CAT Mock Test 7

6. The number of literate females in Rural Noland is 1000 less than the number of literate females in Urban Noland. What is the population of Noland?

7. Ashish, Binay and Joseph can do a job in 20, 30 and 40 days respectively. The three started the job together; Ashish left the job 4 days before it was completed and Binay left the job 3 days before it was completed. In how many days was the job completed?

8. A bookseller sells only three books – A, B and C – on Sundays and their Selling Price are in the ratio 2 : 3 : 4 respectively. The bookseller makes 40%, 30% and 20% profit on selling A, B and C respectively. If the bookseller made an overall profit of 30% on a Sunday when he sold at least one copy of each of the three books, then which of the following statements is definitely true regarding that day?

9. In how many ways can the letters of the word MELANCHOLY be arranged such that E appears before A and A appears before O?

10. The sum of the coefficients of the polynomial

(x – 1)⁶(x – 2)⁴ + (x – 2)⁵(x + 1)⁶ + (x + 1)²(x + 2)³ is

11. The figure given below shows a circle with center O and radius 8 cm. BD is a chord of the circle and A is a point on the minor arc BD. C is a point on BD such that AC is perpendicular to BD. The length of AC is 4 cm and BC is 12 cm. What is the length (in cm) of CD?

12. What is the number of common terms in the two sequences given below?

S1 ≡ 4, 10, 16, 22, …., 562.

S2 ≡ 3, 8, 13, 18, …., 573.

13. A merchant marks up the cost of cloth by 30% and then gives a discount of 20% on the Marked Price to all his customers. What is his profit/loss percentage in winter when the meter-scale shrinks by 10% due to cold?

14. The question given below is followed by two statements, A and B. Mark the answer using the following instructions:

Mark (a) if the question can be answered by using Statement A alone, but cannot be answered by using Statement B alone.

Mark (b) if the question can be answered by using Statement B alone, but cannot be answered by using Statement A alone.

Mark (c) if the question can be answered by using either statement alone.

Mark (d) if the question cannot be answered by any of the two statements.

Q. In x-y plane, a circle passes through the points (2, 5) and (–4, 13). What is the equation of the circle?

A. The circle passes through the point (–10, 21).

B. The radius of the circle is of length 6 units.

15. In how many ways can six letters – A, B, C, D, E and F – be written in a circular arrangement such that D is adjacent to B and is diametrically opposite E?

16. For how many positive integer values of ‘x’ is ||||x – 1| – 2| – 3| – 4| < 5?

Directions for questions 17 to 19 : Answer the questions on the basis of the information given below.

Scientists have recently discovered a new planet and have named it Zeltrion. The inhabitants of Zeltrion are called Vulcans. The total land area of Zeltrion is 100,000 km². There are many islands on Zeltrion but the Vulcans are found only on twelve of them. The table given below shows some data regarding these twelve islands.

Population Density of an Island = The number of Vulcans living on the Island/The total land area of the Island (in km² )

Each of the twelve islands is given a Density Rating based on the criteria given below.

(i) The islands with Population Density of more than or equal to 10⁵ Vulcans/km² are given a Density Rating of 1.

(ii) The islands with Population Density of more than or equal to 10⁴ Vulcans/km² but less than 105 Vulcans/km2 are given a Density Rating of 2.

(iii) The islands with Population Density of less than 10⁴ Vulcans/km² are given a Density Rating of 3.

17. In how many islands is the Population Density more than 70,000 Vulcans/km²?

18. How many islands are given the Density Rating of 3?

19. The Population Density of how many islands is more than that of Gran?

20. For how many real values of ‘x’ is log_x log₄ log₃ log₉ 27^x2-2x+6 = 0?

21. The graph of ‘3 – x’ against ‘y + 5’ is as shown below. (All the graphs in this question are drawn to scale and the same scale has been used on each axis.)

Which of the following shows the graph of y against x?

22. The roots of x² + 3x + c = 0 are α and β while the roots of x² + 21x + d = 0 are β and γ. If α, β and γ are in Arithmetic Progression, then what is the value of c/d?

23. Arjun and Bheem are standing at point A on a circular track with circumference 300 m. Cherry is standing at point B which is diametrically opposite point A on the track. All three of them start running simultaneously on the track; Arjun and Cherry run in clockwise direction at 3 m/s and 4 m/s respectively while Bheem runs in anticlockwise direction at 5 m/s. After how much time from the start will Cherry be equidistant from Arjun and Bheem for the first time?

24. The question given below is followed by two statements, A and B. Mark the answer using the following instructions:

Mark (a) if the question cannot be answered even by using both the statements together.

Mark (b) if the question can be answered by using one of the statements alone, but cannot be answered by using the other statement alone.

Mark (c) if the question can be answered by using either statement alone.

Mark (d) if the question can be answered by using both the statements together, but cannot be answered by using either statement alone.

Q. At the time of Shyam’s birth, the difference between the ages of his mother and his only sister Leela was equal to the difference between the ages of his father and his mother. The present age of Shyam is the same as the age of his mother at the time of his birth. If Shyam’s father is older than Shyam’s mother, then what is the present age of Shyam’s father?

A. Shyam’s father is 40 years older than Leela.

B. Shyam’s mother was 20 years old when Leela was born.

25. How many numbers are there between 0 and 500 which when divided by 3, 4, 6 and 8 leave remainders 1, 2, 4 and 6 respectively?

26. In triangle ABC, AB = 4 cm, BC = 3 cm and AC = 5 cm. Points D and E are chosen on AB and AC respectively such that ∠BDC = ∠ACBand ∠BEC = ∠ABC. What is AD/AE ?

Directions for questions 27 to 29: Answer the questions on the basis of the information given below.

Bell Electronics sells only five products – Laptops, Desktops, Printers, Netbooks and Tablets. The pie chart given below shows the percentage contribution of each product in the total revenue of Rs. 500 crores generated by Bell Electronics in the fiscal year 2010-11.

For analysing the data, the fiscal year 2010-11 was divided into four quarters (Qtr) of three months each. The line graph given below shows the quarter-wise percentage break-up of the total revenue generated by each product in the fiscal year 2010-11.

