“Everybody pretty much agrees that the relationship between elephants and people has dramatically changed,” [says psychologist Gay] Bradshaw. . . . “Where for centuries humans and elephants lived in relatively peaceful coexistence, there is now hostility and violence. Now, I use the term ‘violence’ because of the intentionality associated with it, both in the aggression of humans and, at times, the recently observed behavior of elephants.” . . .
Typically, elephant researchers have cited, as a cause of aggression, the high levels of testosterone in newly matured male elephants or the competition for land and resources between elephants and humans. But. . . Bradshaw and several colleagues argue. . . that today’s elephant populations are suffering from a form of chronic stress, a kind of specieswide trauma. Decades of poaching and culling and habitat loss, they claim, have so disrupted the intricate web of familial and societal relations by which young elephants have traditionally been raised in the wild, and by which established elephant herds are governed, that what we are now witnessing is nothing less than a precipitous collapse of elephant culture. . . .
Elephants, when left to their own devices, are profoundly social creatures. . . . Young elephants are raised within an extended, multitiered network of doting female caregivers that includes the birth mother, grandmothers, aunts and friends. These relations are maintained over a life span as long as 70 years. Studies of established herds have shown that young elephants stay within 15 feet of their mothers for nearly all of their first eight years of life, after which young females are socialized into the matriarchal network, while young males go off for a time into an allmale social group before coming back into the fold as mature adults. . . .
This fabric of elephant society, Bradshaw and her colleagues [demonstrate], ha[s] effectively been frayed by years of habitat loss and poaching, along with systematic culling by government agencies to control elephant numbers and translocations of herds to different habitats. . . . As a result of such social upheaval, calves are now being born to and raised by ever younger and inexperienced mothers. Young orphaned elephants, meanwhile, that have witnessed the death of a parent at the hands of poachers are coming of age in the absence of the support system that defines traditional elephant life. “The loss of elephant elders,” [says] Bradshaw . . . "and the traumatic experience of witnessing the massacres of their family, impairs normal brain and behavior development in young elephants.”
What Bradshaw and her colleagues describe would seem to be an extreme form of anthropocentric conjecture if the evidence that they’ve compiled from various elephant researchers. . . weren’t so compelling. The elephants of decimated herds, especially orphans who’ve watched the death of their parents and elders from poaching and culling, exhibit behavior typically associated with posttraumatic stress disorder and other traumarelated disorders in humans: abnormal startle response, unpredictable asocial behavior, inattentive mothering and hyperaggression. . . .
[According to Bradshaw], “Elephants are suffering and behaving in the same ways that we recognize in ourselves as a result of violence. . . . Except perhaps for a few specific features, brain organization and early development of elephants and humans are extremely similar.”
 The passage makes all of the following claims EXCEPT:
 elephant mothers are evolving newer ways of rearing their calves to adapt to emerging threats.
 the elephant response to deeply disturbing experiences is similar to that of humans.
 human actions such as poaching and culling have created stressful conditions for elephant communities.
 elephants establish extended and enduring familial relationships as do humans.
Again, the evidence for choice 2 can been found in the second last paragraph; anthropocentric means concerning humans or brought by/caused by humans. Thus both options 2 and 3 can be safely eliminated.
The clue to the choice 4 can be found in the third paragraph, which says that elephants are profoundly social creatures. For option1 we have no evidence.
 Which of the following statements best expresses the overall argument of this passage?
 Recent elephant behaviour could be understood as a form of specieswide traumarelated response.
 Elephants, like the humans they are in conflict with, are profoundly social creatures.
 The relationship between elephants and humans has changed from one of coexistence to one of hostility.
 The brain organisation and early development of elephants and humans are extremely similar.
Though option 4 is visible in the paragraph, it is not the central idea. The central idea seems to be focusing on the change in the elephants’ attitude towards humans. Option 1 captures the key argument of the passage.
Like option 4, option 2, though true as per the passage, is not the key focus of the passage.
Option 3 might look like a good choice, but there is a flaw in the option. The passage is not focusing on the relationship between elephants and humans, though the passage starts on that note. The author is more focused on bringing to our attention the aggressive behavior of elephants and tries to find out the causes of that aggression.
Option 1 is the best choice because bulk of the passage is dedicated to how and why the elephants behave aggressively (specieswidetraumarelated response)
 Which of the following measures is Bradshaw most likely to support to address the problem of elephant aggression?
 Funding of more studies to better understand the impact of testosterone on male elephant aggression.
 The development of treatment programmes for elephants drawing on insights gained from treating posttraumatic stress disorder in humans.
 Studying the impact of isolating elephant calves on their early brain development, behaviour and aggression.
 Increased funding for research into the similarity of humans and other animals drawing on insights gained from humanelephant similarities.
Option 1 goes out because the testosterone issue is not at all a concern or the bone of contention. Moreover, by understanding it, how would we be able to address the problem concerning elephant aggression.
Option 2 could indeed help us address the problem of elephant aggression because the trauma experienced by elephants is very similar to stress disorder in humans, and because elephants are social creatures just as humans are, insights gained from treating posttraumatic stress disorder in humans might help us address the problem of elephant aggression. Option 2 is the right choice
Both option 3 and 4 are not likely to contribute in any ways to addressing the problem of elephant aggression. If yes, then there must a strong evidence for that in the passage, but we have no such evidence.
 In paragraph 4, the phrase, “The fabric of elephant society . . . has(s) effectively been frayed by . . .” is:
 an accurate description of the condition of elephant herds today.
 a metaphor for the effect of human activity on elephant communities.
 an exaggeration aimed at bolstering Bradshaw’s claims.
 an ode to the fragility of elephant society today.
Option 1 is incorrect because the statement is not a description but an assertion of a condition that exists today.
Both option 3 and 4 are not in tune with the author’s purpose. The author is not exaggerating the disintegration of elephant society. He is, in fact, being quite sympathetic.
Option 4 suggests that the society has become frail on its own, without any external cause. But human activity is the cause and that has frayed the fabric. Thus, option 4 too is not correctly expressing the idea given in the question.
 In the first paragraph, Bradshaw uses the term “violence” to describe the recent change in the humanelephant relationship because, according to him:
 there is a purposefulness in human and elephant aggression towards each other.
 elephant herds and their habitat have been systematically destroyed by humans.
 humanelephant interactions have changed their character over time.
 both humans and elephants have killed members of each other’s species.
Option 2 says ‘systematically destroyed’. There is no evidence of ‘systematic destruction’ of elephant herds by humans. It is an extreme choice.
Option 3 is true as per the passage, but that is not the reason behind the author’s using the term ‘violence’ to describe the recent change in the humanelephant relationship.
Option 4 is incorrect but the author is focusing on elephants’ aggression towards humans, something that should not be necessarily interpreted as ‘killing’
The only thing worse than being lied to is not knowing you’re being lied to. It’s true that plastic pollution is a huge problem, of planetary proportions. And it’s true we could all dwvg o more to reduce our plastic footprint. The lie is that blame for the plastic problem is wasteful consumers and that changing our individual habits will fix it.
Recycling plastic is to saving the Earth what hammering a nail is to halting a falling skyscraper. You struggle to find a place to do it and feel pleased when you succeed. But your effort is wholly inadequate and distracts from the real problem of why the building is collapsing in the first place. The real problem is that singleuse plastic—the very idea of producing plastic items like grocery bags, which we use for an average of 12 minutes but can persist in the environment for half a millennium—is an incredibly reckless abuse of technology. Encouraging individuals to recycle more will never solve the problem of a massive production of singleuse plastic that should have been avoided in the first place.
As an ecologist and evolutionary biologist, I have had a disturbing window into the accumulating literature on the hazards of plastic pollution. Scientists have long recognized that plastics biodegrade slowly, if at all, and pose multiple threats to wildlife through entanglement and consumption. More recent reports highlight dangers posed by absorption of toxic chemicals in the water and by plastic odors that mimic some species’ natural food. Plastics also accumulate up the food chain, and studies now show that we are likely ingesting it ourselves in seafood. . . .
Beginning in the 1950s, big beverage companies like CocaCola and AnheuserBusch, along with Phillip Morris and others, formed a nonprofit called Keep America Beautiful. Its mission is/was to educate and encourage environmental stewardship in the public. . . . At face value, these efforts seem benevolent, but they obscure the real problem, which is the role that corporate polluters play in the plastic problem. This clever misdirection has led journalist and author Heather Rogers to describe Keep America Beautiful as the first corporate greenwashing front, as it has helped shift the public focus to consumer recycling behavior and actively thwarted legislation that would increase extended producer responsibility for waste management. . . . [T]he greatest success of Keep America Beautiful has been to shift the onus of environmental responsibility onto the public while simultaneously becoming a trusted name in the environmental movement. . . .
So what can we do to make responsible use of plastic a reality? First: reject the lie. Litterbugs are not responsible for the global ecological disaster of plastic. Humans can only function to the best of their abilities, given time, mental bandwidth and systemic constraints. Our huge problem with plastic is the result of a permissive legal framework that has allowed the uncontrolled rise of plastic pollution, despite clear evidence of the harm it causes to local communities and the world’s oceans. Recycling is also too hard in most parts of the U.S. and lacks the proper incentives to make it work well.
