# CAT 2007 LRDI | Previous Year CAT Paper

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

The proportion of male students and the proportion of vegetarian students in a school are given below. The school has a total of 800 students, 80% of whom are in the Secondary Section and rest equally divided between Class 11 and 12.

**1. CAT 2007 LRDI | DI - Tables & Graphs**

What is the percentage of vegetarian students in Class 12?

- A.
40

- B.
45

- C.
50

- D.
55

- E.
60

Answer: Option A

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**Explanation** :

From the table given in the question,

Total students = 800

Students in Secondary = 0.8 × 800 = 640

Students in Class 11 = (800 – 640)/2 = 80

Students in Class 12 = 80

Males in Class 11 = 0.55 × 80 = 44

Males in Class 12 = 0.6 × 80 = 48

∴ Males in Secondary = 0.475 × 800 – 44 – 48 = 288

Vegetarians in Class 11 = 0.5 × 80 = 40

Vegetarians in Secondary = 0.55 × 640 = 352

Vegetarians in Class 12 = 800 × 0.53 – 40 – 352 = 32

∴ The percentage of vegetarians in class 12 = 32 × 100/80 = 40%

Hence, option (a).

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**2. CAT 2007 LRDI | DI - Tables & Graphs**

In Class 12, twenty five per cent of the vegetarians are male. What is the difference between the number of female vegetarians and male non-vegetarians?

- A.
less than 8

- B.
10

- C.
12

- D.
14

- E.
16

Answer: Option E

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**Explanation** :

Vegetarian Males in Class 12 = 0.25 × 32 = 8

∴ Non-vegetarian Males in class 12 = 48 – 8 = 40

∴ Vegetarian females in class 12 = Vegetarians in class 12 – Male vegetarians in class 12

= 32 – 8 = 24 (We derived the number of vegetarians in the class in the previous question)

∴ Required difference = 40 – 24 = 16

Hence, option (e).

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**3. CAT 2007 LRDI | DI - Tables & Graphs**

What is the percentage of male students in the secondary section?

- A.
40

- B.
45

- C.
50

- D.
55

- E.
60

Answer: Option B

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**Explanation** :

In the first question, we derived the number of males in class secondary section as 288 and the total number of students in the section as 640.

∴ Percentage of male students in secondary section = 288 × 100/640 = 45%

Hence, option (b).

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**4. CAT 2007 LRDI | DI - Tables & Graphs**

In the Secondary Section, 50% of the students are vegetarian males. Which of the following statements is correct?

- A.
Except vegetarian males, all other groups have same number of students.

- B.
Except non-vegetarian males, all other groups have same number of students.

- C.
Except vegetarian females, all other groups have same number of students.

- D.
Except non-vegetarian females, all other groups have same number of students

- E.
All of the above groups have the same number of students.

Answer: Option C

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**Explanation** :

(This question was not considered for evaluation as there was an error in the question)

“50% of the students are vegetarian males” contradicts the data given initially.

Interpreting it as “50% of the males are vegetarian”, we have the following:

In secondary,

Vegetarian males = 144

Non-vegetarian males = 144

Vegetarian females = 352 –144 = 208

Non-vegetarian females = 352 – 208 = 144

∴ Except vegetarian females, all other groups have same number of students.

Hence, option (c).

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

The following table shows the break-up of actual costs incurred by a company in last five years (year 2002 to year 2006) to produce a particular product.

The production capacity of the company is 2000 units. The selling price for the year 2006 was Rs. 125 per unit. Some costs change almost in direct proportion to the change in volume of production, while others do not follow any obvious pattern of change with respect to the volume of production and hence are considered fixed. Using the information provided for the year 2006 as the basis for projecting the figures for the year 2007, answer the following questions.

**5. CAT 2007 LRDI | DI - Tables & Graphs**

What is the approximate cost per unit in rupees, if the company produces and sells 1400 units in the year 2007?

- A.
104

- B.
107

- C.
110

- D.
115

- E.
116

Answer: Option B

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**Explanation** :

Observing the values through the years, we can say that Material, Labour and Operating costs directly vary with the change in volume of production.

