CAT Mock Test - 20


53 Questions MCQ Test CAT Mock Test Series 2020 | CAT Mock Test - 20


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This mock test of CAT Mock Test - 20 for CAT helps you for every CAT entrance exam. This contains 53 Multiple Choice Questions for CAT CAT Mock Test - 20 (mcq) to study with solutions a complete question bank. The solved questions answers in this CAT Mock Test - 20 quiz give you a good mix of easy questions and tough questions. CAT students definitely take this CAT Mock Test - 20 exercise for a better result in the exam. You can find other CAT Mock Test - 20 extra questions, long questions & short questions for CAT on EduRev as well by searching above.
QUESTION: 1

The attempt to conceive imaginatively a better ordering of human society than the destructive and cruel chaos in which mankind has hitherto existed is by no means modern: it is at least as old as Plato, whose ``Republic'' set the model for the Utopias of subsequent philosophers. Whoever contemplates the world in the light of an ideal—whether what he seeks be intellect, or art, or love, or simple happiness, or all together—must feel a great sorrow in the evils that men needlessly allow to continue, and—if he be a man of force and vital energy—an urgent desire to lead men to the realization of the good which inspires his creative vision. It is this desire which has been the primary force moving the pioneers of Socialism and Anarchism, as it moved the inventors of ideal commonwealths in the past. In this there is nothing new. What is new in Socialism and Anarchism, is that close relation of the ideal to the present sufferings of men, which has enabled powerful political movements to grow out of the hopes of solitary thinkers. It is this that makes Socialism and Anarchism important and it is this that makes them dangerous to those who batten, consciously or unconsciously upon the evils of our present order of society.
 
The great majority of men and women, in ordinary times, pass through life without ever contemplating or criticising, as a whole, either their own conditions or those of the world at large. They find themselves born into a certain place in society, and they accept what each day brings forth, without any effort of thought beyond what the immediate present requires. Almost as instinctively as the beasts of the field, they seek the satisfaction of the needs of the moment, without much forethought, and without considering that by sufficient effort the whole conditions of their lives could be changed. A certain percentage, guided by personal ambition, make the effort of thought and will which is necessary to place themselves among the more fortunate members of the community; but very few among these are seriously concerned to secure for all the advantages which they seek for themselves. It is only a few rare and exceptional men who have that kind of love toward mankind at large that makes them unable to endure patiently the general mass of evil and suffering, regardless of any relation it may have to their own lives. These few, driven by sympathetic pain, will seek, first in thought and then in action, for some way of escape, some new system of society by which life may become richer, more full of joy and less full of preventable evils than it is at present. But in the past such men have, as a rule, failed to interest the very victims of the injustices which they wished to remedy. The more unfortunate sections of the population have been ignorant, apathetic from excess of toil and weariness, timorous through the imminent danger of immediate punishment by the holders of power, and morally unreliable owing to the loss of self-respect resulting from their degradation. To create among such classes any conscious, deliberate effort after general amelioration might have seemed a hopeless task, and indeed in the past it has generally proved so. But the modern world, by the increase of education and the rise in the standard of comfort among wage-earners, has produced new conditions, more favorable than ever before to the demand for radical reconstruction. It is above all the Socialists, and in a lesser degree the Anarchists, who have become the exponents of this demand.
 
 
What is perhaps most remarkable in regard to both Socialism and Anarchism is the association of a widespread popular movement with ideals for a better world. The ideals have been elaborated, in the first instance, by solitary writers of books, and yet powerful sections of the wage-earning classes have accepted them as their guide in the practical affairs of the world. In regard to Socialism this is evident; but in regard to Anarchism it is only true with some qualification.
 
excerpted from ''proposed road to freedom'' by Bertand Russel
 
According to the information provided in the passage, men can be classified :
           
I. as timid followers
II. as altruistic iconoclasts
III. as self-interested savants
IV. as learned self-seekers
 

Solution:
In the second paragraph of the passage, the author portrays men in different lights. Let’s analyze all the choices given to us:
as timid followers: people happy to follow the current system of functioning
as altruistic iconoclasts: men who are willing to go against conventional systems for the good of others.
as self-interested savants: this is not implied in the passage as nowhere does he refer to selfish individual as savants (Someone who has been admitted to membership in a scholarly field).
as learned self-seekers: as selfish individuals only seeking their own gain
Thus, option 4 is the correct choice. 
QUESTION: 2

Figure 1
Figure 2
 
 
What is the ratio of the total voters of Maharashtra to the total voters of CPI (M)? Given that total number of voters in Maharashtra is 1,530,200 and the total number of voters of CPI in India is 47,022.

Solution:
Using Figure 1 alone,
The total number of voters of CPI = 47022
So total voters in India = (47022 � 100)/ 3 = 1,567,400
Total number of voters in Maharashatra = 1,530,200
Total number of voters of CPI (M) = (8 � 1,567,400)/100 = 125,392
(Total of 1,567,400 has been calculated based on CPI's vote)
So the required ratio = 1,530,200 : 125,392
So Figure 1 alone is sufficient.
 
Using Figure 2 alone, 
Total no. of voters in Maharashatra = 1,530,200
But it does not provide information about the total number of voters of CPI (M). 
So, figure 2 is not sufficient. 
QUESTION: 3

The attempt to conceive imaginatively a better ordering of human society than the destructive and cruel chaos in which mankind has hitherto existed is by no means modern: it is at least as old as Plato, whose ``Republic'' set the model for the Utopias of subsequent philosophers. Whoever contemplates the world in the light of an ideal—whether what he seeks be intellect, or art, or love, or simple happiness, or all together—must feel a great sorrow in the evils that men needlessly allow to continue, and—if he be a man of force and vital energy—an urgent desire to lead men to the realization of the good which inspires his creative vision. It is this desire which has been the primary force moving the pioneers of Socialism and Anarchism, as it moved the inventors of ideal commonwealths in the past. In this there is nothing new. What is new in Socialism and Anarchism, is that close relation of the ideal to the present sufferings of men, which has enabled powerful political movements to grow out of the hopes of solitary thinkers. It is this that makes Socialism and Anarchism important and it is this that makes them dangerous to those who batten, consciously or unconsciously upon the evils of our present order of society.
 
The great majority of men and women, in ordinary times, pass through life without ever contemplating or criticising, as a whole, either their own conditions or those of the world at large. They find themselves born into a certain place in society, and they accept what each day brings forth, without any effort of thought beyond what the immediate present requires. Almost as instinctively as the beasts of the field, they seek the satisfaction of the needs of the moment, without much forethought, and without considering that by sufficient effort the whole conditions of their lives could be changed. A certain percentage, guided by personal ambition, make the effort of thought and will which is necessary to place themselves among the more fortunate members of the community; but very few among these are seriously concerned to secure for all the advantages which they seek for themselves. It is only a few rare and exceptional men who have that kind of love toward mankind at large that makes them unable to endure patiently the general mass of evil and suffering, regardless of any relation it may have to their own lives. These few, driven by sympathetic pain, will seek, first in thought and then in action, for some way of escape, some new system of society by which life may become richer, more full of joy and less full of preventable evils than it is at present. But in the past such men have, as a rule, failed to interest the very victims of the injustices which they wished to remedy. The more unfortunate sections of the population have been ignorant, apathetic from excess of toil and weariness, timorous through the imminent danger of immediate punishment by the holders of power, and morally unreliable owing to the loss of self-respect resulting from their degradation. To create among such classes any conscious, deliberate effort after general amelioration might have seemed a hopeless task, and indeed in the past it has generally proved so. But the modern world, by the increase of education and the rise in the standard of comfort among wage-earners, has produced new conditions, more favorable than ever before to the demand for radical reconstruction. It is above all the Socialists, and in a lesser degree the Anarchists, who have become the exponents of this demand.
 
What is perhaps most remarkable in regard to both Socialism and Anarchism is the association of a widespread popular movement with ideals for a better world. The ideals have been elaborated, in the first instance, by solitary writers of books, and yet powerful sections of the wage-earning classes have accepted them as their guide in the practical affairs of the world. In regard to Socialism this is evident; but in regard to Anarchism it is only true with some qualification.
 
excerpted from ''proposed road to freedom'' by Bertand Russel
 
If you were to ask one pertinent question to the author of the passage, what would it be?

Solution: This is a different question type that requires innovative thinking. First things first, what is the central idea of the passage? The passage revolves around Socialism and Anarchism for sure but at the core of the passage is the idea that human society is given to better ordering now, and things are slowly beginning to change, and a better human life and ideals have found acceptance. The next logical step would be with regards to these ideals being implemented on a larger scale for the betterment of human life and society. This thought process is reflected by option 3. The other options deflect from the central theme of the passage, and rather focus on Socialism/Anarchism instead. These are important but the central question is when they have a positive impact on human life.
QUESTION: 4
The attempt to conceive imaginatively a better ordering of human society than the destructive and cruel chaos in which mankind has hitherto existed is by no means modern: it is at least as old as Plato, whose ``Republic'' set the model for the Utopias of subsequent philosophers. Whoever contemplates the world in the light of an ideal—whether what he seeks be intellect, or art, or love, or simple happiness, or all together—must feel a great sorrow in the evils that men needlessly allow to continue, and—if he be a man of force and vital energy—an urgent desire to lead men to the realization of the good which inspires his creative vision. It is this desire which has been the primary force moving the pioneers of Socialism and Anarchism, as it moved the inventors of ideal commonwealths in the past. In this there is nothing new. What is new in Socialism and Anarchism, is that close relation of the ideal to the present sufferings of men, which has enabled powerful political movements to grow out of the hopes of solitary thinkers. It is this that makes Socialism and Anarchism important and it is this that makes them dangerous to those who batten, consciously or unconsciously upon the evils of our present order of society.
 
