CAT 2007 Question Paper with Answer Key PDF is available for download. The exam was conducted on November 18, 2007. CAT 2007 paper was rated tough by the test-takers. A total of 75 questions appeared in CAT 2007 question paper divided into 3 sections- Quantitative Ability, Data Interpretation and Logical Reasoning, and Verbal Ability. Each section carried 25 questions.
Candidates preparing for CAT 2025 can download the CAT 2007 question paper with the solution PDF to get a better idea about the type of questions asked in the paper and their difficulty level.
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CAT 2007 Question Paper with Solution PDF
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Question 1:
Consider the set \( S = \{2, 3, 4, \ldots, 2n+1\} \), where \( n \) is a positive integer larger than 2007. Define \( X \) as the average of the odd integers in \( S \) and \( Y \) as the average of the even integers in \( S \). What is the value of \( X - Y \)?
Ten years ago, the ages of the members of a joint family of eight people added up to 231 years. Three years later, one member died at the age of 60 and a child was born during the same year. After another three years, one more member died, again at 60, and a child was born during the same year. The current average age of this eight-member joint family is nearest to:
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A function \( f(x) \) satisfies \( f(1) = 3600 \) and \( f(1) + f(2) + \ldots + f(n) = n^2 f(n) \) for all positive integers \( n > 1 \). What is the value of \( f(9) \)?
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Suppose you have a currency, named Miso, in three denominations: 1 Miso, 10 Misos and 50 Misos. In how many ways can you pay a bill of 107 Misos?
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A confused bank teller transposed the rupees and paise when he cashed a cheque for Shailaja, giving her rupees instead of paise and paise instead of rupees. After buying a toffee for 50 paise, Shailaja noticed that she was left with exactly three times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount?
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How many pairs of positive integers \( m, n \) satisfy \[ \frac{1}{m} + \frac{4}{n} = \frac{1}{12}, \]
where \( n \) is an odd integer less than 60?
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The average weight of a class of 100 students is 45 kg. The class consists of two sections, I and II, each with 50 students. The average weight, \( W_I \), of Section I is smaller than the average weight \( W_{II} \) of Section II. If the heaviest student, Deepak, of Section II is moved to Section I, and the lightest student, Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched.
A: \( W_{II} - W_I = 1.0 \)
B: Moving Deepak from Section II to I (without any move to II) makes the average weights of the two sections equal.
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ABC Corporation needs at least 400 kilolitres of water in its factory at all times. It considers a spherical tank with uniform wall thickness. The outer diameter of the tank is 10 m. Is the tank capacity adequate?
A: The inner diameter of the tank is at least 8 meters.
B: The tank weighs 30,000 kg when empty, and is made of material with density 3 g/cc.
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Consider integers \( x, y, z \). What is the minimum possible value of \( x^2 + y^2 + z^2 \)?
A: \( x + y + z = 89 \)
B: Among \( x, y, z \) two are equal.
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Rahim plans to draw a square JKLM with point O on side JK but is not successful. Why?
A: The length of OM is twice that of OL.
B: The length of OM is 4 cm.
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What is the time difference between City A and City B?
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What is the plane’s cruising speed in km per hour?
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The maximum guaranteed return to Shabnam is:
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What strategy will maximize the guaranteed return to Shabnam?
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For general \( n \), how many enemies will each member of \( S \) have?
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For general \( n \), consider any two members of \( S \) that are friends. How many other members of \( S \) will be common friends of both these members?
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In a tournament, there are \( n \) teams \( T_1, T_2, \ldots, T_n \), with \( n > 5 \). Each team consists of \( k \) players, \( k > 3 \). The following pairs of teams have one player in common: \( T_1 \& T_2, T_2 \& T_3, \ldots, T_{n-1} \& T_n, T_n \& T_1 \). No other pair of teams has any player in common. How many players are participating in the tournament, considering all the \( n \) teams together?
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Consider four-digit numbers for which the first two digits are equal and the last two digits are also equal. How many such numbers are perfect squares?
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How many units should Mr. David produce daily?
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What is the maximum daily profit, in rupees, that Mr. David can realize from his business?
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The price of Darjeeling tea (in rupees per kilogram) is \( 100 + 0.10n \) on the \( n^{th} \) day of 2007 (\( n = 1, 2, \ldots, 100 \)), and then remains constant. The price of Ooty tea (in rupees per kilogram) is \( 89 + 0.15n \) on the \( n^{th} \) day of 2007 (\( n = 1, 2, \ldots, 365 \)). On which date in 2007 will the prices of these two varieties of tea be equal?
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Two circles with centres P and Q cut each other at two distinct points A and B. The circles have the same radii and neither P nor Q falls within the intersection of the circles. What is the smallest range that includes all possible values of the angle AQP in degrees?
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A quadratic function \( f(x) \) attains a maximum of 3 at \( x = 1 \). The value of the function at \( x = 0 \) is 1. What is the value \( f(x) \) at \( x = 10 \)?
