CAT 2025 — Slot 1
Full paper, free to view. Pick a section below, click any question to see the answer and explanation.
VARC topics covered: Arts And Literature RC, Economics & Society RC, Odd One Out, Para Completion, Para Summary, Parajumble, Psychology RC, Science And Technology RC
Often the well intentioned music lover or the traditionally-minded professional composer asks two basic questions when faced with the electronic music phenomena: (1) . . . is this type of artistic creation music at all? and, (2) given that the product is accepted as music of a new type or order, is not such music "inhuman"? . . . As Lejaren Hiller points out in his book Experimental Music (coauthor Leonard M. Isaacson), two questions which often arise when music is discussed are: (a) the substance of musical communication and its symbolic and semantic significance, if any, and (b) the particular processes, both mental and technical, which are involved in creating and responding to musical composition. The ever-present popular concept of music as a direct, open, emotional expression and as a subjective form of communication from the composer, is, of course still that of the nineteenth century, when composers themselves spoke of music in those terms . . . But since the third decade of our century many composers have preferred more objective definitions of music, epitomized in Stravinsky's description of it as "a form of speculation in terms of sound and time". An acceptance of this more characteristic twentieth-century view of the art of musical composition will of course immediately bring the layman closer to an understanding of, and sympathetic response to, electronic music, even if the forms, sounds and approaches it uses will still be of a foreign nature to him.
A communication problem however will still remain. The principal barrier that electronic music presents at large, in relation to the communication process, is that composers in this medium are employing a new language of forms . . . where terms like 'densities', 'indefinite pitch relations', 'dynamic serialization', 'permutation', etc., are substitutes (or remote equivalents) for the traditional concepts of harmony, melody, rhythm, etc. . . . When the new structural procedures of electronic music are at last fully understood by the listener the barriers between him and the work he faces will be removed. . . .
The medium of electronic music has of course tempted many kinds of composers to try their hand at it . . . But the serious-minded composer approaches the world of electronic music with a more sophisticated and profound concept of creation. Although he knows that he can reproduce and employ melodic, rhythmic patterns and timbres of a traditional nature, he feels that it is in the exploration of sui generis languages and forms that the aesthetic magic of the new medium lies. And, conscientiously, he plunges into this search.
The second objection usually levelled against electronic music is much more innocent in nature. When people speak—sometimes very vehemently—of the 'inhuman' quality of this music they seem to forget that the composer is the one who fires the machines, collects the sounds, manipulates them, pushes the buttons, programs the computer, filters the sounds, establishes pitches and scales, splices tape, thinks of forms, and rounds up the over-all structure of the piece, as well as every detail of it.
The goal of the author over the course of this passage is to:
differentiate the modern composer from the nineteenth century composer.
differentiate between electronic music and other forms of music.
defend the "serious-minded composer" from Lejaren Hiller and Stravinsky.
defend electronic music from certain common charges.
defend electronic music from certain common charges.
Throughout the passage, the author addresses two charges against electronic music, that it is not music at all, and that it is inhuman, and systematically refutes both. The discussion of Stravinsky's definition, the communication problem, and the composer's creative role all serve to defend electronic music from these criticisms.
Why Option A is
Incorrect: Differentiating modern from nineteenth century composers is only a supporting point used to establish a broader definition of music, it is not the goal of the passage itself.
Why Option B is
Incorrect: The author is not primarily distinguishing electronic music from other forms but defending it against those who would deny it musical status altogether.
Why Option C is
Incorrect: The author is not defending the serious-minded composer from Hiller or Stravinsky, both of whom are cited approvingly to support the defence of electronic music.
Why Option D is Correct: The passage addresses both common objections to electronic music head-on, arguing that electronic music qualifies as music under a modern definition and that the inhuman charge overlooks the composer's active creative role.
Key Takeaway: Identify the overall argumentative stance of a passage by checking what both the opening question and the closing paragraph are doing, since they typically frame and close the same central defence.
What relation does the "communication problem" mentioned in paragraph 2 have to the questions that the author recounts at the beginning of the passage?
Unfamiliar forms and terms might get in the way of our seeing electronic music as music, but this can be overcome.
Its unfamiliar "language of forms" and novel terms mean that we cannot see electronic music as music since it does not employ traditional musical concepts.
None; they are unrelated to one another and form parts of different discussions.
The communication problem is what allows us to see electronic music as music because music must be difficult to understand.
Unfamiliar forms and terms might get in the way of our seeing electronic music as music, but this can be overcome.
The author acknowledges the communication barrier created by electronic music's unfamiliar language of forms and terms, but frames this as an obstacle that can be overcome once listeners fully understand the new structural procedures. So the communication problem relates to the first question about whether electronic music qualifies as music by noting that unfamiliar forms are a temporary barrier, not a permanent disqualification.
Why Option B is
Incorrect: This overstates the passage's claim, the author does not say the unfamiliar language means electronic music cannot be seen as music, only that it presents a communication difficulty that can be resolved through understanding.
Why Option C is
Incorrect: The communication problem is directly connected to the passage's opening questions, specifically to whether the listener can recognise electronic music as music, making them clearly related.
Why Option D is
Incorrect: The author does not argue that music must be difficult to understand, this inverts the passage's actual claim that the barrier can and should be removed through understanding.
Why Option A is Correct: This correctly captures the passage's position, that the unfamiliar language of forms does get in the way of seeing electronic music as music, but this barrier is not insurmountable and can be overcome once the listener is familiar with the new structural language.
Key Takeaway: When a passage identifies a problem and then frames it as surmountable, the correct answer will reflect both the existence of the barrier and the possibility of overcoming it.
The mention of Stravinsky's description of music in the first paragraph does all the following EXCEPT:
help us determine which sounds are musical and which are not.
respond to and expand upon earlier understandings of music.
complicate our notion of what is communicated through music.
allow us to classify electronic music as music.
help us determine which sounds are musical and which are not.
Stravinsky's definition describes music as "a form of speculation in terms of sound and time," which is broad enough to include electronic music, thereby expanding what counts as music, responding to the earlier emotional-expression definition, and making musical communication seem more abstract. However, this definition says nothing about which specific sounds are musical and which are not, it redefines what music does, not what materials qualify as musical.
Why Option B is
Incorrect: The Stravinsky quote does respond to and expand upon the nineteenth century emotional definition of music, broadening the concept significantly.
Why Option C is
Incorrect: Moving from an emotional to a speculative definition of music does complicate our notion of what is communicated through music, shifting it from feelings to something more abstract.
Why Option D is
Incorrect: By defining music in abstract terms of sound and time, Stravinsky's definition becomes broad enough to classify electronic music as music, which the author explicitly points out.
Why Option A is Correct: Stravinsky's definition broadens what music is at a conceptual level but does not provide any criterion for determining which specific sounds are musical versus non-musical, so it does not help with that distinction.
Key Takeaway: When asked what a quote does not do, check whether each function listed is actually performed by the quote in context, rather than broadly related to the topic.
From the context in which it is placed, the phrase "sui generis" in paragraph 3 suggests which one of the following?
Particular
Generic
Unaesthetic
Indescribable
Particular
The passage states that the serious-minded composer feels that it is in the exploration of "sui generis languages and forms" that the aesthetic magic of the new medium lies, contrasting this with merely reproducing traditional patterns. The phrase is used to describe languages and forms that are unique and distinct to the medium itself, that is, particular to electronic music.
Why Option B is
Incorrect: "Generic" means common or ordinary, which is the opposite of what "sui generis" means in this context, where the composer is seeking out what is distinctively unique about the new medium.
Why Option C is
Incorrect: Nothing in the passage suggests the composer considers these languages unaesthetic, in fact the opposite is true since they are described as containing the "aesthetic magic" of the new medium.
Why Option D is
Incorrect: "Indescribable" does not fit because the passage describes these forms in terms of exploration and aesthetic value, not as something beyond description.
Why Option A is Correct: "Particular" captures the sense of unique or distinctive, meaning languages and forms specific to electronic music that are not simply borrowed from traditional music, which is exactly how the phrase is used.
Key Takeaway: Use the surrounding context, especially contrasts and comparisons, to determine a phrase's meaning rather than relying solely on prior knowledge.
Understanding the key properties of complex systems can help us clarify and deal with many new and existing global challenges, from pandemics to poverty . . . A recent study in Nature Physics found transitions to orderly states such as schooling in fish (all fish swimming in the same direction), can be caused, paradoxically, by randomness, or 'noise' feeding back on itself. That is, a misalignment among the fish causes further misalignment, eventually inducing a transition to schooling. Most of us wouldn't guess that noise can produce predictable behaviour. The result invites us to consider how technology such as contact-tracing apps, although informing us locally, might negatively impact our collective movement. If each of us changes our behaviour to avoid the infected, we might generate a collective pattern we had aimed to avoid: higher levels of interaction between the infected and susceptible, or high levels of interaction among the asymptomatic.
Complex systems also suffer from a special vulnerability to events that don't follow a normal distribution or 'bell curve'. When events are distributed normally, most outcomes are familiar and don't seem particularly striking. Height is a good example: it's pretty unusual for a man to be over 7 feet tall; most adults are between 5 and 6 feet, and there is no known person over 9 feet tall. But in collective settings where contagion shapes behaviour — a run on the banks, a scramble to buy toilet paper — the probability distributions for possible events are often heavy-tailed. There is a much higher probability of extreme events, such as a stock market crash or a massive surge in infections. These events are still unlikely, but they occur more frequently and are larger than would be expected under normal distributions.
What's more, once a rare but hugely significant 'tail' event takes place, this raises the probability of further tail events. We might call them second-order tail events; they include stock market gyrations after a big fall and earthquake aftershocks. The initial probability of second-order tail events is so tiny it's almost impossible to calculate — but once a first-order tail event occurs, the rules change, and the probability of a second-order tail event increases.
The dynamics of tail events are complicated by the fact that they result from cascades of other unlikely events. When COVID-19 first struck, the stock market suffered stunning losses followed by an equally stunning recovery. Some of these dynamics are potentially attributable to former sports bettors, with no sports to bet on, entering the market as speculators rather than investors. The arrival of these new players might have increased inefficiencies and allowed savvy long-term investors to gain an edge over bettors with different goals. . . .
One reason a first-order tail event can induce further tail events is that it changes the perceived costs of our actions and changes the rules that we play by. This game-change is an example of another key complex systems concept: nonstationarity. A second, canonical example of nonstationarity is adaptation, as illustrated by the arms race involved in the coevolution of hosts and parasites [in which] each has to 'run' faster, just to keep up with the novel solutions the other one presents as they battle it out in evolutionary time.
All of the following inferences are supported by the passage EXCEPT that:
examples like runs on banks and toilet paper scrambles illustrate how contagion can amplify local choices into system-wide cascades that surprise participants and lead to patterns they did not intend to create.
learning can change the rules that actors face. So, a rare shock can alter payoffs and raise the odds of subsequent large disturbances within the same system, which supports the idea of second-order tail events.
heavy-tailed events make extreme outcomes more frequent and larger than bell curve expectations. This complicates forecasting and risk management in collective settings shaped by contagion and copying behaviour.
the text attributes the COVID-19 pandemic rebound in financial markets solely to displaced sports bettors and treats their entry as the overriding cause of the rapid recovery across assets and time horizons.
the text attributes the COVID-19 pandemic rebound in financial markets solely to displaced sports bettors and treats their entry as the overriding cause of the rapid recovery across assets and time horizons.
The passage uses the example of displaced sports bettors entering the financial market as one possible factor in the COVID-19 market dynamics, framed as "some of these dynamics are potentially attributable" to them. This is explicitly tentative and partial, not a singular, overriding explanation for the market's behaviour.
Why Option A is
Incorrect: The passage explicitly discusses runs on banks and toilet paper scrambles as examples of contagion-driven behaviour generating collective outcomes participants did not intend, directly supporting this inference.
Why Option B is
Incorrect: The passage discusses nonstationarity and how a first-order tail event changes the rules and raises the probability of further large disturbances, directly supporting this inference about learning changing the rules actors face.
Why Option C is
Incorrect: The passage explicitly states heavy-tailed events make extreme outcomes more frequent and larger than bell-curve expectations, supporting this inference about complicating forecasting and risk management.
Why Option D is Correct: The passage attributes market dynamics only partially and tentatively to sports bettors, using the phrase "potentially attributable," and does not claim this was the sole or overriding cause of the recovery, making this inference an overstatement not supported by the passage.
Key Takeaway: Tentative or partial attributions in a passage must not be read as sole or definitive explanations, any inference overstating a partial claim into a complete causal explanation is invalid.
