CAT Model Question Paper

Sir recently I have done BBA and now I am looking to take part in to MBA entrance CAT and here I don’t know which type question ask in exam question paper so can give me link here I can download CAT model question papers?

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The CAT (Common Admission Test) is an entrance exam for the India Institutes of Management (IIMs) & other top MBA colleges in India.

Exam Pattern:
The CAT test is administered online & includes multiple-choice questions.
Negative-mark penalties for wrong answers.
It includes three sections that cover arithmetical problem solving, statistics, geometry, data interpretation, logical reasoning, puzzles, and English language skills.

List of few questions of CAT exam are given below:
1. A shop stores x kg of rice. The first customer buys half this amount plus half a kg of rice. The second customer buys half the remaining amount plus half a kg of rice. Then the third customer also buys half the remaining amount plus half a kg of rice. Thereafter, no rice is left in the shop. Which of the following best describes the value of x?
(1) 2 ≤ x ≤ 6 (2) 5 ≤ x ≤ 8 (3) 9 ≤ x ≤ 12 (4) 11≤ x ≤ 14 (5) 13 ≤ x ≤ 18

Directions for Questions 2 and 3:
Let f(x) = ax2 + bx + c, where a, b and c are certain constants and a ≠ 0.
It is known that f (5) = −3f (2) and that 3 is a root of f(x) = 0.

2. What is the other root of f(x) = 0?
(1) −7 (2) − 4 (3) 2 (4) 6 (5) cannot be determined

3. What is the value of a + b + c?

(1) 9 (2) 14 (3) 13 (4) 37 (5) cannot be determined

4. The number of common terms in the two sequences 17, 21, 25, … , 417 and 16, 21, 26, … , 466 is
(1) 78 (2) 19 (3) 20 (4) 77 (5) 22 Test Form Number:

Directions for Questions 5 and 6: The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

5. Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is
(1) 60 (2) 75 (3) 45 (4) 90 (5) 72

6. Neelam rides her bicycle from her house at A to her club at C, via B taking the shortest path. Then the number of possible shortest paths that she can choose is
(1) 1170 (2) 630 (3) 792 (4) 1200 (5) 936

7. Let f(x) be a function satisfying f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what

8. The integers 1, 2, …, 40 are written on a blackboard. The following operation is then repeated 39 times: In each repetition, any two numbers, say a and b, currently on the blackboard are erased and a new number a + b – 1 is written. What will be the number left on the board at the end?
(1) 820 (2) 821 (3) 781 (4) 819 (5) 780

9. Suppose, the speed of any positive integer n is defined as follows: seed(n) = n, if n < 10 = seed(s(n)), otherwise, where s(n) indicates the sum of digits of n. For example, seed(7) = 7, seed(248) = seed(2 + 4 + 8) = seed(14) = seed(1 + 4) = seed(5) = 5 etc. How many positive integers n, such that n < 500, will have seed(n) = 9?
(1) 39 (2) 72 (3) 81 (4) 108 (5) 55

10. In a triangle ABC, the lengths of the sides AB and AC equal 17.5 cm and 9 cm respectively. Let D be a point on the line segment BC such that AD is perpendicular to BC. If AD = 3 cm, then what is the radius (in cm) of the circle circumscribing the triangle ABC?
(1) 17.05 (2) 27.85 (3) 22.45 (4) 32.25 (5) 26.25

11. What are the last two digits of 72008?
(1) 21 (2) 61 (3)01 (4)41 (5)81

12. If the roots of the equation x3− ax2 +bx – c =0 are three consecutive integers, then what is the smallest possible value of b?

13. Consider obtuse-angled triangles with sides 8 cm, 15 cm and x cm. If x is an integer, then how many such triangles exist?
(1) 5 (2) 21 (3) 10 (4) 15 (5) 14

14. How many integers, greater than 999 but not greater than 4000, can be formed with the digits 0, 1, 2, 3 and 4, if repetition of digits is allowed? (1) 499 (2) 500 (3) 375 (4) 376 (5) 501

15. What is the number of distinct terms in the expansion of (a +b + c)20?
(1) 231 (2) 253 (3) 242 (4) 210 (5) 228

16. Consider a square ABCD with midpoints E, F, G, H of AB, BC, CD and DA respectively. Let L denote the line passing through F and H. Consider points P and Q, on L and inside ABCD, such that the angles APD and BQC both equal 120°. What is the ratio of the area of ABQCDP to the remaining area inside ABCD?

