4 : 3 : 3. So the average realisation per cubic metre of sales is indeed the weighted average.
This is given as $\frac{[(4 \times 5.26) + (3 \times 14.28) + (3 \times 20)]}{(4 + 3 + 3)}$ = Rs. 12.4

= Rs. 13 (Approximately)

41. CAT 1998 LRDI | DI - Tables & Graphs

In the previous question, if in 1994, prices increased by 5%, 1% and 10% while the volume sales break-up was 40%, 30% and 30% for plywood, saw timber and logs respectively, then what was the average realisation?

A.
18.95
B.
16.45
C.
13.15
D.
10.25

Answer: Option C

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Explanation :

The only change would be the accounting for price increase. This is given as $\frac{(4 \times 5.26 \times 1.05) + (3 \times 14.28 \times 1.01) + (3 \times 20 \times 1.10)}{(4 + 3 + 3)}$ = Rs. 13.15

Direction: Answer the question based on the following information.

The following operations are defined for real numbers.
a # b = a + b, if a and b both are positive else a # b = 1
a ∇ b = (a × b)^{a + b} if a × b is positive else a ∇ b = 1.

42. CAT 1998 LRDI | LR - Operator Based Questions

$\frac{(2 \neq 1)}{(1 \nabla 2)} =$

A.
1/8
B.
1
C.
3/8
D.
3

Answer: Option C

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Explanation :

Since both 2 and 1 are positive, (2 # 1) = 2 + 1 = 3.
(1∇2)= (1× 2)¹⁺² = 23 = 8.
Thus, the given expression is equal to $\frac{3}{8} .$

43. CAT 1998 LRDI | LR - Operator Based Questions

$\frac{\{((1 # 1) # 2) - (10^{1.3} \nabla \log_{10} 0.1)\}}{(1 \nabla 2)} =$

A.
3/8
B.
$\frac{4 \times \log_{10} 0.1}{8}$
C.
$\frac{(4 + 10^{13})}{8}$
D.
None of these

Answer: Option A

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Explanation :

Let us first simplify the numerator. Since 1 is positive,
(1 # 1) is 1 + 1 = 2 which again is positive. Then
(1 # 1) # 2 = 2 # 2 = 2 + 2 = 4
Now note that log₁₀ 0.1
= log₁₀ 10^–1 = –1
Then 10^1.3log₁₀ 0.1= 10^1.3× (–1) is negative.
So 10^1.3 ∇ log₁₀ 0.1 = 1
Hence, the numerator is equal to 4 –1 = 3
Since 1 × 2 = 2 is positive, (1∇2) = (1× 2)¹⁺² = 2³ = 8.
So the denominator = 8. Hence, the answer is $\frac{3}{8} .$

44. CAT 1998 LRDI | LR - Operator Based Questions

$(\frac{(X # - Y)}{(- X \nabla Y)}) = \frac{3}{8},$ then which of the following must be true?

A.
X = 2, Y = 1
B.
X > 0, Y < 0
C.
X, Y both positive
D.
X, Y both negative

45. CAT 1998 LRDI | LR - Logical Connectives

P, Q, R and S are four statements. Relation between these statements is as follows.

I. If P is true, then Q must be true.
II. If Q is true, then R must be true.
III. If S is true, then either Q is false or R is false.

Which of the following must be true?

A.
If P is true, then S is false
B.
If S is false, then Q must be true
C.
If Q is true, then P must be true
D.
If R is true, then Q must be true

Direction: Answer the questions based on the following information.

A, B, C and D are to be seated in a row. But C and D cannot be together. Also B cannot be at the third place.

46. CAT 1998 LRDI | LR - Arrangements

Which of the following must be false?

A.
A is at the first place
B.
A is at the second place
C.
A is at the third place
D.
A is at the fourth place

47. CAT 1998 LRDI | LR - Arrangements

If A is not at the third place, then which of the following options does C have?

A.
The first place only
B.
The third place only
C.
The first and third place only
D.
Any of the places

48. CAT 1998 LRDI | LR - Arrangements

If A and B are together, then which of the following must be necessarily true?

A.
C is not at the first place
B.
A is at the third place
C.
D is at the first place
D.
C is at the first place

Direction: Answer the questions based on the following information.

Amar, Akbar and Anthony are three friends. Only three colours are available for their shirts, viz. red, green and blue. Amar does not wear red shirt. Akbar does not wear green shirt. Anthony does not wear blue shirt.

49. CAT 1998 LRDI | LR - Selection & Distribution

If Akbar and Anthony wear the same colour of shirts, then which of the following is not true?

A.
Amar wears blue and Akbar wears green
B.
Amar wears green and Akbar wears red
C.
Amar wears blue and Akbar does not wear blue
D.
Anthony wears red

50. CAT 1998 LRDI | LR - Selection & Distribution

If two of them wear the same colour, then how many of the following must be false?

I. Amar wears blue and Akbar does not wear green
II. Amar does not wear blue and Akbar wears blue
III. Amar does not wear blue and Akbar does not wear blue
IV. Amar wears green, Akbar does not wear red, Anthony does not wear green

A.
None
B.
1
C.
2
D.
3

51. CAT 1998 LRDI | DI - Games & Tournaments

A, B, C, D, ..., X, Y, Z are the players who participated in a tournament. Everyone played with every other player exactly once. A win scores 2 points, a draw scores 1 point and a loss scores 0 point. None of the matches ended in a draw. No two players scored the same score. At the end of the tournament, by ranking list is published which is in accordance with the alphabetical order. Then

A.
M wins over N
B.
N wins over M
C.
M does not play with N
D.
None of these

CAT 1998 LRDI | Previous Year CAT Paper

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