CSAT 2019: every question, solved
80 questions from the official UPSC Prelims 2019 paper, in paper order. Tap an option; the answer and the reason appear instantly.
Read the passage
Political theorists no doubt have to take history of injustice, for example, untouchability, seriously. The concept of historical injustice takes note of a variety of historical wrongs that continue into the present in some form or the other and tend to resist repair. Two reasons might account for resistance to repair. One, not only are the roots of injustice buried deep in history, injustice itself constitutes economic structures of exploitation, ideologies of discrimination and modes of representation. Two, the category of historical injustice generally extends across a number of wrongs such as economic deprivation, social discrimination and lack of recognition. This category is complex, not only because of the overlap between a number of wrongs, but because one or the other wrong, generally discrimination, tends to acquire partial autonomy from others. This is borne out by the history of repair in India.
What is the main idea that we can infer from the passage ?
Answer (d) & explanation
The main idea is that it is hard, if not impossible, to repair every form of historical injustice (d). Step 1: the passage says historical wrongs "tend to resist repair" because they are deep-rooted and overlap with one another. That matches (d). Step 2: option (b) says injustice is inevitable and always beyond repair. "Tend to resist" is softer than "always", so (b) overstates. Step 3: option (a) fails because the passage says theorists "have to take" untouchability seriously; it does not say they ignored it. Option (c) blames bad economies, which the passage never says.
Tip: match the strength of the option to the passage. "Tend to" fits "difficult", not "always" or "never".
Answer as per the official UPSC answer key.
Read the passage
Political theorists no doubt have to take history of injustice, for example, untouchability, seriously. The concept of historical injustice takes note of a variety of historical wrongs that continue into the present in some form or the other and tend to resist repair. Two reasons might account for resistance to repair. One, not only are the roots of injustice buried deep in history, injustice itself constitutes economic structures of exploitation, ideologies of discrimination and modes of representation. Two, the category of historical injustice generally extends across a number of wrongs such as economic deprivation, social discrimination and lack of recognition. This category is complex, not only because of the overlap between a number of wrongs, but because one or the other wrong, generally discrimination, tends to acquire partial autonomy from others. This is borne out by the history of repair in India.
On the basis of the above passage, the following assumptions have been made :
- 1. Removal of economic discrimination leads to removal of social discrimination.
- 2. Democratic polity is the best way to repair historical wrongs.
Which of the above assumptions is/are valid ?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: the passage says discrimination gains "partial autonomy" from other wrongs. That means it can live on by itself. So removing economic discrimination need not remove social discrimination. Assumption 1 fails. Step 2: assumption 2 calls democracy the best way to repair historical wrongs. The passage never mentions democracy. So 2 fails. Step 3: so options (a), (b) and (c) fail.
Tip: "partial autonomy" is a key phrase: it means one problem does not simply depend on another. When an option brings in a new idea, like democracy, that the passage never raised, it cannot be a valid assumption.
Answer as per the official UPSC answer key.
Read the passage
Education plays a great transformatory role in life, particularly so in this rapidly changing and globalizing world. Universities are the custodians of the intellectual capital and promoters of culture and specialized knowledge. Culture is an activity of thought, and receptiveness to beauty and human feelings. A merely well informed man is only a bore on God’s earth. What we should aim at is producing men who possess both culture and expert knowledge. Their expert knowledge will give them a firm ground to start from and their culture will lead them as deep as philosophy and as high as art. Together it will impart meaning to human existence.
On the basis of the above passage, the following assumptions have been made :
- 1. A society without well educated people cannot be transformed into a modern society.
- 2. Without acquiring culture, a person’s education is not complete.
Which of the above assumptions is/are valid ?
Answer (b) & explanation
Only assumption 2 is valid (b). Step 1: the passage says "a merely well informed man is only a bore" and that education must give "both culture and expert knowledge". So education without culture is incomplete. Assumption 2 holds. Step 2: assumption 1 says a society cannot be transformed without well-educated people. The passage talks about what good education is, not about how societies modernise. "Cannot" is too absolute and not argued. Step 3: so options (a), (c) and (d) fail.
Tip: this passage echoes the thinker A. N. Whitehead. In CSAT, quoted lines are the best evidence; pick the assumption that rests directly on them.
Answer as per the official UPSC answer key.