Which one of the options below best summarises the passage?
The passage explains how social outcomes generally follow normal distributions. So, extreme events are negligible, and policy should stabilise averages rather than learn from large shocks in fast-changing collective settings.
The passage explains how noise can create order, then shows why complex systems with contagion are vulnerable to heavy-tailed cascades. It also explains why early shocks change rules through nonstationarity with a market illustration during the COVID-19 disruption.
The passage explains how speculative entrants always produce inefficiency after health shocks. Therefore, long-term investors invariably profit when new participants push prices away from fundamentals under pandemic conditions and comparable crises.
The passage explains how nonstationarity works in evolutionary biology and rejects applications in markets or public health because adaptation is exclusive to parasite-host systems and cannot arise in technology-mediated social dynamics.
The passage explains how noise can create order, then shows why complex systems with contagion are vulnerable to heavy-tailed cascades. It also explains why early shocks change rules through nonstationarity with a market illustration during the COVID-19 disruption.
The passage explains how noise can create order through the fish schooling example, then explains heavy-tailed distributions and why complex systems are vulnerable to extreme events, then discusses second-order tail events, and illustrates these with the COVID-19 market example and the concept of nonstationarity through the host-parasite coevolution example.
Why Option A is
Incorrect: The passage explicitly argues the opposite, that extreme events do not follow normal distributions and are more frequent than expected, contradicting the idea that extreme events are negligible and policy should only stabilise averages.
Why Option C is
Incorrect: The passage does not claim speculative entrants always produce inefficiency or that long-term investors invariably profit, these are stated as possible outcomes in one specific scenario, not universal conclusions.
Why Option D is
Incorrect: The passage explicitly applies nonstationarity to markets and public health, not just biology, and the host-parasite example is used as an analogy to illustrate a broader concept, not as a boundary excluding other settings.
Why Option B is Correct: This captures the passage's full arc, from noise producing order, through heavy-tailed vulnerability and cascading tail events, to the market illustration during COVID-19, and the nonstationarity concept.
Key Takeaway: A summary must capture each stage of the passage's argument in sequence, rather than selecting only one section while misrepresenting or omitting the others.
Which one of the following observations would most strengthen the passage's claim that a first-order tail event raises the probability of further tail events in complex systems?
In epidemic networks, initial super-spreading episodes are isolated spikes after which outbreak sizes match the baseline distribution from independent contact models across comparable cities with no rise in the frequency or size of later extreme clusters.
River discharge records show water levels fit a normal distribution with thin tails that match laboratory data, regardless of storms or floods.
After a major equity crash, researchers find dense clusters of large daily moves for several weeks, with extreme days occurring far more often than in normal circumstances for assets with customarily low volatility profiles.
Following large earthquakes, regional seismic activity returns to baseline within hours with no aftershock sequence once data are adjusted for reporting effects, which suggests independence across events rather than any elevation in subsequent tail probabilities.
After a major equity crash, researchers find dense clusters of large daily moves for several weeks, with extreme days occurring far more often than in normal circumstances for assets with customarily low volatility profiles.
The passage claims that once a first-order tail event occurs, the rules change and the probability of a second-order tail event increases, meaning further extreme events become more frequent. Option C directly supports this by showing that after a major equity crash, dense clusters of large daily moves appear for several weeks, with extreme days occurring far more often than normally expected.
Why Option A is
Incorrect: This describes isolated spikes with no subsequent increase in frequency or size, which directly contradicts the passage's claim that first-order tail events raise the probability of further tail events.
Why Option B is
Incorrect: This describes thin-tailed normal distributions for river discharge, which is evidence against heavy-tailed behaviour and does not support the claim about tail events increasing further tail event probability.
Why Option D is
Incorrect: This describes seismic activity returning to baseline quickly with no aftershock sequence, directly contradicting the passage's specific use of earthquake aftershocks as an example of second-order tail events.
Why Option C is Correct: This directly illustrates the passage's claim by showing that following a major market crash, extreme days cluster and occur far more often than baseline conditions would predict, consistent with a first-order event raising the probability of further tail events.
Key Takeaway: To strengthen a claim about cascading tail events, look for evidence of elevated frequency of extreme outcomes after an initial shock, not just the initial shock itself.
The passage suggests that contact tracing apps could inadvertently raise risky interactions by altering local behaviour. Which one of the assumptions below is most necessary for that suggestion to hold?
Most users uninstall apps within a week, which leaves only highly exposed individuals participating. This neutralises any systematic bias in routing decisions and prevents any predictable change in aggregate contact patterns.
Individuals base movement choices partly on observed infections and on the behaviour of others. So, local responses interact, which turns many small adjustments into large scale patterns that can frustrate the intended aim of risk reduction.
App alerts always include precise location to within one metre and deliver real time updates for all users, which ensures that the data feed is perfectly accurate regardless of privacy settings, power limits, or network conditions.
Urban networks have uniform traffic conditions at all hours, which allows perfectly predictable routing independent of personal choices, social signals, or crowd reactions and, therefore, makes interdependence negligible in city movement decisions.
Individuals base movement choices partly on observed infections and on the behaviour of others. So, local responses interact, which turns many small adjustments into large scale patterns that can frustrate the intended aim of risk reduction.
For contact tracing apps to inadvertently raise risky interactions, it must be the case that individual responses to app alerts interact with each other and scale up into collective patterns that differ from the intended outcome. Without this assumption that local individual choices aggregate into large-scale emergent patterns, the app's intended risk reduction could not paradoxically increase risk.
Why Option A is
Incorrect: If most users uninstall the app, the mechanism through which collective patterns form via widespread behavioural responses would be broken, making the scenario of inadvertent risk increase less plausible rather than supporting it.
Why Option C is
Incorrect: Perfect accuracy of app alerts is not a necessary condition for the argument, the concern is about how collective movement patterns emerge from many individual decisions, not about the precision of the data itself.
Why Option D is
Incorrect: If urban networks have uniform traffic independent of personal choices, the interdependence of individual decisions that drives the collective pattern change would not exist, undermining rather than supporting the passage's suggestion.
Why Option B is Correct: This captures the necessary assumption, that individual movement decisions based on app information interact and aggregate, turning many local adjustments into a large-scale pattern that frustrates the app's intended purpose of reducing risk.
Key Takeaway: For assumption questions, identify the minimum condition the argument requires, specifically the mechanism connecting the initial action, here app alerts, to the unintended collective outcome described.
How can we know what someone else is thinking or feeling, let alone prove it in court? In his 1863 book, A General View of the Criminal Law of England, James Fitzjames Stephen, among the most celebrated legal thinkers of his generation, was of the opinion that the assessment of a person's mental state was an inference made with "little consciousness." In a criminal case, jurors, doctors, and lawyers could watch defendants—scrutinizing clothing, mannerisms, tone of voice—but the best they could hope for were clues. . . . Rounding these clues up to a judgment about a defendant's guilt, or a defendant's life, was an act of empathy and imagination. . . . The closer the resemblance between defendants and their judges, the easier it was to overlook the gap that inference filled. Conversely, when a defendant struck officials as unlike themselves, whether by dint of disease, gender, confession, or race, the precariousness of judgments about mental state was exposed.
In the nineteenth century, physicians who specialized in the study of madness and the care of the insane held themselves out as experts in the new field of mental science. Often called alienists or mad doctors, they were the predecessors of modern psychiatrists, neurologists, and psychologists. . . . The opinions of family and neighbors had once been sufficient to sift the sane from the insane, but a growing belief that insanity was a subtle condition that required expert, medical diagnosis pushed physicians into the witness box. . . . Lawyers for both prosecution and defense began to recruit alienists to assess defendants' sanity and to testify to it in court.
Irresponsibility and insanity were not identical, however. Criminal responsibility was a legal concept and not, fundamentally, a medical one. Stephen explained: "The question 'What are the mental elements of responsibility?' is, and must be, a legal question. It cannot be anything else, for the meaning of responsibility is liability to punishment." . . . Nonetheless, medical and legal accounts of what it meant to be mentally sound became entangled and mutually referential throughout the nineteenth century. Lawyers relied on medical knowledge to inform their opinions and arguments about the sanity of their clients. Doctors commented on the legal responsibility of their patients. Ultimately, the fields of criminal law and mental science were both invested in constructing an image of the broken and damaged psyche that could be contrasted with the whole and healthy one. This shared interest, and the shared space of the criminal courtroom, made it nearly impossible to consider responsibility without medicine, or insanity without law. . . .
Physicians and lawyers shared more than just concern for the mind. Class, race, and gender bound these middle-class, white, professional men together, as did family ties, patriotism, Protestantism, business ventures, the alumni networks of elite schools and universities, and structures of political patronage. But for all their affinities, men of medicine and law were divided by contests over the borders of criminal responsibility, as much within each profession as between them. Alienists steadily pushed the boundaries of their field, developing increasingly complex and capacious definitions of insanity. Eccentricity and aggression came to be classified as symptoms of mental disease, at least by some.
The last paragraph of the passage refers to "middle-class, white, professional men". Which one of the following qualities best describes the connection among them?
The borders of criminal responsibility.
The opinions of family and neighbours.
Eccentricity and aggression.
Empathy and imagination.
The borders of criminal responsibility.
The passage uses the example of displaced sports bettors entering the financial market as one possible factor in the COVID-19 market dynamics, framed as "some of these dynamics are potentially attributable" to them. This is explicitly tentative and partial, not a singular, overriding explanation for the market's behaviour. The last paragraph explicitly states that despite all the shared class, race, professional, and personal ties among these men, they were divided by contests over the borders of criminal responsibility, both within and between the professions of medicine and law. The passage focuses on this contest as the key tension defining their relationship despite their many affinities.
Why Option B is
Incorrect: The opinions of family and neighbours are mentioned earlier in the passage as what was once sufficient to assess sanity, not as a quality connecting the professional men described in the last paragraph.
Why Option C is
Incorrect: Eccentricity and aggression are mentioned as symptoms that alienists began classifying as mental disease, a specific development within the field, not the central bond or division among these professional men.
Why Option D is
Incorrect: Empathy and imagination are mentioned in the first paragraph as the qualities used by jurors to assess mental state, not as something connecting the professional men discussed in the last paragraph.
Why Option A is Correct: The passage explicitly states that despite all their shared qualities, these men were divided by contests over the borders of criminal responsibility, making this the most precise description of what connected and defined their relationship.
Key Takeaway: When a paragraph lists many shared qualities but then identifies one key dividing issue, that dividing issue is usually what the question about connections among the group is pointing toward.
According to the passage, who or what was an "alienist"?
Professionals who pushed the boundaries of their fields till they became unrecognisable in the nineteenth century.
Physicians who specialised in the study of madness and the care of the insane in the nineteenth century.
Physicians and lawyers who were responsible for the condition of immigrants or 'aliens' in the nineteenth century.
Physicians and lawyers who were responsible for examining accounts of extraterrestrials or 'aliens' in the nineteenth century.
Professionals who pushed the boundaries of their fields till they became unrecognisable in the nineteenth century.
The passage defines alienists directly in the second paragraph as physicians who specialised in the study of madness and the care of the insane, noting they were the predecessors of modern psychiatrists, neurologists and psychologists.
Why Option A is
Incorrect: While alienists did push the boundaries of their field over time, this is a later development described separately, not the definition of what an alienist was.
Why Option C is
Incorrect: The passage makes no connection between alienists and immigrants or "aliens" in the sense of foreign nationals, this interpretation confuses the word "alienist" with its superficially similar term.
Why Option D is
Incorrect: Extraterrestrials are entirely absent from the passage, this is a fanciful misreading of the term.
Why Option B is Correct: This matches the passage's explicit definition, physicians specialising in madness and care of the insane in the nineteenth century.
Key Takeaway: For definition questions, locate the passage's explicit definitional statement rather than inferring a meaning from the word's sound or etymology.
Study the following sets of concepts and identify the set that is conceptually closest to the concerns and arguments of the passage.
Empathy, Prosecution, Knowledge, Business.
Judgement, Belief, Accounts, Patronage.
Assessment, Empathy, Prosecution, Patriotism.
Judgement, Insanity, Punishment, Responsibility.
Judgement, Insanity, Punishment, Responsibility.
The passage is centrally about how judgments about mental state are made in legal contexts, how insanity as a concept relates to legal responsibility, how punishment is tied to the definition of responsibility, and how these concepts became entangled between medicine and law throughout the nineteenth century.
Why Option A is
Incorrect: While empathy and prosecution appear in the passage, knowledge and business are peripheral and do not represent the conceptual core of the argument.
