CAT 2024 — Slot 1
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VARC topics covered: Economics & Society RC, Nature And Environment RC, Odd One Out, Para Completion, Para Summary, Science And Technology RC
. . . [T]he idea of craftsmanship is not simply nostalgic. . . . Crafts require distinct skills, an allround approach to work that involves the whole product, rather than individual parts, and an attitude that necessitates devotion to the job and a focus on the communal interest. The concept of craft emphasises the human touch and individual judgment. Essentially, the crafts concept seems to run against the preponderant ethos of management studies which, as the academics note, have long prioritised efficiency and consistency. . . . Craft skills were portrayed as being primitive and traditionalist.
The contrast between artisanship and efficiency first came to the fore in the 19th century when British manufacturers suddenly faced competition from across the Atlantic as firms developed the "American system" using standardised parts. . . . the worldwide success of the Singer sewing machine showed the potential of a mass-produced device. This process created its own reaction, first in the form of the Arts and Crafts movement of the late 19th century, and then again in the "small is beautiful" movement of the 1970s. A third crafts movement is emerging as people become aware of the environmental impact of conventional industry.
There are two potential markets for those who practise crafts. The first stems from the existence of consumers who are willing to pay a premium price for goods that are deemed to be of extra quality. . . . The second market lies in those consumers who wish to use their purchases to support local workers, or to reduce their environmental impact by taking goods to craftspeople to be mended, or recycled.
For workers, the appeal of craftsmanship is that it allows them the autonomy to make creative choices, and thus makes a job far more satisfying. In that sense, it could offer hope for the overall labour market. Let the machines automate dull and repetitive tasks and let workers focus purely on their skills, judgment and imagination. As a current example, the academics cite the "agile" manifesto in the software sector, an industry at the heart of technological change. The pioneers behind the original agile manifesto promised to prioritise "individuals and interactions over processes and tools". By bringing together experts from different teams, agile working is designed to improve creativity.
But the broader question is whether crafts can create a lot more jobs than they do today. Demand for crafted products may rise but will it be easy to retrain workers in sectors that might get automated (such as truck drivers) to take advantage? In a world where products and services often have to pass through regulatory hoops, large companies will usually have the advantage.
History also suggests that the link between crafts and creativity is not automatic. Medieval craft guilds were monopolies which resisted new entrants. They were also highly hierarchical with young men required to spend long periods as apprentices and journeymen before they could set up on their own; by that time the innovative spirit may have been knocked out of them. Craft workers can thrive in the modern era, but only if they don't get too organised.
We can infer from the passage that medieval crafts guilds resembled mass production in that both:
did not necessarily promote creativity.
discouraged innovation by restricting entry through strict rules.
did not always employ egalitarian production processes.
focused excessively on product quality.
did not necessarily promote creativity.
The passage states that medieval craft guilds were hierarchical, with long apprenticeships that may have knocked the innovative spirit out of young workers by the time they could set up on their own. This shows that guilds, despite being associated with crafts, did not necessarily foster creativity, just as mass production, focused on efficiency and consistency, also does not necessarily promote creativity. Both systems, in their own way, suppressed individual creative input.
Why Option B is
Incorrect: Mass production is not described in the passage as restricting entry, this is a feature specific to guilds, not something shared by both.
Why Option C is
Incorrect: The passage does not discuss egalitarian production processes for either guilds or mass production, this is not the basis of comparison being drawn.
Why Option D is
Incorrect: Mass production is associated with efficiency and consistency, not necessarily an excessive focus on quality, so this is not a shared trait between the two systems.
Why Option A is Correct: Both guilds and mass production are shown to not necessarily encourage creativity, guilds through their hierarchical apprenticeship structure, and mass production through its prioritisation of efficiency over individual judgment.
Key Takeaway: When comparing two systems mentioned in a passage, identify the precise shared outcome the passage implies, rather than assuming surface-level similarities that aren't explicitly supported.
Which one of the following statements is NOT inconsistent with the views stated in the passage?
We need to support the crafts; only then can we retain the creativity intrinsic to their production.
Creativity in the crafts could be stifled if the market for artisan goods becomes too organised.
The Arts and Crafts movement was initially inspired by the "American system" of production.
The agile movement in software is a throwback to the tenets of the medieval crafts guilds.
Creativity in the crafts could be stifled if the market for artisan goods becomes too organised.
The passage ends by stating that craft workers can thrive in the modern era only if they don't get too organised, drawing on the example of guilds becoming monopolistic and hierarchical. This directly supports the idea that an overly organised market for crafts could stifle the very creativity crafts are meant to nurture.
Why Option A is
Incorrect: The passage does not suggest that support for crafts is the only way to retain creativity, it instead cautions that crafts and creativity are not automatically linked, especially if crafts become too organised.
Why Option C is
Incorrect: The passage states the Arts and Crafts movement was a reaction against the American system of standardised mass production, not inspired by it.
Why Option D is
Incorrect: The agile movement is presented as a positive contrast to the hierarchical structure of medieval guilds, not as a throwback to their tenets.
Why Option B is Correct: This aligns directly with the passage's closing caution that craft workers can thrive only if they avoid becoming too organised, implying that excessive organisation could stifle creativity.
Key Takeaway: For "not inconsistent" questions, find the option that directly echoes a specific claim in the passage rather than one that contradicts or misattributes a causal relationship.
The author questions the ability of crafts to create substantial employment opportunities presently because:
the low scale of crafts production will not be able to absorb the mass of redundant labour.
regulatory requirements could make it difficult for small crafts outfits to compete.
workers made redundant by automation are unlikely to opt for crafts-related work.
crafts guilds tend to resist new entrants and are unlikely to accept large numbers of trainees.
regulatory requirements could make it difficult for small crafts outfits to compete.
The passage states that in a world where products and services often have to pass through regulatory hoops, large companies will usually have the advantage, implying small crafts outfits will struggle to compete under such regulatory requirements, limiting their ability to scale up and create substantial employment.
Why Option A is
Incorrect: The passage does not frame the issue in terms of absorption capacity for redundant labour directly, it specifically raises regulatory hurdles as the structural challenge.
Why Option C is
Incorrect: The passage raises a question about whether workers in automated sectors can be retrained for crafts, but this is posed as an open question, not stated as the reason the author doubts crafts' employment potential.
Why Option D is
Incorrect: This refers to a separate historical point about guilds resisting new entrants, not the specific present-day employment concern the author raises about regulatory hoops favouring large companies.
Why Option B is Correct: This matches the passage's specific point about regulatory hoops giving large companies an advantage, directly explaining the author's doubt about crafts' ability to create substantial employment.
Key Takeaway: Locate the exact reasoning given in the passage for a stated doubt or concern, rather than a plausible but unstated alternative explanation.
The most recent revival in interest in the crafts is a result of the emergence of all of the following EXCEPT:
support for individual creations as opposed to mass-produced objects.
concerns about the environmental impact of mass production.
a niche market for discerning buyers of quality products.
a greater interest in buying locally produced goods.
support for individual creations as opposed to mass-produced objects.
The passage attributes the most recent crafts revival specifically to growing awareness of the environmental impact of conventional industry. Support for individual creations over mass-produced objects is mentioned earlier as a general appeal of crafts and a separate market category, not specifically as the cause of the most recent revival.
Why Option B is
Incorrect (as a candidate for the exception): The passage explicitly attributes the emerging third crafts movement to environmental impact concerns about conventional industry.
Why Option C is
Incorrect (as a candidate for the exception): The passage explicitly mentions a market of consumers willing to pay a premium for quality goods, a niche market for discerning buyers, as one of the existing reasons crafts persist.
Why Option D is
Incorrect (as a candidate for the exception): The passage explicitly mentions consumers wanting to support local workers as one of the markets driving interest in crafts.
Why Option A is Correct: Support for individual creations over mass production is a general, ongoing appeal of crafts mentioned earlier in the passage, not specifically identified as a cause of the most recent revival, making it the exception.
Key Takeaway: Distinguish between general, long-standing appeals of a phenomenon and the specific, recent causes the passage attributes to its latest resurgence.
Oftentimes, when economists cross borders, they are less interested in learning from others than in invading their garden plots. Gary Becker, for instance, pioneered the idea of human capital. To do so, he famously tackled topics like crime and domesticity, applying methods honed in the study of markets to domains of nonmarket life. He projected economics outward into new realms: for example, by revealing the extent to which humans calculate marginal utilities when choosing their spouses or stealing from neighbors. At the same time, he did not let other ways of thinking enter his own economic realm: for example, he did not borrow from anthropology or history or let observations of nonmarket economics inform his homo economicus. Becker was a picture of the imperial economist in the heyday of the discipline's bravura.
Times have changed for the once almighty discipline. Economics has been taken to task, within and beyond its ramparts. Some economists have reached out, imported, borrowed, and collaborated—been less imperial, more open. Consider Thomas Piketty and his outreach to historians. The booming field of behavioral economics—the fusion of economics and social psychology—is another case. Having spawned active subfields, like judgment, decisionmaking and a turn to experimentation, the field aims to go beyond the caricature of Rational Man to explain how humans make decisions….
It is important to underscore how this flips the way we think about economics. For generations, economists have presumed that people have interests—"preferences," in the neoclassical argot—that get revealed in the course of peoples' choices. Interests come before actions and determine them. If you are hungry, you buy lunch; if you are cold, you get a sweater. If you only have so much money and can't afford to deal with both your growling stomach and your shivering, which need you choose to meet using your scarce savings reveals your preference.
Psychologists take one look at this simple formulation and shake their heads. Increasingly, even some mainstream economists have to admit that homo economicus doesn't always behave like the textbook maximizer; irrational behavior can't simply be waved away as extraeconomic expressions of passions over interests, and thus the domain of other disciplines…. This is one place where the humanist can help the economist. If narrative economics is going to help us understand how rivals duke it out, who wins and who loses, we are going to need much more than lessons from epidemiological studies of viruses or intracranial stimuli.
Above all, we need politics and institutions. Shiller [the Nobel prize winning economist] connects perceptions of narratives to changes in behavior and thence to social outcomes. He completes a circle that was key to behavioral economics and brings in storytelling to make sense of how perceptions get framed. This cycle (perception to behavior to society) was once mediated or dominated by institutions: the political parties, lobby groups, and media organizations that played a vital role in legitimating, representing, and excluding interests. Yet institutions have been stripped from Shiller's account, to reveal a bare dynamic of emotions and economics, without the intermediating place of politics.
We can infer from the passage that the term "homo economicus" refers to someone who:
is not influenced by the preferences and choices of others.
believes in borrowing and collaborating with other disciplines in their work.
makes rational decisions based on their own preferences.
maximises their opportunities based on nonmarket choices.
makes rational decisions based on their own preferences.
The passage explains that the term refers to a model in economics where people's interests, or preferences, come before and determine their actions and choices, which is essentially the idea of the rational maximiser making decisions based on personal preferences.
Why Option A is
Incorrect: The passage does not characterise homo economicus through independence from others' preferences, the discussion centres on a person's own preferences driving their own choices.
Why Option B is
Incorrect: This is the opposite of homo economicus, the passage shows homo economicus as a closed, self-contained model resistant to incorporating other disciplines, like in Becker's imperial approach to economics.
Why Option D is
Incorrect: The passage describes homo economicus through market-based rational decision making, not specifically through nonmarket choices, which is rather Becker's broader application of economic reasoning to nonmarket domains.
Why Option C is Correct: This matches the passage's explanation, that interests determine choices, with the classic example given being the trade-off between buying lunch or a sweater based on one's own preferences.
Key Takeaway: Define a term strictly based on the passage's own explanation, rather than associations from the surrounding context that describe related but distinct ideas.
"Times have changed for the once almighty discipline." We can infer from this statement and the associated paragraph that the author is being:
sarcastic about how economists, who earlier shunned other disciplines, are now beginning to incorporate them in their analyses.
disparaging of economists' inability to precisely predict market behaviour, and are now borrowing from other disciplines to remedy this.
judgemental about the ability of economic tools to accurately manage crises leading to the downfall of this lofty science.
critical of economists' openly borrowing and collaborating across disciplines to explain how humans make decisions.
sarcastic about how economists, who earlier shunned other disciplines, are now beginning to incorporate them in their analyses.
