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Section I
This section contains 25 questions
- The price of Darjeeling tea (in rupees per kilogram) is 100 + 0.10 n , on the n th^ day of 2007 ( n = 1, 2, ..., 100), and then remains constant. On the other hand, the price of Ooty tea (in rupees per kilogram) is 89 + 0.15 n , on the n th^ day of 2007 ( n = 1, 2, ..., 365). On which date in 2007 will the prices of these two varieties of tea be equal? (1) May 21 (2) April 11 (3) May 20 (4) April 10 (5) June 30
- 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 of f ( x ) at x = 10? (1) – 119 (2) – 159 (3) – 110 (4) - (5) -
- 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? (1) Between 0 and 90 (2) Between 0 and 30 (3) Between 0 and 60 (4) Between 0 and 75 (5) Between 0 and 45
Directions for Questions 4 and 5:
Let S be the set of all pairs ( i , j ) where 1 ≤ i ≤ j < n and n ≥ 4. Any two distinct members of S
are called “friends” if they have one constituent of the pairs in common and “enemies”
otherwise. For example, if n = 4, then S = {(1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4)}. Here, (1,
- and (1, 3) are friends, (1,2) and (2, 3) are also friends, but (1,4) and (2, 3) are enemies.
- For general n , how many enemies will each member of S have? (1) n – 3 (2)
(3) 2 n – 7
- 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?
(2) 2 n – 6 (3)
(4) n – 2 (5)
Directions for Questions 6 and 7:
Shabnam is considering three alternatives to invest her surplus cash for a week. She wishes
to guarantee maximum returns on her investment. She has three options, each of which can
be utilized fully or partially in conjunction with others.
Option A: Invest in a public sector bank. It promises a return of +0.10%
Option B: Invest in mutual funds of ABC Ltd. A rise in the stock market will result in a
return of +5%, while a fall will entail a return of – 3%
Option C: Invest in mutual funds of CBA Ltd. A rise in the stock market will result in a
return of – 2.5%, while a fall will entail a return of +2%
- The maximum guaranteed return to Shabnam is (1) 0.25% (2) 0.10% (3) 0.20% (4) 0.15% (5) 0.30%
- What strategy will maximize the guaranteed return to Shabnam? (1) 100% in option A (2) 36% in option B and 64% in option C (3) 64% in option B and 36% in option C (4) 1/3 in each of the three options (5) 30% in option A, 32% in option B and 38% in option C
No other pair of teams has any player in common. How many players are participating in the tournament, considering all the n teams together?
(1) n ( k – 1) (2) k ( n – 1) (3) n ( k – 2) (4) k ( k – 2) (5) ( n – 1)( k – 1)
Directions for Questions 12 and 13:
Mr. David manufactures and sells a single product at a fixed price in a niche market. The
selling price of each unit is Rs. 30. On the other hand, the cost, in rupees, of producing x
units is 240 + bx + cx^2 , where b and c are some constants. Mr. David noticed that doubling
the daily production from 20 to 40 units increases the daily production cost by 66.66%.
However, an increase in daily production from 40 to 60 units results in an increase of only
50% in the daily production cost. Assume that demand is unlimited and that Mr. David can
sell as much as he can produce. His objective is to maximize the profit.
- How many units should Mr. David produce daily? (1) 130 (2) 100 (3) 70 (4) 150 (5) Cannot be determined
- What is the maximum daily profit, in rupees, that Mr. David can realize from his business? (1) 620 (2) 920 (3) 840 (4) 760 (5) Cannot be determined
Directions for Questions 14 and 15:
Let a 1 = p and b 1 = q, where p and q are positive quantities. Define: an = pb n − 1 bn = qb n − 1, for even n > 1 and a n = pa n − 1 bn = qa n − 1, for odd n > 1.
- If p = 1/3 and q = 2/3, then what is the smallest odd n such that an + bn < 0.01? (1) 7 (2) 13 (3) 11 (4) 9 (5) 15
Directions for Questions 16 through 19:
Each question is followed by two statements A and B. Answer each question using the following instructions.