17. Three consecutive positive integers are raised to the first, second and third powers respectively and then added. The sum so obtained is a perfect square whose square root equals the total of the three original integers. Which of the following best describes the minimum, say m, of these three integers?
(1) 1 ≤ m ≤ 3 (2) 4 ≤ m ≤ 6 (3) 7 ≤ m ≤ 9 (4) 10 ≤ m ≤ 12 (5) 13 ≤ m ≤ 15

19. Two circles, both of radii 1 cm, intersect such that the circumference of each one passes through the centre of the circle of the other. What is the area (in sq cm) of the intersecting region?

20. Rahim plans to drive from city A to station C, at the speed of 70 km per hour, to catch a train arriving there from B. He must reach C at least 15 minutes before the arrival of the train. The train leaves B, located 500 km south of A, at 8:00 am and travels at a speed of 50 km per hour. It is known that C is located between west and northwest of B, with BC at 60° to AB. Also, C is located between south and southwest of A with AC at 30° to AB. The latest time by which Rahim must leave A and still catch the train is closest to
(1) 6:15 am (2) 6:30 am (3) 6:45 am (4) 7:00 am (5) 7:15 am

21. Consider a right circular cone of base radius 4 cm and height 10 cm. A cylinder is to be placed inside the cone with one of the flat surface resting on the base of the cone. Find the largest possible total surface area (in sq. cm) of the cylinder.

Directions for Questions 22 and 23: Five horses, Red, White, Grey, Black and Spotted participated in a race. As per the rules of the race, the persons betting on the winning horse get four times the bet amount and those betting on the horse that came in second get thrice the bet amount. Moreover, the bet amount is returned to those betting on the horse that came in third, and the rest lose the bet amount. Raju bets Rs. 3000, Rs. 2000 Rs. 1000 on Red, White and Black horses respectively and ends up with no profit and no loss.

22. Which of the following cannot be true?
1) At least two horses finished before Spotted (2) Red finished last (3) There were three horses between Black and Spotted (4) There were three horses between White and Red (5) Grey came in second

23. Suppose, in addition, it is known that Grey came in fourth. Then which of the following cannot be true?
(1) Spotted came in first (2) Red finished last (3) White came in second (4) Black came in second (5) There was one horse between Black and White

Directions for Questions 24 and 25: Marks (1) if Q can be answered from A alone but not from B alone. Marks (2) if Q can be answered from B alone but not from A alone. Marks (3) if Q can be answered from A alone as well as from B alone. Marks (4) if Q can be answered from A and B together but not from any of them alone. Marks (5) if Q cannot be answered even from A and B together. In a single elimination tournament, any player is eliminated with a single loss. The tournament is played in multiple rounds subject to the following rules: (a) If the number of players, say n, in any round is even, then the players are grouped in to n/2 pairs. The players in each pair play a match against each other and the winner moves on to the next round. (b) If the number of players, say n, in any round is odd, then one of them is given a bye, that is, he automatically moves on to the next round. The remaining (n − 1) players are grouped into (n − 1)/2 pairs. The players in each pair play a match against each other and the winners moves on to the next round. No player gets more than one bye in the entire tournament. Thus, if n is even, then n/2 players move on to the next round while if n is odd, then (n + 1)/2 players move on to the next round. The process is continued till the final round, which obviously is played between two players. The winner in the final round is the champion of the tournament.

24. Q: What is the number of matches played by the champion? A: The entry list for the tournament consists of 83 players. B: The champion received one bye.

25. Q: If the number of players, say n, in the first round was between 65 and 128, then what is the exact value of n? A: Exactly one player received a bye in the entire tournament. B: One player received a bye while moving on to the fourth round from third round

SECTION II This section contains 25 questions Directions for Questions 26 to 28: Answer the following questions based on the information given below: For admission to various affiliated colleges, a university conducts a written test with four different sections, each with a maximum of 50 marks. The following table gives the aggregate as well as the sectional cut-off marks fixed by six different colleges affiliated to the university. A student will get admission only if he/she gets marks greater than or equal to the cut-off marks in each of the section and his/her aggregate marks are at least equal to the aggregate cut-off marks as specified by the college.