The phrase "once almighty discipline" carries an ironic tone, highlighting how economics, which once resisted outside influence under figures like Becker, is now embracing collaboration with other disciplines like history and psychology. The tone is sarcastic about this shift in posture from imperial dominance to openness.
Why Option B is
Incorrect: The author's point is not about economists' inability to predict markets, but about their changing openness to other disciplines, this option misattributes the reason for the shift.
Why Option C is
Incorrect: This frames the tone as judgemental about economic tools failing during crises, which is not the focus of this specific statement or paragraph, the paragraph is about disciplinary openness, not crisis management failure.
Why Option D is
Incorrect: This claims the author is critical of the new collaborative approach, but the broader passage actually treats this shift positively as something that helps economics, especially through behavioral economics.
Why Option A is Correct: This captures the sarcastic tone toward how a once insular, imperial discipline is now embracing the very disciplines it had previously shunned.
Key Takeaway: Identify tone by closely reading the specific word choices, like "once almighty," which signal irony about a reversal in attitude or behaviour.
The author critiques Shiller's approach to behavioural economics for:
ignoring the marginal role that media and politics play in influencing people's behaviour.
denigrating the role of institutions while creating a link between behavioural economics and perceptions.
linking emotions and rational behaviour without considering the mediation of social institutions.
relying excessively on storytelling as the main influence on the formation of perceptions.
linking emotions and rational behaviour without considering the mediation of social institutions.
The author critiques Shiller specifically for stripping institutions out of his account, leaving only a bare dynamic of emotions and economics without the mediating role that politics and institutions traditionally played between perception, behaviour and society.
Why Option A is
Incorrect: The passage does not say Shiller ignores a "marginal role" of media and politics, it specifically says institutions have been stripped entirely from his account, a stronger claim than just a marginal role being ignored.
Why Option B is
Incorrect: This is close but reverses the framing slightly, the critique is that Shiller links perceptions to behaviour while removing institutions, not that he denigrates institutions while still creating the link, the issue is the absence of institutional mediation itself.
Why Option D is
Incorrect: The critique is not about excessive reliance on storytelling itself, storytelling is presented as a useful tool, the actual critique is about the missing institutional mediation in the overall framework.
Why Option C is Correct: This precisely matches the passage's critique, that Shiller connects emotions and economic behaviour without the mediating role of political and social institutions that once linked perception, behaviour and society.
Key Takeaway: When a critique involves an omission, focus on exactly what is said to be missing from the model, rather than rephrasing it as a different kind of flaw.
In the first paragraph the author is making the point that economists like Becker:
benefitted from the application of their principles and concepts to non-economic phenomena.
had begun to borrow concepts from other disciplines but were averse to the latter applying economic principles.
used economics to analyse non-market behaviour, without incorporating perspectives from other areas of inquiry.
tended to guard their discipline from poaching by academics from other subject areas.
used economics to analyse non-market behaviour, without incorporating perspectives from other areas of inquiry.
The passage describes how Becker applied economic methods to nonmarket domains like crime and domesticity, projecting economics outward, but did not let other disciplines like anthropology or history inform his own economic thinking, keeping the discipline closed in one direction.
Why Option A is
Incorrect: The passage does not focus on whether Becker personally benefited from this one-directional application, it focuses on the imbalance of borrowing.
Why Option B is
Incorrect: This reverses the passage's claim, Becker did not borrow from other disciplines at all, he only exported economic methods outward without importing ideas back.
Why Option D is
Incorrect: The passage does not describe Becker as guarding against other academics studying economic topics, it describes him as unwilling to incorporate non-economic perspectives into his own analysis, a different point.
Why Option C is Correct: This matches the passage's description of Becker analysing nonmarket behaviour, like crime and marriage, using economic tools, while never importing insights from other disciplines into his economic thinking.
Key Takeaway: Pay attention to the direction of intellectual exchange described in a passage, exporting one's own methods is different from refusing to import others' methods, and a precise answer should reflect exactly which direction is being criticised.
Landing in Australia, the British colonists weren't much impressed with the small-bodied, slender-snooted marsupials called bandicoots. "Their muzzle, which is much too long, gives them an air exceedingly stupid," one naturalist noted in 1805. They nicknamed one type the "zebra rat" because of its black-striped rump. Silly-looking or not, though, the zebra rat—the smallest bandicoot, more commonly known today as the western barred bandicoot—exhibited a genius for survival in the harsh outback, where its ancestors had persisted for some 26 million years. Its births were triggered by rainfall in the bone-dry desert. It carried its breath-mint-size babies in a backward-facing pouch so mothers could forage for food and dig shallow, camouflaged shelters.
Still, these adaptations did not prepare the western barred bandicoot for the colonial-era transformation of its ecosystem, particularly the onslaught of imported British animals, from cattle and rabbits that damaged delicate desert vegetation to ravenous house cats that soon developed a taste for bandicoots. Several of the dozen-odd bandicoot species went extinct, and by the 1940s the western barred bandicoot, whose original range stretched across much of the continent, persisted only on two predator-free islands in Shark Bay, off Australia's western coast.
"Our isolated fauna had simply not been exposed to these predators," says Reece Pedler, an ecologist with the Wild Deserts conservation program.
Now Wild Deserts is using descendants of those few thousand island survivors, called Shark Bay bandicoots, in a new effort to seed a mainland bandicoot revival. They've imported 20 bandicoots to a preserve on the edge of the Strzelecki Desert, in the remote interior of New South Wales. This sanctuary is a challenging place, desolate much of the year, with one of the world's most mercurial rainfall patterns—relentless droughts followed by sudden drenching floods.
The imported bandicoots occupy two fenced "exclosures," cleared of invasive rabbits (courtesy of Pedler's sheepdog) and of feral cats (which slunk off once the rabbits disappeared). A third fenced area contains the program's Wild Training Zone, where two other rare marsupials (bilbies, a larger type of bandicoot, and mulgaras, a somewhat fearsome fuzzball known for sucking the brains out of prey) currently share terrain with controlled numbers of cats, learning to evade them. It's unclear whether the Shark Bay bandicoots, which are perhaps even more predator-naive than their now-extinct mainland bandicoot kin, will be able to make that kind of breakthrough.
For now, though, a recent surge of rainfall has led to a bandicoot joey boom, raising the Wild Deserts population to about 100, with other sanctuaries adding to that number. There are also signs of rebirth in the landscape itself. With their constant digging, the bandicoots trap moisture and allow for seed germination so the cattle-damaged desert can restore itself. They have a new nickname—a flattering one, this time. "We call them ecosystem engineers," Pedler says.
According to the text, the western barred bandicoots now have a flattering name because they have:
aided in altering an arid environment.
led a revival in preserving the species.
grown fivefold in terms of population.
led to a surge and increase of rainfall.
aided in altering an arid environment.
The passage explains that the bandicoots earned their new nickname, "ecosystem engineers," because their constant digging traps moisture and allows for seed germination, helping the cattle-damaged desert restore itself, directly tying their flattering name to their role in altering and improving the arid environment.
Why Option B is
Incorrect: While the bandicoots are part of a conservation revival effort, the flattering nickname specifically refers to their ecological impact through digging, not to the act of being preserved or revived itself.
Why Option C is
Incorrect: The passage mentions a population increase to about 100, which is a result of the rainfall surge and joey boom, not the reason behind their nickname, which is tied to their ecological digging behaviour.
Why Option D is
Incorrect: The bandicoots do not cause rainfall, rainfall surges are described as triggering their population boom, not as a result of their behaviour, this reverses the cause and effect described in the passage.
Why Option A is Correct: This matches the passage's explicit explanation, that their digging traps moisture and enables seed germination, helping restore the cattle-damaged desert, which is why they are now called ecosystem engineers.
Key Takeaway: Trace a nickname or label back to the exact behaviour or impact the passage attributes to it, rather than other facts about the same subject mentioned nearby.
Which one of the following options does NOT represent the characteristics of the western barred bandicoot?
Shallow diggers having an elongated muzzle.
Smallest black striped marsupial that uses camouflage and digs.
Look of a rat but with a baby pouch and a slender snout.
Long thin nose, black striped back, pouch for joeys.
Smallest black striped marsupial that uses camouflage and digs.
The passage describes the western barred bandicoot as having a long muzzle, black-striped rump, a backward-facing pouch, and the ability to dig shallow camouflaged shelters. Option B incorrectly calls it the smallest "black striped marsupial," when the passage specifically calls it the smallest bandicoot, not the smallest marsupial overall, a broader and unsupported claim.
Why Option A is
Incorrect (as a candidate for not representing the bandicoot): This matches the passage's description of shallow digging for shelters and an elongated muzzle.
Why Option C is
Incorrect (as a candidate for not representing the bandicoot): This matches the rat-like appearance, backward-facing pouch and slender snout described in the passage.
Why Option D is
Incorrect (as a candidate for not representing the bandicoot): This matches the long muzzle, black-striped rump and pouch for carrying joeys described in the passage.
Why Option B is Correct: This incorrectly broadens the description from "smallest bandicoot" to "smallest black striped marsupial," a claim about being the smallest among all marsupials that the passage does not support.
Key Takeaway: Watch for subtly broadened claims, like extending "smallest of its specific type" to "smallest among a broader category," which the passage doesn't actually support.
The text uses the word 'exclosures' because Wild Deserts has adopted a measure of:
restoring cattle damaged deserts to green landscapes.
ridding the main desert of feral cats and large bilbies.
excluding animals to make the islands predator-free.
barring the entry of invasive species.
barring the entry of invasive species.
The passage describes the exclosures as fenced areas cleared of invasive rabbits and feral cats, designed to keep these harmful, non-native predator species out so that the imported bandicoots could thrive without predation. This matches the general measure of barring entry of invasive species.
Why Option A is
Incorrect: Restoring cattle-damaged deserts to green landscapes is a separate, later effect of the bandicoots' digging behaviour, not the specific purpose of the exclosures themselves.
Why Option B is
Incorrect: The exclosures are not described as ridding the main desert of large bilbies, bilbies are mentioned separately as another rare marsupial sharing a different fenced training zone with cats, not removed by the exclosures.
Why Option C is
Incorrect: The islands in Shark Bay, not the exclosures on the mainland sanctuary, are the predator-free locations historically, the exclosures are a separate, newer mainland conservation measure.
Why Option D is Correct: This matches the passage's description of exclosures as fenced areas specifically cleared of invasive rabbits and feral cats, directly reflecting the measure of barring invasive species from entering.
Key Takeaway: Match a described measure to the precise location and purpose given in the passage, rather than to a similar but distinct conservation detail mentioned elsewhere.
Which one of the following statements provides a gist of this passage?
The onslaught of animals, such as cattle, rabbits and housecats, brought in by the British led to the extinction of the western barred bandicoot.
The negligent attitude of the British colonists towards these bandicoots evidenced by the names given to them led to their annihilation.
Marsupials are going extinct due to the colonial era transformation of the ecosystem which also destroyed natural vegetation.
A type of bandicoots was nearly wiped out by invasive species but rescuers now pin hopes on a remnant island population.
A type of bandicoots was nearly wiped out by invasive species but rescuers now pin hopes on a remnant island population.
The passage traces the western barred bandicoot's decline due to invasive species brought by colonists, its survival only on isolated islands, and the current conservation effort using descendants of those island survivors to attempt a mainland revival, which is the overall arc the passage builds toward.
Why Option A is
Incorrect: This captures only the cause of decline, the invasive species, but omits the passage's larger arc about the current conservation revival effort based on island survivors.
Why Option B is
Incorrect: This focuses on the colonists' naming attitude as the cause of near extinction, but the passage attributes the actual decline to invasive predator species, not to the naming itself, which is a minor narrative detail.
Why Option C is
Incorrect: This generalises to "marsupials" broadly and to ecosystem transformation, but the passage's specific focus is the western barred bandicoot's near extinction and the targeted conservation effort, not marsupials in general.
Why Option D is Correct: This captures the passage's full arc, the near extinction caused by invasive species, and the current conservation hope resting on the descendants of the surviving island population.