The great majority of men and women, in ordinary times, pass through life without ever contemplating or criticising, as a whole, either their own conditions or those of the world at large. They find themselves born into a certain place in society, and they accept what each day brings forth, without any effort of thought beyond what the immediate present requires. Almost as instinctively as the beasts of the field, they seek the satisfaction of the needs of the moment, without much forethought, and without considering that by sufficient effort the whole conditions of their lives could be changed. A certain percentage, guided by personal ambition, make the effort of thought and will which is necessary to place themselves among the more fortunate members of the community; but very few among these are seriously concerned to secure for all the advantages which they seek for themselves. It is only a few rare and exceptional men who have that kind of love toward mankind at large that makes them unable to endure patiently the general mass of evil and suffering, regardless of any relation it may have to their own lives. These few, driven by sympathetic pain, will seek, first in thought and then in action, for some way of escape, some new system of society by which life may become richer, more full of joy and less full of preventable evils than it is at present. But in the past such men have, as a rule, failed to interest the very victims of the injustices which they wished to remedy. The more unfortunate sections of the population have been ignorant, apathetic from excess of toil and weariness, timorous through the imminent danger of immediate punishment by the holders of power, and morally unreliable owing to the loss of self-respect resulting from their degradation. To create among such classes any conscious, deliberate effort after general amelioration might have seemed a hopeless task, and indeed in the past it has generally proved so. But the modern world, by the increase of education and the rise in the standard of comfort among wage-earners, has produced new conditions, more favorable than ever before to the demand for radical reconstruction. It is above all the Socialists, and in a lesser degree the Anarchists, who have become the exponents of this demand.
 
 
What is perhaps most remarkable in regard to both Socialism and Anarchism is the association of a widespread popular movement with ideals for a better world. The ideals have been elaborated, in the first instance, by solitary writers of books, and yet powerful sections of the wage-earning classes have accepted them as their guide in the practical affairs of the world. In regard to Socialism this is evident; but in regard to Anarchism it is only true with some qualification.
 
excerpted from ''proposed road to freedom'' by Bertand Russel
 
 
It can be inferred from the passage that Socialism and Anarchism pose a threat to:
Solution: The answer to this question can be directly inferred from the lines: It is this that makes Socialism and Anarchism important, and it is this that makes them dangerous to those who batten, consciously or unconsciously upon the evils of our present order of society.
QUESTION: 5
The attempt to conceive imaginatively a better ordering of human society than the destructive and cruel chaos in which mankind has hitherto existed is by no means modern: it is at least as old as Plato, whose ``Republic'' set the model for the Utopias of subsequent philosophers. Whoever contemplates the world in the light of an ideal—whether what he seeks be intellect, or art, or love, or simple happiness, or all together—must feel a great sorrow in the evils that men needlessly allow to continue, and—if he be a man of force and vital energy—an urgent desire to lead men to the realization of the good which inspires his creative vision. It is this desire which has been the primary force moving the pioneers of Socialism and Anarchism, as it moved the inventors of ideal commonwealths in the past. In this there is nothing new. What is new in Socialism and Anarchism, is that close relation of the ideal to the present sufferings of men, which has enabled powerful political movements to grow out of the hopes of solitary thinkers. It is this that makes Socialism and Anarchism important and it is this that makes them dangerous to those who batten, consciously or unconsciously upon the evils of our present order of society.
 
The great majority of men and women, in ordinary times, pass through life without ever contemplating or criticising, as a whole, either their own conditions or those of the world at large. They find themselves born into a certain place in society, and they accept what each day brings forth, without any effort of thought beyond what the immediate present requires. Almost as instinctively as the beasts of the field, they seek the satisfaction of the needs of the moment, without much forethought, and without considering that by sufficient effort the whole conditions of their lives could be changed. A certain percentage, guided by personal ambition, make the effort of thought and will which is necessary to place themselves among the more fortunate members of the community; but very few among these are seriously concerned to secure for all the advantages which they seek for themselves. It is only a few rare and exceptional men who have that kind of love toward mankind at large that makes them unable to endure patiently the general mass of evil and suffering, regardless of any relation it may have to their own lives. These few, driven by sympathetic pain, will seek, first in thought and then in action, for some way of escape, some new system of society by which life may become richer, more full of joy and less full of preventable evils than it is at present. But in the past such men have, as a rule, failed to interest the very victims of the injustices which they wished to remedy. The more unfortunate sections of the population have been ignorant, apathetic from excess of toil and weariness, timorous through the imminent danger of immediate punishment by the holders of power, and morally unreliable owing to the loss of self-respect resulting from their degradation. To create among such classes any conscious, deliberate effort after general amelioration might have seemed a hopeless task, and indeed in the past it has generally proved so. But the modern world, by the increase of education and the rise in the standard of comfort among wage-earners, has produced new conditions, more favorable than ever before to the demand for radical reconstruction. It is above all the Socialists, and in a lesser degree the Anarchists, who have become the exponents of this demand.
 
 
What is perhaps most remarkable in regard to both Socialism and Anarchism is the association of a widespread popular movement with ideals for a better world. The ideals have been elaborated, in the first instance, by solitary writers of books, and yet powerful sections of the wage-earning classes have accepted them as their guide in the practical affairs of the world. In regard to Socialism this is evident; but in regard to Anarchism it is only true with some qualification.
 
excerpted from ''proposed road to freedom'' by Bertand Russel
 
It can be inferred that hindrance(s) to the collective improvement of man was/were:
 
I. a weary population afraid of challenging established systems and viewpoints.
II. Basic poverty which made them focused only on their day to day survival.
III. low levels of education
 
Solution:
The answer for this question can be found in the parts highlighted below:  They find themselves born into a certain place in society, and they accept what each day brings forth, without any effort of thought beyond what the immediate present requires. Almost as instinctively as the beasts of the field, they seek the satisfaction of the needs of the moment, without much forethought, and without considering that by sufficient effort the whole conditions of their lives could be changed.   The more unfortunate sections of the population have been ignorant, apathetic from excess of toil and weariness, timorous through the imminent danger of immediate punishment by the holders of power, and morally unreliable owing to the loss of self-respect resulting from their degradation. To create among such classes any conscious, deliberate effort after general amelioration might have seemed a hopeless task, and indeed in the past it has generally proved so. But the modern world, by the increase of education and the rise in the standard of comfort among wage-earners, has produced new conditions, more favorable than ever before to the demand for radical reconstruction.
 
 
II and III are actually derivations from the last line highlighted above. Effectively, this line states the condition of the modern world, a condition which was not present previously and acted as a hindrance. Thus, option 3 is the correct answer in this case. 
 
QUESTION: 6
The most notable distinction between living and inanimate things is that the former maintain themselves by renewal. A stone when struck resists. If its resistance is greater than the force of the blow struck, it remains outwardly unchanged. Otherwise, it is shattered into smaller bits. Never does the stone attempt to react in such a way that it may maintain itself against the blow, much less so as to render the blow a contributing factor to its own continued action. While the living thing may easily be crushed by superior force, it none the less tries to turn the energies which act upon it into means of its own further existence. If it cannot do so, it does not just split into smaller pieces (at least in the higher forms of life), but loses its identity as a living thing.
 
As long as it endures, it struggles to use surrounding energies in its own behalf. It uses light, air, moisture, and the material of soil. To say that it uses them is to say that it turns them into means of its own conservation. As long as it is growing, the energy it expends in thus turning the environment to account is more than compensated for by the return it gets: it grows. Understanding the word "control" in this sense, it may be said that a living being is one that subjugates and controls for its own continued activity the energies that would otherwise use it up. Life is a self-renewing process through action upon the environment.
 
In all the higher forms this process cannot be kept up indefinitely. After a while they succumb; they die. The creature is not equal to the task of indefinite self-renewal. But continuity of the life process is not dependent upon the prolongation of the existence of any one individual. Reproduction of other forms of life goes on in continuous sequence. And though, as the geological record shows, not merely individuals but also species die out, the life process continues in increasingly complex forms. As some species die out, forms better adapted to utilize the obstacles against which they struggled in vain come into being. Continuity of life means continual readaptation of the environment to the needs of living organisms.
 
We have been speaking of life in its lowest terms—as a physical thing. But we use the word "Life" to denote the whole range of experience, individual and racial. When we see a book called the Life of Lincoln we do not expect to find within its covers a treatise on physiology. We look for an account of social antecedents; a description of early surroundings, of the conditions and occupation of the family; of the chief episodes in the development of character; of signal struggles and achievements; of the individual's hopes, tastes, joys and sufferings. In precisely similar fashion we speak of the life of a savage tribe, of the Athenian people, of the American nation. "Life" covers customs, institutions, beliefs, victories and defeats, recreations and occupations.
 
We employ the word "experience" in the same pregnant sense. And to it, as well as to life in the bare physiological sense, the principle of continuity through renewal applies. With the renewal of physical existence goes, in the case of human beings, the recreation of beliefs, ideals, hopes, happiness, misery, and practices. The continuity of any experience, through renewing of the social group, is a literal fact. Education, in its broadest sense, is the means of this social continuity of life. Every one of the constituent elements of a social group, in a modern city as in a savage tribe, is born immature, helpless, without language, beliefs, ideas, or social standards. Each individual, each unit who is the carrier of the life-experience of his group, in time passes away. Yet the life of the group goes on.
The definition of life for a lower and a higher form of being is:
Solution: From the given paragraph, the definition of life for a lower and a higher form of being is only fractionally related to each other. This is only so in the physical sense and in all other ways, the definition of life differentiates for the two.
QUESTION: 7
The humanities transmit, through time and across cultures, diverse expressions of the human condition, allowing us to contextualize, illuminate, and pass on an essential legacy of culture, history and heritage.
 
I believe that social media poses a grave threat to the humanities because it lacks the depth, nuance and permanence that make genuine, meaningful interactions about the human condition possible.  Everything that social media communication represents- immediacy, impermanence, collectivism- is contrary and harmful to the thoughtfulness, permanence and individualistic experiences necessary to humanities discourse. Social media is creating a hive mind, a group think that devalues the human condition in favor of the immediate, the marketable and the shallow. In social media, there is no difference between us and others; we look the same, we talk the same, we fill the same space. The real purpose of social media is to gauge measure and ultimately control the behavior of the crowd for marketing purposes. And as social media, and its values of pliable, identifiable collectives based on mutual interests, migrates from the Web to become more ubiquitous in our everyday lives--try attending a movie or buying a meal, the reductionist conversation that it engenders comes with it.
 
The first negative impact that social media has on the humanities is a multiple-choice format and physical structure that allows only for a very limited, narrow type of communication. There is no room for individual creativity or representation. Humanities also require background and context to impart ideas but social media is an equivalency and framework vacuum that decontextualizes and trivializes information in a way that renders it nearly meaningless. The brevity of communication through social media precludes explanation and circumstance.  Within social media, all information is equally important. There are no little or big facts; all data is expressed in compact bites of equal weight. The inability to separate the trivial from the significant leaves us unable to glean consequential substance from what we are saying to each other: the very purpose of the humanities. Lastly, social media creates and archives no history. The humanities are about expanding, describing, understanding and transmitting through the generations, the human condition. The purpose of social media is to understand ever larger groups of people at the expense of the individual. Humanities is exactly the opposite: understanding the individual for the sake of the masses.
 
