sample paper for CAT exam
this sample paper provides you a basic understanding of all the types of questions related to CAT and any management entrance exam. The sample paper consists of two parts- quantitative analysis and data interpretation and verbal ability.
QUANTITATIVE ABILITY AND DATA INTERPRETATION
1) Let A be a two-digit number and B be another two digit number formed by reversing the digits of A. IF A+B+( product of digits of number A)=145, then what is the sum of the digits of A.
2) Given that f(1)=1, f(2x)=4f(x)+6 and f(x+2)=f(x)+12x+12 for all real values of x. what is the value of f(20)?
3) Sammy’s wrist watch lagged behind by 12 min on Thursday at 6.00 am while it was 16 min ahead on Saturday at 9.00 pm in the same week. At what time did the watch show correct time?
a) 9 pm on Friday
b) 9 am on Friday
c) 1.30 pm on Friday
d) 12.30 pm on Saturday
Directions for question 4 and 5: answer the questions on the basis of the following information below.
Five friends namely- Anu, Banu, Cara, Dia and Emily- are playing on the sea shore and collecting pebbles. Pebbles collected by each of them are of red or blue or green colors only. The aggregate number of red, blue and green pebbles collected by each of them was 15, 11 and 22 respectively. Here is some partial information of amount of pebbles collected by each.
Cara collected 4 red, banu 3 and anu has collected a total of 10 pebbles among which 4 are green. The no of blue colored pebbles with each of the friend is a prime no. the no of pebbles of each color with Emily is same. No of pebbles with Cara is double the no of pebbles with Emily. Total no of pebbles with Banu is 50% more than the total no of pebbles with Dia. Ratio of the no of red pebbles to the no of green pebbles with banu as well as Dia is 1:2.
4) For how many friends the ratio of no of blue pebbles to green pebbles is 1:2?
5) What is the ratio of total no of pebbles with A and D?
6) Ajay, Vijay and Dhananjay purchased 1, 10 and 25 notebooks for a total of Rs. 14, Rs. 130 and Rs. 300respectively from a stationary shop. In his transaction with Ajay and Dhananjay, the shopkeeper made a profit of p% and q% respectively such that p=2q. How much profit did the shopkeeper make in his transaction with Vijay?(Assume that the shopkeeper bought each note book at the same price)
7) A book shelf can accommodate 6 books from left to right. If 10 identical books on each of the languages French, German, Spanish and English are available, in how many ways can the book-shelf be filled such that books on the same language are not put adjacently?
Direction for question 9: following question is followed by two statements, I and II. Answer each question using the following instructions:
a) If the question can be answered by using either of the statements alone.
b) If the question can be answered by using one of the statements alone but not by using the other statement alone.
c) If the question can be answered by using both the statements together, but cannot be answered by using either statement alone.
d) If the question can be answered using both statements together.
8) Is X a perfect square? (X not equal to 0)
I. X can be written as the sum of three positive integers in only one way.
- 7*X is a perfect square.
9) If Sn=12-22+32-42+……. + (2n-1)2-(2n)2+ (2n+1)2, then which of the following is correct?
10) A tower stands at a point Q on the ground. The angle of elevation of the top of the tower from a point R which is south of Q is 600. The angle of elevation of the top of the tower from a point S to the west of R is 300. If the height of the tower is 10 m, then find the distance between the points S and R.
d) None of these
11) How many multiples of 18 are less than 3500 and are 2 more than the square of a natural number?
12) If a3-xb5x=ax+5b3x, then x log(log b/log a) is equal to
a) Log a
b) Log b
c) X log a
d) None of these
13) Anil completes an assignment in 10 to 15 days and Mukesh takes 15 to 20 days to finish the same assignment. If they work on alternate days and both of them take a break together on every third day, then which of the following is correct regarding the number of days in which the assignment may be completed?
a) Less than or equal to 25 days
b) More than 18 days
c) More than or equal to 17 days
d) More than 25 days
14) Each of Amit, Bosco, Chris and Deepak bought 56 pencils each out of which a total of 64 pencils were found to be broken. If the no of unbroken pencils with Chris is 60% and 75% more than that of Amit and Bosco respectively, then find the no of broken pencils with Deepak.