26. Aditya did not get a call from even a single college. What could be the maximum aggregate marks obtained by him?
(1) 181 (2) 176 (3) 184 (4) 196 (5) 190

27. Bhama got calls from all colleges. What could be the minimum aggregate marks obtained by her?
(1) 180 (2) 181 (3) 196 (4) 176 (5) 184

28. Charlie got calls from two colleges. What could be the minimum marks obtained by him in a section?
(1) 0 (2) 21 (3) 25 (4) 35 (5) 41

Directions for Questions 29 to 32: Answer the following questions based on the information given below: The bar chart below shows the revenue received, in million US Dollars (USD), from subscribers to a particular Internet service. The data covers the period 2003 to 2007 for the United States (US) and Europe. The bar chart also shows the estimate revenues from the subscription to this service for the period 2008 to 2010.

29. While the subscription in Europe has been growing steadily towards that of the US, the growth rate in Europe seems to be declining. Which of the following is closest to the percent change in growth rate of 2007 (over 2006) relative to the growth rate of 2005 (over 2004)?
(1) 17 (2) 20 (3) 35 (4) 60 (5) 100

30. The difference between the estimated subscription in Europe in 2008 and what it would have been if it were computed using the percentage growth rate of 2007 (over 2006), is closest to :
(1) 50 (2) 80 (3) 20 (4) 10 (5) 0

31. In 2003, sixty percent of subscribers in Europe were men. Given that woman subscribers increase at the rate of 10 percent per annum and men at the rate of 5 percent per annum, what is the approximate percentage growth of subscribers between 2003 and 2010 in Europe? The subscription prices are volatile and may change each year.
(1) 62 (2) 15 (3) 78 (4) 84 (5) 50

32. Consider the annual percent change in the gap between subscription revenues in the US and Europe. What is the year in which the absolute value of this change is the highest?
(1) 03-04 (2) 05-06 (3) 06-07 (4) 08-09 (5) 09-10

Directions for Questions 33 to 35: Answer the following Questions based on the information given below. There are 100 employees in an organization across five departments. The following table gives the departement-wise distribution of average age, average basic pay and allowances. The gross pay of an employee is the sum of his/her basic pay and allowances. There are limited numbers of employees considered for transfer/promotion across departments. Whenever a person is transferred/promoted from a department of lower average age to a department of higher average age, he/she will get an additional allowance of 10% of basic pay over and above his/her current allowance. There will not be any change in pay structure if a person is transferred/promoted from a department with higher average age to a department with lower average age. Questions below are independent of each other.

33. There was a mutual transfer of an employee between Marketing and Finance departments and transfer of one employee from Marketing to HR. As a result, the average age of Finance department increased by one year and that of marketing department remained the same. What is the new average age of HR department?
(1) 30 (2) 35 (3) 40 (4) 45 (5) cannot be determined

34. What is the approximate percentage change in the average gross pay of the HR department due to transfer of a 40-yr old person with basic pay of Rs. 8000 from the Marketing department? (1) 9% (2) 11% (3) 13% (4) 15% (5) 17%

35. If two employees (each with a basic pay of Rs. 6000) are transferred from Maintenance department to HR department and one person (with a basic pay of Rs. 8000) was transferred from Marketing department to HR department, what will be the percentage change in average basic pay of HR department?
(1) 10.5% (2) 12.5% (3) 15% (4) 30% (5)40%

Directions for Questions 36 to 40: Answer the following questions based on the information given below: Abdul, Bikram and Chetan are three professional traders who trade in shares of a company XYZ Ltd. Abdul follows the strategy of buying at the opening of the day at 10 am and selling the whole lot at the close of the day at 3 pm. Bikram follows the strategy of buying at hourly intervals: 10 am , 11 am, 12 noon, 1 pm and 2 pm, and selling the whole lot at the close of the day. Further, he buys an equal number of shares in each purchase. Chetan follows a similar pattern as Bikram but his strategy is somewhat different. Chetan’s total investment amount is divided equally among his purchases. The profit or loss made by each investor is the difference between the sale value at the close of the day less the investment in purchase. The “return” for each investor is defined as the ratio of the profit or loss to the investment amount expressed as a percentage.