 In the second paragraph, the phrase “what hammering a nail is to halting a falling skyscraper” means:
 relying on emerging technologies to mitigate the illeffects of plastic pollution.
 encouraging the responsible production of plastics by firms.
 focusing on consumer behaviour to tackle the problem of plastics pollution.
 focusing on singleuse plastic bags to reduce the plastics footprint.
He further adds in the second para “Recycling plastic is to saving the Earth what hammering a nail is to halting a falling skyscraper”. He suggests that neither recycling nor change in consumer behavior is going to solve the problem. The right answer is 3
 In the first paragraph, the author uses “lie” to refer to the:
 blame assigned to consumers for indiscriminate use of plastics.
 understatement of the enormity of the plastics pollution problem.
 understatement of the effects of recycling plastics.
 fact that people do not know they have been lied to.
 The author lists all of the following as negative effects of the use of plastics EXCEPT the:
 slow pace of degradation or nondegradation of plastics in the environment.
 air pollution caused during the process of recycling plastics.
 adverse impacts on the digestive systems of animals exposed to plastic.
 poisonous chemicals released into the water and food we consume.
 Which of the following interventions would the author most strongly support:
 completely banning all singleuse plastic bags.
 having all consumers change their plastic consumption habits.
 recycling all plastic debris in the seabed.
 passing regulations targeted at producers that generate plastic products.
If we pass regulations targeted at producers of plastics, we might be able to change the situation. Thus option 4 is the right choice.
 It can be inferred that the author considers the Keep America Beautiful organisation:
 an innovative example of a collaborative corporate social responsibility initiative.
 a sham as it diverted attention away from the role of corporates in plastics pollution.
 an important step in sensitising producers to the need to tackle plastics pollution.
 a "greenwash" because it was a benevolent attempt to improve public recycling habits.
Economists have spent most of the 20th century ignoring psychology, positive or otherwise. But today there is a great deal of emphasis on how happiness can shape global economies, or — on a smaller scale — successful business practice. This is driven, in part, by a trend in "measuring" positive emotions, mostly so they can be optimized. Neuroscientists, for example, claim to be able to locate specific emotions, such as happiness or disappointment, in particular areas of the brain. Wearable technologies, such as Spire, offer datadriven advice on how to reduce stress.
We are no longer just dealing with "happiness" in a philosophical or romantic sense — it has become something that can be monitored and measured, including by our behavior, use of social media and bodily indicators such as pulse rate and facial expressions.
There is nothing automatically sinister about this trend. But it is disquieting that the businesses and experts driving the quantification of happiness claim to have our best interests at heart, often concealing their own agendas in the process. In the workplace, happy workers are viewed as a "winwin." Work becomes more pleasant, and employees, more productive. But this is now being pursued through the use of performanceevaluating wearable technology, such as Humanyze or Virgin Pulse, both of which monitor physical signs of stress and activity toward the goal of increasing productivity.
Cities such as Dubai, which has pledged to become the "happiest city in the world," dream up evermore elaborate and intrusive ways of collecting data on wellbeing — to the point where there is now talk of using CCTV cameras to monitor facial expressions in public spaces. New ways of detecting emotions are hitting the market all the time: One company, Beyond Verbal, aims to calculate moods conveyed in a phone conversation, potentially without the knowledge of at least one of the participants. And Facebook [has] demonstrated . . . that it could influence our emotions through tweaking our news feeds — opening the door to evermore targeted manipulation in advertising and influence.
As the science grows more sophisticated and technologies become more intimate with our thoughts and bodies, a clear trend is emerging. Where happiness indicators were once used as a basis to reform society, challenging the obsession with money that G.D.P. measurement entrenches, they are increasingly used as a basis to transform or discipline individuals.
Happiness becomes a personal project, that each of us must now work on, like going to the gym. Since the 1970s, depression has come to be viewed as a cognitive or neurological defect in the individual, and never a consequence of circumstances. All of this simply escalates the sense of responsibility each of us feels for our own feelings, and with it, the sense of failure when things go badly. A society that deliberately removed certain sources of misery, such as precarious and exploitative employment, may well be a happier one. But we won't get there by making this single, often fleeting emotion, the overarching goal.
 In the author’s opinion, the shift in thinking in the 1970s:
 introduced greater stress into people’s lives as they were expected to be responsible for their own happiness.
 was a welcome change from the earlier view that depression could be cured by changing circumstances.
 put people in touch with their own feelings rather than depending on psychologists.
 reflected the emergence of neuroscience as the authority on human emotions.
The author suggests that before 1970 people thought that depression was a result of one’s circumstances. Option b is incorrect, as it speaks about how depression could be cured, while the passage has nothing about it.
As the second part of the extract suggests, people, after 1970, became more responsible towards their happiness, as it became clear that depression was not a result of circumstances but of neurological or cognitive defects.
Option 1 is the best choice.
 The author’s view would be undermined by which of the following research findings?
 There is a definitive move towards the adoption of wearable technology that taps into emotions.
 A proliferation of gyms that are collecting data on customer wellbeing.
 Individuals worldwide are utilising technologies to monitor and increase their wellbeing.
 Stakeholders globally are moving away from collecting data on the wellbeing of individuals.
As the science grows more sophisticated and technologies become more intimate with our thoughts and bodies, a clear trend is emerging. Where happiness indicators were once used as a basis to reform society, challenging the obsession with money that G.D.P. measurement entrenches, they are increasingly used as a basis to transform or discipline individuals.
The author in the last sentence says that happiness indicators are used as a basis to transform or discipline individuals. Option 4 clearly weakens the author’s argument by saying that stakeholders are moving away from collecting data on the wellbeing of individuals. Thus, option 4 is undermining or weakening the author’s argument.
All the other three choices are supportive of the author’s views given in the paragraph.
 According to the author, Dubai:
 develops sophisticated technologies to monitor its inhabitants’ states of mind.
 incentivises companies that prioritise worker welfare.
 collaborates with Facebook to selectively influence its inhabitants’ moods.
 is on its way to becoming one of the world’s happiest cities.
Cities such as Dubai, which has pledged to become the "happiest city in the world," dream up evermore elaborate and intrusive ways of collecting data on wellbeing — to the point where there is now talk of using CCTV cameras to monitor facial expressions in public spaces…
Thus, option 1 is the right choice. There is no evidence for option 2 and 3, while option 4 says that it is on its way to becoming one of the world’s happiest cities. However, the passage says that Dubai wants to become. It doesn’t mean that it is likely to become the happiest city in the world.
 According to the author, wearable technologies and social media are contributing most to:
 happiness as a “personal project”.
 disciplining individuals to be happy.
 depression as a thing of the past.
 making individuals aware of stress in their lives.
 From the passage we can infer that the author would like economists to:
 correlate measurements of happiness with economic indicators.
 measure the effectiveness of Facebook and social media advertising.
 incorporate psychological findings into their research cautiously.
 work closely with neuroscientists to understand human behaviour.
When researchers at Emory University in Atlanta trained mice to fear the smell of almonds (by pairing it with electric shocks), they found, to their consternation, that both the children and grandchildren of these mice were spontaneously afraid of the same smell. That is not supposed to happen. Generations of schoolchildren have been taught that the inheritance of acquired characteristics is impossible. A mouse should not be born with something its parents have learned during their lifetimes, any more than a mouse that loses its tail in an accident should give birth to tailless mice. . . .
Modern evolutionary biology dates back to a synthesis that emerged around the 1940s60s, which married Charles Darwin’s mechanism of natural selection with Gregor Mendel’s discoveries of how genes are inherited. The traditional, and still dominant, view is that adaptations – from the human brain to the peacock’s tail – are fully and satisfactorily explained by natural selection (and subsequent inheritance). Yet [new evidence] from genomics, epigenetics and developmental biology [indicates] that evolution is more complex than we once assumed. . . .
In his book On Human Nature (1978), the evolutionary biologist Edward O Wilson claimed that human culture is held on a genetic leash. The metaphor [needs revision]. . . . Imagine a dogwalker (the genes) struggling to retain control of a brawny mastiff (human culture). The pair’s trajectory (the pathway of evolution) reflects the outcome of the struggle. Now imagine the same dogwalker struggling with multiple dogs, on leashes of varied lengths, with each dog tugging in different directions. All these tugs represent the influence of developmental factors, including epigenetics, antibodies and hormones passed on by parents, as well as the ecological legacies and culture they bequeath. . . .
The received wisdom is that parental experiences can’t affect the characters of their offspring. Except they do. The way that genes are expressed to produce an organism’s phenotype – the actual characteristics it ends up with – is affected by chemicals that attach to them. Everything from diet to air pollution to parental behaviour can influence the addition or removal of these chemical marks, which switches genes on or off. Usually these socalled ‘epigenetic’ attachments are removed during the production of sperm and eggs cells, but it turns out that some escape the resetting process and are passed on to the next generation, along with the genes. This is known as ‘epigenetic inheritance’, and more and more studies are confirming that it really happens. Let’s return to the almondfearing mice. The inheritance of an epigenetic mark transmitted in the sperm is what led the mice’s offspring to acquire an inherited fear. . . .