As human beings, our only real method of connection is through authentic communication. Studies show that only 7% of communication is based on the written or verbal word. A whopping 93% is based on nonverbal body language. This is where social media gets dicey. Every relevant metric shows that we are interacting at breakneck speed and frequency through social media. But are we really communicating? With 93% of our communication context stripped away, we are now attempting to forge relationships and make decisions based on phrases, Abbreviations, Snippets, Emoticons, and which may or may not be accurate representations of the truth. In an ironic twist, social media has the potential to make us less social; a surrogate for the real thing. For it to be a truly effective communication vehicle, all parties bear a responsibility to be genuine, accurate, and not allow it to replace human contact altogether. In the workplace, the use of electronic communication has overtaken face-to-face and voice-to-voice communication by a wide margin. With these two trends at play, leaders must consider the impact on business relationships and the ability to effectively collaborate, build trust, and create employee engagement and loyalty.
 
Passage Source: Valley Advocate (Article name: Social Media Flaws and the Humanities)
The author adopts all of the following approaches towards Social media except:
Solution: This is a question where you need to use logic in order to answer the question. The one simple attitude adopted by the author of the passage towards social media is that of ‘criticism’. All options that fall within the ambit of criticism are acceptable here, and these include options A, B and D. Option C is the odd one out. Though it appears to be correct, on close perusal, we find that the tone actually states ‘harshly judgmental’. The author has been judgmental for sure, but has he been harshly so (meaning unfair in this context)? That is something we cannot conclude from the given context.
QUESTION: 8
What is the approximate average selling price of ice cream per ton (in millions Rs.) of all the six companies taken together?
Solution:
Total sales of all the six companies taken together = Rs.64 billion or Rs.64000 million
Average selling price (in million Rs.) per ton = 64000/3500 = Rs.18.3 million.
QUESTION: 9
The expenditure incurred in ice cream production by Dairy Queen was Rs.10.54 million per ton in the year 2012. What is the approximate percentage profit (as the percentage of expenditure) that Dairy Queen has earned?
Solution:
Quantity of ice cream sold by Dairy Queen in the year 2012 = (15 � 3500)/100 = 525 tons
Total expenditure incurred (in million Rs.) by Dairy Queen = 10.54 � 525 = 5533.5
Total sales achieved by Dairy Queen = (11 � 64000)/100 = Rs. 7040 million
Dairy Queen‘s profits in the year 2012 = 7040 – 5533.5 = Rs. 1504.5 million 
So, approximate profit percentage = (1504.5 � 100) / 5533.5 = 27.2 % 
QUESTION: 10
What is the approximate marked price (in million Rs.) per ton of Dippin Dots, if the discount per ton of Dippin Dots is 10% of the selling price?
Solution:
Marked price = Selling price + Discount   
Quantity of the ice cream sold by Dippin Dots = (21 � 3500)/100 = 735 tons
Total sales of Dippin Dots = (29 � 64000)/100 = Rs.18560 million
Now, per ton selling price of Dippin Dots' ice cream = 18560 / 735 = Rs. 25.25 million 
Discount = 10% of 25.25 = Rs. 2.525 million
So, marked price = 25.25 + 2.525 = Rs. 27.775 million or Rs.27.8 (approx.). 
QUESTION: 11
It is known that the profits earned by Blue Bunny and Dione are 20% and 25% of their respective total sales of the year 2012. What is the approximate ratio of the cost price per ton of Blue Bunny's ice cream to that of Dione ice cream?
Solution:
Quantity of the ice cream sold by Blue Bunny = (18 � 3500)/100 = 630 tons
Total sales of Blue Bunny = (17 � 64000)/100 = Rs. 10880 million
Now, per ton selling price of Blue Bunny's ice cream = 10880 / 630 = Rs. 17.27 million 
So, cost price per ton of Blue Bunny's ice cream = 0.8 � 17.27 = Rs. 13.82 million
 
Quantity of ice cream sold by Dione in the year 2050 = (16 � 3500)/100 = 560 tons
Total sales of Dione = (13 � 64000)/100 = Rs. 8320 million
Now, per ton selling price of Dione's ice cream = 8320 / 560 = Rs. 14.86 million 
So, cost price per ton of Dione's ice cream = 0.75 � 14.86 = Rs. 11.15 million
 
Therefore, the required approximate ratio = 14/11
 
QUESTION: 12
In order to promote sales, a shopkeeper is preparing a display of chocolates in blue and pink gift packs. Each gift pack will contain exactly three different chocolates from amongst 5 Star, Bournville, Crackle, Dairy Milk, Fruit n Nut, Gems and Silk. No chocolate can be packed in both gift packs. From past experience, the shopkeeper knows that:
 
The Bournville and the Dairy Milk must be on display in the blue and pink gift packs respectively.
The Gems can neither be displayed in the gift pack with the Dairy Milk nor in the gift pack with the 5 Star.
The Fruit n Nut and the Silk must be on display in the same gift pack.
If Silk is displayed in the blue gift pack, which of the following pairs of chocolates must be displayed in the pink gift pack?
Solution:
If Silk is displayed in the blue pack, then fruit n Nut is also displayed in the blue pack.
Now, Gems cannot be displayed in the pink pack.
So, the pink pack contains Dairy Milk, crackle and 5 Star.
The best answer is option 2.
 
QUESTION: 13
In order to promote sales, a shopkeeper is preparing a display of chocolates in blue and pink gift packs. Each gift pack will contain exactly three different chocolates from amongst 5 Star, Bournville, Crackle, Dairy Milk, Fruit n Nut, Gems and Silk. No chocolate can be packed in both gift packs. From past experience, the shopkeeper knows that:
 
The Bournville and the Dairy Milk must be on display in the blue and pink gift packs respectively.
The Gems can neither be displayed in the gift pack with the Dairy Milk nor in the gift pack with the 5 Star.
The Fruit n Nut and the Silk must be on display in the same gift pack.
If Silk is displayed in the pink gift pack, which of the following pairs of chocolates could be displayed in the blue gift pack?
Solution: If Silk is displayed in the pink pack, then fruit n Nut is also displayed in the pink pack.The blue pack will now contain Bournville, Gems and it may have Crackle. The best answer is option 4.
QUESTION: 14
Worst Price, a leading retailer, was running a special sales promotion at its outlet in which, for every 1000 rupees that a customer spent on buying any items at the shop, the customer would get 1 reward point. The marketing department classified the total number of customers into seven different sections – G1, G2, G3,G4, G5, G6, G7 according to their respective number of reward point. The following pie chart gives the percentage wise break up of the number of customers classified into each of these seven sections. In the pie chart, the values given in the brackets alongside each section give the minimum and maximum number of reward point got by any customer classified into that section.
To encourage customers to spend more at their outlets the management decided to give cash return to some of the customers from among whose who had at least 18 reward points. While deciding the cash return the management decided to classify the customers with different reward points into different groups-P to U- according to their number of reward points , as given in the table below:
 
Group
No. of reward point
Cash Return (Rs.)
P
18,19,20
1000
Q
21,22,23,24,25
1200
R
26,27,28,29,30
1400
S
31,32,33,34,35
1600
T
36,37,38,39,40
1800
U
41,42,43,44,45
2000
The number of customers selected for receiving a cash return were different for different groups However, within each group, the management selected an equal number of customers with each of the different number of reward points classified into that group. For example, in group P, of the total number of customers selected for receiving a cash return, the number of customers with 18 reward points is same as that with 19 reward points, which, in turn, is same as that with 20 reward points.
The percentage wise distribution of the total value of the cash returns offered by the management to the customers belonging to the different groups is given in the following graph:
Total amount paid as cash return Rs. 300000
How many customers with 38 reward points were paid a cash return?
Solution: 8 people with 38 reward points  were paid a cash return.
QUESTION: 15
Worst Price, a leading retailer, was running a special sales promotion at its outlet in which, for every 1000 rupees that a customer spent on buying any items at the shop, the customer would get 1 reward point. The marketing department classified the total number of customers into seven different sections – G1, G2, G3,G4, G5, G6, G7 according to their respective number of reward point. The following pie chart gives the percentage wise break up of the number of customers classified into each of these seven sections. In the pie chart, the values given in the brackets alongside each section give the minimum and maximum number of reward point got by any customer classified into that section.
To encourage customers to spend more at their outlets the management decided to give cash return to some of the customers from among whose who had at least 18 reward points. While deciding the cash return the management decided to classify the customers with different reward points into different groups-P to U- according to their number of reward points , as given in the table below:
 
Group
No. of reward point
Cash Return (Rs.)
P
18,19,20
1000
Q
21,22,23,24,25
1200
R
26,27,28,29,30
1400
S
31,32,33,34,35
1600
T
36,37,38,39,40
1800
U
41,42,43,44,45
2000
The number of customers selected for receiving a cash return were different for different groups However, within each group, the management selected an equal number of customers with each of the different number of reward points classified into that group. For example, in group P, of the total number of customers selected for receiving a cash return, the number of customers with 18 reward points is same as that with 19 reward points, which, in turn, is same as that with 20 reward points.
The percentage wise distribution of the total value of the cash returns offered by the management to the customers belonging to the different groups is given in the following graph:
Total amount paid as cash return Rs. 300000
For which section of customers is the number of customers selected for receiving a cash return the highest, when expressed as a percentage of the total number of customers in that section?
Solution:
The value of G4 is more than that for any other section.
QUESTION: 16
Worst Price, a leading retailer, was running a special sales promotion at its outlet in which, for every 1000 rupees that a customer spent on buying any items at the shop, the customer would get 1 reward point. The marketing department classified the total number of customers into seven different sections – G1, G2, G3,G4, G5, G6, G7 according to their respective number of reward point. The following pie chart gives the percentage wise break up of the number of customers classified into each of these seven sections. In the pie chart, the values given in the brackets alongside each section give the minimum and maximum number of reward point got by any customer classified into that section.
To encourage customers to spend more at their outlets the management decided to give cash return to some of the customers from among whose who had at least 18 reward points. While deciding the cash return the management decided to classify the customers with different reward points into different groups-P to U- according to their number of reward points , as given in the table below:
 
Group
No. of reward point
Cash Return (Rs.)
P
18,19,20
1000
Q
21,22,23,24,25
1200
R
26,27,28,29,30
1400
S
31,32,33,34,35
1600
T
36,37,38,39,40
1800
U
41,42,43,44,45
2000
The number of customers selected for receiving a cash return were different for different groups However, within each group, the management selected an equal number of customers with each of the different number of reward points classified into that group. For example, in group P, of the total number of customers selected for receiving a cash return, the number of customers with 18 reward points is same as that with 19 reward points, which, in turn, is same as that with 20 reward points.
The percentage wise distribution of the total value of the cash returns offered by the management to the customers belonging to the different groups is given in the following graph:
Total amount paid as cash return Rs. 300000
What was the total amount paid as cash return to customers with 37 credits or more?
Solution:
The total amount paid as cash return to people with reward points 37 and above was 1800 � 8 � 4 + 2000 � 6 � 5 = 57,600 + 60,000 = 1,17,600
 
QUESTION: 17
38 fruits, apples, oranges, plums and guavas, are distributed among 4 people A, B, C and D. Each one gets a minimum of one fruits of each type and a maximum of four fruits of each type. There are 12 apples. There are two females, each of whom has the highest number of fruits. D, who has 3 plums, has 5 fruits less than the person who has the highest number of fruits. A has 4 apples and 4 plums and does not have the lowest number of fruits. B has an equal number of apples, oranges and guavas only. C has an equal number of oranges, guavas and plums only. None of the friends has an equal number of fruits of each type.
 