Read the passage
Soil, in which nearly all our food grows, is a living resource that takes years to form. Yet it can vanish in minutes. Each year 75 billion tonnes of fertile soil is lost to erosion. That is alarming — and not just for food producers. Soil can trap huge quantities of carbon dioxide in the form of organic carbon and prevent it from escaping into the atmosphere.
On the basis of the above passage, the following assumptions have been made :
- 1. Large scale soil erosion is a major reason for widespread food insecurity in the world.
- 2. Soil erosion is mainly anthropogenic.
- 3. Sustainable management of soils helps in combating climate change.
Which of the above assumptions is/are valid ?
Answer (b) & explanation
Only assumption 3 is valid (b). Step 1: the passage says soil traps carbon dioxide as organic carbon. Keeping soils healthy keeps this carbon out of the air. So sustainable soil care helps fight climate change. Assumption 3 holds. Step 2: assumption 2 says erosion is mainly anthropogenic (man-made). The passage names no cause of erosion, so 2 fails. Step 3: assumption 1 says erosion is a major reason for present food insecurity worldwide. The passage claims no such current crisis. So 1 fails, and options (a), (c) and (d) fail.
Tip: soil is the largest land store of carbon, holding more than plants and the air together. That is why soil health is a climate topic.
Answer as per the official UPSC answer key.
Read the passage
Inequality is visible, even statistically measurable in many instances, but the economic power that drives it is invisible and not measurable. Like the force of gravity, power is the organising principle of inequality, be it of income, or wealth, gender, race, religion and region. Its effects are seen in a pervasive manner in all spheres, but the ways in which economic power pulls and tilts visible economic variables remain invisibly obscure.
On the basis of the above passage, the following assumptions have been made :
- 1. Economic power is the only reason for the existence of inequality in a society.
- 2. Inequality of different kinds, income, wealth, etc. reinforces power.
- 3. Economic power can be analysed more through its effects than by direct empirical methods.
Which of the above assumptions is/are valid ?
Answer (b) & explanation
Only assumption 3 is valid (b). Step 1: the passage says economic power is "invisible and not measurable", yet its effects are seen everywhere. So we study power through its effects. Assumption 3 holds. Step 2: assumption 1 calls economic power the only reason for inequality. The passage does not say "only", so 1 overstates. Step 3: assumption 2 says inequality reinforces power. But the passage runs the other way: power drives inequality. So 2 reverses the direction. Options (a), (c) and (d) fail.
Tip: watch the direction of cause and effect. "A causes B" is not the same as "B causes A", and CSAT often flips them to set a trap.
Answer as per the official UPSC answer key.
Read the passage
Climate change may actually benefit some plants by lengthening growing seasons and increasing carbon dioxide. Yet other effects of a warmer world, such as more pests, droughts, and flooding, will be less benign. How will the world adapt ? Researchers project that by 2050, suitable croplands for four commodities — maize, potatoes, rice and wheat — will shift, in some cases pushing farmers to plant new crops. Some farmlands may benefit from warming, but others won’t. Climate alone does not dictate yields; political shifts, global demand, and agricultural practices will influence how farms fare in the future.
Which one of the following is the most logical and rational inference that can be made from the above passage ?
Answer (a) & explanation
The inference is that farmers who modernise and diversify will be better placed (a). Step 1: the passage says croplands will shift and "agricultural practices will influence how farms fare". So farmers who adapt their methods and grow varied crops gain. That is (a). Step 2: option (d) calls climate the most important factor. But the passage says "climate alone does not dictate yields". So (d) fails. Step 3: option (b), loss of crop diversity, is not stated. Option (c) predicts a great increase in farmland and output, which the passage never claims.
Tip: when a passage says "X alone does not decide", reject options that make X the main or only factor.
Answer as per the official UPSC answer key.
Read the passage
A bat’s wings may look like sheets of skin. But underneath, a bat has the same five fingers as an orangutan or a human, as well as a wrist connected to the same cluster of wrist bones connected to the same long bones of the arm. What can be more curious than that the hand of a man, formed for grasping, that of a mole for digging, the leg of the horse, the paddle of the porpoise, and the wing of the bat, should all be constructed on the same pattern ?
Which one of the following is the most logical, scientific and rational inference that can be made from the above passage ?
Answer (d) & explanation
The inference is that man and these animals share an evolutionary history (d). Step 1: the passage says limbs used for very different jobs are "constructed on the same pattern". The same bone plan in a human hand, a bat's wing and a whale's flipper points to a common ancestor. That is (d). Step 2: options (a) and (b) call this biodiversity. But similar structure shows sameness, the opposite of diversity. Step 3: option (c) calls it a coincidence. That is unscientific; such matching patterns are evidence of shared descent.