27. Which product generated the maximum revenue in the 3^rd quarter of the fiscal year?

28. In which quarter was the revenue generated by Laptops equal to the revenue generated by Desktops?

29. What was the ratio of the revenue generated by Printers in the 2^nd quarter to the revenue generated by Laptops in the 4^th quarter?

30. How many four-digit even numbers are there which have 0 and 1 as two of the digits and the remaining two are distinct digits among 2, 4 and 6? 

31. A paragraph is given below from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way.

Take it from Jeff Gardner, who received an $11,000 bill from Verizon after spending four days in Jamaica. Before the trip, Mr. Gardner, who runs a fly-fishing business in Grayling, said he called Verizon to find out what it would cost to use his cell phone for calls and his wireless air card to check e-mail on his laptop while in the Caribbean. He said he was told that calls would be about $2 a minute and that there would be no extra charges for data as he was on an unlimited plan.

32. A paragraph is given below from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way.

The life of Man, viewed outwardly, is but a small thing in comparison with the forces of Nature. The slave is doomed to worship Time and Fate and Death, because they are greater than anything he finds in himself, and because all his thoughts are of things which they devour. But, great as they are, to think of them greatly, to feel their passionless splendor, is greater still. And such thought makes us free men; we no longer bow before the inevitable in Oriental subjection, but we absorb it, and make it a part of ourselves.

33. A paragraph is given below from which the last sentence has been deleted. From the given options, choose the one that completes the paragraph in the most appropriate way.

The moviemakers are getting top-level access to the most classified mission in history from an administration that has tried to throw more people in jail for leaking classified information than the Bush administration. It was clear that the White House had outsourced the job of manning up the president's image to Hollywood when Boal got welcomed to the upper echelons of the White House.

Directions for questions 34 to 37: The passage given below is followed by a set of four questions. Choose the most appropriate answer to each question.

One word is missing in the American debate over the debt crisis: austerity. It's a revealing absence. In spite of the vast deficit, and despite the U.S. being the home of individualism, no way is being offered for individuals to make a difference by changing their lifestyles.

In the U.K., we've become familiar with talk of the "new age of austerity." Politicians of both left and right use the expression to frame the narrative about the cuts we're now facing. While both sides "warn" about this coming era, austerity is not negative in the British psyche. Here, associations with wartime soften it. Austerity is associated with personal changes which benefited society and made sense to people who learned to tackle wastefulness, to "make do and mend." Long before the current cuts, austerity was making a comeback here, associated with the environmental issues of recycling, cutting consumption and reducing our carbon footprint. Indeed, the New Economics Foundation recently launched the New Home Front, arguing that wartime lifestyles are positive models for reducing our environmental impact. When we think growing our own vegetables, staycations rather than vacations, cycling rather than driving, it has a fashionable appeal.

Not so in the U.S. In the five months I spent there earlier this year, I never heard the word austerity in political discussion. The Republican discourse is all about how the government is spending too much. The government must tighten its belt. There was nothing about individuals living beyond their means.

Yet the U.S. deficit is founded on overconsumption, made possible by too much consumer credit and, less well recognised, too much environmental credit. In the current war of words in Congress, there are no references to the immoral lending that encouraged people who could not afford it to invest in the American dream. That's what led to the property crash and the financial crisis. That has disappeared totally from political argument. From individuals I heard nothing about the need for prosperous people to change their ways. There are, of course, many worthy "green shoots," such as the "locavore" movement or the "greening the campus" initiative at the university I was visiting, where a newly appointed sustainability officer tries to cut energy use. But people like him have their work cut out. The whole of the east coast and the rust belt
are vast, shocking landscapes to which many Americans seem oblivious.

This is a society which has lived not just beyond its economic means but beyond its environmental ones too as the hundreds of miles of abandoned buildings, abandoned cars, and endless highways bear witness to.

Yet the American dream survives. You're either in it, or out of it. Being out means destitution. Individual lifestyles are boom or bust. In the U.K. I know many people who reject consumerism, getting involved in poorly paid environmental or political work. We regard them as rather honourable. In the U.S., if you don't have money you don't count.

34. What is the central idea of the passage?

35. It can be inferred that the author approaches the lack of American austerity with

36. According to the passage, all of these are associated with the British sense of austerity except for

37. Which of the following cannot be inferred from the passage?

38. The question given below is followed by two statements, A and B. Mark the answer using the following instructions:

Mark (a) if the question can be answered by using Statement A alone, but cannot be answered by using Statement B alone.
Mark (b) if the question can be answered by using Statement B alone, but cannot be answered by using Statement A alone.
Mark (c) if the question can be answered by using either statement alone.
Mark (d) if the question cannot be answered even by using both the statements together.

Q. Ankit, Binay and Chintu have different ages and they play different sports among Cricket, Tennis and Football. The youngest among the three does not play Tennis. Chintu is not the oldest among the three. Who among the three plays Football?

A. Ankit plays Cricket.

B. Ankit is not the oldest among the three.

Directions for questions 39 and 40: Answer the questions on the basis of the information given below.

There are four friends – Akansh, Nakul, Phalguni and Sharad. Two of them were born in Delhi, one was born
in Mumbai and one was born in Kolkata. It is also known that:
(i) Nakul was not born in Mumbai.
(ii) Sharad was not born in Kolkata.
(iii) Phalguni and Akansh were born in different cities.
(iv) If Sharad was born in Mumbai then Akansh was not born in Kolkata.
(v) If Phalguni was born in Kolkata then Sharad was not born in Mumbai.
(vi) If Nakul was born in Kolkata then Akansh was not born in Delhi.
(vii) If Akansh was born in Kolkata then Sharad was not born in Delhi.
(viii) If Phalguni was born in Delhi then Akansh was not born in Mumbai.

39. In which city was Phalguni born?

40. In which city was Akansh born?

Directions for questions 41 and 42: The passage given below is followed by a set of two questions. Choose the most appropriate answer to each question.

In the story "Indian artists to boycott major show in Israel", my views have been presented in a way that completely belies my life-long career in art based on the conviction that art and politics (and most certainly culture and politics) are interlocked in complex ways. And that artists can make a significant contribution to ongoing history through protests, boycotts, refusals, and direct address within and beyond their art practice.