What was the total number of plums?
Solution:
We know that D has 3 plums. Since each of them gets a minimum of 1 fruits of each type, D will have at least 1 each of apples, oranges and guavas. So, the minimum number of fruits with D will be 6. If D has 6 fruits, then the two females will have 11 fruits each. So, the number of fruits with the four friends will be 11, 11, 10 and 6. If D has 7 fruits, then the four friends will have 12, 12, 7 and 7 fruits. If D has 8 fruits, then the four friends will have 13, 13, 8 and 4 fruits. D cannot have more than 8 fruits; otherwise, one of the friends will get only 1 fruits.
 
Suppose D has 7 fruit. Since A has 4 apples and 4 plums, A must have 12 fruit. So, one of B and C must have 12 fruit and the other must have 7 fruit. Each of B and C has the same number of fruit of three different types. The one who has 12 fruit cannot have 3 fruit of each type and must therefore have 2, 2, 2 and 6 fruit. Since this is not possible, we can rule out the possibility that D has 7 fruit.
Suppose D has 8 fruit. Since A has 4 apples and 4 plums, A must have 13 fruit and consequently, one of B and C must have 13 fruit and the other must have 4 fruit. The one who has 4 fruit will have 1 fruit of each type. But this contradicts the information that B and C have an equal number of fruit of three types only. These rules out the possibility that D has 8 fruit
 
D must, therefore, have 6 fruit and the other three friends must have 11, 11 and 10 fruit. D must have 1 each of apples, oranges and guavas and 3 plums. Suppose A has 10 fruit and B and C have 11 fruit each. The only way B and C can have 11 fruit each is if they have 3 fruit each of 3 different types and 2 fruit of the fourth type. So, one of B and C will have 3 apples and the other will have 2 apples. So, the total number of apples with A, B, C and D is 4 + 3 + 2 + 1 = 10. This contradicts the information that the total number of apples is 12. Thus, A must have 11 fruit, one of B and C must have 11 fruit and the other must have 10 fruit and D has 6 fruit. Based on this, there are four different ways in which the fruit can be distributed.
 
Case 1
 
Case 2
 
A
B
C
D
Total
 
 
A
B
C
D
Total
Apples
4
3
4
1
12
 
Apples
4
3
4
1
12
Oranges
2
3
2
1
8
 
Oranges
1
3
2
1
7
Guavas
1
3
2
1
7
 
Guavas
2
3
2
1
8
Plums
4
2
2
3
11
 
Plums
4
2
2
3
11
Total
11
11
10
6
38
 
Total
11
11
10
6
38
 
 
 
 
 
 
 
 
 
 
 
 
 
Case 3
 
Case 4
 
A
B
C
D
Total
 
 
A
B
C
D
Total
Apples
4
4
3
1
12
 
Apples
4
4
3
1
12
Oranges
2
2
3
1
8
 
Oranges
1
2
3
1
7
Guavas
1
2
3
1
7
 
Guavas
2
2
3
1
8       
Plums
4
2
2
3
11
 
Plums
4
2
2
3
11
Total
11
10
11
6
38
 
Total
11
10
11
6
38
 
B has an equal number of apples, oranges and guavas only. C has an equal number of oranges, guavas and plums only. So case-3 & case-4 are rejected.
The total number of plums is 4 + 2 + 2 + 3 = 11.
QUESTION: 18
38 fruits, apples, oranges, plums and guavas, are distributed among 4 people A, B, C and D. Each one gets a minimum of one fruits of each type and a maximum of four fruits of each type. There are 12 apples. There are two females, each of whom has the highest number of fruits. D, who has 3 plums, has 5 fruits less than the person who has the highest number of fruits. A has 4 apples and 4 plums and does not have the lowest number of fruits. B has an equal number of apples, oranges and guavas only. C has an equal number of oranges, guavas and plums only. None of the friends has an equal number of fruit of each type.
 
The females together had how many more fruits than the males had together?
Solution: We know that D has 3 plums. Since each of them gets a minimum of 1 fruits of each type, D will have at least 1 each of apples, oranges and guavas. So, the minimum number of fruits with D will be 6. If D has 6 fruits, then the two females will have 11 fruits each. So, the number of fruits with the four friends will be 11, 11, 10 and 6. If D has 7 fruits, then the four friends will have 12, 12, 7 and 7 fruits. If D has 8 fruits, then the four friends will have 13, 13, 8 and 4 fruits. D cannot have more than 8 fruits; otherwise, one of the friends will get only 1 fruits. Suppose D has 7 fruit. Since A has 4 apples and 4 plums, A must have 12 fruit. So, one of B and C must have 12 fruit and the other must have 7 fruit. Each of B and C has the same number of fruit of three different types. The one who has 12 fruit cannot have 3 fruit of each type and must therefore have 2, 2, 2 and 6 fruit. Since this is not possible, we can rule out the possibility that D has 7 fruit.Suppose D has 8 fruit. Since A has 4 apples and 4 plums, A must have 13 fruit and consequently, one of B and C must have 13 fruit and the other must have 4 fruit. The one who has 4 fruit will have 1 fruit of each type. But this contradicts the information that B and C have an equal number of fruit of three types only. This rules out the possibility that D has 8 fruit. D must, therefore, have 6 fruit and the other three friends must have 11, 11 and 10 fruit. D must have 1 each of apples, oranges and guavas and 3 plums. Suppose A has 10 fruit and B and C have 11 fruit each. The only way B and C can have 11 fruit each is if they have 3 fruit each of 3 different types and 2 fruit of the fourth type. So, one of B and C will have 3 apples and the other will have 2 apples. So, the total number of apples with A, B, C and D is 4 + 3 + 2 + 1 = 10. This contradicts the information that the total number of apples is 12. Thus, A must have 11 fruit, one of B and C must have 11 fruit and the other must have 10 fruit and D has 6 fruit. Based on this, there are four different ways in which the fruit can be distributed. 
Case 1
 
Case 2
 
A
B
C
D
Total
 
 
A
B
C
D
Total
Apples
4
3
4
1
12
 
Apples
4
3
4
1
12
Oranges
2
3
2
1
8
 
Oranges
1
3
2
1
7
Guavas
1
3
2
1
7
 
Guavas
2
3
2
1
8
Plums
4
2
2
3
11
 
Plums
4
2
2
3
11
Total
11
11
10
6
38
 
Total
11
11
10
6
38
 
 
 
 
 
 
 
 
 
 
 
 
 
Case 3
 
Case 4
 
A
B
C
D
Total
 
 
A
B
C
D
Total
Apples
4
4
3
1
12
 
Apples
4
4
3
1
12
Oranges
2
2
3
1
8
 
Oranges
1
2
3
1
7
Guavas
1
2
3
1
7
 
Guavas
2
2
3
1
8       
Plums
4
2
2
3
11
 
Plums
4
2
2
3
11
Total
11
10
11
6
38
 
Total
11
10
11
6
38

B has an equal number of apples, oranges and guavas only. C has an equal number of oranges, guavas and plums only. So case-3 & case-4 are rejected.
The females had a total of 22 fruit and the males had a total of 16 fruit. The difference is 6.
 
QUESTION: 19
38 fruits, apples, oranges, plums and guavas, are distributed among 4 people A, B, C and D. Each one gets a minimum of one fruits of each type and a maximum of four fruits of each type. There are 12 apples. There are two females, each of whom has the highest number of fruits. D, who has 3 plums, has 5 fruits less than the person who has the highest number of fruits. A has 4 apples and 4 plums and does not have the lowest number of fruits. B has an equal number of apples, oranges and guavas only. C has an equal number of oranges, guavas and plums only. None of the friends has exactly the same composition of all fruits as any other friend.
 
Who are the two females in this group of 4 people?
Solution:
We know that D has 3 plums. Since each of them gets a minimum of 1 fruits of each type, D will have at least 1 each of apples, oranges and guavas. So, the minimum number of fruits with D will be 6. If D has 6 fruits, then the two females will have 11 fruits each. So, the number of fruits with the four friends will be 11, 11, 10 and 6. If D has 7 fruits, then the four friends will have 12, 12, 7 and 7 fruits. If D has 8 fruits, then the four friends will have 13, 13, 8 and 4 fruits. D cannot have more than 8 fruits; otherwise, one of the friends will get only 1 fruits.
 
Suppose D has 7 fruit. Since A has 4 apples and 4 plums, A must have 12 fruit. So, one of B and C must have 12 fruit and the other must have 7 fruit. Each of B and C has the same number of fruit of three different types. The one who has 12 fruit cannot have 3 fruit of each type and must therefore have 2, 2, 2 and 6 fruit. Since this is not possible, we can rule out the possibility that D has 7 fruit.
Suppose D has 8 fruit. Since A has 4 apples and 4 plums, A must have 13 fruit and consequently, one of B and C must have 13 fruit and the other must have 4 fruit. The one who has 4 fruit will have 1 fruit of each type. But this contradicts the information that B and C have an equal number of fruit of three types only. These rules out the possibility that D has 8 fruit
 
D must, therefore, have 6 fruit and the other three friends must have 11, 11 and 10 fruit. D must have 1 each of apples, oranges and guavas and 3 plums. Suppose A has 10 fruit and B and C have 11 fruit each. The only way B and C can have 11 fruit each is if they have 3 fruit each of 3 different types and 2 fruit of the fourth type. So, one of B and C will have 3 apples and the other will have 2 apples. So, the total number of apples with A, B, C and D is 4 + 3 + 2 + 1 = 10. This contradicts the information that the total number of apples is 12. Thus, A must have 11 fruit, one of B and C must have 11 fruit and the other must have 10 fruit and D has 6 fruit. Based on this, there are four different ways in which the fruit can be distributed.
 