Key Takeaway: A gist should capture both the problem and the passage's central resolution or current effort, not just one half of the narrative.
In the summer of 2022, subscribers to the US streaming service HBO MAX were alarmed to discover that dozens of the platform's offerings — from the Covid-themed heist thriller Locked Down to the recent remake of The Witches — had been quietly removed from the service . . . The news seemed like vindication to those who had long warned that streaming was more about controlling access to the cultural commons than expanding it, as did reports (since denied by the show's creators) that Netflix had begun editing old episodes of Stranger Things to retroactively improve their visual effects.
What's less clear is whether the commonly prescribed cure for these cultural ills — a return to the material pleasures of physical media — is the right one. While the makers of Blu-ray discs claim they have a shelf life of 100 years, such statistics remain largely theoretical until they come to pass, and are dependent on storage conditions, not to mention the continued availability of playback equipment. The humble DVD has already proved far less resilient, with many early releases already beginning to deteriorate in quality. Digital movie purchases provide even less security. Any film "bought" on iTunes could disappear if you move to another territory with a different rights agreement and try to redownload it. It's a bold new frontier in the commodification of art: the birth of the product recall. After a man took to Twitter to bemoan losing access to Cars 2 after moving from Canada to Australia, Apple clarified that users who downloaded films to their devices would retain permanent access to those downloads, even if they relocated to a hemisphere where the [content was] subject to a different set of rights agreements. Thanks to the company's ironclad digital rights management technology, however, such files cannot be moved or backed up, locking you into watching with your Apple account.
Anyone who does manage to acquire Digital Rights Management free (DRM-free) copies of their favourite films must nonetheless grapple with ever-changing file format standards, not to mention data decay — the gradual process by which electronic information slowly but surely corrupts. Only the regular migration of files from hard drive to hard drive can delay the inevitable, in a sisyphean battle against the ravages of digital time.
In a sense, none of this is new. Charlie Chaplin burned the negative of his 1926 film A Woman of the Sea as a tax write-off. Many more films have been lost through accident, negligence or plain indifference. During a heatwave in July 1937, a Fox film vault in New Jersey burned down, destroying a majority of the silent films produced by the studio.
Back then, at least, cinema was defined by its ephemerality: the sense that a film was as good as gone once it left your local cinema. Today, with film studios keen to stress the breadth of their back catalogues (or to put in Hollywood terms, the value of their IPs), audiences may start to wonder why those same studios seem happy to set the vault alight themselves if it'll help next quarter's numbers.
Which one of the following statements about art best captures the arguments made in the passage?
In the age of online subscription services, it is time to change our understanding of classic works of art being primarily immutable and easily available to the public.
As art is increasingly created, stored and distributed digitally, access to it is counterintuitively likely to be made more difficult by the rapid churn in technology and the whims of host platforms.
Accepting retroactive changes to works of art is dangerous because it will encourage creators to not put enough effort into the original attempt, given that they can always edit or update their work later.
Works of art belong to the cultural commons and hence must remain available in perpetuity, irrespective of who pays for access to them.
As art is increasingly created, stored and distributed digitally, access to it is counterintuitively likely to be made more difficult by the rapid churn in technology and the whims of host platforms.
The passage describes how streaming services remove content unpredictably, digital purchases can vanish due to shifting rights agreements, and even physical media like DVDs and Blu-rays face long-term durability concerns, all suggesting that despite the digital age's promise of broader access, technology and platform decisions are making access to art more precarious, not more secure.
Why Option A is
Incorrect: The passage does not argue that classic works of art were ever truly "immutable," it shows that ephemerality and loss have always existed, the issue is more about access uncertainty in the digital era specifically.
Why Option C is
Incorrect: The passage does not argue that retroactive changes will discourage creators from putting in effort, this speculation about creator behaviour is not the argument the passage makes.
Why Option D is
Incorrect: The passage doesn't argue art "must" remain available in perpetuity as a moral imperative, it instead describes the current reality of precarious access without making this kind of normative claim.
Why Option B is Correct: This matches the passage's overall argument, that despite digital media's promise of easy access, technological churn and platform decisions are making access to art counterintuitively more difficult and uncertain.
Key Takeaway: Distinguish between a passage's descriptive observations about a trend and a normative claim about what should happen, since incorrect options often slip into prescriptive territory the passage doesn't actually argue for.
Which one of the following statements, if true, would best invalidate the main argument of the passage?
Recent research has irrefutably proven that Blu-Ray discs have a shelf life of at least 100 years.
Studios and streaming services have committed to giving customers perpetual and platform independent access to the original digital content they have paid for.
When moving to a different geographical location, customers can easily use Virtual Private Networks (VPNs) to bypass geo-blocking and regain access to their content on any streaming service.
Improved cloud storage services have made it possible for movie collections to now be preserved in perpetuity, without the need to keep migrating the files.
Studios and streaming services have committed to giving customers perpetual and platform independent access to the original digital content they have paid for.
The passage's main argument is that digital and physical media access is precarious due to platform decisions, shifting rights agreements, and technological decay. If studios and streaming services committed to giving customers perpetual, platform-independent access to content they've paid for, this would directly remove the precariousness the passage centers its argument on, invalidating the main concern.
Why Option A is
Incorrect: Even with a proven 100-year shelf life for Blu-ray discs, this does not address the passage's broader argument about digital purchases, streaming removals, and shifting rights agreements, which remain unresolved.
Why Option C is
Incorrect: VPN workarounds for geo-blocking address only the specific issue of regional restrictions, not the passage's broader concern about content being removed from platforms entirely or facing format and decay issues.
Why Option D is
Incorrect: Improved cloud storage addressing file migration concerns would help with data decay specifically, but it would not resolve the deeper issue of platforms removing content or restricting access based on rights agreements.
Why Option B is Correct: This directly addresses the passage's core argument about precarious and platform-dependent access, by removing the very uncertainty and rights-based restrictions the passage centers its concern around.
Key Takeaway: To invalidate a passage's main argument, find the option that removes the central uncertainty or problem the passage is built around, not one that addresses only a peripheral detail.
Which of the following statements is suggested by the sentence "Back then, at least, cinema was defined by its ephemerality: the sense that a film was as good as gone once it left your local cinema"?
Around a century ago, people were more accepting of not having access to films once they left the local cinema.
Today, films are expected to be available for a long time, since they are no longer tied solely to their stay at the local cinema.
Cinema is now no longer as ephemeral as it used to be earlier, because the technology used for creating and preserving films has improved manifold.
Presently, there is no reason why film studios should remove access to films once they have left the local cinema.
Today, films are expected to be available for a long time, since they are no longer tied solely to their stay at the local cinema.
The phrase suggests that in the past, people accepted that a film, once it left the cinema, was essentially gone, an attitude of impermanence. By contrast, the passage's broader argument shows that today, audiences expect films to remain available long after their cinema run, since they are no longer tied solely to that brief cinema window, given streaming and digital purchases.
Why Option A is
Incorrect: This focuses on past audience acceptance, but the question asks what this specific statement suggests in the context of contrast with today, not just about historical attitudes alone.
Why Option C is
Incorrect: This claims cinema is "no longer as ephemeral" due to improved preservation technology, but the passage's larger argument is actually that despite improved technology, access remains precarious due to platform and rights issues, not that ephemerality has been resolved.
Why Option D is
Incorrect: This claims there is "no reason" for studios to remove access, but the passage shows there are commercial and practical reasons, like quarterly performance pressures, that lead studios to do exactly this.
Why Option B is Correct: This captures the intended contrast, that audiences today expect long-term availability for films, unlike the past acceptance of cinema's inherent impermanence after leaving theaters.
Key Takeaway: When a statement draws a contrast between past and present attitudes, identify what change in expectation the passage is highlighting, rather than focusing only on the historical half of that contrast.
"Netflix had begun editing old episodes of Stranger Things to retroactively improve their visual effects." What is the purpose of this example used in the passage?
To show that streaming services are controlling access to the cultural commons rather than expanding it.
To show how unsubstantiated reports are leading to an increase in the level of distrust towards streaming services.
To show a practice that justifies the fears of people who feel streaming services cannot be trusted to be custodians of cultural artefacts like film.
To show that art in the digital age, specifically film, is no longer sacrosanct, and may be changed to suit changing tastes or technology.
To show a practice that justifies the fears of people who feel streaming services cannot be trusted to be custodians of cultural artefacts like film.
The passage mentions this example, alongside the HBO Max removals, as evidence that supports the fears of people who have long warned that streaming companies cannot be trusted to faithfully preserve cultural works, since they are willing to alter content retroactively to suit their own purposes.
Why Option A is
Incorrect: This example specifically illustrates retroactive editing of existing content, a different concern from controlling access to the cultural commons, which is more directly illustrated by the HBO Max content removals mentioned earlier.
Why Option B is
Incorrect: The passage explicitly notes that the report was "since denied by the show's creators," but it still uses the example to illustrate the broader pattern of distrust, the purpose isn't about highlighting that the report itself is unsubstantiated, but about what it represents to people already suspicious of streaming services.
Why Option D is
Incorrect: This is a closely related but broader claim about art generally no longer being "sacrosanct," when the passage's specific use of this example is to support the fears already raised about streaming services' trustworthiness as custodians, a more specific point than this general claim about art's mutability.
Why Option C is Correct: This precisely matches how the passage frames the example, as something that seemed like vindication to those who had long warned streaming was more about controlling access than expanding it, directly supporting their existing fears about streaming services as untrustworthy custodians.
Key Takeaway: When the passage explicitly frames an example as supporting a previously stated suspicion or fear, identify that exact framing rather than choosing a broader or more generic interpretation of the example's purpose.
The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Scientific research shows that many animals are very intelligent and have sensory and motor abilities that dwarf ours. Dogs are able to detect diseases such as cancer and diabetes and warn humans of impending heart attacks and strokes. Elephants, whales, hippopotamuses, giraffes, and alligators use low-frequency sounds to communicate over long distances, often miles. Many animals also display wide-ranging emotions, including joy, happiness, empathy, compassion, grief, and even resentment and embarrassment. It's not surprising that animals share many emotions with us because we also share brain structures, located in the limbic system, that are the seat of our emotions.
The advanced sensory and motor abilities of animals is the reason why they can display wide-ranging emotions.
The similarity in brain structure explains why animals show emotions typically associated with humans.
Animals can show emotions which are typically associated with humans.
Animals are more intelligent than us in sensing danger and detecting diseases.
Animals can show emotions which are typically associated with humans.
The passage links animals displaying human-like emotions to the fact that humans and animals share brain structures in the limbic system, which is the seat of emotions. This shared brain structure is presented as the explanation for why animals display these emotions.
Why Option A is
Incorrect: This incorrectly attributes animals' emotional display to their sensory and motor abilities, when the passage actually attributes it to shared brain structure.
Why Option C is
Incorrect: This only states the fact that animals show human-like emotions but omits the explanation for why, the shared brain structure, which the passage explicitly provides.
Why Option D is
Incorrect: This focuses only on animals' sensory abilities in disease detection, ignoring the passage's broader point about animals' emotional similarity to humans and its underlying explanation.
Why Option B is Correct: This captures both pieces, the fact that animals display human-like emotions and the passage's explicit explanation, the similarity in brain structure.
Key Takeaway: A complete summary should include not just what the passage states but also the explanation it provides for that claim.
There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Comprehending a wide range of emotions, Renaissance music nevertheless portrayed all emotions in a balanced and moderate fashion.
Paragraph: A volume of translated Italian madrigals were published in London during the year of 1588. This sudden public interest facilitated a surge of English Madrigal writing as well as a spurt of other secular music writing and publication. (1). This music boom lasted for thirty years and was as much a golden age of music as British literature was with Shakespeare and Queen Elizabeth I. (2). The rebirth in both literature and music originated in Italy and migrated to England; the English madrigal became more humorous and lighter in England as compared to Italy. Renaissance music was mostly polyphonic in texture. (3). Extreme use of and contrasts in dynamics, rhythm, and tone colour do not occur. (4). The rhythms in Renaissance music tend to have a smooth, soft flow instead of a sharp, well-defined pulse of accents.