Some bare facts: I signed the Palestine Campaign for the Academic and Cultural Boycott of Israel in 2010, which makes my stand against the state of Israel/in support of the Palestinian cause, self-evident. Added to that, I am not invited to show in the forthcoming exhibition of Indian art in Tel Aviv, so there cannot be even a remote reason for me to renege or prevaricate on the issue of a boycott.

Even if artists who were invited by the curators did not refuse this invitation right away, a subsequent campaign could make them reflect on their decision. Pushpamala N.'s initiative could, and should, provoke artists to explore and extend and revise their political position and related action. Each one of us will respond to a greater or lesser degree to a historical moment, a place, a movement, to express our solidarity. But one does not need to recount at every point all the ills that beset the world's nation-states and thus cancel every political call on that basis.

I further believe that a political position of any complexity allows artists to use imaginative and intellectual resources in their mode of political intervention: protests and boycotts, open letters in the press, to the state, to the institution concerned, an artist's statement through the work and as a textual support to be displayed or published in the catalogue.

41. A suitable title to the passage would be

42. Which one of these has not been mentioned as a means by which art can contribute to politics?

43. Five sentences are given below, labeled A, B, C, D and E. They need to be arranged in a logical order to form a coherent paragraph/passage. From the given options, choose the most appropriate one.

A. The guy who is throwing out the garbage offers customers a cup of water.
B. It's not all those quirky British sandwiches, thin and understated with ingredients like free-range egg mayonnaise and avocado-and-pine-nut filling.
C. The manager swings by to commiserate about the sweltering weather.
D. No, it's the employees.
E. The cashier is asking New Yorkers how they are doing - and genuinely seems to want an answer.

44. Five sentences are given below, labeled A, B, C, D and E. They need to be arranged in a logical order to form a coherent paragraph/passage. From the given options, choose the most appropriate one.

A. If that is not enough to energize the White House, here are a few more facts.
B. For all of the talk of "big government," there is no way to cut that much in discretionary programs without crippling basic functions.
C. To avoid across-the-board cuts, Congress must enact at least another $1.2 trillion in deficit reduction measures over the 10 years.
D. Lawmakers could eliminate the Federal Bureau of Investigation, the Centers for Disease Control and Prevention, the National Institutes of Health and Head Start and still not cut $110 billion annually.
E. According to the latest CBS News Poll, 63 percent support raising taxes on households that earn more than $250,000 a year to help address the deficit.

45. There are two gaps in the sentence given below. From the pairs of words given, choose the one that fills the gaps most appropriately

Sure, at times we Indians get frustrated with the functioning of our ……… state and its …………. institutions, but it would be naïve to believe that we cherish our freedoms any less than someone living in a Western democracy.

Directions for questions 46 to 48: Answer the questions on the basis of the information given below.

Four security officers – Andrew, Joseph, Parry and Lucas – were responsible for guarding the Kohinoor diamond during a 1-day exhibition held recently. The exhibition started at 10 a.m. and finished at 5 p.m. The officers operated in 1-hour shifts and at least one officer guarded the diamond in each of the seven shifts. None of the officers operated in two consecutive shifts and none of them joined or left a shift midway.

It is also known that:

(i) Andrew operated in exactly four shifts.
(ii) Two officers were operating at 12:40 p.m. One of the two was Joseph.
(iii) Parry operated in exactly three shifts. He was operating at 01:20 p.m.
(iv) Lucas operated in exactly two shifts and he operated alone in both of them.
(v) Each of the four officers operated in at least two shifts. Joseph and Parry never operated together in any of the shifts.

46. In how many shifts did Joseph operate?

47. How many shifts were there in which just one of the four officers operated?

48. At what time did Joseph leave for his home if it is known that he left immediately after his last shift ended on the day of the exhibition?

49. The word given below has been used in sentences in four different ways. Choose the option corresponding to the sentence in which the usage of the word is incorrect or inappropriate.

Hack

(a) He has been hacking around all day and not studying for his exam.
(b) The US was alerted of a major terror strike after it hacked into the email account of a suspected terror group.
(c) His reputation was hacked for bits.
(d) The best way would be to hack up that piece of wood so it can fit in the truck.

50. The word given below has been used in sentences in four different ways. Choose the option corresponding to the sentence in which the usage of the word is incorrect or inappropriate.

Hang

(a) He hangs about with people much older than him.
(b) She has managed to hang it up and pull through despite all the challenges faced.
(c) He hung a left at the wrong corner.
(d) I need a career to hang my hat on.

51. The word given below has been used in sentences in four different ways. Choose the option corresponding to the sentence in which the usage of the word is incorrect or inappropriate. 

Opt

(a) Once you opt in for interiors in this design institute it will be difficult for you to change track later in your profession.
(b) MPs hoped to reverse Britain's opt-out from the treaty.
(c) After a few moments of indecision, he opted for the black car.
(d) When he realized the risks involved he decided to opt out of the chit fund.

52. The question given below is followed by two statements, A and B. Mark the answer using the following instructions:

Mark (a) if the question can be answered by using Statement A alone, but cannot be answered by using Statement B alone.
Mark (b) if the question can be answered by using Statement B alone, but cannot be answered by using Statement A alone.
Mark (c) if the question can be answered by using either statement alone.
Mark (d) if the question cannot be answered by any of the two statements.

Q. Four friends – Ram, Raheem, Shyam and Shameem – are standing in a row in the descending order of their heights, not necessarily in the given order. Raheem is standing adjacent to Shameem and Shyam is standing at one of the ends of the row. Who is the shortest among the four?

A. Shameem is shorter than Shyam and Ram is standing at one of the ends of the row.
B. Exactly one person is standing between Shyam and Shameem.

Directions for questions 53 to 55: The passage given below is followed by a set of three questions. Choose the most appropriate answer to each question.

Nevertheless, Dumont's magnum opus remains his Homo hierarchicus published in French in 1967 (1970 and 1972 for the English translations). It is an impressive  synthetic work with a strong theoretical background, in which the author presented his understanding of the Indian caste society as a whole. According to Dumont, people were ascribed an unequal status from birth and ranked from the Untouchables (who did not then call themselves Dalits) at the bottom to the Brahmins at the top according to the degree of purity attached to each caste collectively as well as to each individual.