Epigenetics is only part of the story. Through culture and society, [humans and other animals] inherit knowledge and skills acquired by [their] parents. . . . All this complexity . . . points to an evolutionary process in which genomes (over hundreds to thousands of generations), epigenetic modifications and inherited cultural factors (over several, perhaps tens or hundreds of generations), and parental effects (over singlegeneration timespans) collectively inform how organisms adapt. These extragenetic kinds of inheritance give organisms the flexibility to make rapid adjustments to environmental challenges, dragging genetic change in their wake – much like a rowdy pack of dogs.
 The Emory University experiment with mice points to the inheritance of:
 psychological markers
 acquired characteristics
 personality traits
 acquired parental fears
 Which of the following best describes the author's argument?
 Darwin’s and Mendel’s theories together best explain evolution.
 Mendel’s theory of inheritance is unfairly underestimated in explaining evolution.
 Wilson’s theory of evolution is scientifically superior to either Darwin’s or Mendel’s.
 Darwin’s theory of natural selection cannot fully explain evolution.
Thus 1 is the best choice, as the author attributes inheritance to much more than natural selection and mendelian gentics. The other negative opinions expressed in the other options cannot be seen anywhere in the passage.
 Which of the following, if found to be true, would negate the main message of the passage?
 A study affirming the influence of sociocultural markers on evolutionary processes.
 A study highlighting the criticality of epigenetic inheritance to evolution.
 A study indicating the primacy of ecological impact on human adaptation.
 A study affirming the sole influence of natural selection and inheritance on evolution.
We can see clear evidence in these lines: All these tugs represent the influence of developmental factors, including epigenetics, antibodies and hormones passed on by parents, as well as the ecological legacies and culture they bequeath.
 The passage uses the metaphor of a dog walker to argue that evolutionary adaptation is most comprehensively understood as being determined by:
 extra genetic, genetic, epigenetic and genomic legacies.
 sociocultural, genetic, epigenetic, and genomic legacies
 ecological, hormonal, extra genetic and genetic legacies.
 genetic, epigenetic, developmental factors, and ecological legacies.
We can see clear evidence in these lines: All these tugs represent the influence of developmental factors, including epigenetics, antibodies and hormones passed on by parents, as well as the ecological legacies and culture they bequeath.
 In the first paragraph, the author laments the fact that:
 there is no recognition of the Indian soldiers who served in the Second World War.
 the new war memorial will be built right next to India Gate.
 India lost thousands of human lives during the Second World War.
 funds will be wasted on another war memorial when we already have the India Gate memorial.
The phrase ‘airbrushed out of existence’ has that regret in the tone. Thus 1 is the right choice.
The] Indian government [has] announced an international competition to design a National War Memorial in New Delhi, to honour all of the Indian soldiers who served in the various wars and counterinsurgency campaigns from 1947 onwards. The terms of the competition also specified that the new structure would be built adjacent to the India Gate – a memorial to the Indian soldiers who died in the First World War. Between the old imperialist memorial and the proposed nationalist one, India’s contribution to the Second World War is airbrushed out of existence.
The Indian government’s conception of the war memorial was not merely absentminded. Rather, it accurately reflected the fact that both academic history and popular memory have yet to come to terms with India’s Second World War, which continues to be seen as little more than mood music in the drama of India’s advance towards independence and partition in 1947. Further, the political trajectory of the postwar subcontinent has militated against popular remembrance of the war. With partition and the onset of the IndiaPakistan rivalry, both of the new nations needed fresh stories for selflegitimisation rather than focusing on shared wartime experiences.
However, the Second World War played a crucial role in both the independence and partition of India. . . . The Indian army recruited, trained and deployed some 2.5 million men, almost 90,000 of which were killed and many more injured. Even at the time, it was recognised as the largest volunteer force in the war. . . .
India’s material and financial contribution to the war was equally significant. India emerged as a major militaryindustrial and logistical base for Allied operations in southeast Asia and the Middle East. This led the United States to take considerable interest in the country’s future, and ensured that this was no longer the preserve of the British government.
Other wartime developments pointed in the direction of India’s independence. In a stunning reversal of its longstanding financial relationship with Britain, India finished the war as one of the largest creditors to the imperial power.
Such extraordinary mobilization for war was achieved at great human cost, with the Bengal famine the most extreme manifestation of widespread wartime deprivation. The costs on India’s home front must be counted in millions of lives.
Indians signed up to serve on the war and home fronts for a variety of reasons. . . . [M]any were convinced that their contribution would open the doors to India’s freedom. . . . The political and social churn triggered by the war was evident in the massive waves of popular protest and unrest that washed over rural and urban India in the aftermath of the conflict. This turmoil was crucial in persuading the Attlee government to rid itself of the incubus of ruling India. . . .
Seventy years on, it is time that India engaged with the complex legacies of the Second World War. Bringing the war into the ambit of the new national memorial would be a fitting – if not overdue – recognition that this was India’s War.
 The phrase “mood music” is used in the second paragraph to indicate that the Second World War is viewed as:
 setting the stage for the emergence of the India–Pakistan rivalry in the subcontinent.
 a tragic period in terms of loss of lives and national wealth.
 a backdrop to the subsequent independence and partition of the region.
 a part of the narrative on the illeffects of colonial rule on India.
Passage Overview: In the passage the author seems to be stressing on “India’s contribution to the second world war, and its consequences, something which has been ignored both by academicians and the Indian government”
This question is a kind of interpretation question. If we don’t know the meaning of the phrase ‘mood music’, we must try to the see the context in which it has been used. By the way, ‘mood music’ is recorded music that is played in the background to make the audience relax. So if you know the meaning, you can straightaway mark 3 as the answer. A backdrop is a background just as mood music is played in the background. Even from the passage it is clear that to the Indian government and Indian academicians, India’s contribution to the second world war is just a little more than a mood music, in other words it is not a significant contribution, something that the author seems to be lamenting. Option 3 is the right choice.
 The author lists all of the following as outcomes of the Second World War EXCEPT:
 independence of the subcontinent and its partition into two countries.
 US recognition of India’s strategic location and role in the War.
 largescale deaths in Bengal as a result of deprivation and famine.
 the large financial debt India owed to Britain after the War.
We could have marked option 4 directly, as it is stating exactly opposite of what is given in the passage. It was not India but Britain that owed large financial debt. India was one of the biggest creditors to Britain, the passage says. This means that it was India had lent resources to Britain.
 The author claims that omitting mention of Indians who served in the Second World War from the new National War Memorial is:
 a reflection of the academic and popular view of India’s role in the War.
 appropriate as their names can always be included in the India Gate memorial.
 a reflection of misplaced priorities of the postindependence Indian governments.
 is something which can be rectified in future by constructing a separate memorial.
yet to come to terms with India’s Second World War”. The other choices are neither stated nor implied in the paragraph.
.
 The author suggests that a major reason why India has not so far acknowledged its role in the Second World War is that it:
 blames the War for leading to the momentous partition of the country.
 wants to forget the human and financial toll of the War on the country.
 has been focused on building an independent, noncolonial political identity.
 views the War as a predominantly Allied effort, with India playing only a supporting role.
The last sentence of the second paragraph says: With partition and the onset of the IndiaPakistan rivalry, both of the new nations needed fresh stories for selflegitimization rather than focusing on shared wartime experiences. “Selflegitimization” would mean selfassertion, or establishing oneself as a strong legal entity. This makes option 3 the right choice. Moreover, none of the other options have any hint in the paragraph. Option 1 and 4 go out because the author asserts that India did make a significant contribution to the war. Option might seem a tempting choice, but there is no hint for it.
 The four sentences (labelled 1,2,3,4) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper sequence of order of the sentences and key in this sequence of four numbers as your answer:
 Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out. Choose its number as your answer and key it in.
 Translators are like bumblebees.
 Though long since scientifically disproved, this factoid is still routinely trotted out.
 Similar pronouncements about the impossibility of translation have dogged practitioners since Leonardo Bruni’s De interpretatione recta, published in 1424.
 Bees, unaware of these deliberations, have continued to flit from flower to flower, and translators continue to translate.
 In 1934, the French entomologist August Magnan pronounced the flight of the bumblebee to be aerodynamically impossible
 The four sentences (labelled 1, 2, 3, and 4) given in this question, when properly sequenced, form a coherent paragraph. Decide on the proper order for the sentences and key in this sequence of four numbers as your answer.

The passage given below is followed by four summaries. Choose the option that best captures the author’s position.
Production and legitimation of scientific knowledge can be approached from a number of perspectives. To study knowledge production from the sociology of professions perspective would mean a focus on the institutionalization of a body of knowledge. The professionsapproach informed earlier research on managerial occupation, business schools and management knowledge. It however tends to reify institutional power structures in its understanding of the links between knowledge and authority. Knowledge production is restricted in the perspective to the selected members of the professional community, most notably to the university faculties and professional colleges. Power is understood as a negative mechanism, which prevents the nonprofessional actors from offering their ideas and information as legitimate knowledge.
 Professionsapproach aims at the institutionalization of knowledge but restricts knowledge production as a function of a select few.
 The study of knowledge production can be done through many perspectives.
 Professionsapproach focuses on the creation of institutions of higher education and disciplines to promote knowledge production
 The professionsapproach has been one of the most relied upon perspective in the study of management knowledge production.
The above simplification helps us arrive at option 1 as the right choice. Options 3 and 4 are against the author’s stand in the passage. Option 2 is not the core message, but an inference that can be derived from the above passage.

The passage given below is followed by four summaries. Choose the option that best captures the author’s position.