15) A square ABCD has vertices A (-1, 3), B (3, 3), C (3,-1) AND D (-1,-1). The points P and Q lie on AB and BC respectively such that AP: PB is2:3 and BQ: QC IS 3:1. The line AQ and PD intersect at the point S. find the slope of the line CS.
16) For which of the following values of p, the equation x3+px2+x+p=0 will have either no real roots or exactly two real roots between x=1 and x=-1?
d) All of these
17) Rectangular tiles each of size 70 cm by 20 cm are to be laid horizontally on a rectangular floor of size 120 cm*130 cm, such that tiles do not overlap. A tile can be placed in any orientation so long as its edges are parallel to the edges of the floor. No tile should overshoot any edge of the floor. The maximum possible no of tiles that can accommodated on the floor is
18) What is the remainder when 8643 is divided by 132?
19) If x2+y2=3axy, y2+z2=4byz and z2+x2=5czx, then which of the following condition is satisfied?
20) In triangle ABC, D, E and F are the points of trisection of BC, AC and AB respectively such that AE: EC=2: 1, AF: FB=1: 2 and BD: DC=1: 2. Which of the following statements are true?
a) Area of triangle EDC=2/9 area of triangle ABC
b) Area of triangle FBD=2/7 area of BFEC
c) Area of triangle DEF=1/3 area of triangle ABC
d) None of these
21) Find the no of positive integer solutions of the equation 7x+3y=123, such that x is always less than y.
22) Mrs. And Mr. Tarak travel from Delhi to Agra and break the journey at Mathura in between. Somewhere between Delhi and Mathura, Mrs. Tarak asks, ’’how far have we travelled?’’ Mr. Tarak replies, ‘’ half as far as the distance from here to Mathura’’. Somewhere between Mathura and Agra, exactly 300 km from the point where she asked the first question, Mrs. Tarak asks, ‘’ how far have we to go?’’ Mr. Tarak replies “half as far as the distance from Mathura to here’’. The distance between Delhi to Agra is
a) 200 km
b) 400 km
c) 450 km
d) 300 km
23) The co-ordinates of the vertices of a triangle are A (2, 5), B (-3, 0) and C (-2, 4). A line ‘L’ passes through the Centroid of the triangle ABC and the point (1, 1). What is the shortest distance of the line from the origin?
a) 0 units
b) 1 unit
c) 1/sq-rt(2) units
d) Sqrt(2) units
24) Three integers are chosen at random without replacement from the first 20 positive integers. The probability that their product is even is
Directions for questions 25 to 27: answer on the basis of the following information.
Bicycle industry 1997-2002
|Production (‘000’ units)||7,721||8,907||9,913||10,895||9,813|
|Export quantity(‘000’ units)||1,204||1,092.2||1,009||949.2||750.7|
|Export value (Rs. crore)||147.6||144.4||141.0||128.8||95.0|
|Total sales (Rs. crore)||892.1||841.3||965.9||1,002.3||1,021.8|
Domestic sales (‘000’units) = production-export quantity
Domestic sales (Rs. crore) = total sales-export value
25) The highest approximate average export price per bicycle in any one of the time periods given was
a) Rs. 1,320
b) Rs. 1,360
c) Rs. 1,400
d) Rs. 1,270
26) What is the largest percentage increase in domestic consumption (in terms of the no of cycles) for any time period over the previous time period?
27) What was the percentage change in capacity utilization in 2001-02 over that in 1997-98, if the capacity increased by 40% during that period? [capacity utilization= (production/capacity)*100]
a) 9% decrease
b) 5% decrease
c) 5% increase
d) 18% increase
Directions for questions 28 to 30: answer the questions on the basis of the information given below.
The following is a student’s report card from a two hours management entrance test. For every correct answer she gets 3 marks, but for every wrong answer she loses 1 mark.
|Test area||No. of questions||Attempted questions||Wrong answers|
|1) reading comprehension(RC)||50||43||13|
|3) verbal ability (VA)||50||38||11|
|4) Data interpretation(DI)||40||32||09|
28) What percentage of the total maximum score did the candidate score?