Why Option B is
Incorrect: Judgment and belief appear in the passage, but accounts and patronage are mentioned only as background contextual details about the shared social world of these professionals, not as central concerns of the argument.
Why Option C is
Incorrect: Assessment, empathy and prosecution appear in the passage but patriotism is a social background detail, not a conceptual concern of the passage's core argument.
Why Option D is Correct: Judgment, insanity, punishment and responsibility are the four concepts that the passage explicitly develops and interconnects, through Stephen's definition of responsibility as liability to punishment, the legal versus medical concept of insanity, and the difficulty of judging mental state in court.
Key Takeaway: When asked for conceptual closeness, identify the terms that the passage explicitly defines, argues about, and interconnects, rather than terms that merely appear incidentally.
"Conversely, when a defendant struck officials as unlike themselves, whether by dint of disease, gender, confession, or race, the precariousness of judgments about mental state was exposed." Which one of the following best describes the use of the word "confession" in this sentence?
Referring to the practice of 'confession' in some faiths, here it is a metaphor for the religion of the defendant.
Referring to the gender, race or disease claimed as a defence by the defendant, here it is a synonym for 'professing' a gender, race, or disease.
Referring to the defendant's confession of his or her crime as false, because 'dint' is an archaic form of 'didn't' or 'did not'.
The defendants struck out at the officials and then confessed to the act.
Referring to the practice of 'confession' in some faiths, here it is a metaphor for the religion of the defendant.
The sentence lists disease, gender, confession, and race as qualities that could make a defendant seem unlike the officials judging them. In this list, "confession" functions most naturally as referring to religious confession, meaning the defendant's religious affiliation, which, like race or gender, could mark them as different from the predominantly Protestant professional judges described elsewhere in the passage.
Why Option B is
Incorrect: While this option offers a grammatically creative reading, "professing" a gender or race is not a natural reading of "confession" in this context, and the option creates an awkward construction to make the word fit.
Why Option C is
Incorrect: "Dint" is not an archaic form of "didn't," it is an archaic word meaning "by means of" or "by force of," so this interpretation is based on a factual error about the word's meaning.
Why Option D is
Incorrect: This completely misreads the sentence, which is not about defendants physically striking officials but about how defendants appeared to officials, and "confession" here is not about admitting to a crime.
Why Option A is Correct: In the context of a society where the judges and officials were predominantly Protestant, a defendant's religious affiliation, like race or gender, could mark them as unlike the officials, exposing the precariousness of the judgment, making "confession" as a metaphor for religious faith the most coherent reading.
Key Takeaway: When a word appears in a list alongside other demographic or social categories, interpret it as a social marker consistent with the others in the list rather than in its most literal or common sense.
Studies showing that income inequality plays a positive role in economic growth are largely based on three arguments. The first argument focuses on investment indivisibilities wherein large sunk costs are required when implementing new fundamental innovations. Without stock markets and financial institutions to mobilize large sums of money, a high concentration of wealth is needed for individuals to undertake new industrial activities accompanied by high sunk costs . . . [One study] shows the relation between economic growth and income inequality for 45 countries during 1966-1995. [It was found] that the increase in income inequality has a significant positive relationship with economic growth in the short and medium term. Using system GMM, [another study estimated] the relation between income inequality and economic growth for 106 countries during 1965-2005 period. The results show that income inequality has a positive impact on economic growth in the short run, but the two are negatively correlated in the long run. The second argument is related to moral hazard and incentives . . . Because economic performance is determined by the unobservable level of effort that agents make, paying compensations without taking into account the economic performance achieved by individual agents will fail to elicit optimum effort from the agents. Thus, certain income inequalities contribute to growth by enhancing worker motivation . . . and by giving motivation to innovators and entrepreneurs . . . Finally, [another study] point[s] out that the concentration of wealth or stock ownership in relation to corporate governance contributes to growth. If stock ownership is distributed and owned by a large number of shareholders, it is not easy to make quick decisions due to the conflicting interests among shareholders, and this may also cause a free-rider problem in terms of monitoring and supervising managers and workers. . . .
Various studies have examined the relationships between income inequality and economic growth, and most of these assert that a negative correlation exists between the two. . . . Analyzing 159 countries for 1980-2012, they conclude that there exists a negative relation between income inequality and economic growth; when the income share of the richest 20% of population increases by 1%, the GDP decreases by 0.08%, whereas when the income share of the poorest 20% of population increases by 1%, the GDP increases by 0.38%. Some studies find that inequality has a negative impact on growth due to poor human capital accumulation and low fertility rates . . . while [others] point out that inequality creates political instability, resulting in lower investment. . . . [Some economists] argue that widening income inequality has a negative impact on economic growth because it negatively affects social consensus or social capital formation. One important research topic is the correlation between democratization and income redistribution. [Some scholars] explain that social pressure for income redistribution rises as income inequality increases in a democratic society. In other words, when democratization extends suffrage to a wider class of people, the increased political power of low- and middle-income voters results in broader support for income redistribution and social welfare expansion. However . . . if the rich have more political influence than the poor, the democratic system actually worsens income inequality rather than improving it.
Which one of the options below best summarises the passage?
The passage claims that evaluating the effect of income inequality on economic growth without considering both short- and long-term consequences is misguided.
The passage confines its discussion to financing gaps and corporate control while undercutting cross country evidence and overlooking the significance of concerns regarding human capital accumulation, fertility rates, and income redistribution under democratisation.
The passage argues that income inequality accelerates economic growth while also emphasising the significance of concerns regarding human capital accumulation, fertility rates, and political instability.
The passage outlines investment, incentive, and governance channels through which income inequality may support economic growth and reports short-term gains while noting long-term drawbacks.
The passage outlines investment, incentive, and governance channels through which income inequality may support economic growth and reports short-term gains while noting long-term drawbacks.
The passage's first half outlines three mechanisms through which income inequality may support growth, investment in high sunk-cost activities, incentive effects on workers and innovators, and concentrated ownership improving corporate governance, while noting that short-term gains may not persist in the long run. The second half presents the opposing evidence of a long-term negative relationship between inequality and growth.
Why Option A is
Incorrect: This is a partial claim about the importance of considering short and long-term effects, but it does not capture the passage's actual content, which outlines specific mechanisms and presents both sides of the empirical debate.
Why Option B is
Incorrect: This incorrectly claims the passage confines itself to financing gaps and corporate control, when it also discusses incentives, human capital, fertility rates, political instability and democratisation, so this is inaccurate.
Why Option C is
Incorrect: This says the passage "argues that income inequality accelerates economic growth," but the passage presents both sides, the positive and negative, without taking a single position, making this a misrepresentation.
Why Option D is Correct: This captures both halves accurately, the three investment, incentive, and governance channels that may support growth, the evidence of short-term gains, and the overall complication that long-term outcomes may be negative.
Key Takeaway: When a passage presents both sides of an empirical debate, the correct summary should reflect the structure of the argument, listing channels on one side and acknowledging the opposing evidence, without resolving the debate in favour of either position.
The passage refers to "democratization". Choose the one option below that comes closest to the opposite of this process.
After the emergency decree, the regime shifted toward authoritarianism as suffrage narrowed and opposition parties were deregistered.
Corporate donations were capped and parties received public funding which was portrayed as establishing an oligarchy.
Municipalities adopted participatory budgeting and recall elections which a press release called totalitarianism.
The coalition imposed term limits and strengthened judicial review in order to further entrench autocratic rule.
After the emergency decree, the regime shifted toward authoritarianism as suffrage narrowed and opposition parties were deregistered.
The passage defines democratisation in terms of extending suffrage to a wider class of people, increasing the political power of low- and middle-income voters, and broadening support for income redistribution. The opposite would be a narrowing of suffrage and a shift toward authoritarian rule, which is precisely what Option A describes.
Why Option B is
Incorrect: Capping corporate donations and using public funding is a reform within a democratic system, not a move away from democracy, despite the option labelling it an oligarchy, which is an incorrect framing of what it describes.
Why Option C is
Incorrect: Participatory budgeting and recall elections are expansions of democratic participation, despite the option using the word "totalitarianism," which does not match what the described measures actually represent.
Why Option D is
Incorrect: Term limits and strengthened judicial review are typically mechanisms for reinforcing democratic accountability, not autocratic rule, making the label "autocratic" inconsistent with the described measures.
Why Option A is Correct: Narrowing suffrage and deregistering opposition parties directly reverses the core features of democratisation described in the passage, making authoritarianism the genuine opposite.
Key Takeaway: When evaluating opposites, look at what the measures actually do rather than what labels the options attach to them, since several options use misleading labels that contradict the substance of what they describe.
The primary function of the three-part case for a positive income inequality-economic growth link in the first half of the passage is to show that:
inequality boosts growth in every period and type of economy, regardless of finance or governance conditions.
mature stock markets make wealth concentration unnecessary, yet they might still be harmful to investment.
inequality can aid short-term growth in settings with high sunk costs, incentive alignment, and concentrated ownership.
dispersed ownership speeds corporate decision-making and removes free rider problems.
inequality can aid short-term growth in settings with high sunk costs, incentive alignment, and concentrated ownership.
The passage's three-part case presents conditions under which inequality may support growth, specifically when large sunk costs require concentrated capital, when performance-based pay incentivises worker and innovator effort, and when concentrated ownership improves corporate decision-making and supervision.
Why Option A is
Incorrect: The passage does not claim inequality boosts growth in every period and type of economy, it presents conditions under which this may be true, and explicitly notes the long-run negative correlation across many countries.
Why Option B is
Incorrect: The passage does not argue that mature stock markets make wealth concentration unnecessary or harmful, it argues concentration is needed specifically when stock markets and financial institutions cannot mobilise large sums on their own.
Why Option D is
Incorrect: This reverses the passage's point about ownership, the passage argues that concentrated ownership improves decision-making and removes the free-rider problem, not that dispersed ownership speeds decisions.
Why Option C is Correct: This accurately captures the three specific conditional settings where inequality may aid growth, high sunk costs, incentive alignment, and concentrated ownership, without overstating the claim as universal.
Key Takeaway: When a passage presents a conditional argument, the correct characterisation must preserve those conditions rather than presenting the claim as unconditional or universal.
According to the incentive or moral hazard argument, which one of the designs below is most consistent with the claim that some inequality can raise growth?
Pay rewards on verifiable performance for highly productive workers.
Rents protected by market power that enlarge top incomes without linking pay to results.
Wages are determined by tenure rather than output to ensure equity.
A regime that concentrates stock ownership in relation to corporate governance.
Pay rewards on verifiable performance for highly productive workers.
The moral hazard argument in the passage states that since economic performance depends on unobservable effort, paying rewards without linking them to performance fails to elicit optimal effort. Therefore, performance-linked compensation creates the kind of inequality in pay that motivates workers to exert more effort and drives growth.
Why Option B is
Incorrect: Rents from market power that enlarge top incomes without linking pay to results are exactly what the moral hazard argument argues against, since this creates inequality without any incentive effect on effort or performance.
Why Option C is
Incorrect: Wages determined by tenure rather than output remove the performance-based link entirely, which the passage identifies as failing to elicit optimum effort, making this inconsistent with the moral hazard argument.
Why Option D is
Incorrect: Concentrated stock ownership relates to the third argument about corporate governance, not to the moral hazard or incentive argument, which is specifically about linking pay to individual performance.
Why Option A is Correct: Rewarding verifiable performance for highly productive workers directly reflects the moral hazard argument, since it links compensation to observable results, providing the incentive structure that the passage argues can raise growth.
Key Takeaway: Match a design to the specific mechanism the passage describes for a particular argument, rather than to other arguments that appear nearby in the same passage.
Five jumbled sentences (labelled 1, 2, 3, 4, and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence out and key in the number of that sentence as your answer.
1. Developments both technological and sociocultural have afforded us far greater freedom over death than we had in the past, and while we are still adapting ourselves to that freedom, we now appreciate the moral importance of this freedom.
2. But I believe that a type of freedom we can call freedom over death — that is, a freedom in which we shape the timing and circumstances of how we die — should be central to this conversation.
3. Legalising assisted dying is but a further step in realising this freedom over death.
4. Many people endorse, through their opinions or their choices, our freedom over death, encompassing a right to medical assistance in hastening our deaths.
5. Freedom is a notoriously complex and contested philosophical notion, and I won't pretend to settle any of the big controversies it raises.