Artificial embryo twinning is a relatively lowtech way to make clones. As the name suggests, this technique mimics the natural process that creates identical twins. In nature, twins form very early in development when the embryo splits in two. Twinning happens in the first days after egg and sperm join, while the embryo is made of just a small number of unspecialized cells. Each half of the embryo continues dividing on its own, ultimately developing into separate, complete individuals. Since they developed from the same fertilized egg, the resulting individuals are genetically identical.
 Artificial embryo twinning is lowtech and mimetic of the natural development of genetically identical twins from the embryo after fertilization.
 Artificial embryo twinning is lowtech unlike the natural development of identical twins from the embryo after fertilization.
 Artificial embryo twinning is just like the natural development of twins, where during fertilization twins are formed.
 Artificial embryo twinning is lowtech and is close to the natural development of twins where the embryo splits into two identical twins.

The passage given below is followed by four summaries. Choose the option that best captures the author’s position.
The conceptualization of landscape as a geometric object first occurred in Europe and is historically related to the European conceptualization of the organism, particularly the human body, as a geometric object with parts having a rational, threedimensional organization and integration. The European idea of landscape appeared before the science of landscape emerged, and it is no coincidence that Renaissance artists such as Leonardo da Vinci, who studied the structure of the human body, also facilitated an understanding of the structure of landscape. Landscape which had been a subordinate background to religious or historical narratives, became an independent genre or subject of art by the end of sixteenth century or the beginning of the seventeenth century.
 Landscape became a major subject of art at the turn of the sixteenth century.
 The threedimensional understanding of the organism in Europe led to a similar approach towards the understanding of landscape.
 The study of landscape as an independent genre was aided by the Renaissance artists.
 The Renaissance artists were responsible for the study of landscape as a subject of art.
Option 2 too has some distortions; while the passage says that conceptualization of landscape as geometric object is related to the European conceptualization of the organism as a geometric object, the option says that threedimensional understanding of the organism led to a similar approach…. It should be geometric understanding of the organism.
Option 3 best captures the author’s position, which in the passage is clearly visible as “Renaissance artists also facilitated an understanding of the structure of landscape”.
Option 4 is incorrect because it distorts the fact by saying the Renaissance artists were responsible, while the passage says that they facilitated.
 The four sentences (labelled 1,2,3,4) given in this question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a number. Decide on the proper sequence of order of the sentences and key in this sequence of four numbers as your answer:
 Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.
 In many cases time inconsistency is what prevents our going from intention to action.
 For people to continuously postpone getting their children immunized, they would need to be constantly fooled by themselves.
 In the specific case of immunization, however, it is hard to believe that time inconsistency by itself would be sufficient to make people permanently postpone the decision if they were fully cognizant of its benefits.
 In most cases, even a small cost of immunization was large enough to discourage most people.
 Not only do they have to think that they prefer to spend time going to the camp next month rather than today, they also have to believe that they will indeed go next month.
 Five sentences related to a topic are given below. Four of them can be put together to form a meaningful and coherent short paragraph. Identify the odd one out.
 Displacement in Bengal is thus not very significant in view of its magnitude.
 A factor of displacement in Bengal is the shifting course of the Ganges leading to erosion of river banks.
 The nature of displacement in Bengal makes it an interesting case study.
 Since displacement due to erosion is well spread over a long period of time, it remains invisible.
 Rapid displacement would have helped sensitize the public to its human costs.
 The four sentences (labelled 1, 2, 3, and 4) given in this question, when properly sequenced, form a coherent paragraph. Decide on the proper order for the sentences and key in this sequence of four numbers as your answer.
1600 satellites were sent up by a country for several purposes. The purposes are classified as broadcasting (B), communication (C), surveillance (S), and others (O). A satellite can serve multiple purposes; however a satellite serving either B, or C, or S does not serve O.
The following facts are known about the satellites:
1. The numbers of satellites serving B, C, and S (though may be not exclusively) are in the ratio 2:1:1.
2. The number of satellites serving all three of B, C, and S is 100.
3. The number of satellites exclusively serving C is the same as the number of satellites exclusively serving S. This number is 30% of the number of satellites exclusively serving B.
4. The number of satellites serving O is the same as the number of satellites serving both C and S but not B.
 What best can be said about the number of satellites serving C?
 Must be between 450 and 725
 Cannot be more than 800
 Must be between 400 and 800
 Must be at least 100
 What is the minimum possible number of satellites serving B exclusively?
 100
 200
 500
 250
 If at least 100 of the 1600 satellites were serving O, what can be said about the number of satellites serving S?
 At most 475
 Exactly 475
 At least 475
 No conclusion is possible based on the given information
 If the number of satellites serving at least two among B, C, and S is 1200, which of the following MUST be FALSE?
 The number of satellites serving C cannot be uniquely determined
 The number of satellites serving B is more than 1000
 All 1600 satellites serve B or C or S
 The number of satellites serving B exclusively is exactly 250
The multilayered piechart below shows the sales of LED television sets for a big retail electronics outlet during 2016 and 2017. The outer layer shows the monthly sales during this period, with each label showing the month followed by sales figure of that month. For some months, the sales figures are not given in the chart. The middlelayer shows quarterwise aggregate sales figures (in some cases, aggregate quarterwise sales numbers are not given next to the quarter). The innermost layer shows annual sales. It is known that the sales figures during the three months of the second quarter (April, May, June) of 2016 form an arithmetic progression, as do the three monthly sales figures in the fourth quarter (October, November, December) of that year.
 What is the percentage increase in sales in December 2017 as compared to the sales in December 2016?
 28.57
 22.22
 50.00
 38.46
 In which quarter of 2017 was the percentage increase in sales from the same quarter of 2016 the highest?
 Q1
 Q3
 Q4
 Q2
 During which quarter was the percentage decrease in sales from the previous quarter’s sales the highest?
 Q2 of 2017
 Q1 of 2017
 Q4 of 2017
 Q2 of 2016
 During which month was the percentage increase in sales from the previous month’s sales the highest?
 March of 2017
 October of 2017
 October of 2016
 March of 2016
An ATM dispenses exactly Rs. 5000 per withdrawal using 100, 200 and 500 rupee notes. The ATM requires every customer to give her preference for one of the three denominations of notes. It then dispenses notes such that the number of notes of the customer’s preferred denomination exceeds the total number of notes of other denominations dispensed to her.
 In how many di?erent ways can the ATM serve a customer who gives 500 rupee notes as her preference?
 If the ATM could serve only 10 customers with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, what is the maximum number of customers among these 10 who could have given 500 rupee notes as their preferences?
 What is the maximum number of customers that the ATM can serve with a stock of fifty 500 rupee notes and a sufficient number of notes of other denominations, if all the customers are to be served with at most 20 notes per withdrawal?
 10
 16
 12
 13
 What is the number of 500 rupee notes required to serve 50 customers with 500 rupee notes as their preferences and another 50 customers with 100 rupee notes as their preferences, if the total number of notes to be dispensed is the smallest possible?
 800
 750
 900
 1400
Adriana, Bandita, Chitra, and Daisy are four female students, and Amit, Barun, Chetan, and Deb are four male students. Each of them studies in one of three institutes  X, Y, and Z. Each student majors in one subject among Marketing, Operations, and Finance, and minors in a different one among these three subjects. The following facts are known about the eight students:
1. Three students are from X, three are from Y, and the remaining two students, both female, are from Z.
2. Both the male students from Y minor in Finance, while the female student from Y majors in Operations.
3. Only one male student majors in Operations, while three female students minor in Marketing.
4. One female and two male students major in Finance.
5. Adriana and Deb are from the same institute. Daisy and Amit are from the same institute.
6. Barun is from Y and majors in Operations. Chetan is from X and majors in Finance.
7. Daisy minors in Operations.
 Who are the students from the institute Z?
 Adriana and Bandita
 Adriana and Daisy
 Bandita and Chitra
 Chitra and Daisy
 Which subject does Deb minor in?
 Cannot be determined uniquely from the given information
 Marketing
 Operations
 Finance
 Which subject does Amit major in?
 Operations
 Marketing
 Cannot be determined uniquely from the given information
 Finance
 If Chitra majors in Finance, which subject does Bandita major in?
 Cannot be determined uniquely from the given information
 Marketing
 Finance
 Operations
You are given an n×n square matrix to be ?lled with numerals so that no two adjacent cells have the same numeral. Two cells are called adjacent if they touch each other horizontally, vertically or diagonally. So a cell in one of the four corners has three cells adjacent to it, and a cell in the ?rst or last row or column which is not in the corner has five cells adjacent to it. Any other cell has eight cells adjacent to it.
 What is the minimum number of different numerals needed to ?ll a 3×3 square matrix?
 What is the minimum number of different numerals needed to ?ll a 5×5 square matrix?
 Suppose you are allowed to make one mistake, that is, one pair of adjacent cells can have the same numeral. What is the minimum number of different numerals required to ?ll a 5×5 matrix?
 16
 4
 25
 9
 Suppose that all the cells adjacent to any particular cell must have different numerals. What is the minimum number of different numerals needed to fill a 5×5 square matrix?
 9
 16
 4
 25
Fuel contamination levels at each of 20 petrol pumps P1, P2, …, P20 were recorded as either high, medium, or low.