After this publication, Dumont distanced himself from the sociology of India, feeling that he had achieved what he wanted to say on the caste system. He started a new field of research that dealt with the genesis of the modern individualism grounded on an egalitarian basis, which he contrasted with the inegalitarian caste system. It was the subject of his Homo aequalis (1977), followed by Essays on individualism (1983), and German Ideology: From France to Germany and Back (1991). However, these works belonged to the traditional history of political and philosophical ideas and have no empirical grounding.

Dumont's oeuvre has been discussed and debated by anthropologists in Europe as well as in India. His sociological interpretation of the caste system is both widely acclaimed and highly criticised. The most radical criticism emphasised that Dumont's brilliant analysis of the caste system is taken from a dominant internal viewpoint, whether from its priests (Brahmins) or its princes (Kshatriya), which is well expressed in and legitimised by the classical Sanskrit texts that Dumont widely used. From a sociological point of view,

however, scholars need to question, first, the social conditions of the production of these representations that cannot be taken for granted, and, second, their social usages. The relations of power and domination that structure the Hindu caste system, which are partly denied from a textual viewpoint (and this, of course, cannot be ignored), have to be clearly recognised and analysed. Furthermore, the comparative sociology that Dumont developed was quite often reduced to a binary opposition between individualism and holism, or to a radical confrontation between the equalitarian West and the hierarchical traditional premodern societies, like India, towards which the anthropologist publicly confessed to having a nostalgic inclination.

Nevertheless, the Indian part of his oeuvre stands for a rare coherent sociological enterprise that cannot be ignored or brushed away if one wants to understand the social making of contemporary India.

53. The style of the passage is

54. Which of the following can be inferred from the passage?

55. Which of the following can be inferred from the passage?

56. Given below are five sentences. Each sentence has a pair of words that are italicized. From the italicized words, select the most appropriate words (A or B) to form correct sentences. The sentences are followed by options that indicate the words, which may be selected to correctly complete the set of sentences. From the options given, choose the most appropriate one.

Secrecy enshrouded (A) / ensconced (B) the Party's central committee. 
As the tumour started spreading, his pain got excruciated (A) / exacerbated (B).
She titivated (A) / titillated (B) her hair in the mirror.
The workforce has been pared (A) / paired (B) to the bone.
I want Robert to evaluate the efficacy (A) / effeminacy (B) and safety of the treatment.

57. Given below are five sentences. Each sentence has a pair of words that are italicized. From the italicized words, select the most appropriate words (A or B) to form correct sentences. The sentences are followed by options that indicate the words, which may be selected to correctly complete the set of sentences. From the options given, choose the most appropriate one.

The Queen laid a wreathe (A) / wreath (B) at the war memorial.
After that lengthy exegesis (A) / exigency (B), it's unclear whether the skeptics are gilding the lily or
just protesting too much.
We went sailing on the secluded lake in a little two-person dingy (A) /dinghy (B).
How can we best understand and explicate (A) / expiate (B) 'King Lear'?
He enunciated (A) / emanated (B) his vision of the future.

Directions for questions 58 to 60: Answer the questions on the basis of the information given below.

Each of the five students – Ashish, Bimal, Coral, Disha and Eshan – gave a presentation on each of the five topics – Corruption, Terrorism, Globalisation, Human Cloning and Business & Ethics – in a week starting on Monday and ending on Friday. Exactly five presentations were given on each of the five days, no two of which were on the same topic. No student gave more than one presentation on any of the five days. It is also known that:

(i) Coral gave a presentation on Globalisation on Tuesday.
(ii) Eshan gave a presentation on Human Cloning on Monday.
(iii) Ashish gave a presentation on the same topic on Monday on which Disha gave a presentation on Friday. The topic was not Globalisation.
(iv) Bimal gave a presentation on Corruption, Terrorism and Human Cloning on Monday, Wednesday and Friday respectively.
(v) Disha gave a presentation on Business & Ethics on Wednesday. She didn’t give a presentation on Corruption on Thursday.
(vi) Coral gave a presentation on the same topic on Monday on which Ashish gave a presentation on Friday.

58. On which day of the week did Ashish give a presentation on Corruption?

59. On which topic did Eshan give a presentation on Thursday?

60. Which of the following statement(s) is/are correct?

I. Coral and Disha gave a presentation on Corruption on Friday and Tuesday respectively.

II. Ashish and Eshan gave a presentation on Human Cloning and Terrorism respectively on Tuesday.

Solutions

1. b

Let the regular hexagon be ABCDEF and the equilateral triangle be ACE. From the figure given below, it can be easily observed that the hexagon can be divided into 6 congruent triangles.

We have, AB = BC = OC = OA and AC is common in the triangle ABC and the triangle AOC. Hence the triangle ABC is congruent to the triangle AOC.

Let the area of triangle ABC be a unit². Required ratio = 3a : 6a = 1 : 2.

2. d

Let “x R, y B” denote x Red and y Blue faces such that x + y = 6.

I. “6 R, 0 B” and “0 R, 6 B”:

Only 1 such case is possible for each.

Hence, total 2 possibilities.

II. “5 R, 1 B” and “1 R, 5 B”:

Only 1 such case is possible for each.

Hence, total 2 possibilities.

III. “4 R, 2 B” and “2 R, 4 B”:

In “4 R, 2 B”, the two blue faces are either adjacent or not. So 2 such cases are possible for each. Hence, total 4 possibilities.

IV. “3 R, 3 B”:

One case is when the three blue faces are adjacent to one another. The other case is when one blue face is adjacent to the other two but the other two are not adjacent to each other. Hence, total 2 possibilities.

Total possibilities = 2 + 2 + 4 + 2 = 10.

3. d

Sum of the squares of first n natural numbers

= (n(n+1)(2n+1))/6

By substitution we can see that

1 + 2² + 3² + 4² + … + 16² = 1496.

As 1496 – 64 = 1432, the number whose square was erased must be 8.