Sentences 1, 2, 3 and 5 build a coherent argument about freedom over death, starting with the philosophical complexity of freedom, introducing the specific concept of freedom over death, explaining how developments have expanded this freedom, and concluding that legalising assisted dying is a further step in realising it. Sentence 4 makes a separate empirical claim about what many people already endorse, which duplicates the general thrust without adding a distinct logical step in the argument's progression, and introduces "medical assistance in hastening deaths" as a specific phrase that sits awkwardly between the philosophical framing and the legal conclusion.
Key Takeaway: When four sentences build a logical argument from definition to application, a sentence making a redundant empirical claim about public opinion without advancing the argument is usually the odd one out.
The four sentences (labelled 1, 2, 3, and 4) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer.
1. It can in fact be integrated into any function (education, medical treatment, production, punishment); it can increase the effect of this function, by being linked closely with it; it can constitute a mixed mechanism in which relations of power (and of knowledge) may be precisely adjusted, in the smallest detail, to the processes that are to be supervised; it can establish a direct proportion between 'surplus power' and 'surplus production'.
2. It's a case of 'it's easy once you've thought of it' in the political sphere.
3. The panoptic mechanism is not simply a hinge, a point of exchange between a mechanism of power and a function; it is a way of making power relations function in a function, and of making a function function through these power relations.
4. In short, it arranges things in such a way that the exercise of power is not added on from the outside, like a rigid, heavy constraint, to the functions it invests, but is so subtly present in them as to increase their efficiency by itself increasing its own points of contact.
Sentence 2 introduces the general observation about the panoptic mechanism being simple once understood, using a light tone to frame the discussion. Sentence 1 then explains in detail the many ways the mechanism can be integrated and applied across various functions. Sentence 4 then draws the broader conclusion, that the mechanism arranges power so subtly that it enhances the efficiency of whatever it invests. Sentence 3 closes by offering the most theoretical and precise summary of what the panoptic mechanism is, framing the entire idea as something more than just a hinge or exchange point. This gives the sequence 2143.
Key Takeaway: Move from the casual or accessible observation first, through the detailed application, to the broader inference, and finally to the most abstract or precise theoretical formulation.
The given sentence is missing in the paragraph below. Decide where it best fits among the options 1, 2, 3, or 4 indicated in the paragraph.
Sentence: "Everything is old-world, traditional techniques from Mexico," Ava emphasizes.
Paragraph: The sisters embrace the ways their great-grandfather built and repaired instruments. ____(1) ____. When crafting a Mexican guitarron used in mariachi music, they use tacote wood for the top of the instrument. Once the wood is cut, they carve the neck and heel from a single block using tools like hand saws, chisels and sandpaper rather than modern power tools — and believe that this traditional method improves the tone of the instrument. ____(2) ____. Their store has a three-year waitlist for instruments that take months to create. ____(3) ____. The family's artisanship has attracted stars like Los Lobos, who own custom guitars made by all three generations of the Delgado family. ____(4) ____. For the sisters, involvement in the family business started at an early age. They each built their first instruments at age 9.
Option 1
Option 4
Option 2
Option 3
Option 1
The inserted sentence is Ava's direct emphasis that everything is traditional and old-world, from Mexico. This fits best right after the opening statement about the sisters embracing the ways of their great-grandfather, at Option 1, since it directly underscores the traditional approach mentioned in that opening line before the paragraph moves on to describe specific techniques and materials.
Why Option B is
Incorrect: Option 4 comes right before the closing sentence about the sisters starting their involvement at age 9. Inserting the emphasis on old-world tradition here, after the discussion of famous clients like Los Lobos, breaks the natural transition toward the personal story of the sisters' early involvement.
Why Option C is
Incorrect: Option 2 comes after the description of using tacote wood and hand tools for the guitarron, a mid-paragraph position where the techniques are already being detailed. The inserted sentence works better as an umbrella statement before these details are introduced.
Why Option D is
Incorrect: Option 3 falls right after the sentence about the three-year waitlist, where the paragraph has moved to discussing the store's commercial success and its famous clients. Inserting a general claim about tradition here interrupts the shift toward discussing reputation and clientele.
Why Option A is Correct: Option 1 sits right after the opening line about following the great-grandfather's methods, making it the ideal position for Ava's direct statement that everything is old-world and traditional, before the paragraph elaborates with specific techniques.
Key Takeaway: A speaker's direct emphasis on a theme fits best right after the theme is first introduced, before the supporting details begin.
The given sentence is missing in the paragraph below. Decide where it best fits among the options 1, 2, 3, or 4 indicated in the paragraph.
Sentence: Historically, silver has been, and still is, an important element in the business of 'show' visible in private houses, churches, government and diplomacy.
Paragraph: ____(1) ____. Timothy Schroder put it succinctly in suggesting that electric light and eating in the kitchen eroded this need. As he explained to the author, 'Silver, when illuminated by flickering candlelight, comes alive and almost dances before the eyes, but when lit by electric light, it becomes flat and dead.' ____(2) ____. Domestic and economic changes may have worked against the market, but the London silver trade remained buoyant, thanks to the competition of collectors seeking grand display silver at the top end, and the buyers of 'collectables', like spoons and wine labels and 'novelties', at the bottom. ____(3) ____. Another factor that came into play was the systematic collection building of certain American museums over the period. Boston, Huntington Art Gallery and Williamsburg, among others, were largely supplied by London dealers. ____(4) ____.
Option 4
Option 3
Option 1
Option 2
Option 3
The inserted sentence states that silver has historically been and remains important in the business of show in private houses, churches, government and diplomacy. This fits at Option 3, right after the passage has discussed how the London silver trade remained buoyant through demand from collectors and buyers, and right before the specific factor of American museum collection building is introduced as another reason for the trade's buoyancy. The inserted sentence bridges the domestic market discussion and the broader institutional demand from museums and governments.
Why Option A is
Incorrect: Option 4 is at the very end of the paragraph, after the American museum factor has already been introduced. The inserted sentence about silver's role in display would be redundant at this point since the paragraph has already moved past this general claim.
Why Option C is
Incorrect: Option 1 is at the very beginning, before the explanation of how electric light and candlelight affect the appearance of silver. Starting with a general claim about silver's display importance before any context is established would feel unsupported, since the reader hasn't yet been given the factors affecting the silver trade.
Why Option D is
Incorrect: Option 2 falls right after the explanation of domestic and economic changes working against the silver market, before the statement about the London silver trade remaining buoyant. Inserting the broader claim about silver's display role here would interrupt the passage's direct move from the problem to the explanation of the market's resilience.
Why Option B is Correct: Option 3 comes right after the specific domestic market factors and right before the American museum factor, providing a bridging statement about institutional demand for display silver that naturally introduces the subsequent point about museum collection building.
Key Takeaway: Place a broad bridging claim between two specific market or institutional examples when it naturally connects what came before to what follows.
The four sentences (labelled 1, 2, 3, and 4) given below, when properly sequenced, would yield a coherent paragraph. Decide on the proper sequencing of the order of the sentences and key in the sequence of the four numbers as your answer.
1. But man, woman or otherwise, there is no denying that the quality of our life and character will be significantly shaped by the way we handle our anger.
2. Once the taboos have been broken, women usually experience letting their fists fly as intensely liberating.
3. Though this might seem a stereotype, women—unlike men, who are frequently applauded for unbridled aggression—are often socialized to keep a lid on their ire.
4. Many of them are so at odds with their aggressive feelings that, as a coach, I often have to stop them from pulling their punches and encourage them to extend their arms so their blows might actually reach their fleshy target.
Sentence 3 introduces the generalisation that women, unlike men, are often socialised to suppress their anger. Sentence 4 follows with a specific coaching example of women literally holding back, pulling their punches. Sentence 2 then describes the liberation women experience once those taboos are broken and they allow themselves to express aggression fully. Sentence 1 closes with the broader takeaway that regardless of gender, handling anger well shapes character and quality of life. This gives the sequence 3421.
Key Takeaway: Move from a general social observation, to a specific behavioural example, to the emotional resolution of that behaviour, and finally to the universal conclusion that encompasses the earlier gender-specific point.
Five jumbled sentences (labelled 1, 2, 3, 4, and 5), related to a topic, are given below. Four of them can be put together to form a coherent paragraph. Identify the odd sentence out and key in the number of that sentence as your answer.
1. The Bayeux tapestry was, therefore, an obvious way to tell people about the downfall of the English and the rise of the Normans.
2. So if we take expert in Anglo-Saxon culture Gale Owen-Crocker's idea that the tapestry was originally hung in a square with certain scenes facing each other, people would have stood in the centre.
3. Art historian Linda Neagley has argued that pre-Renaissance people interacted with art visually, kinaesthetically (sensory perception through bodily movement) and physically.
4. That would make it an 11th-century immersive space with scenes corresponding and echoing each other, drawing the viewer's attention, playing on their senses and understanding of the story they thought they knew.
5. The Bayeux tapestry would have been hung at eye level to enable this.
Sentences 3, 5, 2 and 4 build a coherent argument about how people physically interacted with the Bayeux tapestry, through art historian Linda Neagley's argument about visual and kinaesthetic interaction, the idea that it was hung at eye level to enable this, Gale Owen-Crocker's theory about the original square hanging arrangement, and the resulting immersive experience this would have created. Sentence 1 makes a separate historical point about the tapestry being used as a vehicle for the Norman conquest narrative, which does not fit the thread about spatial and sensory interaction with the tapestry.
Key Takeaway: When four sentences describe how a specific object was physically or sensorially experienced, a sentence making a separate historical or propagandistic point about that object's message is usually the odd one out.
The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
Zombie cells may contribute to age-related chronic inflammation: this finding could help scientists understand more about the aging process and why the immune system becomes less effective as we get older. Zombie or "senescent" cells are damaged cells that can no longer divide and grow like normal cells. Scientists think that these cells can contribute to chronic health problems when they accumulate in the body. In younger people, the immune system is more effective at clearing senescent cells from the body through a process called apoptosis, but as we age, this process becomes less efficient. As a result, there is an accumulation of senescent cells in different organs in the body, either through increased production or reduced clearance by the immune system. The zombie cells continue to use energy though they do not divide, and often secrete chemicals that cause inflammation, which if persistent for longer periods of time can damage healthy cells leading to chronic diseases.
Senescent "zombie" cells are inactive or malfunctioning cells that can be found throughout the body.
A younger person's immune system is healthy and is able to clear the damaged cells, but as people age, the zombie cells resist apoptosis, and start accumulating in the body.
Aging leads to less effective apoptosis, and therefore zombie cells start to accumulate in the body, causing inflammation, which accelerates aging and leads to chronic diseases.
Dead cells accelerate chronic inflammation weakening the immune system and lead to aging.
Aging leads to less effective apoptosis, and therefore zombie cells start to accumulate in the body, causing inflammation, which accelerates aging and leads to chronic diseases.
The passage explains that zombie cells accumulate because the immune system becomes less efficient at clearing them as we age, and that these cells cause chronic inflammation by secreting chemicals, which damages healthy cells and leads to chronic diseases.
Why Option A is
Incorrect: This only defines senescent cells as inactive or malfunctioning and found throughout the body, but omits the mechanism of accumulation, the inflammation process, and the link to chronic disease.
Why Option B is
Incorrect: This describes the contrast between young and old immune systems but misrepresents the passage by saying zombie cells "resist apoptosis," when the passage actually says the immune system becomes less efficient at clearing them, not that the cells themselves actively resist.
Why Option C is Correct: This captures the full causal chain, aging leads to less efficient apoptosis, zombie cells accumulate, they cause inflammation, and this leads to chronic disease, matching the passage's core argument precisely.
Why Option D is
Incorrect: This confuses the description by calling the cells "dead" rather than senescent cells that are damaged but still metabolically active, and also reverses causality by implying the cells weaken the immune system rather than accumulating because the immune system weakens.
Key Takeaway: A summary must accurately reflect both the mechanism and the direction of causality described in the passage, not just the end result.
The passage given below is followed by four summaries. Choose the option that best captures the essence of the passage.
In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. The globalized nature of the modern world invites artists to draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred. Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgement. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It's essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.
Artists in a globalised world must navigate between drawing inspiration from diverse cultures respectfully and cultural appropriation that involves borrowing without proper acknowledgement which has broader societal impacts including perpetuating power imbalances.
In today's world of creativity, artists have to decide between respectfully acknowledging works that are inspired by diverse cultures and appropriating elements without respect for their contexts.
In a globalised world, artists must draw from diverse cultural influences to create works that appeal to all, and this results in instances of both inspiration and cultural appropriation.
Artists must navigate the thin line between inspiration and cultural appropriation, where respectful inspiration fosters cultural understanding whereas appropriation involves borrowing without acknowledgement leading to commodification and reinforcement of stereotypes.