1. Contamination levels at three pumps among P1 – P5 were recorded as high.
2. P6 was the only pump among P1 – P10 where the contamination level was recorded as low.
3. P7 and P8 were the only two consecutively numbered pumps where the same levels of contamination were recorded.
4. High contamination levels were not recorded at any of the pumps P16 – P20.
5. The number of pumps where high contamination levels were recorded was twice the number of pumps where low contamination levels were recorded.
 Which of the following MUST be true?
 The contamination level at P10 was recorded as high.
 The contamination level at P13 was recorded as low.
 The contamination level at P20 was recorded as medium.
 The contamination level at P12 was recorded as high.
 What best can be said about the number of pumps at which the contamination levels were recorded as medium?
 Exactly 8
 More than 4
 At least 8
 At most 9
 If the contamination level at P11 was recorded as low, then which of the following MUST be true?
 The contamination level at P12 was recorded as high.
 The contamination level at P14 was recorded as medium.
 The contamination level at P15 was recorded as medium.
 The contamination level at P18 was recorded as low.
 If contamination level at P15 was recorded as medium, then which of the following MUST be FALSE?
 Contamination level at P14 was recorded to be higher than that at P15.
 Contamination levels at P10 and P14 were recorded as the same.
 Contamination levels at P13 and P17 were recorded as the same.
 Contamination levels at P11 and P16 were recorded as the same.
A company administers a written test comprising of three sections of 20 marks each – Data Interpretation (DI), Written English (WE) and General Awareness (GA), for recruitment. A composite score for a candidate (out of 80) is calculated by doubling her marks in DI and adding it to the sum of her marks in the other two sections. Candidates who score less than 70% marks in two or more sections are disqualified. From among the rest, the four with the highest composite scores are recruited. If four or less candidates qualify, all who qualify are recruited.
Ten candidates appeared for the written test. Their marks in the test are given in the table below. Some marks in the table are missing, but the following facts are known:
1. No two candidates had the same composite score.
2. Ajay was the unique highest scorer in WE.
3. Among the four recruited, Geeta had the lowest composite score.
4. Indu was recruited.
5. Danish, Harini, and Indu had scored the same marks the in GA.
6. Indu and Jatin both scored 100% in exactly one section and Jatin’s composite score was 10 more than Indu’s.
 Which of the following statements MUST be true?
1. Jatin's composite score was more than that of Danish.
2. Indu scored less than Chetna in DI.
3. Jatin scored more than Indu in GA.
 Only 2
 Only 1
 Both 1 and 2
 Both 2 and 3
 Which of the following statements MUST be FALSE?
 Chetna scored more than Bala in DI
 Harini’s composite score was less than that of Falak
 Bala’s composite score was less than that of Ester
 Bala scored same as Jatin in DI
 If all the candidates except Ajay and Danish had different marks in DI, and Bala's composite score was less than Chetna's composite score, then what is the maximum marks that Bala could have scored in DI?
 If all the candidates scored different marks in WE then what is the maximum marks that Harini could have scored in WE?
Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.
 Based on the given information, which of the following statements MUST be FALSE?
 The size of the research committee is less than the size of the administration committee
 In the teaching committee the number of educationalists is equal to the number of politicians
 In the administration committee the number of bureaucrats is equal to the number of educationalists
 The size of the research committee is less than the size of the teaching committee
 What is the number of bureaucrats in the administration committee?
 What is the number of educationalists in the research committee?
 Which of the following CANNOT be determined uniquely based on the given information?
 The total number of educationalists in the three committees
 The total number of bureaucrats in the three committees
 The size of the research committee
 The size of the teaching committee
 Let x, y, z be three positive real numbers in a geometric progression such that x < y < z. If 5x, 16y, and 12z are in an arithmetic progression then the common ratio of the geometric progression is
 3/6
 3/2
 5/2
 1/6
Let x = $a$, y = $ar$ and z = $ar^2$
Given that, 5x, 16y and 12z are in AP.
so, 5x + 12z = 32y
On replacing the values of x, y and z, we get
$5a + 12ar^2 = 32ar$
or, $12r^2  32r + 5$ = 0
On solving, $r$ = $\frac{5}{2}$ or $\frac{1}{6}$
For $r$ = $\frac{1}{6}$, x < y < z is not satisfied.
So, $r$ = $\frac{5}{2}$
 A tank is fitted with pipes, some filling it and the rest draining it. All filling pipes fill at the same rate, and all draining pipes drain at the same rate. The empty tank gets completely filled in 6 hours when 6 filling and 5 draining pipes are on, but this time becomes 60 hours when 5 filling and 6 draining pipes are on. In how many hours will the empty tank get completely filled when one draining and two filling pipes are on?
Let the rate of each filling pipes be 'x lts/hr' and the rate of each draining pipes be 'y lts/hr'.
According to the first condition,
Capacity of tank = (6x  5y)×6..........(i)
From the second condition,
Capacity of tank = (5x  6y) × 60.....(ii)
On equating (i) and (ii), we get
(6x  5y) × 6 = (5x  6y)×60
or, 6x  5y = 50x  60y
or, 44x = 55y
or, 4x = 5y
or, x = 1.25y
Capacity of the tank = (6x  5y) × 6 = (7.5y  5y) × 6 = 15y
Effective rate of 2 filling and 1 draining pipes = (2x  y) = (2.5y  y) = 1.5y
Time required = $\frac{\text{15y}}{\text{1.5y}}$hours = 10 hours.
Hence, 10 is the correct answer.
 Given that x^{2018}y^{2017} = 1/2 and x^{2016}y^{2019} = 8, the value of x^{2} + y^{3} is
 35/4
 37/4
 31/4
 33/4
Given that $x^{2018}y^{2017}=\frac{1}{2}$ ... (1)
$x^{2016}y^{2019}=8$ ... (2)
Equation (2)/ Equation (1)
$\frac{y^2}{x^2} = \frac{8}{1/2}$
$\frac{y}{x} = 4$ or $4$
Case 1: When $\frac{y}{x} = 4$
$x^{2018}(4x)^{2017}=\frac{1}{2}$
$x^{2018+2017}(2)^{4034}=\frac{1}{2}$
$x^{4035}=\frac{1}{(2)^{4035}}$
$x=\frac{1}{2}$
Since, $\frac{y}{x} = 4$, => y = 2
Therefore, $x^{2}+y^{3}$ = $\frac{1}{4}+8$ = $\frac{33}{4}$
Case 2: When $\frac{y}{x} = 4$
$x^{2018}(4x)^{2017}=\frac{1}{2}$
$x^{2018+2017}(2)^{4034}=\frac{1}{2}$
$x^{4035}=\frac{1}{(2)^{4035}}$
$x=\frac{1}{2}$
Since, $\frac{y}{x} = 4$, => y = 2
Therefore, $x^{2}+y^{3}$ = $\frac{1}{4}+8$ = $\frac{33}{4}$.
 Point P lies between points A and B such that the length of BP is thrice that of AP. Car 1 starts from A and moves towards B. Simultaneously, car 2 starts from B and moves towards A. Car 2 reaches P one hour after car 1 reaches P. If the speed of car 2 is half that of car 1, then the time, in minutes, taken by car 1 in reaching P from A is
Let the distance between A and B be 4x.
Length of BP is thrice the length of AP.
=> AP = x and BP = 3x
Let the speed of car 1 be s and the speed of car 2 be 0.5s.
Car 2 reaches P one hour (60 minutes) after Car 1 reaches P.
=> x/s + 60 = 3x/0.5s
x/s + 60 = 6x/s
5x/s = 60
x/s = 12
Time taken by car 1 in reaching P from A = x/s = 12 minutes.
Therefore, 12 is the correct answer.
 If \({\log _2}\left( {5 + {{\log }_3}a} \right) = 3\) and \({\log _5}\left( {4a + 12 + {{\log }_2}b} \right) = 3\), then a + b is equal to
 67
 40
 32
 59
$\log_{2}({5+\log_{3}{a}})=3$
=>$5 + \log_{3}{a}$ = 8
=>$ \log_{3}{a}$ = 3
or $a$ = 27
$\log_{5}({4a+12+\log_{2}{b}})=3$
=>$4a+12+\log_{2}{b}$ = 125
Putting $a$ = 27, we get
$\log_{2}{b}$ = 5
or, $b$ = 32
So, $a + b$ = 27 + 32 = 59
 A trader sells 10 litres of a mixture of paints A and B, where the amount of B in the mixture does not exceed that of A. The cost of paint A per litre is Rs. 8 more than that of paint B. If the trader sells the entire mixture for Rs. 264 and makes a pro?t of 10%, then the highest possible cost of paint B, in Rs. per litre, is
 26
 16
 20
 22
Let the price of paint B be x.
Price of paint A = x+8
We know that the amount of paint B in the mixture does not exceed the amount of paint A. Therefore, paint B can at the maximum compose 50% of the mixture.
The seller sells 10 litres of paint at Rs.264 earning a profit of 10%.
=> The cost price of 10 litres of the paint mixture = Rs. 240
Therefore, the cost of 1 litre of the mixture = Rs.24
We have to find the highest possible cost of paint B.
When we increase the cost of paint B, the cost of paint A will increase too. If the cost price of the mixture is closer to the cost of paint B, then the amount of paint B present in the mixture should be greater than the amount of paint A present in the mixture.
