# CAT 1998 LRDI | Previous Year CAT Paper

**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

Answer: Option B

**Explanation** :

If Sita is not sick, it follows that she is careless. One of the either/or conditions hold good.

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**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.
BC

Answer: Option D

**Explanation** :

Ram does not eat hamburgers, so it follows that he does not get a swollen nose. When X, then Y. Not Y, hence not X.

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**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

Answer: Option B

**Explanation** :

If the employees have confidence in the management, it follows that they are hostile. The first of the either/or condition is false, so the second one has to be true.

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**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

Answer: Option D

**Explanation** :

None of the given options relates logically to the given statements.

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**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

Answer: Option A

**Explanation** :

As all irresponsible parents do not shout, it follows that the children cavort. When X, then Y. X, hence Y.

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**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

Answer: Option B

**Explanation** :

If only strong have biceps and no faith is strong, it follows that no faith has biceps. In A, X and Y need not overlap. In B, the Sona and crazy set need not overlap. In D there is no logical conclusion at all.

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**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

Answer: Option B

**Explanation** :

In (C) and (D) the first two statements do not logically lead to the third. In C, we do not know if the hand and the head set overlap. D leads to an unpredictable conclusion. The icicles which are cycles are at least men. In B, if no teeth is yellow, no girl can be yellow, since all girls are teeth.

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**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

Answer: Option A

**Explanation** :

If no sun is not white, it implies that all sun is white. All moon is sun, so it follows that all moon is white. B and C lead to undefined conclusions. In D, there is a possibility that X and Y sets can intersect.

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**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

Answer: Option C

**Explanation** :

If all Ts are square and all squares are rectangular, it follows that all Ts are rectangular. Also, if idiots are bumblers and bumblers fumble, it follows that idiots fumble. In B, there is a possibility that fat and huge sets need not intersect. D plays with words and leads to uncertain conclusion again.

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**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

Answer: Option B

**Explanation** :

Ms Maharashtra was wearing white. Since Ms West Bengal was not the runner-up, she was not wearing green and neither was Ms Andhra Pradesh. Hence, it was Ms Uttar Pradesh who was wearing green saree. So red could have either be worn by Ms West Benga l or by Ms Andhra Pradesh. Now participants wearing yellow saree and white saree were at the ends, but Ms West Bengal did not occupy any of these positions. Hence, it can be concluded that Ms Andhra Pradesh sat at one of the ends and wore yellow, while Ms West Bengal wore red.

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**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

Answer: Option C

**Explanation** :

Ms Maharashtra was wearing white. Since Ms West Bengal was not the runner-up, she was not wearing green and neither was Ms Andhra Pradesh. Hence, it was Ms Uttar Pradesh who was wearing green saree. So red could have either be worn by Ms West Benga l or by Ms Andhra Pradesh. Now participants wearing yellow saree and white saree were at the ends, but Ms West Bengal did not occupy any of these positions.

it can be concluded that Ms Maharashtra and Ms Andhra Pradesh occupied the seats at the end. So Ms West Bengal and Ms Uttar Pradesh, should occupy middle two seats. So the answers could be either (b) or (c). It can further be concluded that since Ms Andhra Pradesh wore yellow, she was the winner and since Ms Uttar Pradesh wore green, she was the runner-up. So these two cannot sit together. Option (b) would contradict this. Hence, (c) is the only option left.

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**12. CAT 1998 LRDI | LR - Arrangements**

Which saree was worn by Ms Andhra Pradesh?

- A.
Yellow

- B.
Red

- C.
Green

- D.
White

Answer: Option A

**Explanation** :

Ms Maharashtra was wearing white. Since Ms West Bengal was not the runner-up, she was not wearing green and neither was Ms Andhra Pradesh. Hence, it was Ms Uttar Pradesh who was wearing green saree. So red could have either be worn by Ms West Benga l or by Ms Andhra Pradesh. Now participants wearing yellow saree and white saree were at the ends, but Ms West Bengal did not occupy any of these positions.

it can be seen that Ms Andhra Pradesh had worn the yellow saree.

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**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

Answer: Option C

**Explanation** :

Ms Maharashtra was wearing white. Since Ms West Bengal was not the runner-up, she was not wearing green and neither was Ms Andhra Pradesh. Hence, it was Ms Uttar Pradesh who was wearing green saree. So red could have either be worn by Ms West Benga l or by Ms Andhra Pradesh. Now participants wearing yellow saree and white saree were at the ends, but Ms West Bengal did not occupy any of these positions.

it can be seen that Ms Uttar Pradesh was the runner-up.

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**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%

Answer: Option A

**Explanation** :

If we were to take the highest quantity supplied from various states in different months, we will get the following table:

Hence, we find that the highest percentage of apples supplied by any state is 99% (J & K in February).

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**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

Answer: Option C

**Explanation** :

If we were to add the quantity of apples supplied by various states, it can be found that HP supplied 2,31,028 tonnes, UP supplied 258 tonnes, and J & K supplied 2,62,735 tonnes. Thus, it was J & K that supplied the maximum number of apples.