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Which of the following best describes \( a_n + b_n \) for even \( n \)?
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If \( p = \frac{1}{3} \) and \( q = \frac{2}{3} \), then what is the smallest odd \( n \) such that \( a_n + b_n < 0.01 \)?
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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?
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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.)
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In what proportion P, Q and S should be mixed to make a diet having at least 60% carbohydrate at the lowest cost per unit?
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The company is planning to launch a balanced diet required for adolescent children.
The 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?
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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.
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Five students Atul, Bala, Chetan, Dev and Ernesto participated in a quiz contest. They were ranked based on scores. Dev ranked higher than Ernesto; Bala ranked higher than Chetan; Chetan’s rank was lower than median. Who got the highest rank?
A: Atul was the last rank holder.
B: Bala was not among the top two rank holders.
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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 with engineering background is 20% more than the number of female employees with engineering background.
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In a football match, at 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.
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What is the approximate cost per unit in rupees, if the company produces and sells 1400 units in the year 2007?
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What is the minimum number of units that the company needs to produce and sell to avoid any loss?
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If the company reduces the price by 5%, it can produce and sell as many units as it desires. How many units should the company produce to maximize its profit?
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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?
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What is the percentage of male students in the secondary section?
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In Class 12, 25% of the vegetarians are male. What is the difference between the number of female vegetarians and male non-vegetarians?
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What is the percentage of vegetarian students in Class 12?
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In the Secondary Section, 50% of the students are vegetarian males. Which of the following statements is correct?
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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. Which country will result in the cheapest package, taking cost of poor quality into account?
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Taking the cost of poor quality into account, which country will be the most expensive for knee replacement?
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What difference in amount in Bahts will it make to a Thai citizen if she gets a hysterectomy done in India instead of in Thailand, including poor quality cost? (Travel cost from Thailand to India is 7500 Bahts, 1 USD = 32.89 Bahts.)
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If the rupee value increases to Rs. 35 for a US Dollar and all else remains the same, what is the approximate difference in cost (in USD) for a Spinal Fusion between Singapore and India, including poor quality?
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What is the lowest price, in rupees, a passenger has to pay for travelling by the shortest route from A to J?
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The company plans to introduce a direct flight between A and J at 5% below the current minimum price. What should the company charge, approximately, in rupees?
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If airports C, D and H are closed, what would be the minimum price from A to J?
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If prices include a margin of 10% over total cost, what is the minimum cost per km for A to J?
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If prices include a 15% margin over total cost, which distance minimizes total cost per km from A to J?
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What is the thematic highlight of the passage?
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Which of the following would have been true if biological linkages structured human society?
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It has been claimed in the passage that "some roles are more absorbing than others". Which of the following reasons support this claim?
A. Some roles carry great expectations from society preventing manifestation of the true self.
B. Society ascribes so much importance to some roles that the conception of self may get aligned with the roles being performed.
C. Some roles require development of skill and expertise leaving little time for manifestation of self.
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A. When I returned to home, I began to read
B. everything I could get my hand on about Israel.
C. That same year Israel’s Jewish Agency sent
D. a Shaliach a sort of recruiter to Minneapolis.
E. I became one of his most active devotees.
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A. So once an economy is actually in a recession,
B. the authorities can, in principle, move the economy
C. out of slump - assuming hypothetically
D. that they know how to - by a temporary stimuli.
E. In the longer term, however, such policies have no affect on the overall behaviour of the economy.
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A. It is sometimes told that democratic
B. government originated in the city-states
C. of ancient Greece. Democratic ideals have been handed to us from that time.
D. In truth, however, this is an unhelpful assertion.
E. The Greeks gave us the word, hence did not provide us with a model.
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In the passage, the expression "like a madonna from a madonna" alludes to
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The sea and 'other creation' leads Rilke to
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According to the passage, the term "adventurers of experience" refers to
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Characters are also part of deep structure. Characters tie events in a story together and provide a thread of continuity and meaning. Stories can be about individuals, groups, projects, or whole organizations, so from an organizational studies perspective, the focal actor(s) determine the level and unit of analysis used in a study. Stories of mergers and acquisitions, for example, are commonplace. In these stories whole organizations are personified as actors. But these macro level stories usually are not told from the perspective of the macro-level participants, because whole organizations cannot narrate their experiences in the first person.
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Nevertheless, photographs still retain some of the magical allure that the earliest daguerreotypes inspired. As objects, our photographs have changed; they have become physically flimsier as they have become more technologically sophisticated. Daguerre produced pictures on copper plates: today many of our photographs never become tangible things, but instead remain filed away on computers and cameras, part of the digital ether that envelops the modern world. At the same time,our patience for the creation of images has also eroded. Children today are used to being tracked from birth by digital cameras and video recorders and they expect to see the results of their poses and performances instantly. The space between life as it is being lived and life as it is being displayed shrinks to a mere second.