Tip: these are called homologous organs: same structure, different use. They are classic evidence for evolution in school biology.
Answer as per the official UPSC answer key.
Read the passage
Around 56 million years ago, the Atlantic Ocean had not fully opened and animals, perhaps including our primate ancestors, could walk from Asia to North America through Europe and across Greenland. Earth was warmer than it is today, but as the Palaeocene epoch gave way to Eocene, it was about to get much warmer still — rapidly and radically. The cause was a massive geologically sudden release of carbon. During this period called Palaeocene-Eocene Thermal Maximum or PETM, the carbon injected into the atmosphere was roughly the amount that would be injected today if humans burned all the Earth’s reserves of coal, oil and natural gas. The PETM lasted for about 1,50,000 years, until the excess carbon was reabsorbed. It brought on drought, floods, insect plagues and a few extinctions. Life on Earth survived — indeed, it prospered — but it was drastically different.
Based on the above passage, the following assumptions have been made :
- 1. Global warming has a bearing on the planet’s biological evolution.
- 2. Separation of land masses causes the release of huge quantities of carbon into the atmosphere.
- 3. Increased warming of Earth’s atmosphere can change the composition of its flora and fauna.
- 4. The present man-made global warming will finally lead to conditions similar to those which happened 56 million years ago.
Which of the assumptions given above are valid ?
Answer (c) & explanation
Assumptions 1 and 3 are valid (c). Step 1: the passage says that after the warming event 56 million years ago (the PETM), life "prospered, but it was drastically different". So warming affects evolution (1) and changes the mix of plants and animals (3). Step 2: assumption 2 says separating land masses released the carbon. The passage gives no cause for the carbon release, so 2 fails. Step 3: assumption 4 predicts that today's warming will lead to the same conditions. The passage makes no forecast, so 4 fails. Options (a), (b) and (d) fail.
Tip: a passage about the past rarely supports a firm prediction about the future. Reject "will finally lead to" type claims.
Answer as per the official UPSC answer key.
The number of times the digit 5 will appear while writing the integers from 1 to 1000 is
Answer (c) & explanation
The digit 5 appears 300 times (c). Step 1: write the numbers 000 to 999 as three-digit strings. There are 1000 strings with 3 places each, so 3000 digits in all. Step 2: each digit 0 to 9 appears equally often: 3000 ÷ 10 = 300. Leading zeros do not affect the count of 5s. Step 3: the number 1000 has no 5, so the answer stays 300. Check another way: 5 appears 100 times in the units place, 100 in the tens and 100 in the hundreds. Options (a), (b) and (d) are wrong.
Tip: from 1 to 999, every non-zero digit appears 300 times. Counting place by place (units, tens, hundreds) is the safest method.
269 and 271 come from counting only the numbers that contain a 5. A number like 55 has two 5s.
Answer as per the official UPSC answer key.
A solid cube is painted yellow, blue and black such that opposite faces are of same colour. The cube is then cut into 36 cubes of two different sizes such that 32 cubes are small and the other four cubes are big. None of the faces of the bigger cubes is painted blue. How many cubes have only one face painted ?
Answer (c) & explanation
1. Volume check: 4 big cubes of side 2 and 32 small cubes of side 1 give 32 + 32 = 64, so the cube is 4 × 4 × 4.
2. The big cubes avoid both blue faces, so they fill the middle two layers between the blue faces. The two blue layers (16 small cubes each) hold the 32 small cubes.
3. In each blue layer only the inner 2 × 2 = 4 cubes have just the blue face painted. The big cubes each touch two side faces. Total = 4 + 4 = 8.
Answer as per the official UPSC answer key.
A and B are two heavy steel blocks. If B is placed on the top of A, the weight increases by 60%. How much weight will reduce with respect to the total weight of A and B, if B is removed from the top of A?
Answer (d) & explanation
The weight falls by 37·5% (d). Step 1: take A = 100 for ease. Putting B on top raises the weight by 60%, so B = 60 and the total = 160. Step 2: removing B takes off 60. Step 3: as a share of the total of 160: 60 ÷ 160 = 3/8 = 37·5%. Option (a), 60%, uses A as the base instead of the total. Options (b) and (c) are also wrong.
