# CAT Math Previous Year Question Paper of 2007

## CAT Sample Papers 2007 for Math

Answer each question using the following instructions:
Mark (1) if the question can be answered by using the statement A alone but not by using
the statement B alone.
Mark (2) if the question can be answered by using the statement B alone but not by using
the statement A alone.
Mark (3) if the question can be answered by using either of the statements alone.
Mark (4) if the question can be answered by using both the statements together but not by
either of the statements
alone.
Mark (5) if the question cannot be answered on the basis of the two statements.

1. In a football match, at the half-time, Mahindra and Mahindra Club was trailing by
three goals. Did it win the match?
A. In the second-half Mahindra and Mahindra Club scored four goals.
B. The opponent scored four goals in the match.

2. In a particular school, sixty students were athletes. Ten among them were also
among the top academic performers. How many top academic performers were in
the school?
A. Sixty per cent of the top academic performers were not athletes.
B. All the top academic performers were not necessarily athletes.

3. Five students Atul, Bala, Chetan, Dev and Ernesto were the only ones who
participated in a quiz contest. They were ranked based on their scores in the
contest. Dev got a higher rank as compared to Ernesto, while Bala got a higher rank
as compared to Chetan. Chetan’s rank was lower than the median. Who among the
five got the highest rank?
A. Atul was the last rank holder.
B. Bala was not among the top two rank holders.

4. Thirty per cent of the employees of a call centre are males. Ten per cent of the
female employees have an engineering background. What is the percentage of male
employees with engineering background?
A. Twenty five per cent of the employees have engineering background.

B. Number of male employees having an engineering background is 20% more than
the number of female employees having an engineering background.
DIRECTIONS for Questions 30 to 33: Answer the following questions 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

5. What is the percentage of vegetarian students in Class 12?
(1) 40
(2) 45
(3) 50
(4) 55
(5) 60

6. 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?
(1) less than 8
(2) 10
(3) 12
(4) 14
(5) 16

7. What is the percentage of male students in the secondary section?
(1) 40
(2) 45
(3) 50
(4) 55
(5) 60

8. In the Secondary Section, 50% of the students are vegetarian males. Which of the
following statements is correct?
(1) Except vegetarian males, all other groups have same number of students.
(2) Except non-vegetarian males, all other groups have same number of students.
(3) Except vegetarian females, all other groups have same number of students.
(4) Except non-vegetarian females, all other groups have same number of students
(5) All of the above groups have the same number of students.

9. What is the approximate cost per unit in rupees, if the company produces and sells
1400 units in the year 2007?
(1) 104
(2) 107
(3) 110
(4) 115
(5) 116

10. What is the minimum number of units that the company needs to produce and sell
to avoid any loss?
(1) 313
(2) 350
(3) 384
(4) 747
(5) 928

11. 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?
(1) 25,400
(2) 24,400
(3) 31,400
(4) 32,900
(5) 32,000

12. 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?
(1) 1400
(2) 1600
(3) 1800
(4) 1900
(5) 2000

Directions for Questions 38 to 41: Answer the following questions 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.

13. 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?
(1) 700
(2) 2500
(3) 4500
(4) 8000
(5) No difference

14. 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.
(1) 23500
(2) 40500
(3) 57500
(4) 67500
(5) 75000

15. 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?
(1) India
(2) Thailand
(3) Malaysia
(4) Singapore
(5) USA

16. Taking the cost of poor quality into account, which country/countries will be the
most expensive for knee replacement?
(1) India
(2) Thailand
(3) Malaysia
(4) Singapore
(5) India and Singapore

Directions for Questions 42 to 46: Answer the following questions 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.

Sector No. Airport of Airport of 1 A B Distance 2 A C 790 1350
Departure Arrival between the
Airports(km.)
560
3 A D 850 1250
4 A E 1245 1600
5 A F 1345 1700
6 A G 1350 2450
7 A H 1950 1850
8 B C 1650 2000
9 B H 1750 1900
10 B I 2100 2450
11 B J 2300 2275
12 C D 460 450
13 C F 410 430
14 C G 910 1100
15 D E 540 590
16 D F 625 700
17 D G 640 750
18 D H 950 1250
19 D J 1650 2450
20 E F 1250 1700
21 E G 970 1150
22 E H 850 875
23 F G 900 1050
24 F I 875 950
25 F J 970 1150
26 G I 510 550
27 G J 830 890
28 H I 790 970
29 H J 400 425
30 I J 460 540

Price (Rs.)
670

17. What is the lowest price, in rupees, a passenger has to pay for travelling by the
shortest route from A to J?
(1) 2275
(2) 2850
(3) 2890
(4) 2930
(5) 3340

18. 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?
(1) 1991
(2) 2161
(3) 2707
(4) 2745
(5) 2783

19. 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?
(1) 2275
(2) 2615
(3) 2850
(4) 2945
(5) 3190

20. 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?
(1) 0.77
(2) 0.88
(3) 0.99
(4) 1.06
(5) 1.08

21. 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?
(1) 2170
(2) 2180
(3) 2315
(4) 2350
(5) 2390

Directions for Questions 47 to 50: Answer the following questions 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.
Composition
Ingredient Carbohydrate % Protein % Fat % Minerals %
O 50 30 10 10
P 80 20 0 0
Q 10 30 50 10
R 5 50 40 5
S 45 50 0 5

22. 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?
(1) O and P
(2) R and S
(3) P and S
(4) Q and R
(5) O and S

23. 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?
(1) One
(2) Two
(3) Three
(4) Four
(5) None

24. 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.
(1) P and Q
(2) P and S
(3) P and R
(4) Q and S
(5) R and S

25. In what proportion P, Q and S should be mixed to make a diet having at least 60%
carbohydrate at the lowest per unit cost?
(1) 2 : 1 : 3
(2) 4 : 1 : 2
(3) 2 : 1 : 4
(4) 3 : 1: 2
(5) 4 : 1 : 1

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