Case 1
 
Case 2
 
A
B
C
D
Total
 
 
A
B
C
D
Total
Apples
4
3
4
1
12
 
Apples
4
3
4
1
12
Oranges
2
3
2
1
8
 
Oranges
1
3
2
1
7
Guavas
1
3
2
1
7
 
Guavas
2
3
2
1
8
Plums
4
2
2
3
11
 
Plums
4
2
2
3
11
Total
11
11
10
6
38
 
Total
11
11
10
6
38
 
 
 
 
 
 
 
 
 
 
 
 
 
Case 3
 
Case 4
 
A
B
C
D
Total
 
 
A
B
C
D
Total
Apples
4
4
3
1
12
 
Apples
4
4
3
1
12
Oranges
2
2
3
1
8
 
Oranges
1
2
3
1
7
Guavas
1
2
3
1
7
 
Guavas
2
2
3
1
8       
Plums
4
2
2
3
11
 
Plums
4
2
2
3
11
Total
11
10
11
6
38
 
Total
11
10
11
6
38
 
B has an equal number of apples, oranges and guavas only. C has an equal number of oranges, guavas and plums only. So case-3 & case-4 are rejected.
So the two females are A and B. Hence the answer is first option.
 
QUESTION: 20
Worst Price, a leading retailer, was running a special sales promotion at its outlet in which, for every 1000 rupees that a customer spent on buying any items at the shop, the customer would get 1 reward point. The marketing department classified the total number of customers into seven different sections – G1, G2, G3,G4, G5, G6, G7 according to their respective number of reward point. The following pie chart gives the percentage wise break up of the number of customers classified into each of these seven sections. In the pie chart, the values given in the brackets alongside each section give the minimum and maximum number of reward point got by any customer classified into that section.
To encourage customers to spend more at their outlets the management decided to give cash return to some of the customers from among whose who had at least 18 reward points. While deciding the cash return the management decided to classify the customers with different reward points into different groups-P to U- according to their number of reward points , as given in the table below:
 
Group
No. of reward point
Cash Return (Rs.)
P
18,19,20
1000
Q
21,22,23,24,25
1200
R
26,27,28,29,30
1400
S
31,32,33,34,35
1600
T
36,37,38,39,40
1800
U
41,42,43,44,45
2000
The number of customers selected for receiving a cash return were different for different groups However, within each group, the management selected an equal number of customers with each of the different number of reward points classified into that group. For example, in group P, of the total number of customers selected for receiving a cash return, the number of customers with 18 reward points is same as that with 19 reward points, which, in turn, is same as that with 20 reward points.
The percentage wise distribution of the total value of the cash returns offered by the management to the customers belonging to the different groups is given in the following graph:
Total amount paid as cash return Rs. 300000
What percentage of the total amount paid as cash- return was to customers with at least 30 and at most 32 reward points?
Solution:
QUESTION: 21
Data given in one question can be used as additional information in all subsequent questions.
 
Colt Arms is a leading provider of advanced weapons and defense systems with an active interest in selling cutting-edge aggressive and defensive weaponry to countries. They are not Rightist or Leftist when it comes to selling their weapons; they call themselves the Opportunists. They sell their weapons to the Leftists, Rightists and the Pacifists, though Pacifists are not their regular customers.
 
In the 1990s, this company had offices in many countries and sold their latest technologies in continents like Europe, America, Asia, Africa and Others. They also have development centers in most technologically rich countries.
 
Below is a table that shows the percentage share of their various development centers located in different countries for the sale of defensive and aggressive Weaponry and Technology (Tech) to some major continents:
 
 
Europe
America
Asia
Africa
Others
 
Weaponry
Tech
Weaponry
Tech
Weaponry
Tech
Weaponry
Tech
Weaponry
Tech
India
16
21
11
30
7
17
13
19
17
8
China
12
25
18
14
13
23
8
26
18
7
Russia
20
6
14
16
18
10
16
15
16
25
Iraq
14
13
13
8
32
20
11
12
17
20
Pakistan
18
19
20
10
15
12
23
13
21
23
Japan
20
16
24
22
15
18
29
15
11
17
 
Given below is the percentage distribution of the total sales of Weapons (PIE – 1) and Technology (PIE – 2) to different continents by Colt Arms:
 
 
The total sale of Weaponry by Colt Arms is 30 lakh units and that of Technology is 40 lakh units
Which of the following development centres sells the highest number of Weaponry units all across the continents shown above?
Solution:
This question should be solved by comparing the percentage values of the different centres and by approximation. If India is compared with Russia, column by column in weaponry, it is noticed that Russia must have sold a greater amount of weaponry units than India. Similarly, when China is compared to Japan, it is clear that Japan sold a greater amount of weaponry units than what China did. Likewise, when we compare Russia with Japan, we see that Japan has definitely sold a greater number of weaponry units than Russia.
As for the remaining ones, the percentage share of total is,
 
Japan: (0.27�0.20) + (0.18�0.24) + (0.16�0.15) + (0.20�0.29) + (0.19�0.11) = 0.2001
Pakistan: (0.27�0.18) + (0.18�0.20) + (0.16�0.15) + (0.20�0.23) + (0.19�0.21) = 0.1945
QUESTION: 22
Data given in one question can be used as additional information in all subsequent questions.
 
Colt Arms is a leading provider of advanced weapons and defense systems with an active interest in selling cutting-edge aggressive and defensive weaponry to countries. They are not Rightist or Leftist when it comes to selling their weapons; they call themselves the Opportunists. They sell their weapons to the Leftists, Rightists and the Pacifists, though Pacifists are not their regular customers.
 
In the 1990s, this company had offices in many countries and sold their latest technologies in continents like Europe, America, Asia, Africa and Others. They also have development centers in most technologically rich countries.
 
Below is a table that shows the percentage share of their various development centers located in different countries for the sale of defensive and aggressive Weaponry and Technology (Tech) to some major continents:
 
 
Europe
America
Asia
Africa
Others
 
Weaponry
Tech
Weaponry
Tech
Weaponry
Tech
Weaponry
Tech
Weaponry
Tech
India
16
21
11
30
7
17
13
19
17
8
China
12
25
18
14
13
23
8
26
18
7
Russia
20
6
14
16
18
10
16
15
16
25
Iraq
14
13
13
8
32
20
11
12
17
20
Pakistan
18
19
20
10
15
12
23
13
21
23
Japan
20
16
24
22
15
18
29
15
11
17
 
Given below is the percentage distribution of the total sales of Weapons (PIE – 1) and Technology (PIE – 2) to different continents by Colt Arms:
 
 
The total sale of Weaponry by Colt Arms is 30 lakh units and that of Technology is 40 lakh units
How many more units of Weaponry than that of Technology were sold by India, Russia and Pakistan together to Europe?
Solution:
Weaponry units sold by India, Russia and Pakistan together to Europe is
[0.27� (0.16+0.20+0.18)] � 3000000 = 437400
Technology units sold by India, Russia and Pakistan together to Europe is
[0.20�(0.21+0.06+0.19)] � 4000000 = 368000
Therefore, difference between the two sales = 437400 - 368000 = 69400 units. 
QUESTION: 23
Data given in one question can be used as additional information in all subsequent questions.
 
Colt Arms is a leading provider of advanced weapons and defense systems with an active interest in selling cutting-edge aggressive and defensive weaponry to countries. They are not Rightist or Leftist when it comes to selling their weapons; they call themselves the Opportunists. They sell their weapons to the Leftists, Rightists and the Pacifists, though Pacifists are not their regular customers.
 
In the 1990s, this company had offices in many countries and sold their latest technologies in continents like Europe, America, Asia, Africa and Others. They also have development centers in most technologically rich countries.
 
Below is a table that shows the percentage share of their various development centers located in different countries for the sale of defensive and aggressive Weaponry and Technology (Tech) to some major continents:
 
 
Europe
America
Asia
Africa
Others
 
Weaponry
Tech
Weaponry
Tech
Weaponry
Tech
Weaponry
Tech
Weaponry
Tech
India
16
21
11
30
7
17
13
19
17
8
China
12
25
18
14
13
23
8
26
18
7
Russia
20
6
14
16
18
10
16
15
16
25
Iraq
14
13
13
8
32
20
11
12
17
20
Pakistan
18
19
20
10
15
12
23
13
21
23
Japan
20
16
24
22
15
18
29
15
11
17
 
Given below is the percentage distribution of the total sales of Weapons (PIE – 1) and Technology (PIE – 2) to different continents by Colt Arms:
 
 
The total sale of Weaponry by Colt Arms is 30 lakh units and that of Technology is 40 lakh units
Sri Lanka is one of the major trading regions in the ‘Others’ category and 3% of the total sales of Weaponry units to the ‘Others’ category is sold to Sri Lanka. If only India and Russia are able to sell to Sri Lanka in the ratio of 7 : 8 for Weaponry, then the number of Weaponry units India selling to Sri Lanka as a percentage of India’s total sales of weaponry units is? (approx).
Solution:
India’s contribution to Sri Lanka’s Weaponry units.
(3/100) � (19/100) � 3000000 � (7/15) = 7980 units.
India’s contribution to the World’s Weaponry units;
[(0.27�0.16) + (0.18�0.11) + (0.16�0.07) + (0.20�0.13) + (0.19�0.17)] � 3000000 = 397500 units or in percentage terms, (7980/397500) � 100 = 2% (approx). 
QUESTION: 24
India played a total of five matches with Pakistan, of which two matches were played in India and three in Pakistan. India scored a different number of goals in each match among 1, 4, 5, 6 and 8 and conceded  a different number of goals among 0, 1, 2, 4 and 6 in the five matches, not necessarily in that order. It is also known that
I. Pakistan scored 4 goals in one of the matches in Pakistan.
II. Compared to one of the other matches, the number of goals scored by India in the 4th match is half of that scored in the other match and the number of goals conceded by India in the 4th match is also half of that conceded in other match.
III. The number of goals India conceded in one of the matches is thrice that it conceded in the match in which it scored 4 goals.
IV. India won the match in which it scored only one goal and it was played in Pakistan but it was not the 4th match.
V. The 3rd match is played in India, and the 4th match is played in Pakistan.
VI. Compared to the 1st match, in the 2nd match the number of goals scored by India is 2 less but the number of goals conceded is 2 more.
 