Mark (1) if the question can be answered by using statement A alone but not by using statement B alone.
Mark (2) if the question can be answered by using statement B alone but not by using statement A alone.
Mark (3) if the question can be answered by using both the statements together but not by using either of the statements alone.
Mark (4) if the question cannot be answered on the basis of the two statements.
- 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, WI, of Section I is smaller than the average weight, W II, of Section II. If the heaviest student, say Deepak, of Section II is moved to Section I, and the lightest student, say Poonam, of Section I is moved to Section II, then the average weights of the two sections are switched, i.e., the average weight of Section I becomes W II and that of Section II becomes W I. What is the weight of Poonam?
A. W II – W I = 1.
times as much as the amount on the cheque. Which of the following is a valid statement about the cheque amount? (1) Over Rupees 13 but less than Rupees 14 (2) Over Rupees 7 but less than Rupees 8 (3) Over Rupees 22 but less than Rupees 23 (4) Over Rupees 18 but less than Rupees 19 (5) Over Rupees 4 but less than Rupees 5
- Consider the set S = {2, 3, 4, ...., 2 n + l}, where n is a positive integer larger than
- 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? (1) 0 (2) 1 (3) n / (4) n +1/2 n (5) 2008
- 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 years 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: (1) 23 years (2) 22 years (3) 21 years (4) 25 years (5) 24 years
- A function f ( x ) satisfies f (1) = 3600, and f (l) + f (2) + ... + f ( n ) = n ² f ( n ), for all
positive integers n >1. What is the value of f (9)? (1) 80 (2) 240 (3) 200 (4) 100 (5) 120
Section II
This section contains 25 questions
Directions for Questions 26 to 29 : Each question is followed by two statements, A and B. 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.
- 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.
- 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.
- 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.
- 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.
- 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.
Directions for Questions 34 to 37: Answer the following questions 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.
Year 2002
Year 2003
Year 2004
Year 2005
Year 2006 Volume of production 1000 900 1100 1200 1200 Costs (Rs.) Material 50,000 45,100 55,200 59,900 60, Labour 20,000 18,000 22,100 24,150 24, Consumables 2,000 2,200 1,800 1,600 1, Rent of building 1,000 1,000 1,100 1,100 1, Rates and taxes 400 400 400 400 400 Repair and maintenance expenses 800 820 780 790 800 Operating cost of machines 30,000 27,000 33,500 36,020 36, Selling and marketing expenses 5,750 5,800 5,800 5,750 5,
- 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
- 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
- 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, (2) 24, (3) 31, (4) 32, (5) 32,
- 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.
Procedure Comparative Costs in USA and some Asian Countries (in US Dollars) USA India Thailand Singapore Malaysia Heart Bypass 130000 10000 11000 18500 9000 Heart Valve Replacement
Angioplasty 57000 11000 13000 13000 11000 Hip Replacement 43000 9000 12000 12000 10000 Hysterectomy 20000 3000 4500 6000 3000 Knee Replacement 40000 8500 10000 13000 8000 Spinal Fusion 62000 5500 7000 9000 6000
- 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
- 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 Departure Airport of Arrival Distance between the Airports(km.)
- 1 A B Price (Rs.)
- 2 A C
- 3 A D
- 4 A E
- 5 A F
- 6 A G
- 7 A H
- 8 B C
- 9 B H
- 10 B I
- 11 B J
- 12 C D
- 13 C F
- 14 C G
- 15 D E
- 16 D F
- 17 D G
- 18 D H
- 19 D J
- 20 E F
- 21 E G
- 22 E H
- 23 F G
- 24 F I
- 25 F J
- 26 G I
- 27 G J
- 28 H I
- 29 H J
- 30 I J
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
- 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
- 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
- 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
- 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
5) BABAB
Directions for Questions 54 to 56 : The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question.