The highest possible cost of paint B will be obtained when the volumes of paint A and paint B in the mixture are equal.
=> (x+x+8)/2 = 24
2x = 40
x = Rs. 20
 In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
 \(\sqrt {12} \)
 \(\sqrt {14} \)
 \(\sqrt {13} \)
 \(\sqrt {11} \)
Given that two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm.
In the diagram we can see that AB = 6 cm, CD = 4 cm and MN = 1 cm.
We can see that M and N are the mid points of AB and CD respectively.
AM = 3 cm and CD = 2 cm. Let 'OM' be x cm.
In right angle triangle AMO,
$AO^2 = AM^2 + OM^2$
$\Rightarrow$ $AO^2 = 3^2 + x^2$ ... (1)
In right angle triangle CNO,
$CO^2 = CN^2 + ON^2$
$\Rightarrow$ $CO^2 = 2^2 + (OM+MN)^2$
$\Rightarrow$ $CO^2 = 2^2 + (x+1)^2$ ... (2)
We know that both AO and CO are the radius of the circle. Hence $AO = CO$
Therefore, we can equate equation (1) and (2)
$3^2+x^2$=$2^2+(x+1)^2$
$\Rightarrow$ x = 2 cm
Therefore, the radius of the circle
$AO = \sqrt{AM^2 + OM^2}$
$\Rightarrow$ $AO=\sqrt{3^2+2^2}=\sqrt{13}$.
 If among 200 students, 105 like pizza and 134 like burger, then the number of students who like only burger can possibly be
 93
 26
 23
 96
It has been given that among 200 students, 105 like pizza and 134 like burger.
The question asks us to find out the number of students who can be liking only burgers among the given values.
The least number of students who like only burger will be obtained when everyone who likes pizza likes burger too.
In this case, 105 students will like pizza and burger and 134105 = 29 students will like only burger. Therefore, the number of students who like only burger cannot be less than 29.
The maximum number of students who like only burger will be obtained when we try to separate the 2 sets as much as possible.
There are 200 students in total. 105 of them like pizza. Therefore, the remaining 95 students can like only burger and 13495 = 39 students can like both pizza and burger. As we can see, the number of students who like burger cannot exceed 95.
The number of students who like only burger should lie between 29 and 95 (both the values are included).
93 is the only value among the given options that satisfies this condition.
 In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?
 27
 28
 26
 25
In an apartment complex, the number of people aged 51 years and above is 30 and there are at most 39 people whose ages are below 51 years. The average age of all the people in the apartment complex is 38 years. What is the largest possible average age, in years, of the people whose ages are below 51 years?
The possible average age of people whose ages are below 51 years will be maximum if the average age of the number of people aged 51 years and above is minimum. Hence, we can say that that there are 30 people having same age 51 years.
Let 'x' be the maximum average age of people whose ages are below 51.
Then we can say that,
$\frac{51*30+39*x}{30+39} = 38$
$\Rightarrow$ $1530+39x = 2622$
$\Rightarrow$ $x = 1092/39 = 28$
 Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will be
 \(164\sqrt 3 \)
 \(188\sqrt 3 \)
 \(248\sqrt 3 \)
 \(192\sqrt 3 \)
We can see that T$_{2}$ is formed by using the mid points of T$_{1}$. Hence, we can say that area of triangle of T$_{2}$ will be (1/4)th of the area of triangle T$_{1}$.
Area of triangle T$_{1}$ = $\frac{\sqrt{3}}{4}*(24)^2$ = $144\sqrt{3}$ sq. cm
Area of triangle T$_{2}$ = $\frac{144\sqrt{3}}{4}$ = $36\sqrt{3}$ sq. cm
Sum of the area of all triangles = T$_{1}$ + T$_{2}$ + T$_{3}$ + ...
$\Rightarrow$ T$_{1}$ + T$_{2}$/$4$ + T$_{3}$/$4^2$ + ...
$\Rightarrow$ $\frac{T_{1}}{1  0.25}$
$\Rightarrow$ $\frac{4}{3}*T_{1}$
$\Rightarrow$ $\frac{4}{3}*144\sqrt{3}$
$\Rightarrow$ $192\sqrt{3}$
 If u^{2} + (u−2v−1)^{2} = −4v(u + v), then what is the value of u + 3v?
 1/4
 0
 1/2
 1/4
Given that $U^{2}+(U2V1)^{2}$= −$4V(U+V)$
$\Rightarrow$ $U^{2}+(U^22UVU2UV+4V^2+2VU+2V+1)$ = −$4V(U+V)$
$\Rightarrow$ $U^{2}+(U^24UV2U+4V^2+4V+1)$ = −$4V(U+V)$
$\Rightarrow$ $2U^24UV2U+4V^2+4V+1=−4UV4V^2$
$\Rightarrow$ $2U^22U+8V^2+4V+1=0$
$\Rightarrow$ $2[U^2U+\frac{1}{4}]+8[V^2+\frac{V}{2}+\frac{1}{16}]=0$
$\Rightarrow$ $2(U\frac{1}{2})^2+8(V+\frac{1}{4})^2=0$
Sum of two square terms is zero i.e. individual square term is equal to zero.
$U\frac{1}{2}$ = 0 and $V+\frac{1}{4}$ = 0
U = $\frac{1}{2}$ and V = $\frac{1}{4}$
Therefore, $U+3V$ = $\frac{1}{2}$+$\frac{1*3}{4}$ = $\frac{1}{4}$.
 If x is a positive quantity such that \({2^x} = {3^{{{\log }_5}2}}\) , then x is equal to
 \(1 + {\log _3}\frac{5}{3}\)
 \({\log _5}8\)
 \(1 + {\log _5}\frac{3}{5}\)
 \({\log _5}9\)
Givne that: $2^{x}=3^{\log_{5}{2}}$
$\Rightarrow$ $2^{x}=2^{\log_{5}{3}}$
$\Rightarrow$ $x=\log_{5}{3}$
$\Rightarrow$ $x=\log_{5}{\frac{3*5}{5}}$
$\Rightarrow$ $x=\log_{5}{5}+\log_{5}{\frac{3}{5}}$
$\Rightarrow$ $x=1+\log_{5}{\frac{3}{5}}$.
 While multiplying three real numbers, Ashok took one of the numbers as 73 instead of 37. As a result, the product went up by 720. Then the minimum possible value of the sum of squares of the other two numbers is
We know that one of the 3 numbers is 37.
Let the product of the other 2 numbers be x.
It has been given that 73x37x = 720
36x = 720
x = 20
Product of 2 real numbers is 20.
We have to find the minimum possible value of the sum of the squares of the 2 numbers.
Let x=a*b
It has been given that a*b=20
The least possible sum for a given product is obtained when the numbers are as close to each other as possible.
Therefore, when a=b, the value of a and b will be $\sqrt{20}$.
Sum of the squares of the 2 numbers = 20 + 20 = 40.
Therefore, 40 is the correct answer.
 Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is
 2 : 5
 4 : 9
 3 : 8
 1 : 3
It is given that EFGH is also a square whose area is 62.5% of that of ABCD. Let us assume that E divides AB in x : 1. Because of symmetry we can se that points F, G and H divide BC, CD and DA in x : 1.
Let us assume that 'x+1' is the length of side of square ABCD.
Area of square ABCD = $(x+1)^2$ sq. units.
Therefore, area of square EFGH = $\frac{62.5}{100}*(x+1)^2$ = $\frac{5(x+1)^2}{8}$ ... (1)
In right angle triangle EBF,
$EF^2 = EB^2 + BF^2$
$\Rightarrow$ $EF = \sqrt{1^2+x^2}$
Therefore, the area of square EFGH = $EF^2$ = $x^2+1$ ... (2)
By equating (1) and (2),
$x^2+1 = \frac{5(x+1)^2}{8}$
$\Rightarrow$ $8x^2+8 = 5x^2+10x+5$
$\Rightarrow$ $3x^210x+3 = 0$
$\Rightarrow$ $(x  3)(3x  1) = 0$
$\Rightarrow$ $x = 3$ or $1/3$
The ratio of length of EB to that of CG = 1 : x
EB : CG = 1 : 3 or 3 : 1.
 A right circular cone, of height 12 ft, stands on its base which has diameter 8 ft. The tip of the cone is cut off with a plane which is parallel to the base and 9 ft from the base. With π = 22/7, the volume, in cubic ft, of the remaining part of the cone is
We are given that diameter of base = 8 ft. Therefore, the radius of circular base = 8/2 = 4 ft
In triangle OAB and OCD
$\frac{OA}{AB} = \frac{OC}{CD}$
$\Rightarrow$ AB = $\frac{3*4}{12}$ = 1 ft.