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**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

Answer: Option C

**Explanation** :

If J & K supplied the highest quantity of apples, it is obvious that it would supply the highest percentage of total apples supplied as well.

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**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

Answer: Option C

**Explanation** :

It is given that in case demand is more than the supply, additional demand is met by taking the stock from the cold storage. So it can be figured out that in all those months when supply was greater than the demand, no stock would have been used from the cold storage. Looking at the table, we can find that during the period May to September, no stock was taken from the cold storage, and hence supply should have been greater than the demand.

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**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

**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)

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**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

**Explanation** :

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

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**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

Answer: Option B

**Explanation** :

It can be seen from the graph that the southern region showed the highest growth in number of households in all the income categories for the period.

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**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

Answer: Option D

**Explanation** :

We only know the total number of households for all four regions combined. Nowhere have they given the region-wise break-up of this value. In the light of this, the given question cannot be answered.

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**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

Answer: Option B

**Explanation** :

It is very clear from the graph that the percentage increase in total number of households for the northern region for upper middle income category is 200%.

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**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

Answer: Option A

**Explanation** :

As seen from the table, the average income of highincome group in 1987-88 is Rs. 75,000.

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**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

**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 $=\frac{(1.02-0.75)}{0.75}=36\%$

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**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

**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

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**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

**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 $\left(\frac{180000}{5}\right)$ = 36000

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**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

**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 = $\left(\frac{120000}{5}\right)$ = 0.24 lakh per acre

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**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

**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

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**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

**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 = $\left(\frac{180000}{500}\right)$ = Rs. 360.

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**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

Answer: Option D

**Explanation** :

We have not been given the cost of one lemon. In the light of this fact, we cannot find the number of lemons produced and hence the required ratio cannot be determined.

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**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

Answer: Option B

**Explanation** :

Profit = Revenue – Variable Cost – Fixed Cost = Revenue – (Variable Cost + Fixed Cost). If we consider (Fixed Cost + Variable cost) as total cost, then as long as the revenue is higher than the total cost, there is a profit. In case the revenue is less than the total cost there would be a loss. If we are to compile the data given in the question it would be as follows:

Thus, we can say that at a production of 12 units, there is a profit of Rs. 2. Above 12 units there is always a profit and below 12 units there is loss. Hence, to make sure there is no loss, one has to manufacture a minimum of 12 units.

* The answer is clearly not indeterminable, it should be 12 units, but among the options given the one closest to it is 10 units

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**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

Answer: Option A

**Explanation** :

Profit = Revenue – Variable Cost – Fixed Cost = Revenue – (Variable Cost + Fixed Cost). If we consider (Fixed Cost + Variable cost) as total cost, then as long as the revenue is higher than the total cost, there is a profit. In case the revenue is less than the total cost there would be a loss. If we are to compile the data given in the question it would be as follows:

It can be seen that at 20 units there is a profit of Rs. 50. Below this the profit will reduce. Hence, to ensure that the profit is at least Rs. 50, then 20 units have to be manufactured.

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**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

Answer: Option B

**Explanation** :

Let us verify for the given options.

Hence, we can see that to maximise profit per unit, we need to manufacture 34 units.

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**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

Answer: Option B

**Explanation** :

Let us verify for the given options.

Extending the above table for 45 units, we get

Thus, it can be figured out that still he has to manufacture 34 units.

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**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

Answer: Option B

**Explanation** :

Profit = Revenue – Variable Cost – Fixed Cost = Revenue – (Variable Cost + Fixed Cost). If we consider (Fixed Cost + Variable cost) as total cost, then as long as the revenue is higher than the total cost, there is a profit. In case the revenue is less than the total cost there would be a loss. If we are to compile the data given in the question it would be as follows:

Referring to the above table, we can see that if the fixed cost increases by Rs. 40, the profit will reduce by Rs. 40. Hence, we can see that at 10 units he will make a loss of Rs. 30 and at 20 units he will make a profit of Rs. 10. Hence, the answer has to be between (b) and (c). Let us verify for them:

Thus, we see that to make sure there is no loss, he has to manufacture 19 units.

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**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

Answer: Option C

**Explanation** :

The data can be represented in the following table.

Thus, we can see that the maximum increase is 50%.

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**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

Answer: Option B

**Explanation** :

Thus, we see that the maximum percentage increase over the period is shown by plywood.

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**38. CAT 1998 LRDI | DI - Tables & Graphs**

If 1 m^{3} = 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

**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.

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**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

**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)

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.

Workspace:

**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

**Explanation** :

Note that one tonne = $\frac{4}{3}$m^{3} = 1.33 m^{3}, for both plywood and saw timber.

In 1993, price of logs = Rs. 20 per cubic metre.