To discover the relation between rules, paradigms, and normal science, consider first how the historian isolates the particular loci of commitment that have been described as accepted rules. Close historical investigation of a given specialty at a given time discloses a set of recurrent and quasi-standard illustrations of various theories in their conceptual, observational, and instrumental applications. These are the community's paradigms, revealed in its textbooks, lectures, and laboratory exercises. By studying them and by practicing with them, the members of the corresponding community learn their trade. The historian, of course, will discover in addition a penumbral area occupied by achievements whose status is still in doubt, but the core of solved problems and techniques will usually be clear. Despite occasional ambiguities, the paradigms of a mature scientific community can be determined with relative ease. That demands a second step and one of a somewhat different kind. When undertaking it, the historian must compare the community's paradigms with each other and with its current research reports. In doing so, his object is to discover what isolable elements, explicit or implicit, the members of that community may have abstracted from their more global paradigms and deploy it as rules in their research. Anyone who has attempted to describe or analyze the evolution of a particular scientific tradition will necessarily have sought accepted principles and rules of this sort. Almost certainly, he will have met with at least partial success. But, if his experience has been at all like my own, he will have found the search for rules both more difficult and less satisfying than the search for paradigms. Some of the generalizations he employs to describe the community's shared beliefs will present more problems. Others, however, will seem a shade too strong. Phrased in just that way, or in any other way he can imagine, they would almost certainly have been rejected by some members of the group he studies. Nevertheless, if the coherence of the research tradition is to be understood in terms of rules, some specification of common ground in the corresponding area is needed. As a result, the search for a body of rules competent to constitute a given normal research tradition becomes a source of continual and deep frustration. Recognizing that frustration, however, makes it possible to diagnose its source. Scientists can agree that a Newton, Lavoisier, Maxwell, or Einstein has produced an apparently permanent solution to a group of outstanding problems and still disagree, sometimes without being aware of it, about the particular abstract characteristics that make those solutions permanent. They can, that is, agree in their identification of a paradigm without agreeing on, or even attempting to produce, a full interpretation or rationalization of it. Lack of a standard interpretation or of an agreed reduction to rules will not prevent a paradigm from guiding research. Normal science can be determined in part by the direct inspection of paradigms, a process that is often aided by but does not depend upon the formulation of rules and assumption. Indeed, the existence of a paradigm need not even imply that any full set of rules exists.
- What is the author attempting to illustrate through this passage? (1) Relationships between rules, paradigms, and normal science. (2) How a historian would isolate a particular ‘loci of commitment’. (3) How a set of shared beliefs evolve in to a paradigm. (4) Ways of understanding a scientific tradition. (5) The frustrations of attempting to define a paradigm of a tradition.
- The term ‘loci of commitment’ as used in the passage would most likely correspond with which of the following? (1) Loyalty between a group of scientists in a research laboratory. (2) Loyalty between groups of scientists across research laboratories. (3) Loyalty to a certain paradigm of scientific inquiry. (4) Loyalty to global patterns of scientific inquiry. (5) Loyalty to evolving trends of scientific inquiry.
- The author of this passage is likely to agree with which of the following? (1) Paradigms almost entirely define a scientific tradition. (2) A group of scientists investigating a phenomenon would benefit by defining a set of rules. (3) Acceptance by the giants of a tradition is a sine qua non for a paradigm to emerge. (4) Choice of isolation mechanism determines the types of paradigm that may emerge from a tradition. (5) Paradigms are a general representation of rules and beliefs of a scientific tradition.
Directions for Questions 57 to 59: Each of the following questions has a paragraph from which the last sentence has been deleted. From the given options, choose the sentence that completes the paragraph in the most appropriate way.
- 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 common place. 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. (1) More generally, data concerning the identities and relationships of the characters in the story are required, if one is to understand role structure and social networks in which that process is embedded. (2) Personification of a whole organization abstracts away from the particular actors and from traditional notions of level of analysis. (3) The personification of a whole organization is important because stories differ depending on who is enacting various events.