29) Assuming that the candidate was given an extra half an hour due to the absent-mindedness of the supervisor and that she completed all 190 questions. What should her accuracy rate have been in questions that were attempted in the last half an hour to fetch her at least 70% of the total score after negative marking?
30) What were the least marks scored by the candidate in any section?
Verbal ability and logical reasoning
Directions for questions 1 to 3: in each question, the word at the top of the table is used in sentence in four different ways. Choose the option in which the usage of the word is incorrect or inappropriate.
a) Everyone is scared of the principal because his harsh words always sting.
b) The sting of the hornet can be fatal.
c) When I met my cousin who had travelled to Africa, a sting of curiosity led me through his 14 journals.
d) I don’t want to work in the kitchen, because the onion fumes will sting through my eyes.
a) The beginning of the movie was slow, but the rest was fast placed and interesting
b) Rest assured that when amit is on the job, it would be finished on time.
c) It’s futile to argue with Shannon, so I said “let the issue rest in here”.
d) The original edition of the Charles Dickens novel rests in the library.
a) The world was shocked to know that Ingrid, the famous singer was suffering from terminal cancer.
b) The company evaluated the losses it was making on the terminal inventories.
c) Dell’s parents first met at an airport terminal waiting for a flight.
d) The terminal buds of the branch were flowered.
34) There are two gaps in the sentence given below. From the pair of words given, choose the one that fills the gap most appropriately.
I should not have______ to talk in such a_____ strain especially when I had not studied the man to whom I was talking.
a) Daring; commanding
b) Ventured; peremptory
c) Try; bold
d) Emboldened; reckless
Directions for questions 35 to 37: each of the following questions has a paragraph from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way.
35) We keep trying to explain away American fundamentalism. Those of us not engaged personally or emotionally in the biggest political and cultural movement of our times-those on the sidelines of history- keep trying to come up with theories with which to discredit the evident allure of the of this punishing yet oddly comforting idea of a deity, this strange god. His invisible hand is everywhere, say his citizens- theologians, caressing and fixing every outcome: Little League games, job searches, test scores, the secret of sexually transmitted diseases, the success or failure of terrorist attack, victory or defeat in battle, at the ballot box, in bed______________
a) A divine love that speaks through hurricanes.
b) Those unable to feel his soothing touch at moments such as this snort at the notion of a god with the patience or the prurience to monitor every tick and twitch of desire.
c) Who would worship such a god?
d) His followers must be dupes or saps or fools their faith illiterate, insane or misinformed, the strength fleeting, hollow an aberration.
36) Existentialism is said to be all about “the death of god”, the meaninglessness of human life and the anxiety that provoke. It is in the face of such anxiety that one needs the courage to make meanings to oneself. The theme gets dutifully traced back to Soren Kierkegaard and Nietzsche, and forward through martin Heidegger, Camus, Jean-Paul Sartre, Paul Tillich, and Victor Frankel, always with a touch of heroism but surrounded by the darkness of despair and ultimate meaninglessness_______.
a) In the early years of existentialism in postwar Europe, the emphasis was indeed on gloom and hopelessness.
b) The books and articles that made the biggest splash- William Barrett’s Irrational Man.
c) That was challenged in the 60s by the celebrations of hipness in the United States at the hands of Norman mailer, in Advertisement for Myself, and some of the Beats.
d) The heady optimism that ruled in those years leavened the old world gloom and turned meaninglessness into a challenge.
37) In 1623 Galileo crafted a metaphor that is still often cited by scientists. Nature, he wrote, is a book in “the language of mathematics”. If we cannot understand that language, we will be doomed to wander about as if “in a dark labyrinth”. Like other metaphors this one has two facets; it is insightful, but it may be misleading if taken literally. It captures our sense that nature’s truths are somehow imposed on us- that they are already imprinted in the world- and underlines the key role played by mathematics in expressing that truths.___________
a) Take out its historical context and placed in ours, the image can be dangerously deceptive.
b) The idea of a book of nature did not, originate with Galileo.
c) For centuries it had been an accepted part of religious doctrine that the world contained two fundamental books.
d) Nature, the first book, is full of signs that reveal a deeper meaning when interpreted according to scripture, the second book, which supplies the ultimate meaning of syntax of nature’s signs.