4. c

Let c = 8k. Hence, b = 8(k + 1) and a = 8(k + 2), where k is a natural number.

As the H.C.F. of ‘k’, ‘k + 1’ and ‘k + 2’ is always 1, we can say that the L.C.M. of ‘k’, ‘k + 1’ and ‘k + 2’ will be

k (k + 1)(k + 2), when k is odd, and

(k (k + 1)(k + 2))/2 when k is even.

The L.C.M. of a, b and c is either 8k (k +1)(k + 2) or 4k (k + 1)(k + 2).

L.C.M < 10000 (given)

For highest value of k we’ll take 4k(k+1)(k+2) < 10000, where k is even.

Hence, k(k + 1)(k + 2) < 2500.

The maximum possible value of k = 12.

The maximum possible value of c = 96.

For questions 5 and 6:

Let the total number of females in Noland be 100Y.
Therefore, the total number of males in Noland = 120Y.
Total Urban population of Noland = Total Rural population of
Noland = 110Y.
The number of literate females in Noland = 80% of 100Y = 80Y
The number of illiterate females in Noland = 100Y – 80Y = 20Y
The number of literate males in Noland = 4 × 20Y = 80Y
The number of illiterate males in Noland = 120Y – 80Y = 40Y
The number of illiterate people in Rural Noland

= 2/3 (20Y + 40Y) = 40Y

The number of illiterate people in Urban Noland = 60Y – 40Y = 20Y

Further analysis leads to the table given below.

L = Literate, I = Illiterate.

5. c

The number of literate males in Rural Noland = 50Y.

The total number of females in Urban Noland  = 60Y + 10Y = 70Y.

Hence, the answer = 50Y : 70Y = 5 : 7.

6. c

Given: 60Y – 20Y = 1000.

Hence, Y = 25 and 220Y = 5,500.

7. b

Let’s assume that the job consists of 120 (L.C.M. of 20, 30 and 40) units of work.

Therefore, Ashish, Binay and Joseph can do 6, 4 and 3 units of work respectively in a day.

If the job took x days to complete, Ashish, Binay and Joseph worked for x – 4, x – 3, and x days respectively.

Hence, 6(x – 4) + 4(x – 3) + 3x = 120.

⇒ x = 12.

8. b

Let the Selling Price of a copy of A, B and C be 2x, 3x and 4x respectively.

Let the Cost Price of a copy of A, B and C be CA, CB and C_C respectively.

Let the number of copies of A, B and C sold on that Sunday be a, b and c respectively.

Hence, 

9. a

There are 10 places in all from which 3 places are to be selected for E, A and O and their order is already fixed. So this can be done in 10C3 ways. The remaining seven letters M, L, N, C, H, L and Y can be arranged in

the remaining 7 places in 7!/2! Ways.

Hence, the answer = ¹⁰C₃ X 7!/2! = 10!/3!2!

10. d

To find the sum of all the coefficients we can put x = 1 in the given polynomial.

Sum of the coefficients = (1 – 1)⁶(1 – 2)⁴ + (1 – 2)⁵ (1 + 1)⁶ + (1 + 1)²(1 + 2)³

= 0 – 64 + 108 = 44.

11. c

Note: All dimensions are in cm.

Construction: Extend AC to meet the circle at E.

Draw perpendicular bisectors OG and OF on chords AE and BD respectively.

Given, AC = 4 and BC = 12.

Let DC = 2x.

Now, AC × CE = BC × CD or 4 × CE = 12 × 2x.

Hence, CE = 6x.

AE = AC + CE = 4 + 6x

EG = AE/2 = 2 + 3x

BD = BC + CD = 12 + 2x and CF = OG = BD/2 - CD  = 6 – x.

As OG is perpendicular to AE, in right triangle EGO:

EG² + OG² = EO²

⇒ (2 + 3x)² + (6 – x)² = 8²
⇒ (4 + 9x² + 12x)+ (36 + x² − 12x) = 64
⇒10x² + 40 = 64

⇒ x = √(12/5)

Hence, CD = 2x = 2√(12/5) cm.

12. d

The first common term of the two sequences is 28. As the common difference of the two sequences are 6 and 5 respectively, we can say that any number of the form ‘30n – 2’, where n is a natural number, will be common to both the sequences. The maximum possible value of such common term will be 30 × 18 – 2 = 540 – 2 = 538. Hence, the number of common terms in S₁ and S₂ is 18.

13. a

Let the Cost of 1 m of the cloth be Rs. 100x. Marked Price of 1 m of cloth

= Rs. 100(1 + 30/100) x = Rs. 130x.

Selling Price of 1 m of cloth (as measured by the scale) after 20% discount

= Rs. 130 (1 - 20/100)x = Rs. 104x.

The merchant is actually giving just 1(1- 10/100) = 0.9m of cloth due to shrinkage of the meter-scale and claiming money for 1 m of cloth.

Cost of 1 m of cloth (as measured by the scale in winter) = Cost of 0.9 m of cloth

= Rs. 0.9×100x = Rs. 90x.

Profit percentage earned by the merchant

= (104x - 90x)/90x = 15.56%.

14. d

From Statement A: The statement cannot be true as the midpoint of (2, 5) and (–10, 21) is (–4, 13). The three points are collinear and a circle cannot pass through three collinear points. So the statement is false and hence cannot help in finding the equation of the circle.

From Statement B: The distance between (2, 5) and (–4, 13) is 10 units which is less than the length of the diameter i.e. 12 units. Hence, two such circles are possible. So we cannot find a unique equation of the circle using this statement.

Note: The number of possible circles with a fixed radius and passing through two fixed points is 2 unless the distance between the two points is equal to the diameter of the circle. The following figure illustrates
this:

AB < Diameter

Hence, the question cannot be answered by any of the two statements.

15. d

If we place D at some position then the position of E will be automatically fixed. B can be placed on either side of D. So we need to select one position out of these two for B. The remaining three positions can be filled by A, C and F in 3! ways.

The total number of ways = 2 × 3! = 12.

16. b

For the highest possible value of integer ‘x’ which satisfies the given inequality, say ^xmax^, all the modulus brackets will open with a positive sign i.e. |x – 1| > 0, ||x – 1| – 2| > 0, |||x – 1| – 2| – 3| > 0 etc.