Artists in a globalised world must navigate between drawing inspiration from diverse cultures respectfully and cultural appropriation that involves borrowing without proper acknowledgement which has broader societal impacts including perpetuating power imbalances.
The passage discusses both respectful inspiration, which builds cultural understanding, and cultural appropriation, which involves borrowing without acknowledgement and leads to commodification, stereotype reinforcement, erasure of cultural context, and broader societal harm including power imbalances.
Why Option B is
Incorrect: This omits the broader societal impacts including perpetuating power imbalances and the erasure of cultural context, which the passage explicitly includes as consequences of cultural appropriation extending beyond just artistic expression.
Why Option C is
Incorrect: This misrepresents the passage by suggesting that drawing from diverse cultural influences necessarily results in both inspiration and appropriation, as if appropriation is an inevitable by-product of cultural exchange, which is not what the passage argues.
Why Option D is
Incorrect: This captures the distinction between inspiration and appropriation but does not include the passage's explicit point that appropriation's impact extends beyond art to broader societal perceptions and power imbalances.
Why Option A is Correct: This captures all the key elements, navigating between respectful inspiration and appropriation, the defining features of each, and the broader societal impacts of appropriation including perpetuating power imbalances.
Key Takeaway: A complete summary must include not just the central distinction being drawn but also the broader consequences the passage explicitly attributes to the negative outcome being described.
At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu.
At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3.
The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher.
1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4.
2. Dolly and Falguni were the only employees who got the same rating across all the quarters.
3. The following is known about ratings given by Lalu:
• Bunty received a rating of 1 in Quarter 2.
• Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
What was Eklavya’s score at the end of Quarter 2?
Step 1:
Using Condition (1), we know that Asha, Bunty, and Chintu belonged to the Elite group at the beginning of Quarter 1. Consequently, Dolly, Eklavya, and Falguni must have been in the Novice group at the same time.
Since Asha, Bunty, and Chintu were all in the Novice group at the beginning of Quarter 4, it follows that Dolly, Eklavya, and Falguni had moved to the Elite group by the beginning of Quarter 4.
From Condition (3) and the ratings assigned by Lalu, Bunty was shifted to the Novice group in Quarter 2. This implies that his Quarter 1 rating was 1. The same condition also tells us that Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
According to Condition (2), Dolly consistently received a rating of 2, while Falguni consistently received a rating of 3 across all three quarters. Therefore, Falguni must have been promoted to the Elite group in Quarter 2.
Since Asha was demoted to the Novice group in Quarter 3, her cumulative score at the end of Quarter 2 could not have exceeded Chintu's cumulative score. Hence, their Quarter 1 ratings must have been 2 and 3 in some order. Also, in Quarter 2, Asha and Chintu received ratings of 1 and 2, respectively.
The deductions obtained so far are summarized in the table below.
Step 2:
By the end of Quarter 2, both Dolly and Eklavya had cumulative scores of 4. However, since Eklavya's rating in Quarter 2 was higher than Dolly's, Eklavya was promoted to the Elite group in Quarter 3.
As Chintu was demoted to the Novice group at the beginning of Quarter 4, his cumulative score after Quarter 3 must have been less than or equal to Eklavya's cumulative score. This leads to the conclusion that Chintu and Eklavya received ratings of 1 and 2, respectively, in Quarter 3.
With these deductions, the entire arrangement is now determined and is represented in the table below.
Eklavya's cumulative score at the end of Quarter 2 was 4.
How many employees changed groups more than once up to the beginning of Quarter 4?
Step 1:
Using Condition (1), we know that Asha, Bunty, and Chintu belonged to the Elite group at the beginning of Quarter 1. Consequently, Dolly, Eklavya, and Falguni must have been in the Novice group at the same time.
Since Asha, Bunty, and Chintu were all in the Novice group at the beginning of Quarter 4, it follows that Dolly, Eklavya, and Falguni had moved to the Elite group by the beginning of Quarter 4.
From Condition (3) and the ratings assigned by Lalu, Bunty was shifted to the Novice group in Quarter 2. This implies that his Quarter 1 rating was 1. The same condition also tells us that Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
According to Condition (2), Dolly consistently received a rating of 2, while Falguni consistently received a rating of 3 across all three quarters. Therefore, Falguni must have been promoted to the Elite group in Quarter 2.
Since Asha was demoted to the Novice group in Quarter 3, her cumulative score at the end of Quarter 2 could not have exceeded Chintu's cumulative score. Hence, their Quarter 1 ratings must have been 2 and 3 in some order. Also, in Quarter 2, Asha and Chintu received ratings of 1 and 2, respectively.
The deductions obtained so far are summarized in the table below.
Step 2:
By the end of Quarter 2, both Dolly and Eklavya had cumulative scores of 4. However, since Eklavya's rating in Quarter 2 was higher than Dolly's, Eklavya was promoted to the Elite group in Quarter 3.
As Chintu was demoted to the Novice group at the beginning of Quarter 4, his cumulative score after Quarter 3 must have been less than or equal to Eklavya's cumulative score. This leads to the conclusion that Chintu and Eklavya received ratings of 1 and 2, respectively, in Quarter 3.
With these deductions, the entire arrangement is now determined and is represented in the table below.
No employee changed groups more than once up to the beginning of Quarter 4.
What was Bunty’s score at the end of Quarter 3?
Step 1:
Using Condition (1), we know that Asha, Bunty, and Chintu belonged to the Elite group at the beginning of Quarter 1. Consequently, Dolly, Eklavya, and Falguni must have been in the Novice group at the same time.
Since Asha, Bunty, and Chintu were all in the Novice group at the beginning of Quarter 4, it follows that Dolly, Eklavya, and Falguni had moved to the Elite group by the beginning of Quarter 4.
From Condition (3) and the ratings assigned by Lalu, Bunty was shifted to the Novice group in Quarter 2. This implies that his Quarter 1 rating was 1. The same condition also tells us that Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
According to Condition (2), Dolly consistently received a rating of 2, while Falguni consistently received a rating of 3 across all three quarters. Therefore, Falguni must have been promoted to the Elite group in Quarter 2.
Since Asha was demoted to the Novice group in Quarter 3, her cumulative score at the end of Quarter 2 could not have exceeded Chintu's cumulative score. Hence, their Quarter 1 ratings must have been 2 and 3 in some order. Also, in Quarter 2, Asha and Chintu received ratings of 1 and 2, respectively.
The deductions obtained so far are summarized in the table below.
Step 2:
By the end of Quarter 2, both Dolly and Eklavya had cumulative scores of 4. However, since Eklavya's rating in Quarter 2 was higher than Dolly's, Eklavya was promoted to the Elite group in Quarter 3.
As Chintu was demoted to the Novice group at the beginning of Quarter 4, his cumulative score after Quarter 3 must have been less than or equal to Eklavya's cumulative score. This leads to the conclusion that Chintu and Eklavya received ratings of 1 and 2, respectively, in Quarter 3.
With these deductions, the entire arrangement is now determined and is represented in the table below.
Bunty’s score at the end of Quarter 3 was 5.
For how many employees can the scores at the end of Quarter 3 be determined with certainty?
Step 1:
Using Condition (1), we know that Asha, Bunty, and Chintu belonged to the Elite group at the beginning of Quarter 1. Consequently, Dolly, Eklavya, and Falguni must have been in the Novice group at the same time.
Since Asha, Bunty, and Chintu were all in the Novice group at the beginning of Quarter 4, it follows that Dolly, Eklavya, and Falguni had moved to the Elite group by the beginning of Quarter 4.
From Condition (3) and the ratings assigned by Lalu, Bunty was shifted to the Novice group in Quarter 2. This implies that his Quarter 1 rating was 1. The same condition also tells us that Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
According to Condition (2), Dolly consistently received a rating of 2, while Falguni consistently received a rating of 3 across all three quarters. Therefore, Falguni must have been promoted to the Elite group in Quarter 2.
Since Asha was demoted to the Novice group in Quarter 3, her cumulative score at the end of Quarter 2 could not have exceeded Chintu's cumulative score. Hence, their Quarter 1 ratings must have been 2 and 3 in some order. Also, in Quarter 2, Asha and Chintu received ratings of 1 and 2, respectively.
The deductions obtained so far are summarized in the table below.
Step 2:
By the end of Quarter 2, both Dolly and Eklavya had cumulative scores of 4. However, since Eklavya's rating in Quarter 2 was higher than Dolly's, Eklavya was promoted to the Elite group in Quarter 3.
As Chintu was demoted to the Novice group at the beginning of Quarter 4, his cumulative score after Quarter 3 must have been less than or equal to Eklavya's cumulative score. This leads to the conclusion that Chintu and Eklavya received ratings of 1 and 2, respectively, in Quarter 3.
With these deductions, the entire arrangement is now determined and is represented in the table below.
The scores of four employees—Bunty, Dolly, Eklavya, and Falguni—at the end of Quarter 3 can be determined with certainty.
Which of the following statements is/are NECESSARILY true?
I. Asha received a rating of 2 in Quarter 1.
II. Asha received a rating of 1 in Quarter 2.
Both I and II
Neither I nor II
Only I
Only II
Only II
Step 1:
Using Condition (1), we know that Asha, Bunty, and Chintu belonged to the Elite group at the beginning of Quarter 1. Consequently, Dolly, Eklavya, and Falguni must have been in the Novice group at the same time.
Since Asha, Bunty, and Chintu were all in the Novice group at the beginning of Quarter 4, it follows that Dolly, Eklavya, and Falguni had moved to the Elite group by the beginning of Quarter 4.
From Condition (3) and the ratings assigned by Lalu, Bunty was shifted to the Novice group in Quarter 2. This implies that his Quarter 1 rating was 1. The same condition also tells us that Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.
According to Condition (2), Dolly consistently received a rating of 2, while Falguni consistently received a rating of 3 across all three quarters. Therefore, Falguni must have been promoted to the Elite group in Quarter 2.
Since Asha was demoted to the Novice group in Quarter 3, her cumulative score at the end of Quarter 2 could not have exceeded Chintu's cumulative score. Hence, their Quarter 1 ratings must have been 2 and 3 in some order. Also, in Quarter 2, Asha and Chintu received ratings of 1 and 2, respectively.
The deductions obtained so far are summarized in the table below.
Step 2:
By the end of Quarter 2, both Dolly and Eklavya had cumulative scores of 4. However, since Eklavya's rating in Quarter 2 was higher than Dolly's, Eklavya was promoted to the Elite group in Quarter 3.
As Chintu was demoted to the Novice group at the beginning of Quarter 4, his cumulative score after Quarter 3 must have been less than or equal to Eklavya's cumulative score. This leads to the conclusion that Chintu and Eklavya received ratings of 1 and 2, respectively, in Quarter 3.
With these deductions, the entire arrangement is now determined and is represented in the table below.
Only Statement II is necessarily true.
Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”.
A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.”
The following information is known.
1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan.
2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal.
3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions.
4. No one responded “Yes” more than twice.
5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan.
6. Clive tapped more times in total than Badal.
How many taps did Clive receive for his question?
Step 1:
Here, one tap represents "Yes", two taps represent "No", and three taps represent "Maybe".
Since every question received at least one "Yes", one "No", and one "Maybe", each person must have received more than 6 taps in total.
Using Conditions (1) and (4), Alia gave 2 "Yes" responses and 2 "No" responses.
From Condition (6), the combined number of taps made by Badal and Clive is:
40 − (6 + 11 + 9) = 14
Also, Clive made more taps than Badal. Along with Condition (4), this implies that Badal made 6 taps, while Clive made 8 taps.
Now, applying Condition (3), let the number of taps received by Badal, Dilshan, and Ehsaan be x each.
Therefore, the taps received by Clive are:
40 − 9 − 3x = 31 − 3x
Since every person received more than 6 taps,
31 − 3x > 6
which gives x < 8.33. Hence, x can only be 7 or 8.
- If x = 7, then Clive would receive 31 − 21 = 10 taps, which is not possible because Badal answered either "Yes" or "No" to Clive's question.
- Therefore, x = 8, giving Clive = 31 − 24 = 7 taps, which satisfies all the conditions.
The deductions obtained so far are summarized in the table below.
Step 2:
Using Condition (5), no person's response to Alia's question matched the response that Alia gave to that person's question. The same condition also applies to Ehsaan.
Applying this constraint completes the entire arrangement, which is shown in the final table below.
Hence, Clive received 7 taps for his question.
Which two people tapped an equal number of times in total?