The other costs are almost constant.

If the production is x units, the variable cost for material, labour and operation is 50x, 20x and 30x respectively.

∴ Total variable cost = 100x

Total fixed cost (using information for 2006) = 1400 + 1200 + 400 + 800 + 5800 = 9600

∴ Total cost of producing x units = 100x + 9600

Now, x = 1400

Cost per unit = (1400 × 100 + 9600)/1400 = 106.85

Hence, option (b).

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**6. CAT 2007 LRDI | DI - Tables & Graphs**

What is the minimum number of units that the company needs to produce and sell to avoid any loss?

- A.
313

- B.
350

- C.
384

- D.
747

- E.
928

Answer: Option C

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**Explanation** :

Observing the values through the years, we can say that Material, Labour and Operating costs directly vary with the change in volume of production.

The other costs are almost constant.

If the production is x units, the variable cost for material, labour and operation is 50x, 20x and 30x respectively.

∴ Total variable cost = 100x

Total fixed cost (using information for 2006) = 1400 + 1200 + 400 + 800 + 5800 = 9600

∴ Total cost of producing x units = 100x + 9600

Now, x = 1400

From the explanation given in the first question, to avoid any loss, 100x + 9600 ≤ 125x

∴ x ≥ 384

Hence, option (c).

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**7. CAT 2007 LRDI | DI - Tables & Graphs**

Given that the company cannot sell more than 1700 units, and it will have to reduce the price by Rs. 5 for all units, if it wants to sell more than 1400 units, what is the maximum profit, in rupees, that the company can earn?

- A.
25,400

- B.
24,400

- C.
31,400

- D.
32,900

- E.
32,000

Answer: Option A

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**Explanation** :

Profit for 1400 units = 1400 × 125 – (1400 × 100 + 9600) = 25400

Profit for (1400 + m) units = (1400 + m) × 120 - ((1400 + m) × 100 + 9600) = 18400 + 20m

Maximum value of m = 300

Maximum profit for 1400 + 300 units = 24400

∴ Maximum profit that the company can earn is 25400.

Hence, option (a).

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**8. CAT 2007 LRDI | DI - Tables & Graphs**

If the company reduces the price by 5%, it can produce and sell as many units as it desires. How many units the company should produce to maximize its profit?

- A.
1400

- B.
1600

- C.
1800

- D.
1900

- E.
2000

Answer: Option E

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**Explanation** :

The new reduced price = 0.95 × 125 = 118.75

Profit = 118.75x – 100x – 9600 = 18.75x – 9600

Profit will be maximum when 18.75x is maximum. As the maximum production capacity is 2000 units, profit is maximum when 2000 units are produced.

Hence, option (e).

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

The table below shows the comparative costs, in US Dollars, of major surgeries in USA and a select few Asian countries.

The equivalent of one US Dollar in the local currencies is given below.

A consulting firm found that the quality of the health services were not the same in all the countries above. A poor quality of a surgery may have significant repercussions in future, resulting in more cost in correcting mistakes. The cost of poor quality of surgery is given in the table below.

**9. CAT 2007 LRDI | DI - Tables & Graphs**

The rupee value increases to Rs. 35 for a US Dollar, and all other things including quality, remain the same. What is the approximate difference in cost, in US Dollars, between Singapore and India for a Spinal Fusion, taking this change into account?

- A.
700

- B.
2500

- C.
4500

- D.
8000

- E.
No difference

Answer: Option B

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**Explanation** :

Cost of spinal fusion in India = Rs. 5500 × 40.928

Cost with the increased value of Rupee = 5500 × 40.928/35 = 6431 USD

Cost of Spinal Fusion in Singapore = 9000 USD

Required difference = 9000 – 6431 = 2569 USD

Hence, option (b).

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**10. CAT 2007 LRDI | DI - Tables & Graphs**

Approximately, what difference in amount in Bahts will it make to a Thai citizen if she were to get a hysterectomy done in India instead of in her native country, taking into account the cost of poor quality? It costs 7500 Bahts for one-way travel between Thailand and India.