Option 1
Option 3
Option 4
Option 2
Option 3
The inserted sentence describes Renaissance music as comprehending a wide range of emotions but portraying them in a balanced and moderate way. This fits right before the explanation of why extreme contrasts in dynamics, rhythm and tone colour do not occur, at Option 3, since the inserted sentence introduces the idea of balance and moderation that the following sentence then elaborates on with specific examples.
Why Option A is
Incorrect: Option 1 comes early, while the passage is still discussing the historical context of madrigal publication and the music boom, before the discussion of Renaissance music's emotional and stylistic qualities even begins.
Why Option C is
Incorrect: Option 4 falls after the explanation of extreme contrasts not occurring, when the passage has moved on to discussing the rhythmic flow of Renaissance music specifically, a more specific point than the general emotional balance the inserted sentence introduces.
Why Option D is
Incorrect: Option 2 comes right after the comparison between English and Italian madrigal styles, before the passage shifts to discussing the polyphonic texture and emotional character of Renaissance music as a whole.
Why Option B is Correct: Option 3 comes right after the mention of polyphonic texture, setting up perfectly for the inserted sentence about emotional balance, which is then immediately supported by the following sentence about the absence of extreme contrasts.
Key Takeaway: Place a general claim, like balance and moderation, right before the specific examples that illustrate it, rather than after them.
There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: Understanding central Asia's role helps developments make more sense not only across Asia but in Europe, the Americas and Africa.
Paragraph: The nations of the Silk Roads are sometimes called 'developing countries', but they are actually some of the world's most highly developed countries, the very crossroads of civilization, in advanced states of disrepair. (1). These countries lie at the centre of global affairs: they have since the beginning of history. Running across the spine of Asia, they form a web of connections fanning out in every direction, routes along which pilgrims and warriors, nomads and merchants have travelled, goods and produce have been bought and sold, and ideas exchanged, adapted and refined. (2). They have carried not only prosperity, but also death and violence, disease and disaster. (3). The Silk Roads are the world's central nervous system, connecting otherwise far-flung peoples and places…. (4). It allows us to see patterns and links, causes and effects that remain invisible if one looks only at Europe, or North America.
Option 3
Option 2
Option 1
Option 4
Option 4
The inserted sentence concludes that understanding central Asia's role helps developments make sense not just across Asia but globally. This fits best at the very end, Option 4, right before the passage's final sentence about seeing patterns invisible if looking only at Europe or North America, since the inserted sentence sets up this concluding point about global interconnectedness.
Why Option A is
Incorrect: Option 3 falls in the middle of describing the Silk Roads as the world's central nervous system, before the passage reaches its broader concluding point about global patterns, making this too early for the concluding statement.
Why Option B is
Incorrect: Option 2 comes after describing the routes carrying prosperity, death, violence and disease, before the metaphor of the central nervous system is introduced, an inappropriate place for the broader concluding statement about global relevance.
Why Option C is
Incorrect: Option 1 comes right after the introduction of these regions as crossroads of civilization, before the passage even describes their web of connections, far too early for a concluding statement about global understanding.
Why Option D is Correct: Option 4 comes right after the central nervous system metaphor and right before the passage's final point about seeing patterns invisible if looking only at the West, making it the natural conclusion connecting the metaphor to the practical insight the passage ends on.
Key Takeaway: A sentence that draws a broader conclusion fits best near the end of a paragraph, right before the passage's own concluding statement, to maintain a smooth logical close.
There is a sentence that is missing in the paragraph below. Look at the paragraph and decide where (option 1, 2, 3, or 4) the following sentence would best fit.
Sentence: The brain isn't organized the way you might set up your home office or bathroom medicine cabinet.
Paragraph: (1). You can't just put things anywhere you want to. The evolved architecture of the brain is haphazard and disjointed, and incorporates multiple systems, each of which has a mind of its own. (2). Evolution doesn't design things and it doesn't build systems—it settles on systems that, historically, conveyed a survival benefit. There is no overarching, grand planner engineering the systems so that they work harmoniously together. (3). The brain is more like a big, old house with piecemeal renovations done on every floor, and less like new construction. (4).
Option 4
Option 1
Option 2
Option 3
Option 1
The inserted sentence states that the brain isn't organized the way you might set up a home office or medicine cabinet, introducing the central metaphor for the disorganised nature of the brain's architecture. This fits best at the very start, Option 1, since the next sentence explicitly follows up with "you can't just put things anywhere you want to," directly continuing this comparison.
Why Option A is
Incorrect: Option 4 is at the very end of the paragraph, after the extended metaphor of the brain as an "old house with piecemeal renovations" has already been introduced, the home office comparison belongs at the start, not after a more developed metaphor has taken over.
Why Option C is
Incorrect: Option 2 comes after the point about evolution not designing things deliberately, a logical continuation that doesn't need the home office comparison inserted before it, the comparison fits better as the paragraph's opening line.
Why Option D is
Incorrect: Option 3 comes right before the "old house" metaphor is introduced, but inserting the home office comparison here would be redundant, since by this point the disorganised nature of the brain has already been thoroughly established without it.
Why Option B is Correct: Option 1 is the very beginning, perfectly suited for introducing the central metaphor that the very next sentence, "you can't just put things anywhere you want to," builds directly upon.
Key Takeaway: When the sentence right after a blank directly continues or builds on the missing sentence's metaphor, that blank is very likely the correct placement.
The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Cartographers design and create maps to communicate information about phenomena located somewhere on our planet. In the past, cartographers did not worry too much about who was going to read their maps. Although some simple "usability" research was done—like comparing whether circle or bar symbols worked best—cartographers knew how to make maps. This has changed now, however, due to all kinds of societal and technological developments. Today, map readers are more demanding—mostly because of the tools they use to read maps. Cartographers, who are also influenced by these trends, are now more interested in seeing if their products are efficient, effective, and appreciated.
Today, cartographers also need to look into the usability of maps because of the new technological developments.
Modern mapmakers evaluate a map's effectiveness, efficiency and satisfaction of the user through a series of experiments.
Maps are being used for a variety of reasons and therefore map readers have become more demanding.
New technological developments have prompted cartographers to experiment with their maps by applying these new innovations.
Today, cartographers also need to look into the usability of maps because of the new technological developments.
The passage describes how cartographers previously didn't worry much about who read their maps, but due to societal and technological developments, they are now more focused on usability, efficiency, effectiveness and user appreciation of their products.
Why Option B is
Incorrect: This claims modern cartographers evaluate maps "through a series of experiments," a specific methodological detail not stated as the defining current practice in the passage, which speaks more generally about increased interest in usability.
Why Option C is
Incorrect: This shifts the cause to "maps being used for a variety of reasons," which is not the stated reason in the passage, the passage attributes the change to societal and technological developments affecting how readers use maps.
Why Option D is
Incorrect: This frames cartographers as experimenting with new innovations themselves, but the passage's focus is on their growing concern for usability and reader experience, not on adopting new mapping technologies themselves.
Why Option A is Correct: This matches the passage's central point, that technological developments have made cartographers more attentive to usability, a shift from their earlier indifference to how maps were read.
Key Takeaway: Choose the summary that reflects the passage's stated cause, here technological developments, rather than an unstated or loosely related cause.
The passage given below is followed by four alternate summaries. Choose the option that best captures the essence of the passage.
Certain codes may, of course, be so widely distributed in a specific language community or culture, and be learned at so early an age, that they appear not to be constructed — the effect of an articulation between sign and referent — but to be 'naturally' given. Simple visual signs appear to have achieved a 'near-universality' in this sense: though evidence remains that even apparently 'natural' visual codes are culture specific. However, this does not mean that no codes have intervened; rather, that the codes have been profoundly naturalized. The operation of naturalized codes reveals not the transparency and 'naturalness' of language but the depth, the habituation and the near-universality of the codes in use. They produce apparently 'natural' recognitions. This has the (ideological) effect of concealing the practices of coding which are present.
Learning linguistic and visual signs at an early age makes all such codes appear natural. This naturalization of codes is the effect of ideology.
Not all codes are natural but certain codes are naturalized and made to appear universal. Ideology aims to hide the mechanism of coding behind signs.
Language and visual signs are codes. However, some of the codes are so widespread that they not only seem naturally given but also hide the mechanism of coding behind the signs.
All codes, linguistic and visual, have a natural origin but some are so widespread that they become universal. This is what hides the mechanism of coding behind signs.
Language and visual signs are codes. However, some of the codes are so widespread that they not only seem naturally given but also hide the mechanism of coding behind the signs.
The passage argues that codes, both linguistic and visual, are not naturally given but are constructed, and that some codes become so widespread and deeply naturalised that they appear natural, which conceals the fact that coding practices are at work behind these supposedly natural signs.
Why Option A is
Incorrect: This claims early learning makes "all such codes" appear natural, which overgeneralises, the passage specifically discusses certain widely distributed codes becoming naturalised, not a blanket claim about all codes through early learning alone.
Why Option B is
Incorrect: This is close but frames the naturalisation as being specifically due to "ideology" aiming to hide coding, when the passage frames the ideological effect as a consequence of naturalisation, not its driving purpose.
Why Option D is
Incorrect: This incorrectly states that all codes have a "natural origin," when the passage's central point is the opposite, that codes are constructed, not naturally given, even when they appear that way due to widespread use.
Why Option C is Correct: This accurately captures the passage's full argument, that codes are constructed, some become so widespread they seem naturally given, and this naturalisation conceals the mechanism of coding behind the signs.
Key Takeaway: Watch for summaries that subtly reverse the passage's claim about origin, mistaking what merely "appears natural" for what the passage says is "naturally given."
Five jumbled up 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 and key in the number of that sentence as your answer.
1. Urbanites also have more and better options for getting around: Uber is ubiquitous; easy-to-rent dockless bicycles are spreading; battery-powered scooters will be next.
2. When more people use buses or trains the service usually improves because public-transport agencies run more buses and trains.
3. Worsening services on public transport, terrorist attacks in some urban metros and a rise in fares have been blamed for this trend.
4. It seems more likely that public transport is being squeezed structurally as people's need to travel is diminishing as a result of smartphones, videoconferencing, online shopping and so on.
5. There has been a puzzling decline in the use of urban public transport in many countries in the west, despite the growth in urban populations and rising employment.
Sentences 5, 3, 4 and 1 form a coherent argument, the puzzling decline in public transport use, possible causes blamed for it, an alternative structural explanation involving smartphones and remote alternatives, and other transportation options that have emerged. Sentence 2, which states that more public transport use generally leads to improved service, introduces a general principle about transit systems that doesn't fit the specific narrative about why public transport usage is declining despite urban growth.
Key Takeaway: Watch for a sentence stating a general principle that, while topically related, does not engage with the specific puzzle or narrative being built by the other sentences.
Five jumbled up 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 and key in the number of that sentence as your answer.
1. Animals have an interest in fulfilling their basic needs, but also in avoiding suffering, and thus we ought to extend moral consideration.
2. Singer viewed himself as a utilitarian, and presents a direct moral theory concerning animal rights, in contrast to indirect positions, such as welfarist views.
3. He argued for extending moral consideration to animals because, similar to humans, animals have certain significant interests.
4. The event that publicly announced animal rights as a legitimate issue within contemporary philosophy was Peter Singer's Animal Liberation text in 1975.
5. As such, we ought to view their interests alongside and equal to human interests, which results in humans having direct moral duties towards animals.
Sentences 4, 2, 3 and 5 build a coherent narrative, Singer's 1975 work establishing animal rights as a philosophical issue, his utilitarian and direct moral approach, his argument for extending moral consideration based on shared significant interests, and the resulting conclusion about equal interest consideration leading to direct moral duties. Sentence 1 makes a similar point about extending moral consideration due to animals' interest in avoiding suffering, but it duplicates the argument made more specifically in sentences 3 and 5, without contributing a distinct, sequential step to the paragraph's logical buildup.
Key Takeaway: When a sentence repeats an idea already covered more specifically by other sentences in the set, it is often the odd one out, even if it is topically consistent with the rest.
