An example of a scientist who could measure without instruments is Enrico Fermi (1901-1954), a physicist who won the Nobel Prize in Physics in 1938. He had a well-developed knack for intuitive, even casual-sounding measurements. One renowned example of his measurement skills was demonstrated at the first detonation of the atom bomb, the Trinity Test site, on July 16, 1945, where he was one of the atomic scientists observing the blast from base camp. While final adjustments were being made to instruments used to measure the yield of the blast, Fermi was making confetti out of a page of notebook paper. As the wind from the initial blast wave began to blow through the camp, he slowly dribbled the confetti into the air, observing how far back it was scattered by the blast (taking the farthest scattered pieces as being the peak of the pressure wave). Fermi concluded that the yield must be greater than 10 kilotons. This would have been news since other initial observers of the blast did not know that lower limit. After much analysis of the instrument readings, the final yield estimate was determined to be 18.6 kilotons. Like Eratosthenes, Fermi was aware of a rule relating one simple observation — the scattering of confetti in the wind — to a quantity he wanted to measure.
The value of quick estimates was something Fermi was familiar with throughout his career. He was famous for teaching his students skills at approximation of fanciful-sounding quantities that, at first glance, they might presume they knew nothing about. The best-known example of such a "Fermi question" was Fermi asking his students to estimate the number of piano tuners in Chicago, when no one knows the answer. His students — science and engineering majors — would begin by saying that they could not possibly know anything about such a quantity. Of course, some solutions would be to simply do a count of every piano tuner perhaps by looking up advertisements, checking with a licensing agency of some sort, and so on. But Fermi was trying to teach his students how to solve problems where the ability to confirm the results would not be so easy. He wanted them to figure out that they knew something about the quantity in question.
Suppose you apply the same logic as Fermi applied to confetti, which of the following statements would be the most appropriate?
Show Hint
- You can calculate the minimum pressure inside the cooker by calculating the maximum distance travelled by any of its parts after it explodes.
- You can calculate the average potency of a firecracker by calculating the distance covered by one of its bigger fragments.
- You can easily find out the average potency of an earthquake by measuring the length of a crack it makes on the surface of the earth.
- You can calculate the exact volume of water stored in a tank by measuring the distance covered by the stream of water coming out of the tap fixed on the lower corner of the tank.
- All of the above conclusions can be drawn.
The Correct Option is A
Solution and Explanation
- Fermi applied simple observations, like the scattering of confetti, to estimate complex quantities. The key is finding a way to link a measurable quantity (distance, in the case of confetti) to the target quantity (blast pressure or yield).
Step 2: Relate the options to Fermi’s logic.
- Option (A) follows a similar pattern: By observing the distance the parts of the cooker travel after an explosion, you can estimate the pressure. This is a simple, intuitive approximation method based on observable outcomes.
Step 3: Eliminate the other options.
- Option (B) and (C) do not seem to connect simple observations with complex quantities in the same way.
- Option (D) involves a more direct measurement, making it unlike the intuitive estimation Fermi used.
Therefore: The correct answer is \boxed{(A)}.
Quick estimate, as per Fermi, is most useful in:
Show Hint
- In finding an approximate that is more useful than existing values.
- In finding out the exact minimum value of an estimate
- In finding out the exact maximum value of an estimate
- In finding out the range of values of an estimate
- In finding out the average value of an estimate
The Correct Option is D
Solution and Explanation
- Fermi’s quick estimation method is useful for approximating quantities when direct measurement is difficult. The goal is not to find the exact value but to estimate the range of possible values. This method gives a rough idea of the lower and upper bounds of the quantity.
Step 2: Eliminate the incorrect options.
- (A) is too vague since Fermi’s method is about approximation, not necessarily improving upon existing values.
- (B) and (C) focus on exact values, which Fermi's method doesn't aim for.
- (E) focuses on averages, which doesn’t align with Fermi's purpose of finding ranges.
Therefore: The correct answer is \boxed{(D)}.
Given below are some statements that attempt to capture the central idea of the passage:
1. It is useful to estimate; even when the exact answer is known.
2. It is possible to estimate any physical quantity.
3. It is possible to estimate the number of units of a newly launched car that can be sold in a city.
4. Fermi was a genius.
Which of the following statements best captures the central idea?