Tip: the base changes everything. A rise of 60% on 100 is a fall of 37·5% on 160. To reverse an increase of x%, the fall is x ÷ (100 + x) × 100. Here 60 ÷ 160 × 100 = 37·5%. Choosing 100 as the starting value makes such sums easy.
the base changes: 60% of A is not 60% of (A + B).
One trap spotted is one mark saved. The PYQ Book lines up every trap UPSC has set, so you walk in prepared. Try the free sample
Answer as per the official UPSC answer key.
Mr 'X' has three children. The birthday of the first child falls on the 5th Monday of April, that of the second one falls on the 5th Thursday of November. On which day is the birthday of his third child, which falls on 20th December?
Answer (b) & explanation
1. April has 30 days. A 5th Monday needs Monday on 29 or 30 April, so 1 April is a Monday or a Sunday.
2. 1 April to 1 November = 214 days = 30 weeks + 4 days. So 1 November is Friday or Thursday. A 5th Thursday in November (30 days) needs 1 November to be Wednesday or Thursday, so 1 November = Thursday.
3. 20 December is 49 days later = exactly 7 weeks. Thursday.
Answer as per the official UPSC answer key.
Consider the following Statements and Conclusions :
Statements :
- 1. Some rats are cats.
- 2. Some cats are dogs.
- 3. No dog is a cow.
Conclusions :
- I. No cow is a cat.
- II. No dog is a rat.
- III. Some cats are rats.
Which of the above conclusions is/are drawn from the statements ?
Answer (c) & explanation
Only conclusion III follows (c). Step 1: "Some rats are cats" can be turned round: some cats are rats. So III is true. Step 2: conclusion I says no cow is a cat. The cats that are dogs cannot be cows, but other cats may still be cows. Nothing rules this out, so I fails. Step 3: conclusion II says no dog is a rat. Nothing links dogs and rats either way, so II fails. Options (a), (b) and (d) fail.
Tip: "some A are B" always means "some B are A". But "some" statements cannot give "no" conclusions. Drawing quick circles (Venn diagrams) shows what must be true and what only may be true.
Answer as per the official UPSC answer key.
The number of parallelograms that can be formed from a set of four parallel lines intersecting another set of four parallel lines, is
Answer (d) & explanation
36 parallelograms can be formed (d). Step 1: a parallelogram needs 2 lines from the first set and 2 lines from the second set. Step 2: ways to choose 2 lines from 4: (1, 2), (1, 3), (1, 4), (2, 3), (2, 4), (3, 4) = 6. This is 4C2. Step 3: each choice from the first set can pair with each choice from the second: 6 × 6 = 36. Option (b), 24, and option (c), 32, miscount. Option (a), 18, halves the answer for no reason.
Tip: for m parallel lines crossing n parallel lines, parallelograms = mC2 × nC2. The formula nC2 = n(n − 1) ÷ 2 gives 4 × 3 ÷ 2 = 6.
Answer as per the official UPSC answer key.
In a school every student is assigned a unique identification number. A student is a football player if and only if the identification number is divisible by 4, whereas a student is a cricketer if and only if the identification number is divisible by 6. If every number from 1 to 100 is assigned to a student, then how many of them play cricket as well as football?
Answer (b) & explanation
8 students play both cricket and football (b). Step 1: a number divisible by both 4 and 6 must be divisible by their LCM, which is 12. It is not 24, because 4 and 6 share the factor 2. Step 2: multiples of 12 up to 100 are 12, 24, 36, 48, 60, 72, 84 and 96. Step 3: that is 8 numbers (100 ÷ 12 = 8, ignoring the remainder). Option (a), 4, uses 24 instead of 12. Options (c) and (d) are wrong.
Tip: "divisible by both" means divisible by the LCM, not the product. LCM of 4 and 6 is 12; multiplying them gives 24, which misses numbers like 12, 36 and 60.
multiplying 4 × 6 = 24 gives 4, a trap option. Use the LCM.
Answer as per the official UPSC answer key.
When a runner was crossing the 12 km mark, she was informed that she had completed only 80% of the race. How many kilometres was the runner supposed to run in this event?
Answer (b) & explanation
The race was 15 km long (b). Step 1: 12 km is 80% of the whole race. Step 2: so the full race = 12 ÷ 0·8 = 12 × 10 ÷ 8 = 15 km. Step 3: check: 80% of 15 = 12. It works. Option (a), 14, and option (c), 16, do not give 12 at 80%. Option (d), 16·5, comes from adding 20% of 12 to 12 plus a little, which is the wrong base.