How many goals did India score in the first match?
Solution:
From (iii), the score in one of the matches is India – Pakistan is 4 – 2.
 
From (iv), the score of one of the matches is 1 – 0.
 
From (ii) and (iii), by looking at the number of goals scored by India, the only possibility of score in 4th match is 4 – 2. In one match the score is 8 – 4. And from (vi) the score of 2nd match is 6 – 6. The score in the first match will be 8 – 4.
As 3rd match is played in India, 1-0 must be the score of the match in Pakistan i.e. the 5th match and 5 – 1 is the score of the 3rd match.
 
 
India
Pakistan
Venue
1st
8
4
Pakistan
2nd
6
6
India
3rd
5
1
India
4th
4
2
Pakistan
5th
1
0
Pakistan
 
India scored 8 goals in the first match.
QUESTION: 25
India played a total of five matches with Pakistan, of which two matches were played in India and three in Pakistan. India scored a different number of goals in each match among 1, 4, 5, 6 and 8 and conceded  a different number of goals among 0, 1, 2, 4 and 6 in the five matches, not necessarily in that order. It is also known that
I. Pakistan scored 4 goals in one of the matches in Pakistan.
II. Compared to one of the other matches, the number of goals scored by India in the 4th match is half of that scored in the other match and the number of goals conceded by India in the 4th match is also half of that conceded in other match.
III. The number of goals India conceded in one of the matches is thrice that it conceded in the match in which it scored 4 goals.
IV. India won the match in which it scored only one goal and it was played in Pakistan but it was not the 4th match.
V. The 3rd match is played in India, and the 4th match is played in Pakistan.
VI. Compared to the 1st match, in the 2nd match the number of goals scored by India is 2 less but the number of goals conceded is 2 more.
 
Which of the following combinations is true of the goals scored by Pakistan?
Solution:
From (iii), the score in one of the matches is India – Pakistan is 4 – 2.
 
From (iv), the score of one of the matches is 1 – 0.
 
From (ii) and (iii), by looking at the number of goals scored by India, the only possibility of score in 4th match is 4 – 2. In one match the score is 8 – 4. And from (vi) the score of 2nd match is 6 – 6. The score in the first match will be 8 – 4.
As 3rd match is played in India, 1-0 must be the score of the match in Pakistan i.e. the 5th match and 5 – 1 is the score of the 3rd match.
 
 
India
Pakistan
Venue
1st
8
4
Pakistan
2nd
6
6
India
3rd
5
1
India
4th
4
2
Pakistan
5th
1
0
Pakistan
 
From the table it is clear that Pakistan scored 1 goal in 3rd match.
QUESTION: 26
India played a total of five matches with Pakistan, of which two matches were played in India and three in Pakistan. India scored a different number of goals in each match among 1, 4, 5, 6 and 8 and conceded  a different number of goals among 0, 1, 2, 4 and 6 in the five matches, not necessarily in that order. It is also known that
I. Pakistan scored 4 goals in one of the matches in Pakistan.
II. Compared to one of the other matches, the number of goals scored by India in the 4th match is half of that scored in the other match and the number of goals conceded by India in the 4th match is also half of that conceded in other match.
III. The number of goals India conceded in one of the matches is thrice that it conceded in the match in which it scored 4 goals.
IV. India won the match in which it scored only one goal and it was played in Pakistan but it was not the 4th match.
V. The 3rd match is played in India, and the 4th match is played in Pakistan.
VI. Compared to the 1st match, in the 2nd match the number of goals scored by India is 2 less but the number of goals conceded is 2 more.
 
The matches that are played in India are the 
Solution:
From (iii), the score in one of the matches is India – Pakistan is 4 – 2.
 
From (iv), the score of one of the matches is 1 – 0.
 
From (ii) and (iii), by looking at the number of goals scored by India, the only possibility of score in 4th match is 4 – 2. In one match the score is 8 – 4. And from (vi) the score of 2nd match is 6 – 6. The score in the first match will be 8 – 4.
As 3rd match is played in India, 1-0 must be the score of the match in Pakistan i.e. the 5th match and 5 – 1 is the score of the 3rd match.
 
 
India
Pakistan
Venue
1st
8
4
Pakistan
2nd
6
6
India
3rd
5
1
India
4th
4
2
Pakistan
5th
1
0
Pakistan
 
The 2nd & 3rd matches are played in India.
QUESTION: 27
India played a total of five matches with Pakistan, of which two matches were played in India and three in Pakistan. India scored a different number of goals in each match among 1, 4, 5, 6 and 8 and conceded  a different number of goals among 0, 1, 2, 4 and 6 in the five matches, not necessarily in that order. It is also known that
I. Pakistan scored 4 goals in one of the matches in Pakistan.
II. Compared to one of the other matches, the number of goals scored by India in the 4th match is half of that scored in the other match and the number of goals conceded by India in the 4th match is also half of that conceded in other match.
III. The number of goals India conceded in one of the matches is thrice that it conceded in the match in which it scored 4 goals.
IV. India won the match in which it scored only one goal and it was played in Pakistan but it was not the 4th match.
V. The 3rd match is played in India, and the 4th match is played in Pakistan.
VI. Compared to the 1st match, in the 2nd match the number of goals scored by India is 2 less but the number of goals conceded is 2 more.
 
In which match Pakistan scored six goals?
Solution:
From (iii), the score in one of the matches is India – Pakistan is 4 – 2.
 
From (iv), the score of one of the matches is 1 – 0.
 
From (ii) and (iii), by looking at the number of goals scored by India, the only possibility of score in 4th match is 4 – 2. In one match the score is 8 – 4. And from (vi) the score of 2nd match is 6 – 6. The score in the first match will be 8 – 4.
As 3rd match is played in India, 1-0 must be the score of the match in Pakistan i.e. the 5th match and 5 – 1 is the score of the 3rd match.
 
 
India
Pakistan
Venue
1st
8
4
Pakistan
2nd
6
6
India
3rd
5
1
India
4th
4
2
Pakistan
5th
1
0
Pakistan
 
In 2nd match Pakistan scored 6 goals.
QUESTION: 28
In a zoo, there are 5 types of animals – herbivores, carnivores, omnivores, frugivores and sanguinivores. It is also known that –
 
(a) Exactly 1/6th of herbivores, 1/3rd of carnivores, 1/5th of omnivores, 1/10th of frugivores and 1/12th of sanguinivores are in the East Wing.
(b) Exactly 1/9th of herbivores, 1/15th of carnivores, 1/7th of omnivores, 1/3rd of frugivores, 1/6th of sanguinivores are in the West Wing.
(c) Exactly 1/2th of herbivores, 1/12th of carnivores, 1/11th of omnivores, 1/5th of frugivores, 1/7th of sanguinivores are in the South Wing.
(d) Exactly 1/5th of herbivores, 1/10th of carnivores, 1/3rd of omnivores, 1/11th of frugivores, 1/5th of sanguinivores are in the North Wing.
(e) All the rest are in the Central Wing.
 
It is also known that at a time the zoo can support a maximum of 2290 animals and at all times, there are animals from each category in the zoo.
Which of the most populated wing?
Solution:
This one can be solved in the following manner – Since, we know that animals cannot be living in parts, therefore, 1/n or 1/m of the same category will ensure that at least n � m of that particular type of animals populate the zoo. (n � m or a multiple of that).
Thus, population of.....
 
Herbivores – must be at least the LCM of (6, 9, 2, 5) = 90 or a multiple of 90
Carnivores – must be at least the LCM of (3, 15, 12, 10) = 60 or a multiple of 60
Omnivores – must be at least the LCM of (5, 7, 11, 3) = 1155 or a multiple of 1155
Frugivores – must be at least the LCM of (10, 3, 5, 11) = 330 or a multiple of 330
Sanguinivores – must be at least the LCM of (12, 6, 7, 5) = 420 or a multiple of 420
We also know that the total population cannot be more than 2290.
Let’s add all the minimum populations of the different types to ascertain the minimum total population limit: 90+60+1155+330+420 = 2055.
Therefore, the populations of
Herbivores – can be 90 or 180 or 270
Carnivores – can be 60, 120, 180 or 240
Omnivores – must be 1155
Frugivores – must be 330
Sanguinivores – must be 420
 
Thus, the number of animals in the different Wings can be thus determined as –
East Wing – Herbivores (15, 30 or 45), Carnivores (20, 40, 60 or 80), Omnivores (231), Frugivores (33), Sanguinivores (35), Total (334, 349, 354, 364, 369, 374, 384, 389, 394, 404, 409, 424)
West Wing – Herbivores (10, 20 or 30), Carnivores (4, 8, 12 or 16), Omnivores (165), Frugivores (110), Sanguinivores (70), Total (359, 363, 367, 369, 371, 373, 377, 379, 381, 383, 387, 391)
South Wing – Herbivores (45, 90 or 135), Carnivores (5, 10, 15 or 20), Omnivores (105), Frugivores (66), Sanguinivores (60), Total (281, 286, 291, 296, 326, 331, 336, 341, 371, 376, 381, 386)
North Wing – Herbivores (18, 36 or 54), Carnivores (6, 12, 18 or 24), Omnivores (385), Frugivores (30), Sanguinivores (84), Total (523, 529, 535, 541, 547, 553, 559, 565, 571, 577)
Central Wing – Herbivores (2, 4 or 6), Carnivores (25, 50, 75 or 100), Omnivores (269), Frugivores (91), Sanguinivores (171), Total (558, 560, 562, 583, 585, 587, 608, 610, 612, 633, 635, 637).
 
Even in the worst case, the population of the Central Wing is higher than any other Wing’s.
QUESTION: 29
In a zoo, there are 5 types of animals – herbivores, carnivores, omnivores, frugivores and sanguinivores. It is also known that –
 
(a) Exactly 1/6th of herbivores, 1/3rd of carnivores, 1/5th of omnivores, 1/10th of frugivores and 1/12th of sanguinivores are in the East Wing.
(b) Exactly 1/9th of herbivores, 1/15th of carnivores, 1/7th of omnivores, 1/3rd of frugivores, 1/6th of sanguinivores are in the West Wing.
(c) Exactly 1/2th of herbivores, 1/12th of carnivores, 1/11th of omnivores, 1/5th of frugivores, 1/7th of sanguinivores are in the South Wing.
(d) Exactly 1/5th of herbivores, 1/10th of carnivores, 1/3rd of omnivores, 1/11th of frugivores, 1/5th of sanguinivores are in the North Wing.
(e) All the rest are in the Central Wing.
 