1. It is useful to estimate; even when the exact answer is known.
2. It is possible to estimate any physical quantity.
3. It is possible to estimate the number of units of a newly launched car that can be sold in a city.
4. Fermi was a genius.
Which of the following statements best captures the central idea?
Show Hint
- 1, 2 and 4
- 2, 3 and 4
- 2 and 3
- 2 only
- 1, 2 and 3
The Correct Option is D
Solution and Explanation
- The passage highlights the concept of estimation, particularly in Fermi’s approach to using intuitive approximations.
- Statement 2 captures this idea directly, emphasizing the ability to estimate any physical quantity, which aligns with Fermi’s method.
Step 2: Evaluate the other options.
- Statement 1 is useful but not central to the main idea of estimation in the context of Fermi’s method.
- Statement 3 is too specific and doesn’t capture the broader point of estimation.
- Statement 4, while complimentary, doesn’t contribute to the central idea of estimation.
Therefore: The correct answer is \boxed{(D)}.
Read the statements given below:
1. Atomic bomb detonation was a result of Fermi's Nobel Prize contribution.
2. Fermi's students respected him as a scientist.
3. Yield of atomic bomb can only be measured in Kilotons.
Which of the following statement(s) can be inferred from the passage?
1. Atomic bomb detonation was a result of Fermi's Nobel Prize contribution.
2. Fermi's students respected him as a scientist.
3. Yield of atomic bomb can only be measured in Kilotons.
Which of the following statement(s) can be inferred from the passage?
Show Hint
- 1, 2
- 2, 3
- 1, 3
- 2 only
- None of the three statements is correct, hence cannot be inferred from the passage.
The Correct Option is
Solution and Explanation
- The passage does not directly attribute the detonation of the atomic bomb to Fermi's Nobel Prize contribution. It mentions that Fermi was observing the blast, but no direct link to his Nobel Prize is made.
Step 2: Analyze statement 2.
- The passage states Fermi's respect from his students for his estimation skills, but it does not specifically mention whether they respected him as a scientist.
Step 3: Analyze statement 3.
- The passage discusses Fermi’s estimation using the confetti method for approximating the atomic bomb’s yield, but it does not state that the yield can only be measured in kilotons.
Therefore: The correct answer is \boxed{(E)}.
Top Questions on Reading Comprehension
No one argues that the rich should be rich because they were born to wealthy parents. Critics of inequality may complain that those who would abolish inheritance taxes, say, are implicitly endorsing hereditary privilege. But no one defends hereditary privilege outright or disputes the principle that careers should be open to talents.
Most of our debates about access to jobs, education, and public o ce proceed from the premise of equal opportunity. Our disagreements are less about the principle itself than about what it requires. For example, critics of a rmative action in hiring and college admissions argue that such policies are inconsistent with equality of opportunity, because they judge applicants on factors other than merit. Defenders of a rmative action reply that such policies are necessary to make equality of opportunity a reality for members of groups that have suffered discrimination or disadvantage.
At the level of principle at least, and political rhetoric, meritocracy has won the day. In democracies throughout the world, politicians of the center-left and center-right claim that their policies are the ones that will enable all citizens, whatever their race or ethnicity, gender or class, to compete on equal terms and to rise as far as their efforts and talents will take them. When people complain about meritocracy, the complaint is usually not about the ideal but about our failure to live up to it: The wealthy and powerful have rigged the system to perpetuate their privilege; the professional classes have gured out how to pass their advantages on to their children, converting the meritocracy into a hereditary aristocracy; colleges that claim to select students on merit give an edge to the sons and daughters of the wealthy and the well-connected. According to this complaint, meritocracy is a myth, a distant promise yet to be redeemed.- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
Look how you turned on
the ceiling fan—it’s too high,
see how it shakes and trembles.