Directions for questions 38 to 40: the passage given below is followed by a set of questions. Choose the most appropriate answer to each question.
Not only mathematics is dependent on us and our thoughts, but in another sense, we and the whole universe of existing things are dependent on mathematics. The apprehension of this purely ideal character is indispensable if we are to understand rightly the place of mathematics as one among the arts. It was formerly supposed that pure reason could decide in some respects as to the nature of the actual world geometry, at least was thought to deal with the space in which we live. But we now know that pure mathematics can never pronounce upon the questions of actual existence. The world of reason in a sense control the world of facts, but it is not at any point creative of fact, and in the application of its results to the world space and time, its certainty and precision are lost among approximations and working hypothesis. The objects considered by mathematicians have in past been mainly of a kind suggested by phenomenon but from such restrictions the abstract imagination should be wholly free. A reciprocal liberty must be accorded; reason cannot be dictated to the world of facts, but fact cannot restrict reasons privilege of dealing with whatever objects its love of beauty may cause to seem worthy of consideration. Here as elsewhere we build up our ideals out of the fragments to be found in the world; and in the end its hard to say whether the result is a creation or discovery.
38) With which of the following is the author agree?
I. Mankind relies on mathematics for its very existence.
- Geometry was believed to deal with space in which we live.
- The world of reason has no control over the world of fact.
a) Only I
b) I and II
c) Only III
d) I and II
39) When the results of pure mathematics are applied to the universe of existing things,
a) Its findings no longer have completely certainty and preciseness.
b) Mathematics ceases to be a science
c) The abstract imagination of the mathematicians is free of restrictions.
d) The nature of the actual world stands revealed.
40) According to Russell, ”a reciprocal liberty” must be obtained between
a) Mathematics and Applied science
b) Reason and facts
c) Mathematical objects and objects created by abstract imagination.
d) The study of pure mathematics and an application of its results.
Directions for questions 41 to 44: the passage given below is followed by a set of questions. Choose the most appropriate answer to each question.
Psychologists interpret narcissism as a compensation mechanism. Many business narcissists believe they have been wronged in the past and that they are ‘owed’. Their feeling of insecurity can be satisfied only by regular adulation, affirmation and recognition. One of the most frequently observed characteristics of the narcissist is capriciousness-inconsistent and unpredictable behavior. Naturally most scientists believe that its origin lies in early childhood. They blame the inconsistent parent who was attentive to all outward, public signs of achievement and success but blind to disapproving feelings. This inconsistency often leads to young adults being confused and never developing a clear sense of who they are or establishing a coherent value system. They are not comfortable in their own skin. This can and does result in a lifelong quest for full self-regard and self-assertion. The wells of the origin of the problem are both deep and murky, and the passions they endanger seem remorseless. Personal and work relationship for narcissists is particularly interesting. Naturally narcissists search them out because they are rare, probably equally dysfunctional people, labeled, complementary narcissists- they could also be called complementary narcissists.
41) Which of the following statements cannot be inferred from the passage?
a) Narcissists seek continual admiration and devotion from their partners.
b) Good parents guide the growth and development of narcissistic behavior in their children.
c) Inconsistency and unpredictability are the main traits of narcissistic behavior.
d) A narcissistic person considers other people as mere accessories or tools which can aid in achieving success.
42) The most appropriate title for the passage might be
a) ‘effects of narcissism’
b) ‘understanding of narcissism’
c) ‘the narcissists and the society’
d) ‘narcissistic behavior at workplace’
43) According to the passage, a narcissist :
a) Thrives on the adulation provided by society.
b) Behaves with consistent predictability.
c) Seeks out the rarest of qualities in people
d) Is a result of inconsistent parenting.