Therefore, the volume of remaining part = Volume of entire cone  Volume of smaller cone
$\Rightarrow$ $\frac{1}{3}*\pi*4^2*12\frac{1}{3}*\pi*1^2*3$
$\Rightarrow$ $\frac{1}{3}*\pi*189$
$\Rightarrow$ $\frac{22}{7*3}*189$
$\Rightarrow$ $198$ cubic ft
 \({\log _{12}}81 = p,then\;3\left( {\frac{{4  p}}{{4 + p}}} \right)\) is equal to
 log_{4}16
 log_{6}8
 log_{6}16
 log_{2}8
Given that: $\log_{12}{81}=p$
$\Rightarrow$ $\log_{81}{12}=\frac{1}{p}$
$\Rightarrow$ $4\log_{3}{3*4}=\frac{1}{p}$
$\Rightarrow$ $1+\log_{3}{4}=\frac{4}{p}$
Using Componendo and Dividendo,
$\Rightarrow$ $\frac{1+\log_{3}{4}1}{1+\log_{3}{4}+1}=\frac{4p}{4+p}$
$\Rightarrow$ $\frac{\log_{3}{4}}{2+\log_{3}{4}}=\frac{4p}{4+p}$
$\Rightarrow$ $\frac{\log_{3}{4}}{\log_{3}{9}+\log_{3}{4}}=\frac{4p}{4+p}$
$\Rightarrow$ $\frac{\log_{3}{4}}{\log_{3}{36}}=\frac{4p}{4+p}$
$\Rightarrow$ $3*\frac{4p}{4+p}=\frac{3\log_{3}{4}}{\log_{3}{36}}$
$\Rightarrow$ $3*\frac{4p}{4+p}=\frac{\log_{3}{64}}{\log_{3}{36}}$
$\Rightarrow$ $3*\frac{4p}{4+p}=\log_{36}{64}$
$\Rightarrow$ $3*\frac{4p}{4+p}=\log_{6^2}{8^2}=\log_{6}{8}$.
 Train T leaves station X for station Y at 3 pm. Train S, traveling at three quarters of the speed of T, leaves Y for X at 4 pm. The two trains pass each other at a station Z, where the distance between X and Z is three?fths of that between X and Y. How many hours does train T take for its journey from X to Y?
Train T starts at 3 PM and train S starts at 4 PM.
Let the speed of train T be t.
=> Speed of train S = 0.75t.
When the trains meet, train t would have traveled for one more hour than train S.
Let us assume that the 2 trains meet x hours after 3 PM. Trains S would have traveled for x1 hours.
Distance traveled by train T = xt
Distance traveled by train S = (x1)*0.75t = 0.75xt0.75t
We know that train T has traveled three fifths of the distance. Therefore, train S should have traveled twofifths the distance between the 2 cities.
=> (xt)/(0.75xt0.75t) = 3/2
2xt = 2.25xt2.25t
0.25x = 2.25
x = 9 hours.
Train T takes 9 hours to cover threefifths the distance. Therefore, to cover the entire distance, train T will take 9*(5/3) = 15 hours.
Therefore, 15 is the correct answer.
 Each of 74 students in a class studies at least one of the three subjects H, E and P. Ten students study all three subjects, while twenty study H and E, but not P. Every student who studies P also studies H or E or both. If the number of students studying H equals that studying E, then the number of students studying H is
Let us draw a Venn diagram using the information present in the question.
It is given that the number of students studying H equals that studying E.
Let 'x' be the total number of students who studied H, and H and P but mot E.We can also say that the same will be the number of students who studied E, and E and P but not H.Therefore,
x + 20 + 10 + x = 74
x = 22
Hence, the number of students studying H = 22 + 10+ 20 = 52
 A wholesaler bought walnuts and peanuts, the price of walnut per kg being thrice that of peanut per kg. He then sold 8 kg of peanuts at a pro?t of 10% and 16 kg of walnuts at a pro?t of 20% to a shopkeeper. However, the shopkeeper lost 5 kg of walnuts and 3 kg of peanuts in transit. He then mixed the remaining nuts and sold the mixture at Rs. 166 per kg, thus making an overall pro?t of 25%. At what price, in Rs. per kg, did the wholesaler buy the walnuts?
 98
 96
 84
 86
Let the price of peanuts be Rs. 100x per kg
Then, the price of walnuts = Rs. 300x per kg
Cost price of peanuts for the shopkeeper = Rs. 110x per kg
Cost price of walnuts for the shopkeeper = Rs. 360x per kg
Total cost incurred to the shopkeeper while buying = Rs.(8 * 110x + 16 * 360x) = Rs. 6640x
Total selling price that the shopkeeper got = Rs. (166 * 16) = Rs. 2656
Profit = 25%
So, cost price = Rs. 2124.80
Therefore, 6640x = 2124.80
On solving, we get x = 0.32
Therefore, price of walnuts = Rs. (300 * 0.32) = Rs. 96 per kg.
 A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is
Let the total number of tests be 'n' and the average by 'A'
Total score = n*A
When 1st 10 tests are excluded, decrease in total value of scores = (nA  20 * 10) = (nA  200)
Also, (n  10)(A + 1) = (nA  200)
On solving, we get 10A  n = 190..........(i)
When last 10 tests are excluded, decrease in total value of scores = (nA  30 * 10) = (nA  300)
Also, (n  10)(A  1) = (nA  300)
On solving, we get 10A + n = 310..........(ii)
From (i) and (ii), we get n = 60
Hence, 60 is the correct answer.
 Raju and Lalitha originally had marbles in the ratio 4:9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5:6. What fraction of her original number of marbles was given by Lalitha to Raju?
 1/4
 7/33
 1/5
 6/19
Let the number of marbles with Raju and Lalitha initially be 4x and 9x.
Let the number of marbles that Lalitha gave to Raju be a.
It has been given that (4x+a)/(9xa) = 5/6
24x + 6a = 45x  5a
11a = 21x
a/x = 21/11
Fraction of original marbles given to Raju by Lalitha = a/9x (Since Lalitha had 9x marbles initially).
a/9x = 21/99
= 7/33.
 Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?
 24, 10
 25, 9
 24, 12
 25, 10
Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?
We know that AC is the diameter and $\angle$ ABC = 90°. AC = 2*13 = 26 cm
In right angle triangle ABC,
$AC^2 = AB^2 + BC^2$
$\Rightarrow$ $AB^2+BC^2=26^2$
$\Rightarrow$ $AB^2+BC^2=676$
Let us check with the options.
Option (A): $24^2+10^2 = 676$. Hence, this is a possible answer.
Option (B): $25^2+9^2 = 706 \neq 676$. Hence, this is an incorrect pair.
Option (C): $25^2+10^2 = 725 \neq 676$. Hence, this is an incorrect pair.
Option (D): $24^2+12^2 = 720 \neq 676$. Hence, this is an incorrect pair.
 In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is
 18√3
 24√3
 32√3
 12√3
In a parallelogram ABCD of area 72 sq cm, the sides CD and AD have lengths 9 cm and 16 cm, respectively. Let P be a point on CD such that AP is perpendicular to CD. Then the area, in sq cm, of triangle APD is
Given that area of parallelogram = 72 sq cm
Area of triangle ABC = $\frac{1}{2}$*area of parallelogram
(1/2)*AB*BC*sinABC = $\frac{1}{2}$*72
sinABC = $\frac{1}{2}$
$\angle$ ABC = 30°
Let us draw a perpendicular CQ from C to AB.
By symmetry we can say that CQ = AP, CP = AQ and QB = PQ,
Therefore, we can say that area of triangle APD = area of triangle CQB
In right angle triangle CQB,
QB = CBcos30° = $16*\frac{\sqrt{3}}{2}$ = $8\sqrt{3}$ cm
CQ = CBsin30° = $16*\frac{1}{2}$ = $8$ cm
Therefore, area of triangle CQB = 1/2*CQ*QB = $1/2*8*8\sqrt{3}$ = $32\sqrt{3}$
Hence, we can say that area of triangle APD = $32\sqrt{3}$.
 In a circle with center O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is
 \({\left( {\frac{\pi }{{3\sqrt 3 }}} \right)^{\frac{1}{2}}}\)
 \({\left( {\frac{\pi }{4}} \right)^{\frac{1}{2}}}\)
 \({\left( {\frac{\pi }{6}} \right)^{\frac{1}{2}}}\)
 \({\left( {\frac{\pi }{{4\sqrt 3 }}} \right)^{\frac{1}{2}}}\)
It is given that radius of the circle = 1 cm
Chord AB subtends an angle of 60° on the centre of the given circle. R be the region bounded by the radii OA, OB and the arc AB.
Therefore, R = $\frac{60°}{360°}$*Area of the circle = $\frac{1}{6}$*$\pi*(1)^2$ = $\frac{\pi}{6}$ sq. cm
It is given that OC = OD and area of triangle OCD is half that of R. Let OC = OD = x.
Area of triangle COD = $\frac{1}{2}*OC*OD*sin60°$
$\frac{\pi}{6*2}$ = $\frac{1}{2}*x*x*\frac{\sqrt{3}}{2}$
$\Rightarrow$ $x^2 = \frac{\pi}{3\sqrt{3}}$
$\Rightarrow$ $x$ = $(\frac{\pi}{3\sqrt{3}})^{\frac{1}{2}}$ cm.
 How many numbers with two or more digits can be formed with the digits 1,2,3,4,5,6,7,8,9, so that in every such number, each digit is used at most once and the digits appear in the ascending order?
It has been given that the digits in the number should appear in the ascending order. Therefore, there is only 1 possible arrangement of the digits once they are selected to form a number.
There are 9 numbers (1,2,3,4,5,6,7,8,9) in total.
2 digit numbers can be formed in $9C_2$ ways.
3 digit numbers can be formed in $9C_3$ ways.
..................................................
..9 digit number can be formed in 9C9 ways.