When all the brackets open with a positive sign, x – 1 – 2 – 3 – 4 < 5 or x < 15 or x_max = 14.

For questions 17 to 19:

The table given below shows the Population Density and the Density Rating of the twelve islands.

17. d

Four islands – Andorian, Bajoran, Chronian and Delvian.

18.b

Two islands – Elerian and Furon.

19.a

Five islands – Andorian, Bajoran, Chronian, Delvian and Halosian.

20.a

log_x log₄ log₃ log₉ 27^x2-2x+6 = 0

=> log₄ log₃ log₉ 27^x2-2x+6 = 1

=>log₃ log₉ 27^x2-2x+6 = 4

=> log₉ 27^x2-2x+6 = 3⁴ = 81

=> 27^{x2-2x+6  = 9}81

=> 3^{3(x2 2x} 6) = 3¹⁶²
⇒ x² − 2x + 6 = 54
⇒ x² − 2x − 48 = 0
⇒(x − 8)(x + 6) = 0
⇒ x = −6 or 8.

But x cannot be equal to –6 as x > 0. Hence, x = 8 is the only real solution of the equation.

21. c

The given graph must be of an equation of type

(3 - x)/(y+5) = -(1/k)

y + 5 = kx – 3k

y = kx – (3k + 5)

This is the equation of a line in the x-y plane, whose slope (k) is greater than zero and it has a negative intercept (of length 3k + 5) on the y-axis. Only one graph satisfies the condition.

22. c

α + β = −3 and β + γ = −21.

Adding the above two equations we get:
α + 2β + γ = −24.

Also, α + γ = 2β.

(
α, β & γare in A.P.)

Solving the above two equations we get β = –6.

Substituting β = –6 in the given quadratic equations,

we get c = –18 and d = 90.

=> c/d = -(1/5)

23. b

We can say that the midpoint of Arjun and Bheem is moving in anticlockwise direction at (5 - 3)/2 1m/s.

The first occasion when Cherry is equidistant from Arjun and Bheem will be when Cherry reaches this midpoint (as Arjun and Bheem are equidistant from the midpoint, they would automatically be equidistant form Cherry as well).

The time taken by Cherry to reach the midpoint

= (circumference/2) /speed of Cherry speed at which = 150/(4 + 1) = 30s.

24. a

Let the present ages (in years) of Shyam, his father, his sister Leela and his mother be S, F, L and M respectively.

M – L = F – M or 2M = L + F

Also, M = 2S.                            …(i)

Hence, 4S = L + F.                   …(ii)

From Statement A:

F – L = 40.

Combining the above equation with (ii) we get,

4S = 2F – 40.

But as S is not known, we cannot find F.

Statement A alone is not sufficient to answer.

From Statement B:

M – L = 20.

Hence F – M = F – (L + 20) = 20 or F – L = 40.

Statement B is identical to Statement A and is not sufficient to answer.

As the two statements give the same information, the question cannot be answered even by using both the statements together.

25. b

L.C.M. of 3, 4, 6 and 8 is 24.

Each remainder left on division is 2 less than the divisor. So if k is a divisor then the dividend must be of the type nk – 2 where n is a natural number. To satisfy the condition for all the four divisors we have to consider
L.C.M. of 3, 4, 6 and 8 in place of nk. So the smallest such number = 24 – 2 = 22. The next number will be 22 + L.C.M. (2, 4, 6 and 8) = 22 + 24 = 46.

A general expression for any number N satisfying the given condition is N = 24k – 2.

If 0 < N < 500, then N can be:

22, 46, 70,... 478.

As 478 = 24 × 20 – 2, the answer is 20.

26. b

For questions 27 to 29:

The data given in the pie chart and the line graph can be used to tabulate the revenue generated by each product in each of the four quarters of the fiscal year 2010-11 as shown below.

27. d

Tablets

28. a

1st quarter

29. b

2 : 3

30. a

Suppose we do not select digit 6 and the four digits are 2, 4, 0 and 1.

CASE I. When digit 1 is at the thousands place:

The digit 0 can be placed at any position.

Total such numbers = 1 × 3 × 2 × 1 = 6.

CASE II. When digit 1 is not at the thousands place:

Possible positions for the digit 1 = 2.

Possible positions for the digit 0, once the digit 1 has been fixed = 2.

Now digits 2 and 4 can be placed at the remaining two positions in 2 ways.

Total such numbers = 2 × 2 × 2 = 8.

Adding the above two cases, there are 14 such numbers.

Similarly, we will get 28 more such numbers when instead of 2 and 4 the digits selected are either 2 and 6 or 4 and 6.

Hence, the answer = 14 × 3 = 42.

31. d

There is a clear logical ending to the paragraph, as it starts with the fact that Mr. Gardner received a bill of $11,000 from Verizon. Option (d) concludes the information in the paragraph. Option (a) is incorrect as it in the second person while the paragraph is in the third person. Option (b) ends with general information while the paragraph is about Mr. Gardner. Option (c) brings in inconsequential data and it cannot be determined if this is negative or positive in context.

32. b

The paragraph discusses man’s life and the thoughts through which he can be freed. Option (b) completes the flow of the passage by referring to liberation and thought. Option (a) can be ruled out as it an imperative sentence and does not match with the tone of the paragraph. (An imperative sentence is a sentence which gives command, makes a request
or expresses a wish).

Examples:

Go to your room. (an order)
Please lend me your book. (a request)
Have a good time at the picnic. (a wish)
Option (c) is incorrect as it refers to a divine fire – there is no mention of a spiritual context in the paragraph. The paragraph ends in the first person, whereas option (c) refers to the spark being kindled in the hearts of others. This does not go with the logical flow of the paragraph. Option (d) is incorrect as it has a negative tone, whereas the paragraph moves towards a positive tone.

33. b

The paragraph discusses the boost that is being planned for the President’s image – the use of the movie medium. Option (a) is incorrect as it refers to Sony and the president’s gutsy decision and both of these are not referred to in the paragraph. Option (b) is the answer as it supports the information in the passage and clarifies how a movie will help boost the president’s image. Option (c) is incorrect as it refers to the campaign and there is no basis for this inference. Option (d) is abstract and does not help to conclude the information in the paragraph.