- A.
23500

- B.
40500

- C.
57500

- D.
67500

- E.
75000

Answer: Option D

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**Explanation** :

Cost of Hysterectomy in Thailand = 4500 + 6000 = 10500 USD

Cost of Hysterectomy in India = 3000 + 5000 = 8000 USD

Travelling cost = 15000 Bahts = 15000/32.89 USD = 456 USD

Required difference = 10500 – 8456 = 2044 USD = 2044 × 32.89 = 67227 Bahts

Hence, option (d).

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**11. CAT 2007 LRDI | DI - Tables & Graphs**

A US citizen is hurt in an accident and requires an angioplasty, hip replacement and a knee replacement. Cost of foreign travel and stay is not a consideration since the government will take care of it. Which country will result in the cheapest package, taking cost of poor quality into account?

- A.
India

- B.
Thailand

- C.
Malaysia

- D.
Singapore

- E.
USA

Answer: Option C

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**Explanation** :

As shown in the table, Malaysia will have the cheapest package.

Hence, option (c).

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**12. CAT 2007 LRDI | DI - Tables & Graphs**

Taking the cost of poor quality into account, which country/countries will be the most expensive for knee replacement?

- A.
India

- B.
Thailand

- C.
Malaysia

- D.
Singapore

- E.
India and Singapore

Answer: Option A

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**Explanation** :

India will be the most expensive for knee replacement.

Hence, option (a).

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

A low-cost airline company connects ten Indian cities, A to J. The table below gives the distance between a pair of airports and the corresponding price charged by the company. Travel is permitted only from a departure airport to an arrival airport. The customers do not travel by a route where they have to stop at more than two intermediate airports.

**13. CAT 2007 LRDI | DI - Routes & Networks**

What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from A to J?

- A.
2275

- B.
2850

- C.
2890

- D.
2930

- E.
3340

Answer: Option D

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**Explanation** :

Possible routes from A to J are as shown in the table .

The shortest distance is by the route A-C-F-J.

The price is 1350 + 430 + 1150 = Rs. 2930

Hence, option (d).

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**14. CAT 2007 LRDI | DI - Routes & Networks**

The company plans to introduce a direct flight between A and J. The market research results indicate that all its existing passengers travelling between A and J will use this direct flight if it is priced 5% below the minimum price that they pay at present. What should the company charge approximately, in rupees, for this direct flight?

- A.
1991

- B.
2161

- C.
2707

- D.
2745

- E.
2783

Answer: Option B

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**Explanation** :

The current market price paid by the customers is Rs. 2275 (A-H-J).

Therefore, the company should charge (2275 × 0.95) = Rs. 2161.25

Hence, option (b).

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**15. CAT 2007 LRDI | DI - Routes & Networks**

If the airports C, D and H are closed down owing to security reasons, what would be the minimum price, in rupees, to be paid by a passenger travelling from A to J?

- A.
2275

- B.
2615

- C.
2850

- D.
2945

- E.
3190

Answer: Option C

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**Explanation** :

If C, D and H are closed, the cheapest route will be A-F-J and it will cost Rs. 2850.

Hence, option (c).

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**16. CAT 2007 LRDI | DI - Routes & Networks**

If the prices include a margin of 10% over the total cost that the company incurs, what is the minimum cost per kilometer that the company incurs in flying from A to J?

- A.
0.77

- B.
0.88

- C.
0.99

- D.
1.06

- E.
1.08

Answer: Option B

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**Explanation** :

The minimum cost per km that the company incurs would correspond to the minimum price per km route.

By observation from the table, minimum price per kilometre is for the route AHJ and is equal to

2275/2350 = 0.97

Minimum cost per kilometre = 0.97/1.1 = 0.88

Hence, option (b).

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**17. CAT 2007 LRDI | DI - Routes & Networks**

If the prices include a margin of 15% over the total cost that the company incurs, which among the following is the distance to be covered in flying from A to J that minimizes the total cost per kilometer for the company?

- A.
2170

- B.
2180

- C.
2315

- D.
2350

- E.
2390

Answer: Option D

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**Explanation** :

Even if the margin for the prices changes the minimum cost per km would correspond to the same route namely A-H-J.