The game of QUIET is played between two teams. Six teams, numbered 1, 2, 3, 4, 5, and 6, play in a QUIET tournament. These teams are divided equally into two groups. In the tournament, each team plays every other team in the same group only once, and each team in the other group exactly twice. The tournament has several rounds, each of which consists of a few games. Every team plays exactly one game in each round.
The following additional facts are known about the schedule of games in the tournament.
1. Each team played against a team from the other group in Round 8.
2. In Round 4 and Round 7, the match-ups, that is the pair of teams playing against each other, were identical. In Round 5 and Round 8, the match-ups were identical.
3. Team 4 played Team 6 in both Round 1 and Round 2.
4. Team 1 played Team 5 ONLY once and that was in Round 2.
5. Team 3 played Team 4 in Round 3. Team 1 played Team 6 in Round 6.
6. In Round 8, Team 3 played Team 6, while Team 2 played Team 5.
How many rounds were there in the tournament?
Step 1:
There are two groups, each consisting of three teams.
Within each group, every team plays the other two teams once. In addition, each team plays every team from the other group exactly twice.
Hence, the number of matches played by each team is:
= 2 × 1 + 3 × 2 = 8
Since there are six teams in total, the total number of matches played is:
= (8 × 6)/2 = 24
Step 2:
From condition (3), Teams 4 and 6 belong to different groups.
From condition (4), Teams 1 and 5 are placed in the same group.
Conditions (5) and (6) allow several fixtures to be filled immediately.
Condition (1) states that Team 1 faced Team 4 in Round 8.
Therefore, the groups must be:
- Group 1: Teams (4, 2, 3)
- Group 2: Teams (6, 1, 5)
Using condition (2), Rounds 5 and 8 have identical fixtures.
The schedule at this stage is:
- Round 1: 4 vs 6
- Round 2: 4 vs 6, 1 vs 5
- Round 3: 3 vs 4
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
Step 3:
Applying condition (2) once again, Rounds 4 and 7 are also identical.
The complete schedule is therefore:
- Round 1: 4 vs 6, 1 vs 2, 3 vs 5
- Round 2: 4 vs 6, 1 vs 5, 2 vs 3
- Round 3: 3 vs 4, 1 vs 2, 5 vs 6
- Round 4: 4 vs 5, 2 vs 6, 1 vs 3
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6, 4 vs 2, 3 vs 5
- Round 7: 4 vs 5, 2 vs 6, 1 vs 3
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
What is the number of the team that played Team 1 in Round 5?
Step 1:
There are two groups, each consisting of three teams.
Within each group, every team plays the other two teams once. In addition, each team plays every team from the other group exactly twice.
Hence, the number of matches played by each team is:
= 2 × 1 + 3 × 2 = 8
Since there are six teams in total, the total number of matches played is:
= (8 × 6)/2 = 24
Step 2:
From condition (3), Teams 4 and 6 belong to different groups.
From condition (4), Teams 1 and 5 are placed in the same group.
Conditions (5) and (6) allow several fixtures to be filled immediately.
Condition (1) states that Team 1 faced Team 4 in Round 8.
Therefore, the groups must be:
- Group 1: Teams (4, 2, 3)
- Group 2: Teams (6, 1, 5)
Using condition (2), Rounds 5 and 8 have identical fixtures.
The schedule at this stage is:
- Round 1: 4 vs 6
- Round 2: 4 vs 6, 1 vs 5
- Round 3: 3 vs 4
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
Step 3:
Applying condition (2) once again, Rounds 4 and 7 are also identical.
The complete schedule is therefore:
- Round 1: 4 vs 6, 1 vs 2, 3 vs 5
- Round 2: 4 vs 6, 1 vs 5, 2 vs 3
- Round 3: 3 vs 4, 1 vs 2, 5 vs 6
- Round 4: 4 vs 5, 2 vs 6, 1 vs 3
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6, 4 vs 2, 3 vs 5
- Round 7: 4 vs 5, 2 vs 6, 1 vs 3
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
Which team among the teams numbered 2, 3, 4, and 5 was not part of the same group?
5
3
2
4
5
Step 1:
There are two groups, each consisting of three teams.
Within each group, every team plays the other two teams once. In addition, each team plays every team from the other group exactly twice.
Hence, the number of matches played by each team is:
= 2 × 1 + 3 × 2 = 8
Since there are six teams in total, the total number of matches played is:
= (8 × 6)/2 = 24
Step 2:
From condition (3), Teams 4 and 6 belong to different groups.
From condition (4), Teams 1 and 5 are placed in the same group.
Conditions (5) and (6) allow several fixtures to be filled immediately.
Condition (1) states that Team 1 faced Team 4 in Round 8.
Therefore, the groups must be:
- Group 1: Teams (4, 2, 3)
- Group 2: Teams (6, 1, 5)
Using condition (2), Rounds 5 and 8 have identical fixtures.
The schedule at this stage is:
- Round 1: 4 vs 6
- Round 2: 4 vs 6, 1 vs 5
- Round 3: 3 vs 4
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
Step 3:
Applying condition (2) once again, Rounds 4 and 7 are also identical.
The complete schedule is therefore:
- Round 1: 4 vs 6, 1 vs 2, 3 vs 5
- Round 2: 4 vs 6, 1 vs 5, 2 vs 3
- Round 3: 3 vs 4, 1 vs 2, 5 vs 6
- Round 4: 4 vs 5, 2 vs 6, 1 vs 3
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6, 4 vs 2, 3 vs 5
- Round 7: 4 vs 5, 2 vs 6, 1 vs 3
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
What is the number of the team that played Team 1 in Round 7?
Step 1:
There are two groups, each consisting of three teams.
Within each group, every team plays the other two teams once. In addition, each team plays every team from the other group exactly twice.
Hence, the number of matches played by each team is:
= 2 × 1 + 3 × 2 = 8
Since there are six teams in total, the total number of matches played is:
= (8 × 6)/2 = 24
Step 2:
From condition (3), Teams 4 and 6 belong to different groups.
From condition (4), Teams 1 and 5 are placed in the same group.
Conditions (5) and (6) allow several fixtures to be filled immediately.
Condition (1) states that Team 1 faced Team 4 in Round 8.
Therefore, the groups must be:
- Group 1: Teams (4, 2, 3)
- Group 2: Teams (6, 1, 5)
Using condition (2), Rounds 5 and 8 have identical fixtures.
The schedule at this stage is:
- Round 1: 4 vs 6
- Round 2: 4 vs 6, 1 vs 5
- Round 3: 3 vs 4
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
Step 3:
Applying condition (2) once again, Rounds 4 and 7 are also identical.
The complete schedule is therefore:
- Round 1: 4 vs 6, 1 vs 2, 3 vs 5
- Round 2: 4 vs 6, 1 vs 5, 2 vs 3
- Round 3: 3 vs 4, 1 vs 2, 5 vs 6
- Round 4: 4 vs 5, 2 vs 6, 1 vs 3
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6, 4 vs 2, 3 vs 5
- Round 7: 4 vs 5, 2 vs 6, 1 vs 3
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
What is the number of the team that played Team 6 in Round 3?
Step 1:
There are two groups, each consisting of three teams.
Within each group, every team plays the other two teams once. In addition, each team plays every team from the other group exactly twice.
Hence, the number of matches played by each team is:
= 2 × 1 + 3 × 2 = 8
Since there are six teams in total, the total number of matches played is:
= (8 × 6)/2 = 24
Step 2:
From condition (3), Teams 4 and 6 belong to different groups.
From condition (4), Teams 1 and 5 are placed in the same group.
Conditions (5) and (6) allow several fixtures to be filled immediately.
Condition (1) states that Team 1 faced Team 4 in Round 8.
Therefore, the groups must be:
- Group 1: Teams (4, 2, 3)
- Group 2: Teams (6, 1, 5)
Using condition (2), Rounds 5 and 8 have identical fixtures.
The schedule at this stage is:
- Round 1: 4 vs 6
- Round 2: 4 vs 6, 1 vs 5
- Round 3: 3 vs 4
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
Step 3:
Applying condition (2) once again, Rounds 4 and 7 are also identical.
The complete schedule is therefore:
- Round 1: 4 vs 6, 1 vs 2, 3 vs 5
- Round 2: 4 vs 6, 1 vs 5, 2 vs 3
- Round 3: 3 vs 4, 1 vs 2, 5 vs 6
- Round 4: 4 vs 5, 2 vs 6, 1 vs 3
- Round 5: 3 vs 6, 2 vs 5, 1 vs 4
- Round 6: 1 vs 6, 4 vs 2, 3 vs 5
- Round 7: 4 vs 5, 2 vs 6, 1 vs 3
- Round 8: 3 vs 6, 2 vs 5, 1 vs 4
Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya's and Ramya's campaigns and the type of campaigns they run. Each campaign is said to have a level of 1 if it is a staid campaign and a level of 2 if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate. If Amiya and Ramya both run campaigns focusing on issues, then
• The percentage of students voting in the election will be 20 times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then 20 × (2 + 2)%, that is, 80% of the students will vote in the election.
• Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive 1/3 of the votes cast, and Ramya will receive the other 2/3.
The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent.
• If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then 10% of the students who would have otherwise voted for Amiya will vote for Ramya, and another 10% who would have otherwise voted for Amiya, will not vote at all.
• If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then 20% of the students who would have otherwise voted for Ramya will vote for Amiya, and another 5% who would have otherwise voted for Ramya, will not vote at all.
• If both run campaigns attacking each other, then 10% of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.
If both of them run staid campaigns attacking the other, then what percentage of students will vote in the election?
64%
36%
60%
40%
36%
Step 1:
The voter turnout percentage is calculated as:
Turnout (%) = 20 × (Sum of the campaign intensity levels of the two candidates)
Thus, the turnout for each combination is:
- Amiya (Staid) vs Ramya (Staid): 20 × (1 + 1)% = 40%
- Amiya (Staid) vs Ramya (Vigorous): 20 × (1 + 2)% = 60%
- Amiya (Vigorous) vs Ramya (Staid): 20 × (2 + 1)% = 60%
- Amiya (Vigorous) vs Ramya (Vigorous): 20 × (2 + 2)% = 80%
The corresponding vote distribution is:
- Staid vs Staid: Amiya = 1/2, Ramya = 1/2
- Staid vs Vigorous: Amiya = 1/3, Ramya = 2/3
- Vigorous vs Staid: Amiya = 2/3, Ramya = 1/3
- Vigorous vs Vigorous: Amiya = 1/2, Ramya = 1/2
Step 2:
From the given conditions, the vote transfers are:
- Attack vs Attack: 10% of Amiya's votes shift to No Vote, and 10% of Ramya's votes also shift to No Vote.
- Attack vs Issues: 10% of Amiya's votes are transferred to Ramya.
- Issues vs Attack: 20% of Ramya's votes move to Amiya, while 5% of Ramya's votes shift to No Vote.
- Issues vs Issues: 10% of Amiya's votes move to No Vote.
The campaign intensity of both candidates is 1.
Therefore, the voter turnout is:
20 × (1 + 1)% = 40%
Initially, each candidate receives half of the votes, i.e., 20% each.
Since 10% of each candidate's votes are lost, each finally secures:
20% × 90% = 18%
Hence, the total percentage of students who cast a valid vote in the election is:
18% + 18% = 36%
What is the minimum percentage of students who will vote in the election?
36%
40%
32%
38%
36%
Step 1:
The voter turnout percentage is calculated as:
Turnout (%) = 20 × (Sum of the campaign intensity levels of the two candidates)
Thus, the turnout for each combination is:
- Amiya (Staid) vs Ramya (Staid): 20 × (1 + 1)% = 40%
- Amiya (Staid) vs Ramya (Vigorous): 20 × (1 + 2)% = 60%
- Amiya (Vigorous) vs Ramya (Staid): 20 × (2 + 1)% = 60%
- Amiya (Vigorous) vs Ramya (Vigorous): 20 × (2 + 2)% = 80%
The corresponding vote distribution is:
- Staid vs Staid: Amiya = 1/2, Ramya = 1/2
- Staid vs Vigorous: Amiya = 1/3, Ramya = 2/3
- Vigorous vs Staid: Amiya = 2/3, Ramya = 1/3
- Vigorous vs Vigorous: Amiya = 1/2, Ramya = 1/2
Step 2:
From the given conditions, the vote transfers are:
- Attack vs Attack: 10% of Amiya's votes shift to No Vote, and 10% of Ramya's votes also shift to No Vote.