36. On a “boom” day the price of XYZ Ltd. keeps rising throughout the day and peaks at the close of the day. Which trader got the minimum return on that day? (1) Bikram (2) Chetan (3) Abdul (4) Abdul or Chetan (5) cannot be determined

37. On a day of fluctuating market prices, the share price of XYZ Ltd. ends with a gain, i.e., it is higher at the close of the day compared to the opening value. Which trader got the maximum return on that day? (1) Bikram (2) Chetan (3) Abdul (4) Bikram or Chetan (5) cannot be determined

38. Which one of the following statements is always true? (1) Abdul will not be the one with the minimum return (2) Return for Chetan will be higher than that of Bikram (3) Return for Bikram will be higher than that of Chetan (4) Return for Chetan cannot be higher than that of Abdul (5) none of the above One day, two other traders, Dane and Emily joined Abdul , Bikram and Chetan for trading in the shares of XYZ Ltd. Dane followed a strategy of buying equal numbers of shares at 10 am, 11 am and 12 noon, and selling the same numbers at 1 pm, 2 pm and 3 pm. Emily, on the other hand, followed the strategy of buying shares using all her money at 10 am and selling all of them at 12 noon and again buying the shares for all the money at 1 pm and again selling all of them at the close of the day at 3 pm. At the close of the day the following was observed: i. Abdul lost money in the transactions. ii. Both Dane and Emily made profits. iii. There was an increase in share price during the closing hour compared to the price at 2 pm. iv. Share price at 12 noon was lower than the opening price.

39. Which of the following is necessarily false?
(1) Share price was at its lowest at 2 pm (2) Share price was at its lowest at 11 am (3) Share price at 1 pm was higher than the share price at 2 pm (4) Share price at 1 pm was higher than the share price at 12 noon (5) none of the above CAT 2008
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40. Share price was at its highest at
(1) 10 am (2) 11 am (3) 12 noon (4) 1 pm (5) cannot be determined

Directions for Questions 41 to 43: Answer the following questions based on the statements given below: (i) There are three houses on each side of the road. (ii) These six houses are labeled as P, Q, R, S, T and U. (iii) The houses are of different colours, namely, Red, Blue, Green, Orange, Yellow and White. (iv) The houses are of different heights. (v) T, the tallest house, is exactly opposite to the Red coloured house. (vi) The shortest house is exactly opposite to the Green coloured house. (vii) U, the Orange coloured house, is located between P and S. (viii) R, the Yellow coloured house, is exactly opposite to P. (ix) Q, the Green coloured house, is exactly opposite to U. (x) P, the White coloured house, is taller than R, but shorter than S and Q.

41. What is the colour of the tallest house?
(1) Red (2) Blue (3) Green (4) Yellow (5) none of these

42. What is the colour of the house diagonally opposite to the Yellow coloured house?
(1) White (2) Blue (3) Green (4) Red (5) none of these

43. Which is the second tallest house?
(1) P (2) S (3) Q (4) R (5) cannot be determined CAT 2008
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Directions for Questions 44 to 47: Answer the following questions based on the information given below: In a sports event, six teams (A, B, C, D, E and F) are competing against each other. Matches are scheduled in two stages. Each team plays three matches in Stage-I and two matches in Stage-II. No team plays against the same team more than once in the event. No ties are permitted in any of the matches. The observations after the completion of Stage-I and Stage-II are as given below. Stage-I: • One team won all the three matches. Two teams lost all the matches. D lost to A but won against C and F. E lost to B but won against C and F. B lost at least one match. F did not play against the top team of Stage-I. Stage-II: The leader of Stage-I lost the next two matches. Of the two teams at the bottom after Stage-I, one team won both matches, while the other lost both matches. One more team lost both matches in Stage-II.