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

And price of saw timber = $\left(\frac{19}{1.33}\right)$ = 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 $\frac{\left[\right(4\times 5.26)+(3\times 14.28)+(3\times 20\left)\right]}{(4+3+3)}$ = Rs. 12.4

= Rs. 13 (Approximately)

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**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

**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

Workspace:

**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**

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

- A.
1/8

- B.
1

- C.
3/8

- D.
3

Answer: Option C

**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 $\frac{3}{8}.$

Workspace:

**43. CAT 1998 LRDI | LR - Operator Based Questions**

$\frac{\left\{\left(\left(1\#1\right)\#2\right)-({10}^{1.3}\nabla {\mathrm{log}}_{10}0.1)\right\}}{(1\nabla 2)}=$

- A.
3/8

- B.
$\frac{4\times {\mathrm{log}}_{10}0.1}{8}$

- C.
$\frac{(4+{10}^{13})}{8}$

- D.
None of these

Answer: Option A

**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 log_{10} 0.1

= log_{10} 10^{–1} = –1

Then 10^{1.3 }log_{10} 0.1= 10^{1.3 }× (–1) is negative.

So 10^{1.3} ∇ log_{10} 0.1 = 1

Hence, the numerator is equal to 4 –1 = 3

Since 1 × 2 = 2 is positive, (1∇2) = (1× 2)^{1+2} = 2^{3} = 8.

So the denominator = 8. Hence, the answer is $\frac{3}{8}.$

Workspace:

**44. CAT 1998 LRDI | LR - Operator Based Questions**

$\left(\frac{\left(X\#-Y\right)}{\left(-X\nabla Y\right)}\right)=\frac{3}{8},$ 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

Answer: Option B

**Explanation** :

The best possible way to solve this is to check each of the given answer choices. In options (a), (c) and (d), either both X and Y are positive or both X and Y are negative.

Since we have (–Y) in the numerator of our expression and (–X) in the denominator, X and Y will never be both positive and neither will XY be positive.

Hence, both the numerator and the denominator of our expression will be 1 and the value will always be 1.

Hence, the only possible answer choice is (b).

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**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

Answer: Option A

**Explanation** :

If P is true, then both Q and R have to be true. For S to be true, either Q or R must be false. Hence, if P is true, S cannot be true.

Workspace:

**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

Answer: Option A

**Explanation** :

Since C and D cannot be together, they can occupy either of the following seats: (1st and 3rd), (1st and 4th) or (2nd and 4th). In the last two cases, since B cannot be in the 3rd place, A will have to be there.

Thus, we can see that A can never be in the 1st place.

Hence, statement (a) is false.

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**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

Answer: Option C

**Explanation** :

Since neither A nor B can be at 3rd place, this place has to be occupied by either D or C. And if either of them occupies this place, the other one has to occupy the 1st place (since D and C cannot be together).

Hence, C can only occupy either 1st or 3rd place.

Workspace:

**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

Answer: Option B

**Explanation** :

If A and B are together, but C and D are not, then the only places that A and B can occupy are 2nd and 3rd.

And since B cannot be at 3rd place, A has to be at 3rd place.

Workspace:

**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

Answer: Option A

**Explanation** :

Amar does not wear red shirt.

Akbar does not wear green shirt.

Anthony does not wear blue shirt.

Since Akbar and Anthony wear same colour, it can neither be green nor blue.

Hence, option (a) is false.

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**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

Answer: Option B

**Explanation** :

If two of them wear the same colour, the following six combinations will exist: since Amar does not wear red, he can either wear blue or green. In either case, the remaining two will have to wear red, Akbar does not wear green, and Anthony does not wear blue. This gives the combinations 1 and 2 below. Similarly, the other combinations can be worked out.

Using this we can evaluate the statements. (I) is true as we can see that in all the cases, if Amar wears blue, Akbar does not wear green. (II) needs not be false always, as in combination 4, we can see that Amar does not wear blue but Akbar wears blue. (III) is also not necessarily false as in combinations 1 and 3, both Amar and Akbar do not wear blue. Statement (IV) is necessarily false since if Amar wears green and Akbar does not wear red, then combination 4 is the only combination possible and hence Anthony should wear green. So only one of the four statements must always be false.

Workspace:

**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

Answer: Option A

**Explanation** :

It can be seen that each of the 26 players played 25 matches.

Since none of the matches ended in a draw, the scores for each of the players has to be even (since a win gives 2 points). So the highest score possible for a player would be 50 and the lowest would be 0.

Since all 26 of them had different scores varying between 0 and 50, the scores should indeed be all the even numbers between 0 and 50. And since the ranks obtained by players are in alphabetical order, it can be concluded that A scored 50, B scored 48, C scored 46 and so on and Z scored 0.

Now the only way A can score 50 is, if he wins all his matches, i.e. he defeats all other players. Now B has scored 48. So he has lost only one of his matches, which incidentally is against A. He must have defeated all other players.

Similarly, C has scored 46 in 25 matches. So he must have lost two matches, (i.e. to A and B) and defeated all other players. So we conclude that a player whose name appears alphabetically higher up in the order has defeated all the players whose name appear alphabetically lower down.

Hence, M should win over N.

Workspace:

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