34. a

The last line of the first paragraph emphasizes on the need for American individuals to change their lifestyle. The next paragraph discusses the need for austerity measures and also compares the American attitude to the British attitude. The author again returns to a comparison with the British in the last two sentences. Option (a) is correct. Option (d) can be ruled out because the author never mentions individualistic/ unique austerity measures.

35. c

It is clear from the beginning of the passage that the author speaks of the lack of austerity measures among the Americans with a negative tone. However, there is no dislike or scorn in the way he writes. Hence, option (a) is ruled out. Option (b) indicates an arrogant or patronizing attitude. Again, this can’t be inferred from the passage. It is true that the author lauds Britain’s austerity measures but he does not look down on the American’s lack of measures. He instead criticizes it because he feels it has been costly for the American’s. Option (c) is the answer. Option (d) is very negative and indicates that the author has lost hope of the American’s ever implementing austerity measures. However, this has also not been indicated in the passage.

36. a

Options (b), (c) and (d) are mentioned in the second paragraph. However, option (a) cannot be inferred. In the last paragraph, the author mentions that he knows “many people who reject consumerism, getting involved in poorly paid environmental or political work.” However, this can’t be inferred as option (a) – it generalizes the author’s opinion.

37. d

The fourth and fifth paragraphs have the answer to his question. The second half of the fourth paragraph reflects the author’s concern for the way the Americans have misused their environmental resources. Options (a) has been mentioned in the fifth paragraph. Option (c) has been mentioned in the fourth paragraph. There is no direct mention of option (b) but
it can be inferred from the second half of the fourth paragraph. Thus, option (a), (b) and (c) can be inferred from the passage. Hence, option (d) is the correct option.

38. d

From Statement A :

Either Binay or Chintu plays Football. Several cases are possible, two of which are given below :

Hence, Statement A alone is not sufficient to answer.

From Statement B:

The statement only indicates that Binay is the oldest among the three, which is not sufficient to answer.

From Statements A and B:

Either Binay or Chintu plays Football. Three cases are possible as shown below.

Hence, the question cannot be answered even by using both the statements together.

For questions 39 and 40 :

Let Akansh, Nakul, Phalguni and Sharad be represented by A, N, P and S respectively.

On the basis of statements (i), (ii) and (iii) the following six cases (I to VI) are possible.

Statements (iv), (v), (vi), (vii) and (viii) contradict cases IV, III, V, II and VI respectively.

Only case I is feasible and so it is the correct arrangement.

39. c

Kolkata

40.b

Mumbai

41.d

The last line of the first paragraph indicates the central idea of the passage and points towards art’s contribution to politics. Option (d) is the answer. Option (a) is incorrect as the emergence of art and politics has not been discussed in the passage. Option (b) is also incorrect as the passage only states that art and politics are interlocked in complex ways. But, this cannot be inferred as a mutually beneficial relationship – a symbiosis. Option (c) is incorrect as art and politics are not merged or do not become one entity.

42.c

Options (a) and (d) have been mentioned in the last line of the passage. Option (b) can be inferred from the second paragraph. However, option (c) cannot be inferred. It also goes against the information in the passage – against the discussion of art’s contribution to politics. The author has mentioned boycott of those political events where the ideology does not match that of the artist’s. However, option (c) has incorrectly generalized the author’s statement.

43.d

There is a strong link between B and D. This link helps rule out option (b). A, C and E are all specific statements with examples related to the employees. The choice between a specific to general or a general to specific leads one to the correct answer. Options (a) and (c) allow a choice that is specific to general, albeit one that is disjointed with the appearance of BD at the end of the sequence. The correct answer is option (d) as it starts with BD and EAC are a substantiation of the assertion in D.

44. b

There is a CBD link. C sets the standard in deficit reduction. B asserts that there is no way to cut out discretionary programs and still not cripple basic functions. D goes on to substantiate B by discussing that even by cutting down a few programs, Congress would not cut even $110 billion annually. It is also clear that before A there must be another statement to establish the need for Congress to act. Hence, E comes before A. The answer is option (b).

45. b

The tone of the author while describing the state and its institutions is negative. Both the words need to complement each other and deliver a logical meaning. ‘Callous’ means  insensitive, indifferent or unconcerned and ‘wobbly’ means weak and unstable. The state has become callous towards the needs and problems of the Indians and its institutions have become weak and infirm which causes frustration among Indians but they cherish their freedom. Option (b) clearly brings out the meaning of the sentence. ‘Amoral’ and ‘apathetic’ appear to be suitable for the first blank. But both options (a) and (c) are incorrect due to the second words paroxysmal and vacillating respectively. ‘Paroxysmal’ means characterized by a sudden strong feeling or expression that is difficult to control. ‘Vacillating’ means to keep changing your opinion or thoughts about something. Hence, options (a) and (c) are negated. Option (d) is irrelevant as the word ‘ribald’ means characterized by coarse indecent humour.

For questions 46 to 48 :

Let Andrew, Joseph, Parry and Lucas be represented by A, J, P and L respectively. Let the shifts be called 1st to 7th (in the order of their occurrence).

From statement (i), it can be concluded that A operated in the 1st, 3rd, 5th and 7th shifts.

From statement (ii), it can be concluded that J operated along with A in the 3rd shift.

From statement (iii), it can be concluded that P operated in the 4th shift.

From statement (iv), it can be concluded that the two shifts in which L operated were 2nd and 6th. Hence, P operated in the 1st and 7th shifts.

From statement (v), it can be concluded that J operated in the 5th shift along with A.

The conclusions made thus far can be shown as given below.

46. b

2

47. b

3

48. a

3 p.m.

49. c

Hacked to bits is the correct phrase and means severely damaged. Hence, option (c) is incorrect. To hack around means to waste time. Hence, option (a) is correct. To hack into means to break into a computer system. Hence, option (b) is correct. Hack up means to chop or cut into small pieces. So option (d) is correct.