44) The word ‘inconsistent parent’ which has been used in the above passage means
a) A parent who doesn’t care about the behavior of his child at social gathering.
b) A parent does not care about his child’s feelings.
c) A parent who does not care about the feelings of his child but only worries about his social success.
d) A parent who is not interested in the overall development of his child but is interested in his social success.
Directions for questions 45to 47: the passage given below is followed by a set of questions. Choose the most appropriate answer to each question.
As long as music has been recorded questions of authenticity and artifice have arisen. There are innumerable examples of artists being lambasted for their insincerity or praised for their integrity and the ‘genuine ’quality of their songs. Whether it’s some long dead Appalachian musician being held up as the last word in musical purity or john Lennon being trashed for the supposed hypocrisy of his imagine no possessions line music has always ignited such troublesome and often spurious arguments. Perhaps it’s because music can possess such direct emotive power that we often seem to place unrealistic expectations which we would not necessarily apply to film makers or writers. Teenage music fans in particular seldom allow for much distance between musicians and their subject matter. For your average teenage listener there is a direct equation between how doomed a musician is and how meaningful their records are. The quest for authenticity in popular music suggests that music has always been subject to such vicarious fantasy and confused notions of sincerity.
45) Which of the following statements, in the light of the above passage, is NOT correct?
a) Fans expect musicians to produce sincere compositions in comparison to the works presented by film-makers.
b) Music has a direct- relationship with human emotions.
c) Teenage fans expect musicians to present contemporary, relevant and modern compositions.
d) Authenticity and artful contrivance have been in question ever since music has been composed and recorded.
46) The most appropriate title for the passage is:
a) Music for real
b) Music in the modern era
c) Authenticity and art forms
d) Modern musical renditions- authentic or contrived
47) Which of the following statements CANNOT be inferred from the passage?
a) Integrity and authenticity in music is important for the artist.
b) Catering to an audience is the prime factor which surpasses authenticity in expression.
c) Teenage fans measure the reputation of an artist on the basis of authenticity in his lyrics.
d) A number of artists have been blamed for hypocritical lyrics.
Directions for questions 48 to 50: each question consists of six sentences; the first and the last sentence are already given in sequence. Arrange the remaining four to form a coherent paragraph.
48) 1. Pension schemes are poison pills: all through the western world, pension schemes have brought governments close to bankruptcy.
- This happens because the governments have used the pension schemes to redistribute income from young workers to retired people.
- As population growth slows down, the no of old people grows, and the burden of supporting them falls on a diminishing no of young people.
- The workers object to having to support the old, while the old people have formed strong lobbies which can topple governments.
- The pension schemes go bankrupt, and governments have to prop them up with subsidies funded out of taxes in the general population.
6. Thus, class conflict is being replaced by age conflict.
49) 1. Physical properties of a shampoo too are very important.
- After the cleaning and rinsing job is done, the hair should comb easily when wet, free of tangles, and be in a manageable condition for combing when dry.
- Thereafter, it should spread easily and disperse quickly into the hair on the scalp.
- Finally, the shampoo should be rinsed out fast, and without leaving hair tacky and sticky.
- A shampoo should be viscous enough to stay on the palm before application over the head.
6. On drying, shampoo hair should retain its natural luster with a healthy bounce without becoming fizzy.
50) 1. It’s not that I don’t think these buzz words have any application in the real world.
- The ideal leader has to be strong omniscient leader who, by sheer Churchillian force of will and personality, could make people yield to his or her vision.
- They do not have any value-but only if you remember that any buzzword, no matter how clever or attractive, must eventually run through that unpredictable filter known as people.
- No management concept is meaningful without a shrewd understanding of people.
- For example, ‘leadership’ was the management of phrase on everyone’s lips a few years ago
6. Not long, thereafter, ‘leadership’ was the management phrase on everyone’s lips a few years ago.
Directions for questions 51 to 53: answer on the basis of information given below.