We know that $nC_0+nC_1+nC_2+.........+nC_n =2^n$
=> $9C_0 + 9C_1+9C_2+....9C_9 = 2^9$
$9C_0 + 9C_1 + ...9C_9 = 512$
We have to subtract $9C_0$ and $9C_1$ from both the sides of the equations since we cannot form single digit numbers.
=> $9C_2 + 9C_3+...+9C_9=51219$
$9C_2+9C_3+...+9C_9=502$
Therefore, $502$ is the right answer.
 The number of integers x such that 0.25 < 2^{x} < 200, and 2^{x} +2 is perfectly divisible by either 3 or 4, is
At $x = 0, 2^x = 1$ which is in the given range [0.25, 200]
$2^x + 2$ = 1 + 2 = 3 Which is divisible by 3. Hence, x = 0 is one possible solution.
At $x = 1, 2^x = 2$ which is in the given range [0.25, 200]
$2^x + 2$ = 2 + 2 = 3 Which is divisible by 4. Hence, x = 1 is one possible solution.
At $x = 2, 2^x = 4$ which is in the given range [0.25, 200]
$2^x + 2$ = 4 + 2 = 6 Which is divisible by 3. Hence, x = 2 is one possible solution.
At $x = 3, 2^x = 8$ which is in the given range [0.25, 200]
$2^x + 2$ = 8 + 2 = 3 Which is not divisible by 3 or 4. Hence, x = 3 can't be a solution.
At $x = 4, 2^x = 16$ which is in the given range [0.25, 200]
$2^x + 2$ = 16 + 2 = 18 Which is divisible by 3. Hence, x = 4 is one possible solution.
At $x = 5, 2^x = 32$ which is in the given range [0.25, 200]
$2^x + 2$ = 32 + 2 = 34 Which is not divisible by 3 or 4. Hence, x = 5 can't be a solution.
At $x = 6, 2^x = 64$ which is in the given range [0.25, 200]
$2^x + 2$ = 64 + 2 = 66 Which is divisible by 3. Hence, x = 6 is one possible solution.
At $x = 7, 2^x = 128$ which is in the given range [0.25, 200]
$2^x + 2$ = 128 + 2 = 130 Which is not divisible by 3 or 4. Hence, x = 7 can't be a solution.
At $x = 8, 2^x = 256$ which is not in the given range [0.25, 200]. Hence, x can't take any value greater than 7.
Therefore, all possible values of x = {0,1,2,4,6}. Hence, we can say that 'x' can take 5 different integer values.
 If f(x + 2) = f(x) + f(x + 1) for all positive integers x, and f(11) = 91, f(15) = 617, then f(10) equals
$f(x + 2) = f(x) + f(x + 1)$
As we can see, the value of a term is the sum of the 2 terms preceding it.
It has been given that $f(11) = 91$ and $f(15) = 617$.
We have to find the value of $f(10)$.
Let $f(10)$ = b
$f(12)$ = b + 91
$f(13)$ = 91 + b + 91 = 182 + b
$f(14)$ = 182+b+91+b = 273+2b
$f(15)$ = 273+2b+182+b = 455+3b
It has been given that 455+3b = 617
3b = 162
=> b = 54
Therefore, 54 is the correct answer.
 In an examination, the maximum possible score is N while the pass mark is 45% of N. A candidate obtains 36 marks, but falls short of the pass mark by 68%. Which one of the following is then correct?
 N ≤ 200.
 243 ≤ N ≤ 252.
 N ≥ 253.
 201 ≤ N ≤ 242.
Total marks = N
Pass marks = 45% of N = 0.45N
Marks obtained = 36
It is given that, obtained marks is 68% less than that pass marks
=>the obtained marks is 32% of the pass marks.
So, 0.32 * 0.45N = 36
On solving, we get N = 250
 Two types of tea, A and B, are mixed and then sold at Rs. 40 per kg. The profit is 10% if A and B are mixed in the ratio 3 : 2, and 5% if this ratio is 2 : 3. The cost prices, per kg, of A and B are in the ratio
 18 : 25
 19 : 24
 21 : 25
 17 : 25
The selling price of the mixture is Rs.40/kg.
Let a be the quantity of tea A in the mixture and b be the quantity of tea B in the mixture.
It has been given that the profit is 10% if the 2 varieties are mixed in the ratio 3:2
Let the cost price of the mixture be x.
It has been given that 1.1x = 40
x = 40/1.1
$\frac{3a+2b}{5} = \frac{40}{1.1}$
$3.3a+2.2b=200$ (1)
The profit is 5% if the 2 varieties are mixed in the ratio 2:3.
$\frac{2a+3b}{5} = \frac{40}{1.05}$
$2.1a+3.15b=200$ (2)
Equating (1) and (2), we get,
$3.3a+2.2b = 2.1a+3.15b$
$1.2a=0.95b$
$\frac{a}{b} = \frac{0.95}{1.2}$
$\frac{a}{b} = \frac{19}{24}$
 John borrowed Rs. 2,10,000 from a bank at an interest rate of 10% per annum, compounded annually. The loan was repaid in two equal instalments, the first after one year and the second after another year. The ?rst instalment was interest of one year plus part of the principal amount, while the second was the rest of the principal amount plus due interest thereon. Then each instalment, in Rs., is
We have to equate the installments and the amount due either at the time of borrowing or at the time when the entire loan is repaid. Let us bring all values to the time frame in which all the dues get settled, i.e, by the end of 2 years.
John borrowed Rs. 2,10,000 from the bank at 10% per annum. This loan will amount to 2,10,000*1.1*1.1 = Rs.2,54,100 by the end of 2 years.
Let the amount paid as installment every year be Rs.x.
John would pay the first installment by the end of the first year. Therefore, we have to calculate the interest on this amount from the end of the first year to the end of the second year. The loan will get settled the moment the second installment is paid.
=> 1.1x + x = 2,54,100
2.1x = 2,54,100
=> x = Rs. 1,21,000.
Therefore, 121000 is the correct answer.
 Let f(x) = min{2x^{2},52−5x}, where x is any positive real number. Then the maximum possible value of f(x) is
f(x) = min (${2x^{2},525x}$)
The maximum possible value of this function will be attained at the point in which $2x^2$ is equal to $525x$.
$2x^2 = 525x$
$2x^2+5x52=0$
$(2x+13)(x4)=0$
=> $x=\frac{13}{2}$ or $x = 4$
It has been given that $x$ is a positive real number. Therefore, we can eliminate the case $x=\frac{13}{2}$.
$x=4$ is the point at which the function attains the maximum value. $4$ is not the maximum value of the function.
Substituting $x=4$ in the original function, we get, $2x^2 = 2*4^2= 32$.
f(x) = $32$.
Therefore, 32 is the right answer.
 The distance from A to B is 60 km. Partha and Narayan start from A at the same time and move towards B. Partha takes four hours more than Narayan to reach B. Moreover, Partha reaches the midpoint of A and B two hours before Narayan reaches B. The speed of Partha, in km per hour, is
 4
 6
 5
 3
Let the time taken by Partha to cover 60 km be x hours.
Narayan will cover 60 km in x4 hours.
Speed of Partha = $\frac{60}{x}$
Speed of Narayan = $\frac{60}{x4}$
Partha reaches the midpoint of A and B two hours before Narayan reaches B.
=> $\frac{30}{\frac{60}{x}} + 2 = \frac{60}{\frac{60}{(x4)}}$
$\frac{x}{2} + 2 = x4$
$\frac{x+4}{2}=x4$
$x+4=2x8$
$x=12$
Partha will take 12 hours to cross 60 km.
=> Speed of Partha = $\frac{60}{12}=5$ Kmph.
 Humans and robots can both perform a job but at di?erent e?ciencies. Fifteen humans and ?ve robots working together take thirty days to ?nish the job, whereas ?ve humans and ?fteen robots working together take sixty days to ?nish it. How many days will ?fteen humans working together (without any robot) take to ?nish it?
 36
 32
 45
 40
Let the efficiency of humans be 'h' and the efficiency of robots be 'r'.
In the first case,
Total work = (15h + 5r) * 30......(i)
In the second case,
Total work = (5h + 15r) * 60......(ii)
On equating (i) and (ii), we get
(15h + 5r) * 30 = (5h + 15r) * 60
Or, 15h + 5r = 10h + 30r
Or, 5h = 25r
Or, h = 5r
Total work = (15h + 5r) * 30 = (15h + h) * 30 = 480h
Time taken by 15 humans = $\frac{\text{480h}}{\text{15h}}$ days= 32 days.
 When they work alone, B needs 25% more time to ?nish a job than A does. They two ?nish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and ?nally B works alone to complete the remaining 5% of the job. In how many days can B alone ?nish the entire job?
 20
 16
 22
 18
Let us assume that A can complete 'a' units of work in a day and B can complete 'b' units of work in a day.
A works alone till half the work is completed.
A and B work together for 4 days and B works alone to complete the last 5% of the work.
=> A and B in 4 days can complete 45% of the work.
Let us assume the total amount of work to be done to be 100 units.
4a + 4b = 45 (1)
B needs 25% more time than A to finish a job.
=> 1.25*b = a (2)
Substituting (2) in (1), we get,
5b+4b = 45
9b = 45
b = 5 units/day
B alone can finish the job in 100/5 = 20 days.