You walk into this room
with your hot ideas
and the ceiling fan has to work harder
to cool down the room
for us. You walk into this room
with your crazy eyes
and the ceiling fan
wants to y loose. It dreams
of becoming a spider lily.- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
Recently, a team of social scientists launched an experiment to test that hypothesis. They recruited 1,500 entrepreneurs in West Africa—a mix of women and men in their 30s, 40s, and 50s—who were running small startups in manufacturing, service, and commerce. They randomly assigned the founders to one of three groups. One was a control group: they went about their business as usual. The other two were training groups: they spent a week learning new concepts, analyzing them in case studies of other entrepreneurs, and applying them to their own startups through role-play and re section exercises. What differed was whether the training focused on cognitive skills or character skills. In cognitive skills training, the founders took an accredited business course created by the International Finance Corporation. They studied nance, accounting, HR, marketing, and pricing, and practiced using what they learned to solve challenges and seize opportunities. In character skills training, the founders attended a class designed by psychologists to teach personal initiative. They studied proactivity, discipline, and determination, and practiced putting those qualities into action. Character skills training had a dramatic impact. After founders had spent merely ve days working on these skills, their rms’ pro ts grew by an average of 30 percent over the next two years. That was nearly triple the bene t of training in cognitive skills. Finance and marketing knowledge might have equipped founders to capitalize on opportunities, but studying proactivity and discipline enabled them to generate opportunities. They learned to anticipate market changes rather than react to them. They developed more creative ideas and introduced more new products. When they encountered nancial obstacles, instead of giving up, they were more resilient and resourceful in seeking loans. Along with demonstrating that character skills can propel us to achieve greater things, this evidence reveals that it’s never too late to build them … Character doesn’t set like plaster—it retains its plasticity. Character is often confused with personality, but they’re not the same. Personality is your predisposition—your basic instincts for how to think, feel, and act. Character is your capacity to prioritize your values over your instincts. Knowing your principles doesn’t necessarily mean you know how to practice them, particularly under stress or pressure. It’s easy to be proactive and determined when things are going well. The true test of character is whether you manage to stand by those values when the deck is stacked against you. If personality is how you respond on a typical day, character is how you show up on a hard day. Personality is not your destiny—it’s your tendency. Character skills enable you to transcend that tendency to be true to your principles. It’s not about the traits you have—it’s what you decide to do with them. Wherever you are today, there’s no reason why you can’t grow your character skills starting now.
- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
This uidity and situational dependence is uniquely human. In other species, in-group/outgroup distinctions re ect degrees of biological relatedness, or what evolutionary biologists call “kin selection.” Rodents distinguish between a sibling, a cousin, and a stranger by smell—xed, genetically determined pheromonal signatures—and adapt their cooperation accordingly. Those murderous groups of chimps are largely made up of brothers or cousins who grew up together and predominantly harm outsiders. Humans are plenty capable of kin-selective violence themselves, yet human group mentality is often utterly independent of such instinctual familial bonds. Most modern human societies rely instead on cultural kin selection, a process allowing people to feel closely related to what are, in a biological sense, total strangers. Often, this requires a highly active process of inculcation, with its attendant rituals and vocabularies. Consider military drills producing “bands of brothers,” unrelated college freshmen becoming sorority “sisters,” or the bygone value of welcoming immigrants into “the American family.” This malleable, rather than genetically xed, path of identity formation also drives people to adopt arbitrary markers that enable them to spot their cultural kin in an ocean of strangers—hence the importance various communities attach to ags, dress, or facial hair. The hipster beard, the turban, and the “Make America Great Again” hat all fulfill this role by sending strong signals of tribal belonging. Moreover, these cultural communities are arbitrary when compared to the relatively axed logic of biological kin selection. Few things show this arbitrariness better than the experience of immigrant families, where the randomness of a visa lottery can radically reshu e a child’s education, career opportunities, and cultural predilections. Had my grandparents and father missed the train out of Moscow that they instead barely made, maybe I’d be a chain smoking Russian academic rather than a Birkenstock-wearing American one, moved to tears by the heroism during the Battle of Stalingrad rather than that at Pearl Harbor. Scaled up from the level of individual family histories, our big-picture group identities—the national identities and cultural principles that structure our lives— are just as arbitrary and subject to the vagaries of history.
- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
- Work, for many on the career track, is greedy. The individual who puts in overtime, weekend time, or evening time will earn a lot more—so much more that, even on an hourly basis, the person is earning more.…The greediness of work means that couples with children or other care responsibilities would gain by doing a bit of specialization. This specialization doesn’t mean catapulting back to the world of Leave It to Beaver. Women will still pursue demanding careers. But one member of the couple will be on call at home, ready to leave the o ce or workplace at a moment’s notice. That person will have a position with considerable exibility and will ordinarily not be expected to answer an e-mail or a call at ten p.m. That parent will not have to cancel an appearance at soccer practice for an M \& A. The other parent, however, will be on call at work and do just the opposite. The potential impact on promotion, advancement, and earnings is obvious. The work of professionals and managers has always been greedy. Lawyers have always burned the midnight oil. Academics have always been judged for their cerebral output and are expected not to turn their brains off in the evenings. Most doctors and veterinarians were once on call 24/7. The value of greedy jobs has greatly increased with rising income inequality, which has soared since the early 1980s. Earnings at the very upper end of the income distribution have ballooned. The worker who jumps the highest gets an ever-bigger reward. The jobs with the greatest demands for long hours and the least exibility have paid disproportionately more, while earnings in other employments have stagnated. Thus, positions that have been more di cult for women to enter in the rst place, such as those in nance, are precisely the ones that have seen the greatest increases in income in the last several decades. The private equity associate who sees the deal through from beginning to end, who did the di cult modeling, and who went to every meeting and late-night dinner, will have maximum chance for a big bonus and the sought-after promotion. Rising inequality in earnings may be one important reason why the gender pay gap among college graduates has remained at in the last several decades, despite improvements in women’s credentials and positions. It may be the reason why the gender earnings gap for college graduates became larger than that between men and women in the entire population in the late 1980s and early 1990s. Women have been swimming upstream, holding their own but going against a strong current of endemic income inequality. Greedy work also means that couple equity has been, and will continue to be, jettisoned for increased family income. And when couple equity is thrown out the window, gender equality generally goes with it, except among same-sex unions. Gender norms that we have inherited get reinforced in a host of ways to allot more of the childcare responsibility to mothers, and more of the family care to grown daughters. 68. Which of the following statements CANNOT be inferred from the passage?
- XAT - 2025
- Verbal and Logical Ability
- Reading Comprehension
Questions Asked in XAT exam
Match the following renowned Indian personalities with their respective awards.
Names Award 1. Shri Ratan Naval Tata A. Dadasaheb Phalke Award 2. Manmohan Singh B. Grammy Awards 3. Zakir Hussain C. Carnegie Medal of Philanthropy 4. Shyam Benegal D. World Statesman Award - XAT - 2025
- Famous personalities and their contributions
Match the following authors with their respective works.
Authors Books 1. Andy Weir A. Dune 2. Cixin Liu B. The Time Machine 3. Stephen Hawking C. The Brief History of Time 4. HG Wells D. The Martian 5. Frank Herbert E. The Three Body Problem - XAT - 2025
- Books and Authors
Match the following airlines with the countries where they are headquartered.
Airlines Countries 1. AirAsia A. Singapore 2. AZAL B. South Korea 3. Jeju Air C. Azerbaijan 4. Indigo D. India 5. Tigerair E. Malaysia - XAT - 2025
- Business and Economy
The diagram below represents a road network connecting five towns, namely Meeren, Lannisport, Winterfell, Oldtown, and Gulltown. The maximum speed limits along any stretch of road are as shown in the diagram. The straight road that connects Meeren to Gulltown passes through Oldtown. Another straight road, running west to east, connecting Meeren to Winterfell, passes through Lannisport. Further, two straight roads, one from Lannisport to Oldtown and another from Winterfell to Gulltown, are perpendicular to the road joining Meeren to Winterfell, and run from south to north.
Consider a car always travelling at the maximum permissible speed, and always taking the shortest route. It takes 1 hour to reach Oldtown from Meeren, 2 hours to reach Gulltown from Oldtown, and 45 minutes to reach Winterfell from Gulltown. (For this problem, always consider the shortest route in terms of distance.)
- XAT - 2025
- Logical and Analytical Reasoning Skills
The plots below depict and compare the average monthly incomes (in Rs. ’000) of males and females in ten cities of India in the years 2005 and 2015. The ten cities, marked A-J in the records, are of different population sizes. For a fair comparison, to adjust for inflation, incomes for both the periods are scaled to 2025 prices. Each red dot represents the average monthly income of females in a particular city in a particular year, while each blue dot represents the average monthly income of males in a particular city in a particular year. The gender gap for a city, for a particular year, is defined as the absolute value of the average monthly income of males, minus the average monthly income of females, in that year.
- XAT - 2025
- Data Interpretation