Tip: if a part and its percentage are given, whole = part ÷ percentage. A common mistake is to add 20% of 12 (giving 14·4); the remaining 20% is of the whole race, not of the part already run.
Answer as per the official UPSC answer key.
Raju has ₹ 9000 with him and he wants to buy a mobile handset; but he finds that he has only 75% of the amount required to buy the handset. Therefore, he borrows ₹ 2000 from a friend. Then
Answer (a) & explanation
Raju still does not have enough money (a). Step 1: ₹ 9000 is 75% of the price. So the price = 9000 ÷ 0·75 = ₹ 12,000. Step 2: he borrows ₹ 2000 and now has 9000 + 2000 = ₹ 11,000. Step 3: he is still ₹ 1000 short. So (a) is right. Options (b), (c) and (d) all assume he has enough. They come from working out 25% of 9000 (₹ 2250) instead of 25% of the price.
Tip: the missing 25% is of the price, not of what he has. Find the whole first (part ÷ percentage), then compare.
75% less would be different. Here ₹ 9000 is 75% of the price.
Answer as per the official UPSC answer key.
In 2002, Meenu's age was one-third of the age of Meera, whereas in 2010, Meenu's age was half the age of Meera. What is Meenu's year of birth?
Answer (b) & explanation
Meenu was born in 1994 (b). Step 1: test the options. Step 2: born 1994: in 2002 Meenu is 8, so Meera is 3 × 8 = 24. In 2010, Meenu is 16 and Meera is 32. 16 is half of 32. It works. Step 3: born 1992: in 2002 Meenu is 10 and Meera 30. In 2010 they are 18 and 38; 18 is not half of 38. So (a) fails. Options (c) and (d) also fail the check.
Tip: algebra works too. Let Meenu be x in 2002, so Meera is 3x. In 2010: 2(x + 8) = 3x + 8, so x = 8. Born 2002 − 8 = 1994. But testing options is often faster in CSAT.
Answer as per the official UPSC answer key.
Rakesh and Rajesh together bought 10 balls and 10 rackets. Rakesh spent ₹ 1300 and Rajesh spent ₹ 1500. If each racket costs three times a ball does, then what is the price of a racket?
Answer (c) & explanation
A racket costs ₹ 210 (c). Step 1: together they spent 1300 + 1500 = ₹ 2800 on 10 balls and 10 rackets. Step 2: let a ball cost b. A racket costs 3b. So 10b + 10 × 3b = 40b = 2800, and b = ₹ 70. Step 3: a racket = 3 × 70 = ₹ 210. Option (a), ₹ 70, is the price of a ball. Options (b) and (d) do not fit. How the cost was split between Rakesh and Rajesh does not matter.
Tip: CSAT often adds extra data to confuse you. Here the separate spends of ₹ 1300 and ₹ 1500 are not needed; only the total matters.
₹ 70 is the ball, not the racket.
Answer as per the official UPSC answer key.
In a conference, out of a total 100 participants, 70 are Indians. If 60 of the total participants are vegetarian, then which of the following statements is/are correct ?
- 1. At least 30 Indian participants are vegetarian.
- 2. At least 10 Indian participants are non-vegetarian.
Select the correct answer using the code given below :
Answer (c) & explanation
Both statements are correct (c). Step 1: the smallest possible overlap of two groups = group A + group B − total. Step 2: Indians and vegetarians: 70 + 60 − 100 = 30. So at least 30 Indians are vegetarian. Statement 1 holds. Step 3: there are 100 − 60 = 40 non-vegetarians. Indians and non-vegetarians: 70 + 40 − 100 = 10. So at least 10 Indians are non-vegetarian. Statement 2 holds. Options (a), (b) and (d) fail.
Tip: remember minimum overlap = A + B − total. Picture it: even if all 30 non-Indians are vegetarian, 30 more vegetarians must be Indian.
Answer as per the official UPSC answer key.
Read the passage
Low-end IoT (Internet of Things) devices are cheap commodity items : addressing security would add to the cost. This class of items is proliferating with new applications; many home appliances, thermostats, security and monitoring devices and personal convenience devices are part of the IoT. So are fitness trackers, certain medical implants and computer-like devices in automobiles. The IoT is expected to expand exponentially — but new security challenges are daunting.