44. The team(s) with the most wins in the event is (are):
(1) A (2) A & C (3) F (4) E (5) B & E

45. The two teams that defeated the leader of Stage-I are:
(1) F & D (2) E & F (3) B & D (4) E & D (5) F & D

46. The only team(s) that won both the matches in Stage-II is (are):
(1) B (2) E & F (3) A, E & F (4) B, E & F (5) B & F

47. The teams that won exactly two matches in the event are:
(1) A, D & F (2) D & E (3) E & F (4) D, E & F (5) D & F CAT 2008
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Directions for Questions 48 to 50: Answer the following questions based on the information given below: Telecom operators get revenue from transfer of data and voice. Average revenue received from transfer of each unit of data is known as ARDT. In the diagram below, the revenue received from data transfer as percentage of total revenue received and the ARDT in US Dollars (USD) are given for various countries.

48. If the total revenue received is the same for the pairs of countries listed in the choices below, choose the pair that has approximately the same volume of data transfer.
(1) Philippines and Austria (2) Canada and Poland (3) Germany and USA (4) UK and Spain (5) Denmark and Mexico

49. It was found that the volume of data transfer in India is the same as that of Singapore. Then which of the following statements are true?
(1) Total revenue is the same in both countries. (2) Total revenue in India is about 2 times that of Singapore (3) Total revenue in India is about 4 times that of Singapore (4) Total revenue in Singapore is about 2 times that of India (5) Total revenue in Singapore is about 4 times that of India

50. It is expected that by 2010, revenue from the data transfer as a percentage of total revenue will triple for India and double for Sweden. Assume that in 2010, the total revenue in India is twice that of Sweden and that the volume of data transfer is the same in both the countries. What is the percentage increase of ARDT in India if there is no change in ARDT in Sweden?
(1) 400% (2) 550% (3) 800% (4) 950% (5) cannot be determined

Directions for Questions 86 to 90: The passage given below is followed by a set of five questions. Choose the most appropriate answer to each question. To summarize the Classic Maya collapse, we can tentatively identify five strands. I acknowledge, however, that Maya archaeologists still disagree vigorously among themselves—in part, because the different strands evidently varied in importance among different parts of the Maya realm; because detailed archaeological studies are available for only some Maya sites; and because it remains puzzling why most of the Maya heartland remained nearly empty of population and failed to recover after the collapse and after re-growth of forests. With those caveats, it appears to me that one strand consisted of population growth outstripping available resources: a dilemma similar to the one foreseen by Thomas Malthus in 1798 and being played out today in Rwanda (Chapter 10), Haiti (Chapter 11), and elsewhere. As the archaeologist David Webster succinctly puts it, "Too many farmers grew too many crops on too much of the landscape." Compounding that mismatch between population and resources was the second strand: the effects of deforestation and hillside erosion, which caused a decrease in the amount of useable farmland at a time when more rather than less farmland was needed, and possibly exacerbated by an anthropogenic drought resulting from deforestation, by soil nutrient depletion and other soil problems, and by the struggle to prevent bracken ferns from overrunning the fields. The third strand consisted of increased fighting, as more and more people fought over fewer resources. Maya warfare, already endemic, peaked just before the collapse. That is not surprising when one reflects that at least 5,000,000 people, perhaps many more, were crammed into an area smaller than the state of Colorado (104,000 square miles). That warfare would have decreased further the amount of land available for agriculture, by creating no-man's lands between principalities where it was now unsafe to farm. Bringing matters to a head was the strand of climate change. The drought at the time of the Classic collapse was not the first drought that the Maya had lived through, but it was the most severe. At the time of previous droughts, there were still uninhabited parts of the Maya landscape, and people at a site affected by drought could save themselves by moving to another site. However, by the time of the Classic collapse the landscape was now full, there was no useful unoccupied land in the vicinity on which to begin anew, and the whole population could not be accommodated in the few areas that continued to have reliable water supplies. As our fifth strand, we have to wonder why the kings and nobles failed to recognize and solve these seemingly obvious problems undermining their society. Their attention was evidently focused on their short-term concerns of enriching themselves, waging wars, erecting monuments, competing with each other, and extracting enough food from the peasants to support all those activities. Like most leaders throughout human history, the Maya kings and nobles did not heed long-term problems, insofar as they perceived them. We shall return to this theme in Chapter

14. Finally, while we still have some other past societies to consider in this book before we switch our attention to the modern world, we must already be struck by some parallels between the Maya and the past societies discussed in