- Attack vs Issues: 10% of Amiya's votes are transferred to Ramya.
- Issues vs Attack: 20% of Ramya's votes move to Amiya, while 5% of Ramya's votes shift to No Vote.
- Issues vs Issues: 10% of Amiya's votes move to No Vote.
To obtain the minimum voting percentage, both candidates must choose a staid campaign.
In this case, the voter turnout is 40%, with each candidate initially receiving 20% of the votes.
Since both candidates attack each other, 10% of each candidate's votes are lost.
Thus, each candidate finally secures:
20% × 90% = 18%
Hence, the minimum percentage of students who cast a valid vote in the election is:
18% + 18% = 36%
If Amiya runs a campaign focusing on issues, then what is the maximum percentage of votes that she can get?
44%
40%
48%
36%
48%
Step 1:
The voter turnout percentage is calculated as:
Turnout (%) = 20 × (Sum of the campaign intensity levels of the two candidates)
Thus, the turnout for each combination is:
- Amiya (Staid) vs Ramya (Staid): 20 × (1 + 1)% = 40%
- Amiya (Staid) vs Ramya (Vigorous): 20 × (1 + 2)% = 60%
- Amiya (Vigorous) vs Ramya (Staid): 20 × (2 + 1)% = 60%
- Amiya (Vigorous) vs Ramya (Vigorous): 20 × (2 + 2)% = 80%
The corresponding vote distribution is:
- Staid vs Staid: Amiya = 1/2, Ramya = 1/2
- Staid vs Vigorous: Amiya = 1/3, Ramya = 2/3
- Vigorous vs Staid: Amiya = 2/3, Ramya = 1/3
- Vigorous vs Vigorous: Amiya = 1/2, Ramya = 1/2
Step 2:
From the given conditions, the vote transfers are:
- Attack vs Attack: 10% of Amiya's votes shift to No Vote, and 10% of Ramya's votes also shift to No Vote.
- Attack vs Issues: 10% of Amiya's votes are transferred to Ramya.
- Issues vs Attack: 20% of Ramya's votes move to Amiya, while 5% of Ramya's votes shift to No Vote.
- Issues vs Issues: 10% of Amiya's votes move to No Vote.
To maximize Amiya's vote share, the voter turnout must be 80%.
Initially, both Amiya and Ramya receive 40% of the votes.
Under the given conditions, 20% of Ramya's votes are transferred to Amiya.
Therefore, Amiya's final vote share is:
= 40% + 20% of 40%
= 40% + 8%
= 48%
Hence, the maximum percentage of votes that Amiya can receive is 48%.
If Ramya runs a campaign attacking Amiya, then what is the minimum percentage of votes that she is guaranteed to get?
12%
18%
15%
30%
15%
Step 1:
The voter turnout percentage is calculated as:
Turnout (%) = 20 × (Sum of the campaign intensity levels of the two candidates)
Thus, the turnout for each combination is:
- Amiya (Staid) vs Ramya (Staid): 20 × (1 + 1)% = 40%
- Amiya (Staid) vs Ramya (Vigorous): 20 × (1 + 2)% = 60%
- Amiya (Vigorous) vs Ramya (Staid): 20 × (2 + 1)% = 60%
- Amiya (Vigorous) vs Ramya (Vigorous): 20 × (2 + 2)% = 80%
The corresponding vote distribution is:
- Staid vs Staid: Amiya = 1/2, Ramya = 1/2
- Staid vs Vigorous: Amiya = 1/3, Ramya = 2/3
- Vigorous vs Staid: Amiya = 2/3, Ramya = 1/3
- Vigorous vs Vigorous: Amiya = 1/2, Ramya = 1/2
Step 2:
From the given conditions, the vote transfers are:
- Attack vs Attack: 10% of Amiya's votes shift to No Vote, and 10% of Ramya's votes also shift to No Vote.
- Attack vs Issues: 10% of Amiya's votes are transferred to Ramya.
- Issues vs Attack: 20% of Ramya's votes move to Amiya, while 5% of Ramya's votes shift to No Vote.
- Issues vs Issues: 10% of Amiya's votes move to No Vote.
To determine the minimum vote share that Ramya is guaranteed to receive, the voter turnout must be 40%.
Initially, both Amiya and Ramya receive 20% of the votes.
Since Ramya adopts a campaign that attacks Amiya, 20% of Ramya's votes are transferred to Amiya, while an additional 5% of her votes are lost.
Therefore, Ramya's final vote share is:
= 20% − 20% of 20% − 5% of 20%
= 20% − 4% − 1%
= 15%
Hence, the minimum percentage of votes that Ramya is guaranteed to receive is 15%.
What is the maximum possible voting margin with which one of the candidates can win?
28%
26%
29%
20%
29%
Step 1:
The voter turnout percentage is calculated as:
Turnout (%) = 20 × (Sum of the campaign intensity levels of the two candidates)
Thus, the turnout for each combination is:
- Amiya (Staid) vs Ramya (Staid): 20 × (1 + 1)% = 40%
- Amiya (Staid) vs Ramya (Vigorous): 20 × (1 + 2)% = 60%
- Amiya (Vigorous) vs Ramya (Staid): 20 × (2 + 1)% = 60%
- Amiya (Vigorous) vs Ramya (Vigorous): 20 × (2 + 2)% = 80%
The corresponding vote distribution is:
- Staid vs Staid: Amiya = 1/2, Ramya = 1/2
- Staid vs Vigorous: Amiya = 1/3, Ramya = 2/3
- Vigorous vs Staid: Amiya = 2/3, Ramya = 1/3
- Vigorous vs Vigorous: Amiya = 1/2, Ramya = 1/2
Step 2:
From the given conditions, the vote transfers are:
- Attack vs Attack: 10% of Amiya's votes shift to No Vote, and 10% of Ramya's votes also shift to No Vote.
- Attack vs Issues: 10% of Amiya's votes are transferred to Ramya.
- Issues vs Attack: 20% of Ramya's votes move to Amiya, while 5% of Ramya's votes shift to No Vote.
- Issues vs Issues: 10% of Amiya's votes move to No Vote.
Here, the voter turnout is 60%.
Case 1: Amiya secures 40% of the votes, while Ramya secures 20%.
Amiya's final vote share:
= 40% + 20% of 20%
= 44%
Ramya's final vote share:
= 20% − 20% of 20% − 5% of 20%
= 20% − 4% − 1%
= 15%
Therefore, the voting margin is:
44% − 15% = 29%
Case 2: Amiya secures 20% of the votes, while Ramya secures 40%.
Amiya's final vote share:
= 20% + 10% of 20% − 10% of 20%
= 16%
Ramya's final vote share:
= 40% + 10% of 20%
= 42%
Therefore, the voting margin is:
42% − 16% = 26%
Hence, the maximum possible voting margin is 29%.
The chart below shows the price data for seven shares -A, B, C, D, E, F, and G as a candlestick plot for a particular day. The vertical axis shows the price of the share in rupees. A share whose closing price (price at the end of the day) is more than its opening price (price at the start of the day) is called a bullish share; otherwise, it is called a bearish share. All bullish and bearish shares are shown in green and red colour respectively.
Daily Share Price Variability (SPV) is defined as (Day's high price - Day's low price)/(Average of the opening and closing prices during the day). Which among the shares A, C, D and F had the highest SPV on that day?
D
F
A
C
D
Daily Share Price Variability (SPV):
For A:
= (2400 − 1200) / [(2200 + 1800)/2]
= 1200 / 2000
= 0.6
For C:
= (1400 − 800) / [(800 + 1200)/2]
= 600 / 1000
= 0.6
For D:
= (1200 − 300) / [(500 + 1000)/2]
= 900 / 750
= 1.2
For F:
= (2000 − 1200) / [(1800 + 1600)/2]
= 800 / 1700
≈ 0.47
Hence, D has the highest SPV value.
Daily Share Price Variability (SPV) is defined as (Day's high price - Day's low price)/(Average of the opening and closing prices during the day). How many shares had an SPV greater than 0.5 on that day?
SPV for A = 0.6
For B:
= (2000 − 1400) / [(2000 + 1700)/2]
= 600 / 1850
≈ 0.32
SPV for C = 0.6
SPV for D = 1.2
For E:
= (1400 − 1100) / [(1300 + 1100)/2]
= 300 / 1200
= 0.25
SPV for F = 0.47
For G:
= (1900 − 1000) / [(1200 + 1700)/2]
= 900 / 1450
≈ 0.62
Hence, 4 companies have an SPV value greater than 0.5.
Daily loss for a share is defined as (Opening price - Closing price)/ (Opening price). Which among the shares A, B, F and G had the highest daily loss on that day?
A
B
F
G
A
Daily loss for A:
= (2200 − 1800) / 2200
= 400 / 2200
≈ 0.18
Daily loss for B:
= (2000 − 1700) / 2000
= 300 / 2000
= 0.15
Daily loss for F:
= (1800 − 1600) / 1800
= 200 / 1800
≈ 0.11
Daily loss for G:
= (1200 − 1700) / 1200
= −500 / 1200
≈ −0.42
Hence, Share A recorded the highest daily loss.
What would have been the percentage wealth gain for a trader, who bought equal numbers of all bullish shares at opening price and sold them at their day's high?
100%
80%
50%
72%
80%
The bullish shares are C, D, and G.
The combined opening price of these three shares is:
= 800 + 500 + 1200
= Rs. 2,500
The combined highest price reached during the day is:
= 1400 + 1200 + 1900
= Rs. 4,500
Therefore, the required percentage increase is:
= ((4500 − 2500) / 2500) × 100
= 80%
The chart below provides complete information about the number of countries visited by Dheeraj, Samantha and Nitesh, in Asia, Europe and the rest of the world (ROW).
The following additional facts are known about the countries visited by them.
1. 32 countries were visited by at least one of them.
2. USA (in ROW) is the only country that was visited by all three of them.
3. China (in Asia) is the only country that was visited by both Dheeraj and Nitesh, but not by Samantha.
4. France (in Europe) is the only country outside Asia, which was visited by both Dheeraj and Samantha, but not by Nitesh.
5. Half of the countries visited by both Samantha and Nitesh are in Europe.
How many countries in Asia were visited by at least one of Dheeraj, Samantha and Nitesh?
How many countries in Europe were visited only by Nitesh?
How many countries in the ROW were visited by both Nitesh and Samantha?
How many countries in Europe were visited by exactly one of Dheeraj, Samantha and Nitesh?
14
12
5
10
12
The number of countries in Europe that were visited by exactly one of Dheeraj, Samantha, and Nitesh = 6 + 2 + 4 = 12.
Six web surfers M, N, O, P, X, and Y each had 30 stars which they distributed among four bloggers A, B, C, and D. The number of stars received by A and B from the six web surfers is shown in the figure below.
The following additional facts are known regarding the number of stars received by the bloggers from the surfers.
1. The numbers of stars received by the bloggers from the surfers were all multiples of 5 (including 0).
2. The total numbers of stars received by the bloggers were the same.
3. Each blogger received a different number of stars from M.
4. Two surfers gave all their stars to a single blogger.
5. D received more stars than C from Y.
What was the total number of stars received by D?
Common Solution:
The available information can initially be represented as follows:
- A receives: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B receives: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C receives: P = 0 (Total = 45)
- D receives: P = 0 (Total = 45)
Since M distributed a distinct number of stars to each blogger, C and D must have received 5 and 15 stars from M, in some order.
Also, O and X are the only web surfers who assigned all their stars to a single blogger.
Since D received more stars than C from Y, D must have received 5 stars from Y, while C received 0 stars from Y.
Thus, the remaining allocations are:
- C: M = 5/15, N = 0/5, O = 0/30, P = 0, X = 30/0, Y = 0
- D: M = 15/5, N = 5/0, O = 30/0, P = 0, X = 0/30, Y = 5
If D were assigned 15 stars from M, D's total would exceed 45.