Alia and Badal
Clive and Ehsaan
Dilshan and Clive
Badal and Dilshan
Alia and Badal
Step 1:
Here, one tap represents "Yes", two taps represent "No", and three taps represent "Maybe".
Since every question received at least one "Yes", one "No", and one "Maybe", each person must have received more than 6 taps in total.
Using Conditions (1) and (4), Alia gave 2 "Yes" responses and 2 "No" responses.
From Condition (6), the combined number of taps made by Badal and Clive is:
40 − (6 + 11 + 9) = 14
Also, Clive made more taps than Badal. Along with Condition (4), this implies that Badal made 6 taps, while Clive made 8 taps.
Now, applying Condition (3), let the number of taps received by Badal, Dilshan, and Ehsaan be x each.
Therefore, the taps received by Clive are:
40 − 9 − 3x = 31 − 3x
Since every person received more than 6 taps,
31 − 3x > 6
which gives x < 8.33. Hence, x can only be 7 or 8.
- If x = 7, then Clive would receive 31 − 21 = 10 taps, which is not possible because Badal answered either "Yes" or "No" to Clive's question.
- Therefore, x = 8, giving Clive = 31 − 24 = 7 taps, which satisfies all the conditions.
The deductions obtained so far are summarized in the table below.
Step 2:
Using Condition (5), no person's response to Alia's question matched the response that Alia gave to that person's question. The same condition also applies to Ehsaan.
Applying this constraint completes the entire arrangement, which is shown in the final table below.
Alia and Badal tapped an equal number of times in total.
What was Clive’s response to Ehsaan’s question?
No
Maybe
Cannot be determined
Yes
No
Step 1:
Here, one tap represents "Yes", two taps represent "No", and three taps represent "Maybe".
Since every question received at least one "Yes", one "No", and one "Maybe", each person must have received more than 6 taps in total.
Using Conditions (1) and (4), Alia gave 2 "Yes" responses and 2 "No" responses.
From Condition (6), the combined number of taps made by Badal and Clive is:
40 − (6 + 11 + 9) = 14
Also, Clive made more taps than Badal. Along with Condition (4), this implies that Badal made 6 taps, while Clive made 8 taps.
Now, applying Condition (3), let the number of taps received by Badal, Dilshan, and Ehsaan be x each.
Therefore, the taps received by Clive are:
40 − 9 − 3x = 31 − 3x
Since every person received more than 6 taps,
31 − 3x > 6
which gives x < 8.33. Hence, x can only be 7 or 8.
- If x = 7, then Clive would receive 31 − 21 = 10 taps, which is not possible because Badal answered either "Yes" or "No" to Clive's question.
- Therefore, x = 8, giving Clive = 31 − 24 = 7 taps, which satisfies all the conditions.
The deductions obtained so far are summarized in the table below.
Step 2:
Using Condition (5), no person's response to Alia's question matched the response that Alia gave to that person's question. The same condition also applies to Ehsaan.
Applying this constraint completes the entire arrangement, which is shown in the final table below.
Clive’s response to Ehsaan’s question was ‘No’.
How many “Yes” responses were received across all the questions?
Step 1:
Here, one tap represents "Yes", two taps represent "No", and three taps represent "Maybe".
Since every question received at least one "Yes", one "No", and one "Maybe", each person must have received more than 6 taps in total.
Using Conditions (1) and (4), Alia gave 2 "Yes" responses and 2 "No" responses.
From Condition (6), the combined number of taps made by Badal and Clive is:
40 − (6 + 11 + 9) = 14
Also, Clive made more taps than Badal. Along with Condition (4), this implies that Badal made 6 taps, while Clive made 8 taps.
Now, applying Condition (3), let the number of taps received by Badal, Dilshan, and Ehsaan be x each.
Therefore, the taps received by Clive are:
40 − 9 − 3x = 31 − 3x
Since every person received more than 6 taps,
31 − 3x > 6
which gives x < 8.33. Hence, x can only be 7 or 8.
- If x = 7, then Clive would receive 31 − 21 = 10 taps, which is not possible because Badal answered either "Yes" or "No" to Clive's question.
- Therefore, x = 8, giving Clive = 31 − 24 = 7 taps, which satisfies all the conditions.
The deductions obtained so far are summarized in the table below.
Step 2:
Using Condition (5), no person's response to Alia's question matched the response that Alia gave to that person's question. The same condition also applies to Ehsaan.
Applying this constraint completes the entire arrangement, which is shown in the final table below.
Six ‘’Yes” responses were received across all the questions.
A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam, Bashir, Chhavi, and Davies, sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs that are sitting on.
The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction (s)he chooses to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
The following information is known.
1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6.
2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.
What is the number of the chair initially occupied by Bashir?
Step 1:
Initially, Aslam and Chhavi are seated next to each other, whereas Bashir and Davies each have an empty chair on both sides. Since the seating arrangement is circular, the relative placement of Aslam and Chhavi can be fixed arbitrarily without affecting the solution.
From Condition (1), the four friends occupy four consecutive chairs only after Turns 2 and 6. If Aslam were to move counterclockwise, they would fail to occupy adjacent chairs at the end of Turn 2. Hence, Aslam must move clockwise in Turn 1, which means Bashir moves counterclockwise.
Using Condition (2), Davies is on Chair 2 after Turn 1, while Chhavi reaches Chair 7 after Turn 2.
The arrangements after Turns 1 and 2 are shown below.
Step 2:
During Turn 3, Chhavi moves counterclockwise and occupies Chair 6.
From Condition (2), Davies must be on Chair 4 after Turn 5. Therefore, in Turn 4, Davies moves clockwise to Chair 4.
In Turn 5, Aslam moves counterclockwise and occupies Chair 7.
Again applying Condition (1), the four friends sit on adjacent chairs only at the end of Turns 2 and 6. Hence, in Turn 6, Bashir moves clockwise and occupies Chair 5.
Finally, in Turn 7, Chhavi can move either clockwise or counterclockwise, ending up on Chair 1 or Chair 3, respectively.
Therefore, Bashir initially occupied Chair 4.
Who sits on the chair numbered 4 at the end of Turn 3?
Bashir
Chhavi
Davies
No one
No one
Step 1:
Initially, Aslam and Chhavi are seated next to each other, whereas Bashir and Davies each have an empty chair on both sides. Since the seating arrangement is circular, the relative placement of Aslam and Chhavi can be fixed arbitrarily without affecting the solution.
From Condition (1), the four friends occupy four consecutive chairs only after Turns 2 and 6. If Aslam were to move counterclockwise, they would fail to occupy adjacent chairs at the end of Turn 2. Hence, Aslam must move clockwise in Turn 1, which means Bashir moves counterclockwise.
Using Condition (2), Davies is on Chair 2 after Turn 1, while Chhavi reaches Chair 7 after Turn 2.
The arrangements after Turns 1 and 2 are shown below.
Step 2:
During Turn 3, Chhavi moves counterclockwise and occupies Chair 6.
From Condition (2), Davies must be on Chair 4 after Turn 5. Therefore, in Turn 4, Davies moves clockwise to Chair 4.
In Turn 5, Aslam moves counterclockwise and occupies Chair 7.
Again applying Condition (1), the four friends sit on adjacent chairs only at the end of Turns 2 and 6. Hence, in Turn 6, Bashir moves clockwise and occupies Chair 5.
Finally, in Turn 7, Chhavi can move either clockwise or counterclockwise, ending up on Chair 1 or Chair 3, respectively.
No one sits on the chair numbered 4 at the end of Turn 3.
Which of the chairs are occupied at the end of Turn 6?
Chairs numbered 4, 5, 6, and 7
Chairs numbered 2, 3, 4, and 5
Chairs numbered 1, 2, 3, and 4
Chairs numbered 1, 2, 6, and 7
Chairs numbered 4, 5, 6, and 7
Step 1:
Initially, Aslam and Chhavi are seated next to each other, whereas Bashir and Davies each have an empty chair on both sides. Since the seating arrangement is circular, the relative placement of Aslam and Chhavi can be fixed arbitrarily without affecting the solution.
From Condition (1), the four friends occupy four consecutive chairs only after Turns 2 and 6. If Aslam were to move counterclockwise, they would fail to occupy adjacent chairs at the end of Turn 2. Hence, Aslam must move clockwise in Turn 1, which means Bashir moves counterclockwise.
Using Condition (2), Davies is on Chair 2 after Turn 1, while Chhavi reaches Chair 7 after Turn 2.
The arrangements after Turns 1 and 2 are shown below.
Step 2:
During Turn 3, Chhavi moves counterclockwise and occupies Chair 6.
From Condition (2), Davies must be on Chair 4 after Turn 5. Therefore, in Turn 4, Davies moves clockwise to Chair 4.
In Turn 5, Aslam moves counterclockwise and occupies Chair 7.
Again applying Condition (1), the four friends sit on adjacent chairs only at the end of Turns 2 and 6. Hence, in Turn 6, Bashir moves clockwise and occupies Chair 5.
Finally, in Turn 7, Chhavi can move either clockwise or counterclockwise, ending up on Chair 1 or Chair 3, respectively.
Chairs numbered 4, 5, 6, and 7 are occupied at the end of Turn 6.
Which of the following BEST describes the friends sitting on chairs adjacent to the one occupied by Bashir at the end of Turn 7?
Aslam and Chhavi
Chhavi only
Davies only
Chhavi and Davies
Davies only
Step 1:
Initially, Aslam and Chhavi are seated next to each other, whereas Bashir and Davies each have an empty chair on both sides. Since the seating arrangement is circular, the relative placement of Aslam and Chhavi can be fixed arbitrarily without affecting the solution.
From Condition (1), the four friends occupy four consecutive chairs only after Turns 2 and 6. If Aslam were to move counterclockwise, they would fail to occupy adjacent chairs at the end of Turn 2. Hence, Aslam must move clockwise in Turn 1, which means Bashir moves counterclockwise.
Using Condition (2), Davies is on Chair 2 after Turn 1, while Chhavi reaches Chair 7 after Turn 2.
The arrangements after Turns 1 and 2 are shown below.
Step 2:
During Turn 3, Chhavi moves counterclockwise and occupies Chair 6.
From Condition (2), Davies must be on Chair 4 after Turn 5. Therefore, in Turn 4, Davies moves clockwise to Chair 4.
In Turn 5, Aslam moves counterclockwise and occupies Chair 7.
Again applying Condition (1), the four friends sit on adjacent chairs only at the end of Turns 2 and 6. Hence, in Turn 6, Bashir moves clockwise and occupies Chair 5.
Finally, in Turn 7, Chhavi can move either clockwise or counterclockwise, ending up on Chair 1 or Chair 3, respectively.
At the end of Turn 7, only Davies is sitting on a chair adjacent to the one occupied by Bashir.
Five countries engage in trade with each other. Each country levies import tariffs on the other countries. The import tariff levied by Country X on Country Y is calculated by multiplying the corresponding tariff percentage with the total imports of Country X from Country Y.
The radar chart below depicts different import tariff percentages charged by each of the five countries on the others.
For example, US (the blue line in the chart) charges 20%, 40%, 30%, and 30% import tariff percentages on imports from France, India, Japan, and UK, respectively. The bar chart depicts the import tariffs levied by each county on other countries. For example, US charged import tariff of 3 billion USD on UK.
Assume that imports from one country to another equals the exports from the latter to the former.
The trade surplus of Country X with Country Y is defined as follows.
Trade surplus = Exports from Country X to Country Y – Imports to Country X from Country Y.
A negative trade surplus is called trade deficit.
How much is Japan’s export to India worth?
7.0 Billion USD
1.75 Billion USD
16.0 Billion USD
8.5 Billion USD
7.0 Billion USD
From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.
From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.
India charged an import tariff of 3.5 billion USD on imports from Japan, which is 50% of the total imports. Hence, Japan’s exports to India are worth 7.0 billion USD.
Which among the following is the highest?
Exports by Japan to UK
Exports by France to Japan
Imports by France from India
Imports by US from France
Imports by US from France
From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.
From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.
Option (1): Exports by Japan to UK = 6 × 1/0.4 = 15 Billion USD
Option (2): Exports by France to Japan = 3 × 1/ 0.3 = 10 Billion USD
Option (3): Imports by France from India = 6.5 × 1/ 0.4 = 16.25 Billion USD
Option (4): Imports by US from France = 6 × 1/0.2 = 30 Billion USD
Hence, option (4) is the correct answer.
What is the trade surplus/trade deficit of India with UK?
Deficit of 15.0 Billion USD
Surplus of 15.0 Billion USD
Surplus of 10.0 Billion USD
Deficit of 10.0 Billion USD
Deficit of 15.0 Billion USD
From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.