Which one of the following statements is the most logical and rational inference that can be made from the above passage ?
Answer (d) & explanation
The inference is that some IoT devices pose a huge threat to internet security (d). Step 1: the passage says cheap IoT (Internet of Things) devices skip security to save cost, yet they spread fast. It adds that "security challenges are daunting". That is (d). Step 2: options (a) and (b) bring in India, which the passage never mentions. Step 3: option (c), comfort from cheap devices, misses the main point, which is the risk.
Tip: IoT means everyday devices linked to the internet, like smart cameras, bulbs and watches. Weakly protected ones can be hijacked in large numbers to attack websites. Pick the option that names the passage's central concern.
Answer as per the official UPSC answer key.
Read the passage
With the digital phenomenon restructuring most social sectors, it is little surprise that global trade negotiations are now eyeing the digital area in an attempt to pre-emptively colonise it. Big Data is freely collected or mined from developing countries, and converted into digital intelligence in developed countries. This intelligence begins to control different sectors and extract monopoly rents. A large foreign company providing cab service, for instance, is not a network of cars and drivers; it is digital intelligence about commuting, public transport, roads, traffic, city events, personal behavioural characteristics of commuters and drivers and so on.
Which one of the following is the most logical and rational corollary to the above passage ?
Answer (b) & explanation
The corollary is that India should protect its digital sovereignty in trade talks (b). Step 1: the passage says global trade talks try to "pre-emptively colonise" the digital space, using data from developing countries. So a developing country like India must guard its data. That is (b). Step 2: option (a) condemns all globalization, which goes far beyond the passage. Step 3: option (c), charging monopoly rents, reverses the passage, which blames big firms for earning such rents. Option (d) invents a proportional link to foreign trade.
Tip: a corollary is a natural next step from the passage. Choose the option that follows directly, not one that condemns a whole system.
Answer as per the official UPSC answer key.
Read the passage
With the digital phenomenon restructuring most social sectors, it is little surprise that global trade negotiations are now eyeing the digital area in an attempt to pre-emptively colonise it. Big Data is freely collected or mined from developing countries, and converted into digital intelligence in developed countries. This intelligence begins to control different sectors and extract monopoly rents. A large foreign company providing cab service, for instance, is not a network of cars and drivers; it is digital intelligence about commuting, public transport, roads, traffic, city events, personal behavioural characteristics of commuters and drivers and so on.
Which of the following is most definitively implied by the above passage ?
Answer (a) & explanation
The passage most clearly implies that Big Data is the key resource in the digital space (a). Step 1: it says data turned into "digital intelligence" lets firms control whole sectors and earn monopoly rents. So data is the central resource. That is (a). Step 2: option (b) says big economies create Big Data. But the passage says much data comes from developing countries, which weakens (b). Step 3: options (c) and (d) say Big Data belongs to developed countries. The passage says rich-country firms grab it, not that access is their right or nature.
Tip: data is often called "the new oil". India's Digital Personal Data Protection Act, 2023 is one response to this concern.
Answer as per the official UPSC answer key.
Read the passage
The rural poor across the world, including India, have contributed little to human-induced climate change, yet they are on the frontline in coping with its effects. Farmers can no longer rely on historical averages for rainfall and temperature, and the more frequent and extreme weather events, such as droughts and floods, can spell disaster. And there are new threats, such as sea level rise and the impact of melting glaciers on water supply. How significant are small farms ? As many as two billion people worldwide depend on them for their food and livelihood. Small-holder farmers in India produce 41 percent of the country’s food grains, and other food items that contribute to local and national food security.
What is the most logical and rational corollary to the above passage ?
Answer (a) & explanation
The corollary is that supporting small farmers is part of any sustainable development agenda (a). Step 1: the passage says small farmers feed about two billion people, yet they face climate shocks first. So helping them is central to sustainable growth. That is (a). Step 2: option (d) says only small farmers can ensure food security. But they grow 41% of India's grain, not all of it. So "only" fails. Step 3: option (b), poor countries have little role in fighting warming, is not supported. Option (c), India will have no food problem, contradicts the passage's warning.
Tip: an "only" option needs the passage to say "all". A 41% share is large but not the whole.
Answer as per the official UPSC answer key.