Therefore, D must receive 5 stars from M, and C must receive 15 stars from M.
The final allocations are:
- A: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C: M = 15, N = 0, O = 0, P = 0, X = 30, Y = 0 (Total = 45)
- D: M = 5, N = 5, O = 30, P = 0, X = 0, Y = 5 (Total = 45)
Each web surfer distributed 30 stars, and every blogger received an equal total of 45 stars.
Hence, the number of stars received by D is:
= (30 × 6) / 4
= 45.
What was the number of stars received by D from Y?
10
5
0
cannot be determined
5
The available information can initially be represented as follows:
- A receives: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B receives: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C receives: P = 0 (Total = 45)
- D receives: P = 0 (Total = 45)
Since M distributed a distinct number of stars to each blogger, C and D must have received 5 and 15 stars from M, in some order.
Also, O and X are the only web surfers who assigned all their stars to a single blogger.
Since D received more stars than C from Y, D must have received 5 stars from Y, while C received 0 stars from Y.
Thus, the remaining allocations are:
- C: M = 5/15, N = 0/5, O = 0/30, P = 0, X = 30/0, Y = 0
- D: M = 15/5, N = 5/0, O = 30/0, P = 0, X = 0/30, Y = 5
If D were assigned 15 stars from M, D's total would exceed 45.
Therefore, D must receive 5 stars from M, and C must receive 15 stars from M.
The final allocations are:
- A: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C: M = 15, N = 0, O = 0, P = 0, X = 30, Y = 0 (Total = 45)
- D: M = 5, N = 5, O = 30, P = 0, X = 0, Y = 5 (Total = 45)
Each web surfer distributed 30 stars, and every blogger received an equal total of 45 stars.
Hence, the number of stars received by D is:
= (30 × 6) / 4
= 45.
How many surfers distributed their stars among exactly 2 bloggers?
The available information can initially be represented as follows:
- A receives: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B receives: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C receives: P = 0 (Total = 45)
- D receives: P = 0 (Total = 45)
Since M distributed a distinct number of stars to each blogger, C and D must have received 5 and 15 stars from M, in some order.
Also, O and X are the only web surfers who assigned all their stars to a single blogger.
Since D received more stars than C from Y, D must have received 5 stars from Y, while C received 0 stars from Y.
Thus, the remaining allocations are:
- C: M = 5/15, N = 0/5, O = 0/30, P = 0, X = 30/0, Y = 0
- D: M = 15/5, N = 5/0, O = 30/0, P = 0, X = 0/30, Y = 5
If D were assigned 15 stars from M, D's total would exceed 45.
Therefore, D must receive 5 stars from M, and C must receive 15 stars from M.
The final allocations are:
- A: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C: M = 15, N = 0, O = 0, P = 0, X = 30, Y = 0 (Total = 45)
- D: M = 5, N = 5, O = 30, P = 0, X = 0, Y = 5 (Total = 45)
Each web surfer distributed 30 stars, and every blogger received an equal total of 45 stars.
Hence, the number of stars received by D is:
= (30 × 6) / 4
= 45.
Which of the following can be determined with certainty?
I. The numbers of stars received by C from M
II. The number of stars received by D from O
Only I
Only II
Both I and II
Neither I nor II
Only I
The available information can initially be represented as follows:
- A receives: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B receives: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C receives: P = 0 (Total = 45)
- D receives: P = 0 (Total = 45)
Since M distributed a distinct number of stars to each blogger, C and D must have received 5 and 15 stars from M, in some order.
Also, O and X are the only web surfers who assigned all their stars to a single blogger.
Since D received more stars than C from Y, D must have received 5 stars from Y, while C received 0 stars from Y.
Thus, the remaining allocations are:
- C: M = 5/15, N = 0/5, O = 0/30, P = 0, X = 30/0, Y = 0
- D: M = 15/5, N = 5/0, O = 30/0, P = 0, X = 0/30, Y = 5
If D were assigned 15 stars from M, D's total would exceed 45.
Therefore, D must receive 5 stars from M, and C must receive 15 stars from M.
The final allocations are:
- A: M = 10, N = 25, O = 0, P = 5, X = 0, Y = 5 (Total = 45)
- B: M = 0, N = 0, O = 0, P = 25, X = 0, Y = 20 (Total = 45)
- C: M = 15, N = 0, O = 0, P = 0, X = 30, Y = 0 (Total = 45)
- D: M = 5, N = 5, O = 30, P = 0, X = 0, Y = 5 (Total = 45)
Each web surfer distributed 30 stars, and every blogger received an equal total of 45 stars.
Hence, the number of stars received by D is:
= (30 × 6) / 4
= 45.
Consider two sets A = {2, 3, 5, 7, 11, 13} and B = {1, 8, 27}. Let f be a function from A to B such that for every element in B, there is at least one element a in A such that f(a) = b. Then, the total number of such functions f is
665
667
537
540
540
Step 1: Total number of functions
Each of the 6 elements of A can be mapped to any of the 3 elements of
B.
Total functions = 3⁶ = 729
Step 2: Subtract functions where one element of B is not used
Choose the missing element of B in 3 ways.
The remaining 2 elements are available for all 6 elements of
A.
Number of such functions = 3 × 2⁶ = 3 × 64 = 192
Remaining functions = 729 − 192 = 537
Step 3: Add back functions where two elements of B are not used
Choose the two missing elements in 3 ways.
In each case, all 6 elements map to the only remaining element.
Number of such functions = 3 × 1 = 3
Hence, required number of onto functions = 537 + 3 = 540
Let x, y, and z be real numbers satisfying
4(x² + y² + z²) = a,
4(x − y − z) = 3 + a
The a equals
3
1⅓
4
1
3
Step 1: Express both equations in simpler form
Let x² + y² + z² = S. Then a = 4S.
Also, x − y − z = (3 + a)/4 = (3 + 4S)/4 = S + 3/4
Step 2: Apply Cauchy–Schwarz Inequality
(x − y − z)² ≤ (1² + (−1)² + (−1)²)(x² + y² + z²)
(x − y − z)² ≤ 3S
Substituting x − y − z = S + 3/4:
(S + 3/4)² ≤ 3S
Step 3: Simplify
S² + (3/2)S + 9/16 ≤ 3S
S² − (3/2)S + 9/16 ≤ 0
16S² − 24S + 9 ≤ 0
(4S − 3)² ≤ 0
Since a square is always non-negative, this is possible only when 4S − 3 = 0 → S = 3/4
Step 4: Find a
a = 4S = 4 × (3/4) = 3
− If the equations x² + mx + 9 = 0, x² + nx + 17 = 0 and x² + (m + n)x + 35 = 0 have a common negative root, then the value of (2m + 3n) is
Step 1: Let the common negative root be r.
r² + mr + 9 = 0
r² + nr + 17 = 0
r² + (m + n)r + 35 = 0
Step 2: Express m and n in terms of r
m = −(r² + 9)/r
n = −(r² + 17)/r
Step 3: Use the third equation
r² + [(−(r² + 9)/r) + (−(r² + 17)/r)]r + 35 = 0
r² − (r² + 9) − (r² + 17) + 35 = 0
9 − r² = 0 → r² = 9
Since the common root is negative, r = −3
Step 4: Find m and n
m = −(9 + 9)/(−3) = 6
n = −(9 + 17)/(−3) = 26/3
Step 5: Compute 2m + 3n
= 2(6) + 3(26/3) = 12 + 26 = 38
Suppose x₁, x₂, x₃, ..., x₁₀₀ are in arithmetic progression such that x₅ = −4 and 2x₆ + 2x₉ = x₁₁ + x₁₃. Then, x₁₀₀ equals
-194
-196
204
206
-194
Step 1: Let the first term be a and common difference be d.
Using x₅ = −4: a + 4d = −4
Step 2: Use the given relation
2(a + 5d) + 2(a + 8d) = (a + 10d) + (a + 12d)
4a + 26d = 2a + 22d
2a + 4d = 0 → a + 2d = 0 → a = −2d
Step 3: Find d
Substitute a = −2d into a + 4d = −4:
−2d + 4d = −4 → 2d = −4 → d = −2
Hence, a = 4
Step 4: Find x₁₀₀
x₁₀₀ = a + 99d = 4 + 99(−2) = 4 − 198 = −194
− Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is
Step 1: Find their hourly efficiencies
Renu takes 15 × 4 = 60 hours to complete the work → efficiency = 1/60 work per hour.
Seema takes 8 × 5 = 40 hours to complete the work → efficiency = 1/40 work per hour.
Step 2: Let Seema work for x days
Then Renu works for 2x days.
Renu works 2 hours/day → Total hours by Renu = 2 × 2x = 4x hours.
Seema works double Renu's hours = 4 hours/day → Total hours by Seema = 4x hours.
Step 3: Form the work equation
Work by Renu = 4x × (1/60) = x/15
Work by Seema = 4x × (1/40) = x/10
x/15 + x/10 = 1 → 2x + 3x = 30 → 5x = 30 → x = 6
When 10¹⁰⁰ is divided by 7, the remainder is
3
4
1
6
4
Step 1: Reduce the base modulo 7
10 ≡ 3 (mod 7) → 10¹⁰⁰ ≡ 3¹⁰⁰ (mod 7)
Step 2: Find the pattern of powers of 3 modulo 7
3¹ ≡ 3, 3² ≡ 2, 3³ ≡ 6, 3⁴ ≡ 4, 3⁵ ≡ 5, 3⁶ ≡ 1 (mod 7)
The remainders repeat every 6 powers.
Step 3: Find the position of 100 in the cycle
100 ÷ 6 leaves remainder 4.
Therefore, 3¹⁰⁰ ≡ 3⁴ ≡ 4 (mod 7)
The sum of all real values of k for which (1/8)^k × (1/32768)^(1/3) = (1/8) × (1/32768)^(1/k), is
2/3
4/3
−2/3
−4/3
−2/3
Step 1: Express all bases as powers of 2
8 = 2³ → 1/8 = 2^(−3)
32768 = 2¹⁵ → 1/32768 = 2^(−15)
Substituting: (2^(−3))^k × (2^(−15))^(1/3) = 2^(−3) × (2^(−15))^(1/k)
Step 2: Simplify the exponents
2^(−3k) × 2^(−5) = 2^(−3) × 2^(−15/k)
2^(−3k − 5) = 2^(−3 − 15/k)
Step 3: Equate the exponents
−3k − 5 = −3 − 15/k
3k + 5 = 3 + 15/k
3k + 2 = 15/k
Step 4: Form and solve the quadratic equation
3k² + 2k = 15 → 3k² + 2k − 15 = 0
Sum of roots = −b/a = −2/3
− For any natural number n let aₙ be the largest integer not exceeding √n. Then the value of a₁ + a₂ + ..... + a₅₀ is
Step 1: Determine the ranges
⌊√n⌋ = 1 for n = 1 to 3 (3 values)
⌊√n⌋ = 2 for n = 4 to 8 (5 values)
⌊√n⌋ = 3 for n = 9 to 15 (7 values)
⌊√n⌋ = 4 for n = 16 to 24 (9 values)
⌊√n⌋ = 5 for n = 25 to 35 (11 values)
⌊√n⌋ = 6 for n = 36 to 48 (13 values)
⌊√n⌋ = 7 for n = 49 to 50 (2 values)
Step 2: Compute the sum
= (1×3) + (2×5) + (3×7) + (4×9) + (5×11) + (6×13) + (7×2)
= 3 + 10 + 21 + 36 + 55 + 78 + 14
= 217
In September, the incomes of Kamal, Amal and Vimal are in the ratio 8 : 6 : 5. They rent a house together, and Kamal pays 15%, Amal pays 12% and Vimal pays 18% of their respective incomes to cover the total house rent in that month. In October, the house rent remains unchanged while their incomes increase by 10%, 12% and 15%, respectively. In October, the percentage of their total income that will be paid as house rent, is nearest to
15.18
13.26
14.84
12.75
13.26
Step 1: Let incomes be 8x, 6x and 5x.