From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.
Import by India from UK = 5 × 1/0.2 = 25 Billion USD
Export from India to UK = 3 × 1/0.3 = 10 Billion USD
Hence, trade deficit of India with UK = 25 – 10 = 15 Billion USD
Among France and UK, who has/have trade surplus(es) with US?
Both France and UK
Only UK
Neither France nor UK
Only France
Only France
From the radar graph, the table below shows the import tariffs (in %) imposed by each country on other countries.
From the bar graph, the table below shows the import tariffs (in Billion USD) imposed by each country on other countries.
Import by France from US = 5.5 × 1/0.3 = 18.33 Billion USD
Export by France to US = 6 × 1/0.2 = 30 Billion USD
So trade surplus of France with US = 30 – 18.33 = 11.66 Billion USD
Import by UK from US = 2.5 × 1/0.2 = 12.5 Billion USD
Export from UK to US = 3 × 1/0.3 = 10 Billion USD
So trade deficit of UK with US = 12.5 – 10 = 2.5 Billion USD
Hence, only France has trade surplus with US.
A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station.
A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments B – C, C – D, and D – E.
The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200.
The following information is known.
1. Segment C – D had an occupancy factor of 95%.
Only segment B – C had a higher occupancy factor.
2. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E.
3. Among the seats reserved on segment D – E,
exactly four-sevenths were from stations before C.
4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E.
5. No tickets were booked from A to B, from B to D and from D to E.
6. The number of tickets booked for any segment was a multiple of 10.
What was the occupancy factor for segment D – E?
84%
35%
70%
77%
70%
Step 1:
From Condition (2), 40 tickets were booked from B to C, while 30 tickets were booked from B to E.
Using Condition (5), there were no bookings on the routes A to B, B to D, and D to E.
From Condition (4), the number of tickets booked from A to C is equal to the number of tickets booked from A to E, and this common value is greater than 30.
Now, applying Condition (3), exactly four-sevenths of the passengers travelling on segment D–E had boarded before Station C, i.e., from Stations A and B.
Since the total occupancy on segment D–E must be divisible by both 7 and 10, the only possible values are 70 and 140.
An occupancy of 70 is not possible because A to E + B to E > 60. Therefore, the occupancy on segment D–E must be 140.
Hence,
A to E + B to E = (4/7) × 140 = 80
Since B to E = 30,
A to E = 80 − 30 = 50
Therefore,
C to E = 140 − (50 + 30) = 60
Step 2:
From Conditions (1) and (6), the occupancy on segment C–D is
0.95 × 200 = 190
Also, the occupancy on segment B–C is 200.
For segment B–C,
AC + AD + AE + BC + BD + BE = 200
Substituting the known values,
50 + AD + 50 + 40 + 0 + 30 = 200
AD = 30
Similarly, for segment C–D,
AD + AE + BD + BE + CD + CE = 190
Substituting the known values,
30 + 50 + 0 + 30 + CD + 60 = 190
CD = 20
The completed booking table is shown below.
The occupancy on segment D–E is:
A to E + B to E + C to E + D to E
= 50 + 30 + 60 + 0 = 140
Hence, the occupancy factor for segment D–E is
(140/200) × 100 = 70%.
How many tickets were booked from Station A to Station E?
Step 1:
From Condition (2), 40 tickets were booked from B to C, while 30 tickets were booked from B to E.
Using Condition (5), there were no bookings on the routes A to B, B to D, and D to E.
From Condition (4), the number of tickets booked from A to C is equal to the number of tickets booked from A to E, and this common value is greater than 30.
Now, applying Condition (3), exactly four-sevenths of the passengers travelling on segment D–E had boarded before Station C, i.e., from Stations A and B.
Since the total occupancy on segment D–E must be divisible by both 7 and 10, the only possible values are 70 and 140.
An occupancy of 70 is not possible because A to E + B to E > 60. Therefore, the occupancy on segment D–E must be 140.
Hence,
A to E + B to E = (4/7) × 140 = 80
Since B to E = 30,
A to E = 80 − 30 = 50
Therefore,
C to E = 140 − (50 + 30) = 60
Step 2:
From Conditions (1) and (6), the occupancy on segment C–D is
0.95 × 200 = 190
Also, the occupancy on segment B–C is 200.
For segment B–C,
AC + AD + AE + BC + BD + BE = 200
Substituting the known values,
50 + AD + 50 + 40 + 0 + 30 = 200
AD = 30
Similarly, for segment C–D,
AD + AE + BD + BE + CD + CE = 190
Substituting the known values,
30 + 50 + 0 + 30 + CD + 60 = 190
CD = 20
The completed booking table is shown below.
The number of tickets booked from Station A to Station E was 50.
How many tickets were booked from Station C?
Step 1:
From Condition (2), 40 tickets were booked from B to C, while 30 tickets were booked from B to E.
Using Condition (5), there were no bookings on the routes A to B, B to D, and D to E.
From Condition (4), the number of tickets booked from A to C is equal to the number of tickets booked from A to E, and this common value is greater than 30.
Now, applying Condition (3), exactly four-sevenths of the passengers travelling on segment D–E had boarded before Station C, i.e., from Stations A and B.
Since the total occupancy on segment D–E must be divisible by both 7 and 10, the only possible values are 70 and 140.
An occupancy of 70 is not possible because A to E + B to E > 60. Therefore, the occupancy on segment D–E must be 140.
Hence,
A to E + B to E = (4/7) × 140 = 80
Since B to E = 30,
A to E = 80 − 30 = 50
Therefore,
C to E = 140 − (50 + 30) = 60
Step 2:
From Conditions (1) and (6), the occupancy on segment C–D is
0.95 × 200 = 190
Also, the occupancy on segment B–C is 200.
For segment B–C,
AC + AD + AE + BC + BD + BE = 200
Substituting the known values,
50 + AD + 50 + 40 + 0 + 30 = 200
AD = 30
Similarly, for segment C–D,
AD + AE + BD + BE + CD + CE = 190
Substituting the known values,
30 + 50 + 0 + 30 + CD + 60 = 190
CD = 20
The completed booking table is shown below.
The number of tickets booked from Station C was = 20 + 60 = 80.
What is the difference between the number of tickets booked to Station C and the number of tickets booked to Station D?
Step 1:
From Condition (2), 40 tickets were booked from B to C, while 30 tickets were booked from B to E.
Using Condition (5), there were no bookings on the routes A to B, B to D, and D to E.
From Condition (4), the number of tickets booked from A to C is equal to the number of tickets booked from A to E, and this common value is greater than 30.
Now, applying Condition (3), exactly four-sevenths of the passengers travelling on segment D–E had boarded before Station C, i.e., from Stations A and B.
Since the total occupancy on segment D–E must be divisible by both 7 and 10, the only possible values are 70 and 140.
An occupancy of 70 is not possible because A to E + B to E > 60. Therefore, the occupancy on segment D–E must be 140.
Hence,
A to E + B to E = (4/7) × 140 = 80
Since B to E = 30,
A to E = 80 − 30 = 50
Therefore,
C to E = 140 − (50 + 30) = 60
Step 2:
From Conditions (1) and (6), the occupancy on segment C–D is
0.95 × 200 = 190
Also, the occupancy on segment B–C is 200.
For segment B–C,
AC + AD + AE + BC + BD + BE = 200
Substituting the known values,
50 + AD + 50 + 40 + 0 + 30 = 200
AD = 30
Similarly, for segment C–D,
AD + AE + BD + BE + CD + CE = 190
Substituting the known values,
30 + 50 + 0 + 30 + CD + 60 = 190
CD = 20
The completed booking table is shown below.
Required difference = (50 + 40) – (30 + 20) = 40.
How many tickets were booked to travel in exactly one segment?
Step 1:
From Condition (2), 40 tickets were booked from B to C, while 30 tickets were booked from B to E.
Using Condition (5), there were no bookings on the routes A to B, B to D, and D to E.
From Condition (4), the number of tickets booked from A to C is equal to the number of tickets booked from A to E, and this common value is greater than 30.
Now, applying Condition (3), exactly four-sevenths of the passengers travelling on segment D–E had boarded before Station C, i.e., from Stations A and B.
Since the total occupancy on segment D–E must be divisible by both 7 and 10, the only possible values are 70 and 140.
An occupancy of 70 is not possible because A to E + B to E > 60. Therefore, the occupancy on segment D–E must be 140.
Hence,
A to E + B to E = (4/7) × 140 = 80
Since B to E = 30,
A to E = 80 − 30 = 50
Therefore,
C to E = 140 − (50 + 30) = 60
Step 2:
From Conditions (1) and (6), the occupancy on segment C–D is
0.95 × 200 = 190
Also, the occupancy on segment B–C is 200.
For segment B–C,
AC + AD + AE + BC + BD + BE = 200
Substituting the known values,
50 + AD + 50 + 40 + 0 + 30 = 200
AD = 30
Similarly, for segment C–D,
AD + AE + BD + BE + CD + CE = 190
Substituting the known values,
30 + 50 + 0 + 30 + CD + 60 = 190
CD = 20
The completed booking table is shown below.
The number of tickets booked to travel in exactly one segment = B to C + C to D = 40 + 20 = 60.
A value of c for which the minimum value of f(x) = x² − 4cx + 8c is greater than the maximum value of g(x) = −x² + 3cx − 2c, is
2
1/2
−1/2
−2
1/2
Step 1: Find the minimum value of f(x). Since the coefficient of x² is positive, the parabola opens upward. The vertex is at x = 2c. Substituting: Minimum value of f(x) = (2c)² − 4c(2c) + 8c = 4c² − 8c² + 8c = −4c² + 8c.
Step 2: Find the maximum value of g(x). Since the coefficient of x² is negative, the parabola opens downward. The vertex is at x = 3c/2. Substituting: Maximum value of g(x) = −(3c/2)² + 3c(3c/2) − 2c = −9c²/4 + 9c²/2 − 2c = 9c²/4 − 2c.
Step 3: Apply the given condition. −4c² + 8c > 9c²/4 − 2c. Multiplying both sides by 4: −16c² + 32c > 9c² − 8c → 25c² − 40c < 0 → 5c(5c − 8) < 0. Therefore, 0 < c < 8/5. Among the options, only 1/2 lies in this range.
Shruti travels a distance of 224 km in four parts for a total travel time of 3 hours. Her speeds in these four parts follow an arithmetic progression, and the corresponding time taken to cover these four parts follow another arithmetic progression. If she travels at a speed of 960 meters per minute for 30 minutes to cover the first part, then the distance, in meters, she travels in the fourth part is
76800
112000
96000
86400
86400
Let the speeds (in m/min) be 960, 960+d, 960+2d, 960+3d and times (in minutes) be 30, 30+t, 30+2t, 30+3t.
Total time = 180 minutes: 30 + (30+t) + (30+2t) + (30+3t) = 180 → 120 + 6t = 180 → t = 10. So times are 30, 40, 50, 60 minutes.
Total distance = 224000 m: 28800 + 40(960+d) + 50(960+2d) + 60(960+3d) = 224000 → 172800 + 320d = 224000 → d = 160.
Fourth part: speed = 960 + 3×160 = 1440 m/min, time = 60 min. Distance = 1440 × 60 = 86400 meters.
In a 3-digit number N, the digits are non-zero and distinct such that none of the digits is a perfect square, and only one of the digits is a prime number. Then, the number of factors of the minimum possible value of N is
Non-zero digits excluding perfect squares (1, 4, 9): allowed digits are 2, 3, 5, 6, 7, 8. Among these, prime digits are 2, 3, 5, 7 and composite digits are 6, 8. Since only one digit is prime, the number must contain both composites (6 and 8) and exactly one prime.
To minimise N: hundreds digit = 6, tens digit = 2 (smallest prime), units digit = 8. So N = 628.
Prime factorisation: 628 = 2² × 157 (157 is prime). Number of factors = (2+1)(1+1) = 6.
Let 3 ≤ x ≤ 6 and [x²] = [x]², where [x] is the greatest integer not exceeding x. If set S represents all feasible values of x, then a possible subset of S is
(3, √10) ∪ [5, √26) ∪ {6}
[3, √10] ∪ [5, √26]
[3, √10] ∪ [4, √17] ∪ {6}
(4, √18) ∪ [5, √27) ∪ {6}
(3, √10) ∪ [5, √26) ∪ {6}
Case 1 (3 ≤ x < 4): [x] = 3, [x]² = 9. Need [x²] = 9 → 9 ≤ x² < 10 → x ∈ [3, √10).