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Mma Ramotswe had a detective agency in Africa, at the foot of Kgale Hill. These were its assets: a tiny white van, two desks, two chairs, a telephone, and an old typewriter. Then there was a teapot,in which Mma Ramotswe - the only private lady detective in Botswana - brewed redbush tea. And three mugs - one for herself, one for her secretary, and one for the client. What else does a detective agency really need? Detective agencies rely on human intuition and intelligence, both of which Mma Ramotswe had in abundance.
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What is the author attempting to illustrate through this passage?
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The term 'loci of commitment' as used in the passage would most likely correspond with which of the following?
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The author of this passage is likely to agree with which of the following?
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The cricket council that was [A] / were [B] elected last March is [A] / are [B] at sixes and sevens over new rules.
The critics censored [A] / censured [B] the new movie because of its social unacceptability.
Amit’s explanation for missing the meeting was credulous [A] / credible [B].
She coughed discreetly [A] / discretely [B] to announce her presence.
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The further [A] / farther [B] he pushed himself, the more disillusioned he grew.
For the crowds it was more of a historical [A] / historic [B] event.
The old man has a healthy distrust [A] / mistrust [B] for all new technology.
This film is based on a real [A] / true [B] story.
One suspects that the compliment [A] / complement [B] was backhanded.
(1) BABAB
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Regrettably [A] / Regretfully [B] I have to decline your invitation.
I am drawn to the poetic, sensual [A] / sensuous [B] quality of her paintings.
He was besides [A] / beside [B] himself with rage when I told him what I had done.
After brushing against a stationary [A] / stationery [B] truck my car turned turtle.
As the water began to rise over [A] / above [B] the danger mark, the signs of an imminent flood were clear.
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Why do islands with considerable degree of isolation provide valuable insights into human history?
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According to the author, why is prediction difficult in history?
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According to the author, which of the following statements would be true?
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Arrange the following sentences in the most logical order to form a coherent paragraph:
A. In America, highly educated women, who are in stronger position in the labour market than less qualified ones, have higher rates of marriage than other groups.
B. Some work supports the Becker thesis, and some appears to contradict it.
C. And, as with crime, it is equally inconclusive.
D. But regardless of the conclusion of any particular piece of work, it is hard to establish convincing connections between family changes and economic factors using conventional approaches.
E. Indeed, just as with crime, an enormous academic literature exists on the validity of the pure economic approach to the evolution of family structures.
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Arrange the following sentences in the most logical order to form a coherent paragraph:
A. Personal experience of mothering and motherhood are largely framed in relation to two discernible or “official” discourses: the “medical discourse and natural childbirth discourse”.
B. At the same time, the need for medical expert guidance is also a feature for contemporary reproduction and motherhood.
C. Similarly, historical work has shown how what are now taken-for-granted aspects of reproduction and mothering practices result from contemporary “pseudoscientific directives” and “managed constructs”.
D. The contrasting, overlapping, and ambiguous strands within these frameworks focus to varying degrees on a woman’s biological tie to her child and predisposition to instinctively know and be able to care for her child.
E. In addition, a third, “unofficial popular discourse” comprising “old wives’ tales” and based on maternal experiences of childbirth has also been noted.
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Arrange the following sentences in the most logical order to form a coherent paragraph:
A. Indonesia has experienced dramatic shifts in its formal governance arrangements since the fall of President Soeharto and the close of his centralized, authoritarian “New Order” regime in 1997.
B. The political system has taken its place in the nearly 10 years since Reformasi began.
C. The mass media, once tightly under Soeharto’s thumb, has experienced significant liberalization.
D. Such developments are seen optimistically by a number of donors and analysts.
E. A different group of analysts paint a picture in which institutional forms have changed, but power relations have not.
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Arrange the following sentences in the most logical order to form a coherent paragraph:
A. I had six thousand acres of land, and had thus got much spare land besides the coffee plantation.
B. The squatters’ land was more intensely alive than the rest of the farm.
C. The squatters are Natives, who with their families hold a few acres on a white man’s farm.
D. The Kikuyu also grew the sweet potatoes.
E. The beans ripened in the fields.
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CAT 2007 Paper Analysis
- The Data Interpretation section comprised moderate level questions, while questions based on Logical Reasoning were easy.
- The Quantitative Aptitude section was rated difficult. 8-9 questions were direct and could be solved without much difficulty.
- In the VARC section, questions related to Reading Comprehension had maximum weightage.
The below-mentioned table shows the detailed section-wise analysis of CAT 2007 question paper.
| Topics | No. Of Questions | Total Marks | Suggested Time | Good Attempts |
|---|---|---|---|---|
| Quantitative Ability | 25 | 100 | 55 | 12-14 |
| Data Interpretation and Logical Reasoning | 25 | 100 | 45 | 14-15 |
| Verbal Ability | 25 | 100 | 50 | 15-17 |
| Total | 75 | 300 | 150 | 45-55 |
CAT Question Papers of Other Years
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