It is also known that at a time the zoo can support a maximum of 2290 animals and at all times, there are animals from each category in the zoo.
Among the following, which is the most populated wing?
Solution:
This one can be solved in the following manner – Since, we know that animals cannot be living in parts, therefore, 1/n or 1/m of the same category will ensure that at least n � m of that particular type of animals populate the zoo. (n � m or a multiple of that).
Thus, population of.....
 
Herbivores – must be at least the LCM of (6, 9, 2, 5) = 90 or a multiple of 90
Carnivores – must be at least the LCM of (3, 15, 12, 10) = 60 or a multiple of 60
Omnivores – must be at least the LCM of (5, 7, 11, 3) = 1155 or a multiple of 1155
Frugivores – must be at least the LCM of (10, 3, 5, 11) = 330 or a multiple of 330
Sanguinivores – must be at least the LCM of (12, 6, 7, 5) = 420 or a multiple of 420
We also know that the total population cannot be more than 2290.
Let’s add all the minimum populations of the different types to ascertain the minimum total population limit: 90+60+1155+330+420 = 2055.
Therefore, the populations of
Herbivores – can be 90 or 180 or 270
Carnivores – can be 60, 120, 180 or 240
Omnivores – must be 1155
Frugivores – must be 330
Sanguinivores – must be 420
 
Thus, the number of animals in the different Wings can be thus determined as –
East Wing – Herbivores (15, 30 or 45), Carnivores (20, 40, 60 or 80), Omnivores (231), Frugivores (33), Sanguinivores (35), Total (334, 349, 354, 364, 369, 374, 384, 389, 394, 404, 409, 424)
West Wing – Herbivores (10, 20 or 30), Carnivores (4, 8, 12 or 16), Omnivores (165), Frugivores (110), Sanguinivores (70), Total (359, 363, 367, 369, 371, 373, 377, 379, 381, 383, 387, 391)
South Wing – Herbivores (45, 90 or 135), Carnivores (5, 10, 15 or 20), Omnivores (105), Frugivores (66), Sanguinivores (60), Total (281, 286, 291, 296, 326, 331, 336, 341, 371, 376, 381, 386)
North Wing – Herbivores (18, 36 or 54), Carnivores (6, 12, 18 or 24), Omnivores (385), Frugivores (30), Sanguinivores (84), Total (523, 529, 535, 541, 547, 553, 559, 565, 571, 577)
Central Wing – Herbivores (2, 4 or 6), Carnivores (25, 50, 75 or 100), Omnivores (269), Frugivores (91), Sanguinivores (171), Total (558, 560, 562, 583, 585, 587, 608, 610, 612, 633, 635, 637).
So, Among East, West or South any one wing can be most populated so answer cannot be determined.
QUESTION: 30
In a zoo, there are 5 types of animals – herbivores, carnivores, omnivores, frugivores and sanguinivores. It is also known that –
 
(a) Exactly 1/6th of herbivores, 1/3rd of carnivores, 1/5th of omnivores, 1/10th of frugivores and 1/12th of sanguinivores are in the East Wing.
(b) Exactly 1/9th of herbivores, 1/15th of carnivores, 1/7th of omnivores, 1/3rd of frugivores, 1/6th of sanguinivores are in the West Wing.
(c) Exactly 1/2th of herbivores, 1/12th of carnivores, 1/11th of omnivores, 1/5th of frugivores, 1/7th of sanguinivores are in the South Wing.
(d) Exactly 1/5th of herbivores, 1/10th of carnivores, 1/3rd of omnivores, 1/11th of frugivores, 1/5th of sanguinivores are in the North Wing.
(e) All the rest are in the Central Wing.
 
It is also known that at a time the zoo can support a maximum of 2290 animals and at all times, there are animals from each category in the zoo.
Which is the least populated wing?
Solution:
This one can be solved in the following manner – Since, we know that animals cannot be living in parts, therefore, 1/n or 1/m of the same category will ensure that at least n � m of that particular type of animals populate the zoo. (n � m or a multiple of that).
Thus, population of.....
 
Herbivores – must be at least the LCM of (6, 9, 2, 5) = 90 or a multiple of 90
Carnivores – must be at least the LCM of (3, 15, 12, 10) = 60 or a multiple of 60
Omnivores – must be at least the LCM of (5, 7, 11, 3) = 1155 or a multiple of 1155
Frugivores – must be at least the LCM of (10, 3, 5, 11) = 330 or a multiple of 330
Sanguinivores – must be at least the LCM of (12, 6, 7, 5) = 420 or a multiple of 420
We also know that the total population cannot be more than 2290.
Let’s add all the minimum populations of the different types to ascertain the minimum total population limit: 90+60+1155+330+420 = 2055.
Therefore, the populations of
Herbivores – can be 90 or 180 or 270
Carnivores – can be 60, 120, 180 or 240
Omnivores – must be 1155
Frugivores – must be 330
Sanguinivores – must be 420
 
Thus, the number of animals in the different Wings can be thus determined as –
East Wing – Herbivores (15, 30 or 45), Carnivores (20, 40, 60 or 80), Omnivores (231), Frugivores (33), Sanguinivores (35), Total (334, 349, 354, 364, 369, 374, 384, 389, 394, 404, 409, 424)
West Wing – Herbivores (10, 20 or 30), Carnivores (4, 8, 12 or 16), Omnivores (165), Frugivores (110), Sanguinivores (70), Total (359, 363, 367, 369, 371, 373, 377, 379, 381, 383, 387, 391)
South Wing – Herbivores (45, 90 or 135), Carnivores (5, 10, 15 or 20), Omnivores (105), Frugivores (66), Sanguinivores (60), Total (281, 286, 291, 296, 326, 331, 336, 341, 371, 376, 381, 386)
North Wing – Herbivores (18, 36 or 54), Carnivores (6, 12, 18 or 24), Omnivores (385), Frugivores (30), Sanguinivores (84), Total (523, 529, 535, 541, 547, 553, 559, 565, 571, 577)
Central Wing – Herbivores (2, 4 or 6), Carnivores (25, 50, 75 or 100), Omnivores (269), Frugivores (91), Sanguinivores (171), Total (558, 560, 562, 583, 585, 587, 608, 610, 612, 633, 635, 637).
 
Either East or South Wing is the least populated
QUESTION: 31
In a zoo, there are 5 types of animals – herbivores, carnivores, omnivores, frugivores and sanguinivores. It is also known that –
 
(a) Exactly 1/6th of herbivores, 1/3rd of carnivores, 1/5th of omnivores, 1/10th of frugivores and 1/12th of sanguinivores are in the East Wing.
(b) Exactly 1/9th of herbivores, 1/15th of carnivores, 1/7th of omnivores, 1/3rd of frugivores, 1/6th of sanguinivores are in the West Wing.
(c) Exactly 1/2th of herbivores, 1/12th of carnivores, 1/11th of omnivores, 1/5th of frugivores, 1/7th of sanguinivores are in the South Wing.
(d) Exactly 1/5th of herbivores, 1/10th of carnivores, 1/3rd of omnivores, 1/11th of frugivores, 1/5th of sanguinivores are in the North Wing.
(e) All the rest are in the Central Wing.
 
It is also known that at a time the zoo can support a maximum of 2290 animals and at all times, there are animals from each category in the zoo.
Which of the following can be the population of the Central Wing?
Solution:
This one can be solved in the following manner – Since, we know that animals cannot be living in parts, therefore, 1/n or 1/m of the same category will ensure that at least n � m of that particular type of animals populate the zoo. (n � m or a multiple of that).
Thus, population of.....
 
Herbivores – must be at least the LCM of (6, 9, 2, 5) = 90 or a multiple of 90
Carnivores – must be at least the LCM of (3, 15, 12, 10) = 60 or a multiple of 60
Omnivores – must be at least the LCM of (5, 7, 11, 3) = 1155 or a multiple of 1155
Frugivores – must be at least the LCM of (10, 3, 5, 11) = 330 or a multiple of 330
Sanguinivores – must be at least the LCM of (12, 6, 7, 5) = 420 or a multiple of 420
We also know that the total population cannot be more than 2290.
Let’s add all the minimum populations of the different types to ascertain the minimum total population limit: 90+60+1155+330+420 = 2055.
Therefore, the populations of
Herbivores – can be 90 or 180 or 270
Carnivores – can be 60, 120, 180 or 240
Omnivores – must be 1155
Frugivores – must be 330
Sanguinivores – must be 420
 
Thus, the number of animals in the different Wings can be thus determined as –
East Wing – Herbivores (15, 30 or 45), Carnivores (20, 40, 60 or 80), Omnivores (231), Frugivores (33), Sanguinivores (35), Total (334, 349, 354, 364, 369, 374, 384, 389, 394, 404, 409, 424)
West Wing – Herbivores (10, 20 or 30), Carnivores (4, 8, 12 or 16), Omnivores (165), Frugivores (110), Sanguinivores (70), Total (359, 363, 367, 369, 371, 373, 377, 379, 381, 383, 387, 391)
South Wing – Herbivores (45, 90 or 135), Carnivores (5, 10, 15 or 20), Omnivores (105), Frugivores (66), Sanguinivores (60), Total (281, 286, 291, 296, 326, 331, 336, 341, 371, 376, 381, 386)
North Wing – Herbivores (18, 36 or 54), Carnivores (6, 12, 18 or 24), Omnivores (385), Frugivores (30), Sanguinivores (84), Total (523, 529, 535, 541, 547, 553, 559, 565, 571, 577)
Central Wing – Herbivores (2, 4 or 6), Carnivores (25, 50, 75 or 100), Omnivores (269), Frugivores (91), Sanguinivores (171), Total (558, 560, 562, 583, 585, 587, 608, 610, 612, 633, 635, 637).
Since out of the given options only 608 is possible as the population of Central Wing.
QUESTION: 32
DIRECTIONS for the question: Mark the best option
A doctor is called to see a sick child. The doctor has prior information that 90% of sick children in that neighborhood have the flu, while the other 10% are sick with measles. A well-known symptom of measles is a rash (the event of having which we denote R). P(R|M) = .95. However, occasionally children with flu also develop rash, so that P(R|F) = 0.08. Upon examining the child, the doctor finds a rash. What is the probability (rounded off to the nearest tenth) that the child has measles?
Solution:
QUESTION: 33
DIRECTIONS for the question: Solve the following question and mark the best possible option.
A family of lines is given by (1+ 2λ) x+ (1 – λ) y + λ = 0, λ being a parameter. The line belonging to this family at the maximum distance from the point (1, 4) is
Solution:  Hence the answer is option C
QUESTION: 34
A lamp lighter has to light 100 gas lamps. To go from one lamp post to the next he takes 60 seconds. Each lamp burns 12 cubic feet of gas per hour. If he lights the first lamp at 7 p.m. then the gas burnt when he lights the last lamp is:
Solution:
Each lamp burns 12 cubic feet of gas per hour, i.e. 1/5 cubic feet of gas per minute.
He takes 1 min. to go from one lamp post to the other.
When he lights the last lamp post, first lamppost will burn for 99 minutes, second for 98 minutes.
Gas used = 1/5 (99 + 98 + 97 +……. + 2 + 1) = 990
Hence the answer is option D
 
QUESTION: 35
Kapoor makes Rs. 20 everyday, from which he spends Rs. 12 for various expenses. Prem makes Rs. 15 a day but has to spend Rs. 14 each day for expenses. If the two of them saved together, how long will it take them to buy a gift for Rs. 82?
Solution:
Kapoor saves = 20-12 = Rs8 everyday and
Prem saves =15-14 = Rs1 everyday,
Total Savings = 8 +1= 9 everyday, but in total, he want to save 82.
So no. of days required = 82/9 = more than 9 ie. 10 Days.
So, Option A  is the correct answer.
 