Case 2 (4 ≤ x < 5): [x] = 4, [x]² = 16. Need [x²] = 16 → x ∈ [4, √17).
Case 3 (5 ≤ x < 6): [x] = 5, [x]² = 25. Need [x²] = 25 → x ∈ [5, √26).
Case 4 (x = 6): [x²] = [36] = 36 = [x]² = 36. So x = 6 is included.
Complete set S = [3, √10) ∪ [4, √17) ∪ [5, √26) ∪ {6}. Option A, (3, √10) ∪ [5, √26) ∪ {6}, is a valid subset. Options B and C incorrectly include √10 and √17/√26 (endpoints not in S). Option D contains values outside S.
Stocks A, B and C are priced at rupees 120, 90 and 150 per share, respectively. A trader holds a portfolio consisting of 10 shares of stock A, and 20 shares of stocks B and C put together. If the total value of her portfolio is rupees 3300, then the number of shares of stock B that she holds, is
Let shares of B = x, so shares of C = 20 − x. Total value: 10×120 + 90x + 150(20−x) = 3300 → 1200 + 90x + 3000 − 150x = 3300 → 4200 − 60x = 3300 → x = 15.
For any natural number k, let aₖ = 3ᵏ. The smallest natural number m for which {(a₁)¹ × (a₂)² × ... × (a₂₀)²⁰} < {a₂₁ × a₂₂ × ... × a₂₀₊ₘ}, is
58
59
56
57
58
LHS = (3¹)¹ × (3²)² × ... × (3²⁰)²⁰ = 3^(1² + 2² + ... + 20²) = 3^2870 (using sum of squares formula: 20×21×41/6 = 2870).
RHS = 3²¹ × 3²² × ... × 3^(20+m) = 3^(21 + 22 + ... + (20+m)) = 3^[m(m+41)/2].
Condition: m(m+41)/2 > 2870 → m(m+41) > 5740.
For m = 57: 57×98 = 5586 < 5740. For m = 58: 58×99 = 5742 > 5740. Hence smallest m = 58.
The number of distinct integers n for which log1/4(n² − 7n + 11) > 0, is
2
infinite
1
0
0
Since the base 1/4 < 1, log₁/₄(x) > 0 implies 0 < x < 1. So we need 0 < n² − 7n + 11 < 1. From n² − 7n + 11 < 1: n² − 7n + 10 < 0 → (n−2)(n−5) < 0 → 2 < n < 5. Integer candidates: n = 3, 4. Checking domain (n² − 7n + 11 > 0): for n = 3: 9 − 21 + 11 = −1 < 0. For n = 4: 16 − 28 + 11 = −1 < 0. Neither satisfies the domain condition. Answer: 0.
The number of distinct pairs of integers (x, y) satisfying the inequalities x > y ≥ 3 and x + y < 14 is
Since x > y, minimum x = y+1. From x + y < 14: (y+1) + y < 14 → y ≤ 6. With y ≥ 3, possible values of y are 3, 4, 5, 6.
For y = 3: x ∈ {4,5,6,7,8,9,10} → 7 pairs. For y = 4: x ∈ {5,6,7,8,9} → 5 pairs. For y = 5: x ∈ {6,7,8} → 3 pairs. For y = 6: x ∈ {7} → 1 pair. Total = 7+5+3+1 = 16.
At a certain simple rate of interest, a given sum amounts to Rs 13920 in 3 years, and to Rs 18960 in 6 years and 6 months. If the same given sum had been invested for 2 years at the same rate as before but with interest compounded every 6 months, then the total interest earned, in rupees, would have been nearest to
3221
3180
3150
3096
3221
Interest for 3.5 years = 18960 − 13920 = ₹5040. Annual SI = 5040/3.5 = ₹1440.
Principal = 13920 − 3×1440 = ₹9600. Rate = (1440/9600)×100 = 15% p.a. → 7.5% per half-year.
CI for 2 years (4 half-years): Amount = 9600 × (1.075)⁴ ≈ 9600 × 1.33547 ≈ ₹12820.5. Interest = 12820.5 − 9600 ≈ ₹3220.5, nearest to ₹3221.
A container holds 200 litres of a solution of acid and water, having 30% acid by volume. Atul replaces 20% of this solution with water, then replaces 10% of the resulting solution with acid, and finally replaces 15% of the solution thus obtained, with water. The percentage of acid by volume in the final solution obtained after these three replacements, is nearest to
23
25
29
27
27
Initial acid = 60 litres.
Step 1 (replace 20% with water): Acid removed = 30% of 40 = 12 L. Acid left = 48 L.
Step 2 (replace 10% with acid): Acid percentage = 48/200 = 24%. Acid removed = 24% of 20 = 4.8 L. Acid left = 43.2 L. Add 20 L pure acid → acid = 63.2 L.
Step 3 (replace 15% with water): Acid percentage = 63.2/200 = 31.6%. Acid removed = 31.6% of 30 = 9.48 L. Acid left = 53.72 L.
Final acid % = (53.72/200) × 100 = 26.86% ≈ 27%.
In a class, there were more than 10 boys and a certain number of girls. After 40% of the girls and 60% of the boys left the class, the remaining number of girls was 8 more than the remaining number of boys. Then, the minimum possible number of students initially in the class was
Let boys = B, girls = G. Remaining: 2B/5 boys, 3G/5 girls. Condition: 3G/5 − 2B/5 = 8 → 3G − 2B = 40.
For integer solutions, let B = 5b, G = 5g → 3g − 2b = 8. For g to be integer, 8+2b ≡ 0 (mod 3) → b ≡ 2 (mod 3). Also B > 10 → b > 2. Smallest valid b = 5 → g = 6. So B = 25, G = 30.
Total = 55. Verification: remaining boys = 10, remaining girls = 18, difference = 8. ✓
A cafeteria offers 5 types of sandwiches. Moreover, for each type of sandwich, a customer can choose one of 4 breads and opt for either small or large sized sandwich. Optionally, the customer may also add up to 2 out of 6 available sauces. The number of different ways in which an order can be placed for a sandwich, is
880
840
800
600
880
Base choices: 5 sandwich types × 4 breads × 2 sizes = 40 ways.
Sauce choices (up to 2 from 6): no sauce = 1, exactly 1 = ⁶C₁ = 6, exactly 2 = ⁶C₂ = 15. Total sauce choices = 22.
Total orders = 40 × 22 = 880.
In the set of consecutive odd numbers {1, 3, 5, ..., 57}, there is a number k such that the sum of all the elements less than k is equal to the sum of all the elements greater than k. Then, k equals
41
39
43
37
41
The set has 29 odd numbers with total sum = 29² = 841. Let k be the m-th odd number, so k = 2m−1.
Sum before k = (m−1)². Sum after k = 841 − m². Setting equal: (m−1)² = 841 − m² → 2m² − 2m − 840 = 0 → m² − m − 420 = 0 → (m−21)(m+20) = 0 → m = 21.
k = 2×21 − 1 = 41.
Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is
38400
38880
34400
47040
38400
Cost to complete task if each works alone: Arun = 24×2160 = ₹51840, Varun = 21×2400 = ₹50400, Tarun = 15×2160 = ₹32400. Tarun is cheapest per unit of work.
Tarun works all 10 days: completes 10/15 = 2/3 of work. Remaining = 1/3. Varun needs (1/3)÷(1/21) = 7 days.
Total cost = 10×2160 + 7×2400 = 21600 + 16800 = ₹38400.
Kamala divided her investment of Rs 100000 between stocks, bonds, and gold. Her investment in bonds was 25% of her investment in gold. With annual returns of 10%, 6%, 8% on stocks, bonds, and gold, respectively, she gained a total amount of Rs 8200 in one year. The amount, in rupees, that she gained from the bonds, was
Let gold = G, bonds = G/4, stocks = 100000 − 5G/4.
Total return: 0.10(100000 − 5G/4) + 0.06(G/4) + 0.08G = 8200 → 10000 − 0.125G + 0.015G + 0.08G = 8200 → 10000 − 0.03G = 8200 → G = 60000.
Bonds = 60000/4 = ₹15000. Gain from bonds = 6% of 15000 = ₹900.
If a − 6b + 6c = 4 and 6a + 3b − 3c = 50, where a, b and c are real numbers, the value of 2a + 3b − 3c is
20
14
18
15
18
Multiply the first equation by 1/2: a/2 − 3b + 3c = 2. Add to the second equation: 6a + a/2 = 52 → 13a/2 = 52 → a = 8.
From second equation: 48 + 3b − 3c = 50 → 3b − 3c = 2. Therefore 2a + 3b − 3c = 16 + 2 = 18.
The (x, y) coordinates of vertices P, Q and R of a parallelogram PQRS are (−3, −2), (1, −5) and (9, 1), respectively. If the diagonal SQ intersects the x-axis at (a, 0), then the value of a is
27/7
10/3
13/4
29/9
29/9
In parallelogram PQRS, S = P + R − Q = (−3+9−1, −2+1+5) = (5, 4).
Slope of SQ = (−5−4)/(1−5) = −9/−4 = 9/4. Line SQ through S(5,4): y − 4 = (9/4)(x−5).
At y = 0: −4 = (9/4)(x−5) → −16 = 9(x−5) → 9x = 29 → a = 29/9.
In a circle with center C and radius 6√2 cm, PQ and SR are two parallel chords separated by one of the diameters. If ∠PQC = 45°, and the ratio of the perpendicular distance of PQ and SR from C is 3 : 2, then the area, in sq. cm, of the quadrilateral PQRS is
4(3 + √14)
4(3√2 + √7)
20(3 + √14)
20(3√2 + √7)
20(3 + √14)
Radius r = 6√2. Let M be midpoint of PQ. △QCM is right-angled with ∠MQC = 45°, so it is 45°–45°–90°. CM = CQ/√2 = 6√2/√2 = 6 cm. So distance of PQ from C = 6 cm.
Distance of SR from C = (2/3)×6 = 4 cm.
Length of PQ = 2√(72−36) = 2√36 = 12 cm. Length of SR = 2√(72−16) = 2√56 = 4√14 cm.
Since chords are on opposite sides of the diameter, distance between them = 6+4 = 10 cm.
Area of trapezium PQRS = 1/2 × (12 + 4√14) × 10 = 5(12 + 4√14) = 20(3 + √14).
The ratio of the number of students in the morning shift and afternoon shift of a school was 13 : 9. After 21 students moved from the morning shift to the afternoon shift, this ratio became 19 : 14. Next, some new students joined the morning and afternoon shifts in the ratio 3 : 8 and then the ratio of the number of students in the morning shift and the afternoon shift became 5 : 4. The number of new students who joined is
110
88
121
99
99
Let initial students be 13x and 9x. After shifting: (13x−21)/(9x+21) = 19/14 → 182x−294 = 171x+399 → x = 63. Morning = 798, Afternoon = 588.
Let new students join as 3k (morning) and 8k (afternoon). (798+3k)/(588+8k) = 5/4 → 3192+12k = 2940+40k → 28k = 252 → k = 9.
Total new students = 11k = 99.
If the length of a side of a rhombus is 36 cm and the area of the rhombus is 396 sq. cm, then the absolute value of the difference between the lengths, in cm, of the diagonals of the rhombus is
Let diagonals be d₁ and d₂. Area = (1/2)d₁d₂ = 396 → d₁d₂ = 792.
Side relation: (d₁/2)² + (d₂/2)² = 36² → d₁² + d₂² = 5184.
(d₁−d₂)² = d₁² + d₂² − 2d₁d₂ = 5184 − 1584 = 3600. |d₁−d₂| = 60.
The number of non-negative integer values of k for which the quadratic equation x² − 5x + k = 0 has only integer roots, is
Let roots be r₁ and r₂. By Vieta's: r₁+r₂ = 5 and r₁r₂ = k ≥ 0. Integer pairs summing to 5: (0,5), (1,4), (2,3) and their reverses. Distinct products: 0×5 = 0, 1×4 = 4, 2×3 = 6. So k ∈ {0, 4, 6} → 3 values.
A shopkeeper offers a discount of 22% on the marked price of each chair, and gives 13 chairs to a customer for the discounted price of 12 chairs to earn a profit of 26% on the transaction. If the cost price of each chair is Rs 100, then the marked price, in rupees, of each chair is
Let marked price = M. Discounted price per chair = 0.78M. Revenue = 12×0.78M = 9.36M.
Cost of 13 chairs = ₹1300. With 26% profit: SP = 1300×1.26 = ₹1638.
9.36M = 1638 → M = ₹175.
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