50. b

To hang about/around is to spend time somewhere not doing much. Hence, (a) is correct. To hang it up means to resign or quit. So (b) is incorrect. The correct idiom is to hang in there which means to persevere and not give up. Hang a left or right means to take a left or right turn. Hence, (c) is correct. Hang one’s hat  means 1: to situate oneself in (as a residence or place of employment) or 2: to have or use as a source of support . Hence, (d) is correct.

51. a

Opt in for is not grammatically correct. The correct phrase is opt for which means to choose. To opt in is to choose to be part or a member of something. Optout is a noun. It means the act of choosing not to be involved in an agreement. Opt for or against means to choose to take or not to take a particular course of action. To opt out means to choose not to be part of
something. The answer is option (a).

52. a

Shyam is standing at one of the ends of the row. Hence, it can be concluded that Shyam is either the shortest or the tallest among the four.

From Statement A:

Since Shameem is shorter than Shyam, it means that Shyam is not the shortest and so he is the tallest among the four. Ram being at the other end of the row, must be the shortest among the four.

From Statement B:

The statement alone is not sufficient to answer.

53. c

The author starts with a discussion on Dumont’s magnum opus, analyses this publication and then moves on to the analyses of his other publication. In the third paragraph, the author presents other opinions and then also presents his opinion. He takes facts and uses them to arrive at an understanding. These are all elements of the analytical style. Option (c) is the
answer. Option (a) is incorrect as discursive style would indicate that the author is attempting to explain something to the reader – this is clearly not the case in the passage. Option (b) is incorrect because there is no narration of events in a sequential manner – there is a reference to dates but these are only part of the process of analysis that the author goes through. A
theoretical style would have used academic references. It would have also used hypothetical frameworks and would have fitted in if the author were trying to explain an ongoing research procedure or study. However, the passage is concerned more with Dumont and his treatment and ideology as opposed to a particular research.

54. c

The passage never reveals Dumont’s personal opinion of the caste system in India. The last line of the penultimate paragraph does state that Dumont confessed to “a nostalgic inclination towards hierarchical traditional pre-modern societies.” However this cannot be read as support for the caste system in India. The line has been written in context of
the style that Dumont developed in comparative sociology. And there is ambiguity as to whether the nostalgic inclination he felt was an inclination to write/ research on the subject matter itself or his individual support for the subject matter. Option (c) can be inferred because it is mentioned in the passage.

55. b

‘Deliberation’ refers to the process of carefully considering or discussing something; a discussion and consideration by a group of persons (as a jury or legislature) of the reasons for and against a measure. Option (b) brings out the information that the author presents in the passage. Refer to the first line of the third paragraph “Dumont’s oeuvre has been discussed
and debated by anthropologists in Europe as well as in India. His sociological interpretation of the caste system is both widely acclaimed and highly criticized”. Hence, option (b) is the correct answer. Option (a) can be ruled out as it does not correctly describe the reception to Dumont’s work. Option (c) cannot be inferred as it goes against the information in the first line of the second paragraph. The tone of option (d) is too positive to match the tone of the author.

56. b

ABAAA

‘Enshroud’ means to cover or surround something completely so that it cannot be seen or understood. If you are ensconced or ensconce yourself somewhere, you are made or make yourself comfortable and safe in that place or position. So ‘enshrouded’ is the apt word for the first sentence. ‘Excruciate’ means to inflict intense pain on; torture, to subject to intense
mental distress. For example: She has long been excruciated by a persistent pain in her knee. Pain cannot excruciate, this construction is grammatically incorrect. On the other hand, ‘exacerbated’ which means worsened is appropriate in the given context. ‘Titivate’ means improve the appearance of somebody/ something by making small changes whereas ‘titillate’
means to interest or excite somebody. Hence, ‘titivate’ is appropriate for the third sentence. ‘Pared to the bone’ means to be reduced to the lowest possible level. ‘Pair’ means to put people or things into groups of two. ‘Efficacy’ means the ability of something, especially a drug or a medical treatment, to produce the results that are wanted; effectiveness. ‘Effeminacy’ refers to the quality or trait of looking, behaving or sounding like a female.

57. c

BABAA

‘Wreathe’ is a verb and it means to surround or cover something. ‘Wreath’ is a noun and it refers to an arrangement of flowers and leaves, especially in the shape of a circle, placed on graves, etc. as a sign of respect for somebody who has died. So, ‘wreath’ (B) is apt for the first sentence. ‘Exegesis’ is a noun and refers to the detailed explanation of a piece of writing,
especially religious writing. ‘Exigency’ is also a noun and it means an urgent need or demand that you must deal with. The modifier ‘lengthy’ suggests ‘exegesis’ to be the apt word. ‘Dingy’ is an adjective and means dark and dirty. On the other hand ‘dinghy’ is a noun and refers to a small open boat that one sails or rows. So, ‘dinghy’ is the apt word for the third sentence. ‘Explicate’ means to explain an idea or a work of literature in a lot of detail. ‘Expiate’ means to accept punishment for something that you have done wrong in order to show that you are sorry. So ‘explicate’ is the apt word for the fourth sentence. ‘Enunciate’ means to express an idea clearly and exactly whereas emanate means to produce or show something; to come out from a source < a sweet scent emanating from the blossoms > , < He emanates power and confidence > , < The sound of loud music emanated from
the building > . Hence, in the given context, ‘enunciated’ is the apt word for the fifth sentence.

For questions 58 to 60:

Let Ashish, Bimal, Coral, Disha and Eshan be represented by A, B, C, D and E respectively.

After filling up the initial data, it can be concluded that B gave a presentation on Business & Ethics and Globalisation on Tuesday and Thursday respectively.

The topic on which A and D gave a presentation on Monday and Friday respectively was not among Corruption, Human Cloning, Business & Ethics and Globalisation. Therefore, from statement (iii), A and D gave a presentation on Terrorism on Monday and Friday respectively. Similarly, from statement (vi), C and A gave a presentation on Business & Ethics on Monday and Friday respectively.

Therefore, D gave a presentation on Globalisation on Monday and from statement (v), D gave a presentation on Corruption and Human Cloning on Tuesday and Thursday respectively.
Further analysis leads to the final table as given below.

58. c

Thursday

59. a

Business & Ethics

60. c

Both I and II