QUESTION: 36
Aditya thinks of a two-digit number, which is equal to the sum of the squares of its digits. What is the sum of the digits of that number?
Solution:
QUESTION: 37
The XY-plane is marked on the ground in preparation for a sack race. The participants start from point P(0, 2) and finish the race at point Q(10, 3). In hopping from P to Q, the participants must touch the X-axis exactly once. What point on the X-axis should a participant touch so that the total distance travelled is the least?
Solution: Take the reflection of point Q in the X-axis and call it Q’ (10, −3). Let the point at which the student touches x-axis be R. Then, by symmetry, RQ = RQ’ and hence minimizing (PR + RQ) is same as minimizing (PR + RQ’). It is evident that for (PR + RQ’) to be minimum, P, R and Q’ should be collinear. So (x, 0) lies on the line joining (0, 2) and (10, −3).If the line touches x-axis then y becomes 0. Thus, x = 4 i.e. line touches x-axis at (4, 0)
QUESTION: 38
Two functions, f(x) and g(x), are defined for all non-negative x as f(x) = |6 – x| and g(x) = � x. The graphs of f(x) and g(x) intersect in the points A and B. Which of the following represents the equation of AB and the coordinates of the mid-point of AB respectively?
Solution:  
QUESTION: 39
What is the highest power of 2 that divides 1015 � (1023 + 20482) completely?
Solution:
The above term can be re-written as: 1038 + 1015 � 20482
We can see that there are two sub-problems to this:
One is what is the highest power of 2 that divides 1038 completely?
Two is what is the highest power of 2 that divides 1015 � 20482 completely?
 
Let us solve each sub-problem independently.
In the first problem, the answer will be 38
In the second problem, the answer will be 15 for the 1015 component.
Now 2048 is 211. So 20482 will be 222
So for the second problem, the answer will be 15 + 22 = 37.
 
Now we have to choose the smaller of the two, since the division has to be complete.
Hence the answer is 37.
 
QUESTION: 40
Two persons A and B started running simultaneously from a point P, around a circular track of length 1000 m, in opposite directions, with speeds of 4 m/s and 1 m/s respectively. The moment they crossed each other, two more persons, C and D, started from P towards A and B respectively, C running around the track in the direction opposite to A, with a speed of 1 m/sec and D running around the track, in the direction   opposite to B, with a speed of 4 m/sec. Which of the following is a possible time when A, B, C and D will all meet at the same point on the track? (Assume that they continue indefinitely to run around the track in their respective directions).
Solution:
When A and B meet, D starts running in the same direction as that of A (or opposite to B) and at the same speed as that of A
(i.e. 4 m/s).
Hence D and A will never meet and therefore it is not possible for all four of A, B, C and D to ever meet at the same point. Hence they all will not meet ever. Option 4. 
QUESTION: 41
3 circles with centres A, B and C and radii R1, R2 and R3 respectively are tangent to each other. If the in-radius of "ABC is 4", what is the ratio of the product of the radii to the sum of the radii?
Solution:
QUESTION: 42
A group of 4 workers can make a wall in 25 days. This group starts the work and after every two days, one additional worker joins the group. Assume that the capacity of each worker is the same. On which day will the work get completed?
Solution: As 4 workers require 25 days to complete the work, so it requires 100 man-days.In first 2 days 4 � 2 = 8 units, in next two days 5 � 2 = 10 units, then 6 � 2 = 12 units, then 7 � 2 = 14 units, then 8 � 2 = 16 units, then 9 � 2 = 18 units, then 10 � 2 = 20 units , total = 98 units. So, 98 units are completed in 14 days.Note that on the 14th day the work is still not complete.On the 15th day 11 workers will complete the remaining 2 units of work. Hence, None of these.
QUESTION: 43
which of the following is possible value of k?
Solution: Hence the answer is option A
QUESTION: 44
Rohit started walking from point A to point B and Vineet started walking from point B to point A, both at 6 a.m. After walking for 2 hours, both met each other and sat down for breakfast, which took 1 hour. Then, both continued their journey. Since they had just had their breakfast, their speeds reduced to half of their initial speeds. After 1 hour, Vineet realised that their keys got exchanged, so he started running towards Rohit at two and a half times his present speed. If the ratio of Rohit’s and Vineet’s initial speeds was 3:2, at what time would Vineet meet Rohit?
Solution:
QUESTION: 45
50 students have weights ranging from 10 kg to 99 kg. While adding all the weights, the digits in the weight of one of the students were reversed. As a result the average weight of the students turned out to be 90% of the correct average weight of the students. What is the maximum possible correct sum of the weights of all the students?
Solution:
Suppose the maximum total is 50x and the corresponding average is x.
Let the correct weight of one of the students be 10a + b.
This weight has been incorrectly recorded as 10b + a.
Based on this, the calculated average is (50x – 10ab + 10b + a)/50 = 0.9x
⇒ 50x – (9a – 9b) = 45x ⇒ 5x = 9(ab).
The maximum value of (ab) can be 9, but this would mean that the two weights are 90 and 9.
This is clearly not possible, as the reversal of 90 i.e. 9 is not a two digit number.
Since it is specified that the weights are 2-digit numbers, we can conclude that the maximum value of (ab) = 8 and the numbers will be 91 and 19.
From this, we get 5x = 9 � 8 = 72.
Therefore, The maximum total weight is  50x = 720 kg. 
QUESTION: 46

DIRECTIONS for the question: Mark the best option.

A tower is 50 meter high. Its shadow is x meter shorter when the sun's altitude is 45� than when it is 30�. Find the value of x.
Solution: Hence option D.
QUESTION: 47
In a shop, there are 12 pairs of gloves of same colour and size. A man steals 4 gloves. What is the probability that at least one left-right matching pair of gloves was stolen?
Solution:
Total number of ways of selecting 4 gloves = 24C4
Number of ways selecting 4 gloves having at least one left-right combination is
(12C112C3) + (12C212C2) + (12C312C1)
Hence, required probability = (12C112C3) + (12C212C2) + (12C312C1) /24C4
 = (2640 + 4356 + 2640)/(10626)
= 4818/5313. 
QUESTION: 48
ABC is an equilateral triangle of side 1 cm. Three circles, each of radius 1 cm, are drawn tangential to each of the sides AB, BC, AC at their midpoints, outside the triangle. Find the ratio of the area of the triangle formed by joining the centres of these circles to the area of the equilateral triangle.
Solution:
QUESTION: 49
Pipes P and Q can fill a cistern in 4 hours and 5 hours respectively while a leak R can empty the cistern in 3 hours. Initially pipe P is opened and then, leak pipe R is opened at the instant when the cistern is exactly half full. Pipe Q is opened at the instant when the cistern is exactly one fourth filled with water. Find the total time taken to fill the complete cistern from the initial moment.
Solution:
Initially when pipe P is opened, then time taken to half fill the cistern = 2 hours.
After that, both pipes P and R are open, then time taken to empty 1/4th of the cistern = 1/4th of (4x3)/(4 – 3) = 3 hours
Now, when all three pipes P, Q and R are open, then time taken to completely fill the cistern (filling the remaining 3/4th cistern) = 3/4th of  (5x4x3)/ (12 + 15 – 20) = 45/7 = 6.42 hours.
Therefore, total time taken to completely fill the cistern = 2 + 3 + 6.42 = 11.42 hrs. 
QUESTION: 50
The 2f(0) + 3f(1) is equal to
Solution:
QUESTION: 51
Let a, b, c be the respective numbers that show up when three fair dice, P1, P2 and P3, are rolled. If z = |(a – 1) (b – 3) (c – 4)|, the probability that z 1 is
 
Solution:
QUESTION: 52
Let P be the product of the first 100 positive odd integers. Find the largest integer k such that P is divisible by 3k.
Solution:
We are interested in all odd numbers from 1 to 199. The powers of 3 can be obtained from all odd multiples of 3, i.e., from 3 � 1, 3 � 3, and so on up to 3 � 65, which is 33 values. Another 3 can be obtained from all odd powers of 9 each, i.e., one 3 each from 9 � 1, 9 � 3, and so on up to 9 � 21, which is 11 values. Another 3 can be obtained from all odd powers of 27 each, i.e., one 3 each from 27 � 1, 27 � 3 and so on up to 27 � 7, which is 4 values. Another 3 can be obtained from all odd powers of 81 each, i.e., one 3 from 81 � 1, which is 1 value. Thus, the number of times 3 appears in the product is 33 + 11 + 4 + 1 = 49. So, 3k = 349. Thus k = 49.
Alternate solution: 200/3 gives quotient 66, then 66/3 gives quotient 22, then 22/3 gives quotient 7 and finally 7/3 gives quotient 2. So, 397 will divide 200!.
Since there are only half as many odd numbers up to 200, the power of 3 should also be approximately half. From the options, the best answer is 49.
QUESTION: 53
DIRECTIONS for the question: Mark the best option:
 
The expression N = 553 + 173 – 723 is exactly divisible by
Solution: a3 + b3 = (a + b) (a2 – ab + b2), So we have553 + 173 – 723 = 72 [552 -55 �17+172 - 722]
= 72[(55 - 72)� (55 + 72)-55� 17+172]
= 72[17� (55 + 72)-55� 17+172], So the number is divisible by 3 and 17.

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