Find the house rent:
Kamal pays 15% of 8x = 1.2x
Amal pays 12% of 6x = 0.72x
Vimal pays 18% of 5x = 0.9x
Total house rent = 1.2x + 0.72x + 0.9x = 2.82x
Step 2: Find the total income in October
Kamal's income = 8x × 1.10 = 8.8x
Amal's income = 6x × 1.12 = 6.72x
Vimal's income = 5x × 1.15 = 5.75x
Total income = 8.8x + 6.72x + 5.75x = 21.27x
Step 3: Find the percentage of income spent on rent
= (2.82x / 21.27x) × 100 = (2.82 / 21.27) × 100 ≈ 13.26%
− The sum of all four-digit numbers that can be formed with the distinct non-zero digits a, b, c, and d, with each digit appearing exactly once in every number, is 153310 + n, where n is a single digit natural number. Then, the value of (a + b + c + d + n) is
Step 1: Find the expression for the total sum
There are 4! = 24 numbers.
Each digit appears 24/4 = 6 times in each place value.
Total sum = 6 × (1000 + 100 + 10 + 1) × (a + b + c + d)
= 6 × 1111 × (a + b + c + d)
= 6666(a + b + c + d)
Step 2: Find n
6666(a + b + c + d) = 153310 + n
6666 × 23 = 153318
153310 + n = 153318 → n = 8
Step 3: Find the sum of the digits
a + b + c + d = 153318 / 6666 = 23
a + b + c + d + n = 23 + 8 = 31
− ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of △ADE is
Step 1: Find the sides of △ADE
E is the midpoint of CD → DE = 56/2 = 28 cm
AD = 45 cm
AE² = AD² + DE² = 45² + 28² = 2025 + 784 = 2809
AE = 53 cm
Sides of △ADE: 28 cm, 45 cm and 53 cm.
Step 2: Find the area of the triangle
Since AD ⊥ DE:
Area = (1/2) × 45 × 28 = 630 cm²
Step 3: Find the semiperimeter
s = (28 + 45 + 53)/2 = 63 cm
Step 4: Find the inradius
Area = r × s → 630 = r × 63 → r = 10 cm
In the XY-plane, the area, in sq. units, of the region defined by the inequalities y ≥ x + 4 and −4 ≤ x² + y² + 4(x − y) ≤ 0 is
2π
4π
π
3π
2π
Step 1: Rewrite the second inequality
Complete the squares:
x² + y² + 4x − 4y = (x+2)² − 4 + (y−2)² − 4 = (x+2)² + (y−2)² − 8
Hence: −4 ≤ (x+2)² + (y−2)² − 8 ≤ 0
Adding 8: 4 ≤ (x+2)² + (y−2)² ≤ 8
This is the annular region between two concentric circles with centre (−2, 2), inner radius 2, outer radius 2√2.
Step 2: Interpret the line
The line y = x + 4. Substituting the centre (−2, 2): 2 = −2 + 4 ✓
The line passes through the centre, dividing the annular region into two equal halves.
The required region satisfies y ≥ x + 4, so it is half the annulus.
Step 3: Find the required area
Area of annulus = π[(2√2)² − 2²] = π(8 − 4) = 4π
Required area = (1/2) × 4π = 2π
− If x is a positive real number such that 4log₁₀x + 4log₁₀₀x + 8log₁₀₀₀x = 13, then the greatest integer not exceeding x, is
Step 1: Convert all logarithms to base 10
log₁₀₀x = log₁₀x / 2
log₁₀₀₀x = log₁₀x / 3
Let log₁₀x = y.
4y + 4(y/2) + 8(y/3) = 13
Step 2: Solve for y
4y + 2y + 8y/3 = 13
Multiply by 3: 12y + 6y + 8y = 39 → 26y = 39 → y = 3/2
Step 3: Find x
x = 10^(3/2) = 10 × √10 ≈ 31.62
Step 4: Find the greatest integer not exceeding x
⌊x⌋ = 31
The selling price of a product is fixed to ensure 40% profit. If the product had cost 40% less and had been sold for 5 rupees less, then the resulting profit would have been 50%. The original selling price, in rupees, of the product is
15
14
10
20
14
Step 1: Let the original cost price be x.
Original selling price = 140% of x = 1.4x
Step 2: Form the second condition
New cost price = 60% of x = 0.6x
New selling price = 1.4x − 5
Since the new profit is 50%:
New selling price = 150% of new cost price = 1.5 × 0.6x = 0.9x
Therefore: 1.4x − 5 = 0.9x
Step 3: Solve for x
0.5x = 5 → x = 10
Step 4: Find the original selling price
Original selling price = 1.4 × 10 = Rs. 14
A glass is filled with milk. Two-thirds of its content is poured out and replaced with water. If this process of pouring out two-thirds the content and replacing with water is repeated three more times, then the final ratio of milk to water in the glass, is
1 : 27
1 : 80
1 : 81
1 : 26
1 : 80
Step 1: Find the fraction of milk left after each operation
Since two-thirds is removed, one-third of the milk remains after each operation.
After 1st operation: Milk = 1/3
After 2nd operation: Milk = (1/3)² = 1/9
After 3rd operation: Milk = (1/3)³ = 1/27
After 4th operation: Milk = (1/3)⁴ = 1/81
Step 2: Find the fraction of water
Water = 1 − 1/81 = 80/81
Step 3: Find the ratio
Milk : Water = (1/81) : (80/81) = 1 : 80
− A fruit seller has a total of 187 fruits consisting of apples, mangoes and oranges. The number of apples and mangoes are in the ratio 5 : 2. After she sells 75 apples, 26 mangoes and half of the oranges, the ratio of number of unsold apples to number of unsold oranges becomes 3 : 2. The total number of unsold fruits is
Step 1: Let initial numbers be
Apples = 5x, Mangoes = 2x, Oranges = 187 − 7x
Step 2: Use the given ratio after selling
Unsold apples = 5x − 75
Unsold oranges = (187 − 7x)/2
(5x − 75) / [(187 − 7x)/2] = 3/2
Cross-multiplying: 2(5x − 75) = 3(187 − 7x)/2
20x − 300 = 561 − 21x → 41x = 861 → x = 21
Step 3: Find the initial number of each fruit
Apples = 105, Mangoes = 42, Oranges = 40
Step 4: Find the unsold fruits
Unsold apples = 105 − 75 = 30
Unsold mangoes = 42 − 26 = 16
Unsold oranges = 40/2 = 20
Total unsold = 30 + 16 + 20 = 66
Two places A and B are 45 kms apart and connected by a straight road. Anil goes from A to B while Sunil goes from B to A. Starting at the same time, they cross each other in exactly 1 hour 30 minutes. If Anil reaches B exactly 1 hour 15 minutes after Sunil reaches A, the speed of Anil, in km per hour, is
18
16
14
12
12
Step 1: Let Anil's speed = x km/h and Sunil's speed = y km/h.
They meet in 1.5 hours: (x + y) × 1.5 = 45 → x + y = 30
Step 2: Express the total travel times
Anil's total time = 45/x
Sunil's total time = 45/y
Given: 45/x = 45/y + 1.25
Step 3: Substitute y = 30 − x
45/x = 45/(30 − x) + 1.25
Multiply by 4: 180/x = 180/(30 − x) + 5
Multiply by x(30 − x):
180(30 − x) = 180x + 5x(30 − x)
5400 − 180x = 180x + 150x − 5x²
5400 = 510x − 5x²
5x² − 510x + 5400 = 0
x² − 102x + 1080 = 0
(x − 12)(x − 90) = 0
Since x + y = 30, x = 90 is not possible. Therefore x = 12 km/h
− There are four numbers such that average of first two numbers is 1 more than the first number, average of first three numbers is 2 more than average of first two numbers, and average of first four numbers is 3 more than average of first three numbers. Then, the difference between the largest and the smallest numbers, is
Step 1: Let the four numbers be a, b, c and d.
First condition: (a + b)/2 = a + 1 → b = a + 2
Step 2: Second condition
(a + b + c)/3 = (a + b)/2 + 2 = a + 3
(2a + 2 + c)/3 = a + 3 → c = a + 7
Step 3: Third condition
(a + b + c + d)/4 = (a + b + c)/3 + 3 = a + 6
(3a + 9 + d)/4 = a + 6 → d = a + 15
Step 4: Find the required difference
The four numbers are a, a+2, a+7, a+15
Difference = (a + 15) − a = 15
An amount of Rs 10000 is deposited in bank A for a certain number of years at a simple interest of 5% per annum. On maturity, the total amount received is deposited in bank B for another 5 years at a simple interest of 6% per annum. If the interests received from bank A and bank B are in the ratio 10 : 13, then the investment period, in years, in bank A is
4
5
3
6
6
Step 1: Find the interest from Bank A
Interest from Bank A = (10000 × 5 × x)/100 = 500x
Maturity amount = 10000 + 500x
Step 2: Find the interest from Bank B
Interest from Bank B = [(10000 + 500x) × 6 × 5]/100 = 3000 + 150x
Step 3: Use the given ratio
500x : (3000 + 150x) = 10 : 13
13 × 500x = 10(3000 + 150x)
6500x = 30000 + 1500x
5000x = 30000 → x = 6
A shop wants to sell a certain quantity (in kg) of grains. It sells half the quantity and an additional 3 kg of these grains to the first customer. Then, it sells half of the remaining quantity and an additional 3 kg of these grains to the second customer. Finally, when the shop sells half of the remaining quantity and an additional 3 kg of these grains to the third customer, there are no grains left. The initial quantity, in kg, of grains is
50
36
42
18
42
Step 1: Work backwards
After the third sale, grains left = 0.
Just before the third sale, let quantity = x.
x/2 − 3 = 0 → x = 6 kg
Step 2: Find the quantity before the second sale
Let quantity before second sale = y.
y/2 − 3 = 6 → y/2 = 9 → y = 18 kg
Step 3: Find the initial quantity
Let initial quantity = z.
z/2 − 3 = 18 → z/2 = 21 → z = 42 kg
If (a + b√n) is the positive square root of (29 − 12√5), where a and b are integers, and n is a natural number, then the maximum possible value of (a + b + n) is
18
22
4
6
18
Step 1: Square both sides
(a + b√n)² = 29 − 12√5
a² + b²n + 2ab√n = 29 − 12√5
Step 2: Compare rational and irrational parts
a² + b²n = 29
ab√n = −6√5
Step 3: Eliminate √n
Squaring: a²b²n = 180
Using b²n = 29 − a²:
a²(29 − a²) = 180 → a⁴ − 29a² + 180 = 0
(a² − 20)(a² − 9) = 0
Since a is an integer: a² = 9 → a = ±3
Step 4: Find b²n
b²n = 29 − 9 = 20
Possible values: b² = 1, n = 20 or b² = 4, n = 5
Step 5: Check each case
Case 1: b² = 1, n = 20 → ab = −3
a = −3, b = 1: −3 + √20 > 0 ✓ → a + b + n = −3 + 1 + 20 = 18
Case 2: b² = 4, n = 5 → ab = −6
a = −3, b = 2: −3 + 2√5 > 0 ✓ → a + b + n = −3 + 2 + 5 = 4
Step 6: Maximum value = 18
The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is
1125π
750π
1125π√2
750π√2
1125π√2
Step 1: Let dimensions be l, b and h.
Sum of all 12 edges: 4(l + b + h) = 144 → l + b + h = 36
Surface area: 2(lb + bh + hl) = 846 → lb + bh + hl = 423
Step 2: Find the sum of squares of the dimensions
(l + b + h)² = l² + b² + h² + 2(lb + bh + hl)
36² = l² + b² + h² + 2 × 423
1296 = l² + b² + h² + 846
l² + b² + h² = 450
Step 3: Find the radius of the sphere
Diagonal² = l² + b² + h² = 450
Diagonal = √450 = 15√2
Radius = (15√2)/2
Step 4: Find the volume of the sphere
Volume = (4/3)πr³ = (4/3)π × ((15√2)/2)³
= (4/3)π × (3375 × 2√2)/8
= (4/3)π × (3375√2)/4
= 1125π√2
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