Five guests-Arvin, Bhanu, Chirag, Dhara, and Emily- are staying in a hotel. Each of these guests ordered one item each for breakfast, lunch and dinner. The items ordered by the guests are distinct. The following table provides information about items ordered by these guests.
|breakfast||Biscuit, eggs, milk, salad, toast|
|Lunch||Burger, continental, dosa, fruits, rice|
|Dinner||Chicken, Chinese, pizza, rotis, upma|
Additional information given:
i. The only items that are classified as ‘non-vegetarian’ are eggs, continental, chicken, and burger. Further, none of arvind, bhanu, and chirag ordered non-veg items.
ii. Bhanu is patient and ordered milk in the breakfast.
iii. The items ordered by chirag have at least two items whose names start with same alphabet. This holds true for dhiraj and Emily also.
iv. Emily ordered exactly two ‘’ non- vegetarian” items but do not order chicken.
v. Out of the guests, one is from south-India and he/she ordered both dosa and upma.
vi. The guest who ordered toast also ordered fruits.
51) Which of the following item is also ordered by the guest who ordered fruits?
52) Which of the following is not the guest who did not order salad?
53) Which of the following items is/are not ordered by the guest who ordered rotis?
d) Both (a) and (b)
Directions for questions 54 to 55: answer on the basis of information given below.
Pinki, qureshi, ritika, sarika, and tanmay are students coming from Delhi, Lucknow, Chandigarh, Meerut, and Kanpur. They have topped in different subjects among mathematics, English, science, geography, Hindi.
i. The student who has topped in Hindi is not from Delhi.
ii. The student from Kanpur has topped in mathematics.
iii. Q comes from Meerut and S from Delhi.
iv. The student from Chandigarh has not topped in science.
v. P has topped in science and T in geography.
54) Which student topped in Hindi?
d) Cannot be determined
55) Which city does the topper of English come from?
d) Cannot be determined
Direction for question 56: following question is followed by two statements, A and B. answer question using the following instruction:
Mark (a) if the question can be answered by using one statement alone but not by using the other statement alone.
Mark (b) if the question can be answered by using either statement alone.
Mark(c) if the question can be answered both the statements together but not by either statement alone.
Mark (d) if the question cannot be answered even by using both the statements together.
56) There are five vendors- anu, vindu, camily, esha and dia- sitting in a row. Which vendor is sitting exactly in the middle?
- Anu is sitting to the right of bindu. Bindu is sitting to the immediate right of Dia.
- Esha is sitting to the right of Dia, who is sitting on one corner.
57) Five thieves- Amar, Bhuvan, Chirag, Dhruv, and Elan- have been assigned five codes namely A, B, C, D, and E. also each thief has been assigned one of the mentioned codes. For none of the thieves, the first alphabet of his name is same as his assigned code. The codes assigned to both Amar and Chirag is neither B nor E. further, the code assigned to both Dhruv and Elan is neither A nor C. if the code assigned to Amar is D, then what is the code assigned to Bhuvan?
Directions for question 58 to 60: answer on the basis of the information below.
Aarti, Bina, Cara, Emily, Fiza and Gita are seven friends who go gymnasium daily. Each of them takes a different day off in a week. Each of them works out in three slots- morning, afternoon and evening with at least two of the seven in each slot. Each of the seven friends sticks to his/her slot for the entire week.
I. Cara goes in the afternoon slot and his day off is not Sunday.
II. Aarti’s day off is Tuesday and she does not work out in the same slot with either bina or gita.
III. None of those who work out in the morning slot has day off on either Wednesday or Friday.
IV. Fiza and Emily are the only two people who work out in evening slot. Dia’s day off is Sunday.
V. Fiza’s day off is the day next to Cara’s day off. Emily’s day off is not Wednesday.
VI. Gita’s day off is not on the previous day of aarti’s day off. Dia works out in morning slot.
VII. Bina and Cara do not work out in the same slot. Bina’s day off is not Thursday.
58) Which of the following group of friends work out in afternoon slot?
a) Cara and Aarti
b) Cara and Fiza
c) Bina, Gita and Dia
d) Bina, Cara and Gita
59) Which of the following is Bina’s day off?
60) Which of the following group of friends work out in the morning slot?
a) Cara and Fiza
b) Cara and Aarti
c) Bina, gita and Dia
d) Aarti, Cara and Fiza