Chapters

2-4. As on Easter Island, Mangareva, and among the Anasazi, Maya environmental and population problems led to increasing warfare and civil strife. As on Easter Island and at Chaco Canyon, Maya peak population numbers were followed swiftly by political and social collapse. Paralleling the eventual extension of agriculture from Easter Island's coastal lowlands to its uplands, and from the Mimbres floodplain to the hills, Copan's inhabitants also expanded from the floodplain to the more fragile hill slopes, leaving them with a larger population to feed when the agricultural boom in the hills went bust. Like Easter Island chiefs erecting ever larger statues, eventually crowned by pukao, and like Anasazi elite treating themselves to necklaces of 2,000 turquoise beads, Maya kings sought to outdo each other with more and more impressive temples, covered with thicker and thicker plaster—reminiscent in turn of the extravagant conspicuous

consumption by modern American CEOs. The passivity of Easter chiefs and Maya kings in the face of the real big threats to their societies completes our list of disquieting parallels.

86. According to the passage, which of the following best represents the factor that has been cited by the author in the context of Rwanda and Haiti? (1) Various ethnic groups competing for land and other resources (2) Various ethnic groups competing for limited land resources (3) Various ethnic groups fighting wit each other (4) Various ethnic groups competing for political power (5) Various ethnic groups fighting for their identity

87. By an anthropogenic drought, the author means (1) A drought caused by lack of rains. (2) A drought caused due to deforestation (3) A drought caused by failure to prevent bracken ferns from overrunning the fields. (4) A drought caused by actions of human beings. (5) A drought caused by climate changes.

88. According to the passage, the drought at the time of Maya collapse had a different impact compared to the droughts earlier because (1) The Maya kings continue to be extravagant when common people were suffering. (2) It happened at the time of collapse of leadership among Mayas. (3) It happened when the Maya population had occupied all available land suited for agriculture. (4) It was followed by internecine warfare among Mayans. (5) Irreversible environmental degradation led to this drought.

89. According to the author, why is it difficult to explain the reasons for Maya collapse? (1) Copan inhabitants destroyed all records of that period. (2) The constant deforestation and hillside erosion have wiped out all traces of the Maya kingdom. (3) Archaeological sites of Mayas do not provide any consistent evidence. (4) It has not been possible to ascertain which of the factors best explains as to why the Maya civilization collapsed. (5) At least five million people were crammed into a small area.

90. Which factor has not been cited as one of the factors causing the collapse of Maya society? (1) Environmental degradation due to excess population (2) Social collapse due to excess population (3) Increased warfare among Maya people (4) Climate change (5) Obsession of Maya population with their own short-term concerns.

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I want to get the syllabus of CAT Exam. So will you provide the syllabus of CAT Exam to me?

As you want to get the syllabus of CAT Exam, so here I am providing the following syllabus of CAT Exam:

CAT Exam Syllabus

Quantitative Ability
Percentages
Profit, Loss and Discount
Speed, Time and Distance
Averages
Linear Equations
Complex Numbers
Binomial Theorem
Surds and Indices
Permutation and Combination
Probability
Set Theory
Geometry
Trigonometry
LCM and HCF
Interest (Simple and Compound)
Number Systems
Quadratic Equations
Ratio and Proportion
Functions
Mensuration
Co-ordinate Geometry
Mixtures and Alligations
Inequalities
Logarithm
Progressions (Sequences & Series)
Time and Work

Data Interpretation
Bar Graphs
Venn Diagrams
Tables
Caselets
Line Charts
Column Graphs
Pie Chart

Logical Reasoning
Clocks
Venn Diagrams
Seating Arrangement
Logical Sequence
Logical Connectives
Calendars
Number and Letter Series
Logical Matching
Binary Logic
Blood Relations
Syllogism
Cubes

Verbal Ability
English Usage or Grammar
Fill in the blanks
Jumbled Paragraph
Vocabulary Based (Synonyms Antonyms)
Analogies or Reverse Analogies
Sentence Correction
Summary Questions
Cloze Passage
Verbal Reasoning
Reading Comprehension
Facts / Inferences / Judgements
Meaning-Usage Match

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