∴ From the table, the distance for the travel = 2350 km

Hence, option (d).

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

A health-drink company’s R&D department is trying to make various diet formulations, which can be used for certain specific purposes. It is considering a choice of 5 alternative ingredients (O, P, Q, R, and S), which can be used in different proportions in the formulations. The table below gives the composition of these ingredients. The cost per unit of each of these ingredients is O: 150, P: 50, Q: 200, R: 500, S: 100.

**18. CAT 2007 LRDI | DI - Tables & Graphs**

The company is planning to launch a balanced diet required for growth needs of adolescent children. This diet must contain at least 30% each of carbohydrate and protein, no more than 25% fat and at least 5% minerals. Which one of the following combinations of equally mixed ingredients is feasible?

- A.
O and P

- B.
R and S

- C.
P and S

- D.
Q and R

- E.
O and S

Answer: Option E

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**Explanation** :

A mixture of O and S in equal proportion satisfies the given constraints as can be seen from the table.

Hence, option (e).

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**19. CAT 2007 LRDI | DI - Tables & Graphs**

For a recuperating patient, the doctor recommended a diet containing 10% minerals and at least 30% protein. In how many different ways can we prepare this diet by mixing at least two ingredients?

- A.
One

- B.
Two

- C.
Three

- D.
Four

- E.
None

Answer: Option A

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**Explanation** :

The diet should contain 10% minerals. P contains no minerals.

∴ P cannot be a part of any mixture.

R and S both contain 5% minerals.

∴ Mix of R and S in any proportion cannot give 10% minerals.

Consider O and R in the proportion x:y

∴ 10x + 5y = 10(x + y)

∴ 5y = 10y, which is not possible.

Similarly, Q and S, O and S, and Q and R are not possible.

Similarly a mix of three ingredients is not possible.

∴ The only possible mix is that of O and Q in equal proportion.

Hence, option (a).

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**20. CAT 2007 LRDI | DI - Tables & Graphs**

Which among the following is the formulation having the lowest cost per unit for a diet having 10% fat and at least 30% protein? The diet has to be formed by mixing two ingredients.

- A.
P and Q

- B.
P and S

- C.
P and R

- D.
Q and S

- E.
R and S

Answer: Option D

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**Explanation** :

Consider the options.

Option 1: P and Q have to be mixed in the proportion 4:1 to achieve 10% fat content. But this does not give 30% protein.

Option 2: P and S do not contain fat.

Option 3: P and R should be mixed in the proportion 3:1 to achieve 10% fat content. But 30% protein content is not achieved.

Option 4: Q and S should be mixed in the proportion 1:4 to achieve 10% fat content and 46% protein content. The cost of this mix per unit would be 6/5.

Option 5: R and S should be mixed in the proportion 1:3 to achieve 10% fat content and 50% protein content. The cost per unit of this mix would be 2.

Therefore, lowest cost is for Q and S.

Hence, option (d).

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**21. CAT 2007 LRDI | DI - Tables & Graphs**

In what proportion should P, Q and S be mixed to make a diet having at least 60% carbohydrate at the lowest per unit cost?

- A.
2 : 1 : 3

- B.
4 : 1 : 2

- C.
2 : 1 : 4

- D.
3 : 1: 2

- E.
4 : 1 : 1

Answer: Option E

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**Explanation** :

P, Q and S contain 80%, 10% and 45% carbohydrates.

To achieve 60% carbohydrates, proportion of P should be maximum. Hence, options 1 and 3 are eliminated.

Option 2: Carbohydrate content = (320 + 10 + 90)/700 = 420/700 = 60%

Cost per unit = (200 + 200 + 200)/700 = 6/7 = 0.857

Option 4: Carbohydrate content = (240 + 10 + 90)/600 < 60%

Option 5: Carbohydrate content = (320 + 10 + 45)/600 = 62.5%

Cost per unit = (200 + 200 + 100)/600 = 5/6 = 0. 833

P, Q and S in the proportion 4 : 1 : 1 has the lowest cost per unit.

Hence, option (e).

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