Read the passage
The rural poor across the world, including India, have contributed little to human-induced climate change, yet they are on the frontline in coping with its effects. Farmers can no longer rely on historical averages for rainfall and temperature, and the more frequent and extreme weather events, such as droughts and floods, can spell disaster. And there are new threats, such as sea level rise and the impact of melting glaciers on water supply. How significant are small farms ? As many as two billion people worldwide depend on them for their food and livelihood. Small-holder farmers in India produce 41 percent of the country’s food grains, and other food items that contribute to local and national food security.
The above passage implies that
- 1. There is a potential problem of food insecurity in India.
- 2. India will have to strengthen its disaster management capabilities.
Which of the above assumptions is/are valid ?
Answer (c) & explanation
Both implications are valid (c). Step 1: the passage says climate shocks hit small farmers, who grow 41% of India's grain. If their output falls, food supply is at risk. So India faces a potential food insecurity problem. Statement 1 holds. Step 2: it says "droughts and floods can spell disaster". To handle such shocks, India must be ready with disaster management. Statement 2 holds. Step 3: so options (a), (b) and (d) fail.
Tip: "potential" and "will have to strengthen" are moderate claims that a warning passage can support. India's National Disaster Management Authority, set up under the Disaster Management Act, 2005, leads such preparedness.
Answer as per the official UPSC answer key.
Read the passage
A changing climate, and the eventual efforts of governments (however reluctant) to deal with it, could have a big impact on investors’ returns. Companies that produce or use large amounts of fossil fuels will face higher taxes and regulatory burdens. Some energy producers may find it impossible to exploit their known reserves, and be left with “stranded assets” — deposits of oil and coal that have to be left in the ground. Other industries could be affected by the economic damage caused by more extreme weather — storms, floods, heat waves and droughts.
On the basis of the above passage, the following assumptions have been made :
- 1. Governments and companies need to be adequately prepared to face the climate change.
- 2. Extreme weather events will reduce the economic growth of governments and companies in future.
- 3. Ignoring climate change is a huge risk for investors.
Which of the above assumptions is/are valid ?
Answer (c) & explanation
Assumptions 1 and 3 are valid (c). Step 1: the passage lists carbon taxes, stranded assets (like coal plants that lose value) and weather damage as threats to investors' returns. So ignoring climate change is a big risk for investors (3). Step 2: since these risks are real, governments and companies must be prepared (1). Step 3: assumption 2 says extreme weather will reduce growth. The passage only says it "could". So 2 is too certain. Options (a), (b) and (d) fail.
Tip: "could" in a passage does not support "will" in an option. Matching the degree of certainty is a common CSAT test.
Answer as per the official UPSC answer key.
Read the passage
Access to schooling for those coming of school age is close to universal, but access to quality exhibits a sharp gradient with socio-economic status. Quotas for the weaker sections in private schools is a provision introduced by the Right of Children to Free and Compulsory Education Act, 2009. The quotas have imposed a debate on issues of social integration and equity in education that private actors had escaped by and large. The idea of egalitarian education system with equality of opportunity as its primary goal appears to be outside the space that private school principals inhabit. Therefore, the imposition of the quotas has led to resistance, sometimes justified.
With reference to the above passage, the following assumptions have been made :
- 1. Making equality of opportunity a reality is the fundamental goal of the Indian education system.
- 2. The present Indian school system is unable to provide egalitarian education.
- 3. Abolition of private schools and establishment of more government schools is the only way to ensure egalitarian education.
Which of the above assumptions is/are valid ?
Answer (b) & explanation
Only assumption 2 is valid (b). Step 1: the passage says school quality "exhibits a sharp gradient with socio-economic status". In plain words, richer children get better schools. So the present system is not equal. Assumption 2 holds. Step 2: assumption 1 calls equality the fundamental goal of Indian education. The passage notes equality is outside private schools' aims, but it does not show it is the system's core goal. So 1 fails. Step 3: assumption 3 says abolishing private schools is the only way. That is extreme and never argued. Options (a), (c) and (d) fail.
Tip: "abolition" and "only way" are extreme words. Passages describing a problem rarely back such drastic fixes.
Answer as per the official UPSC answer key.
Read the passage
A majority of the TB infected in India are poor and lack sufficient nutrition, suitable housing and have little understanding of prevention. TB then devastates families, makes the poor poorer, particularly affects women and children, and leads to ostracisation and loss of employment. The truth is that even if TB does not kill them, hunger and poverty will. Another truth is that deep-seated stigma, lack of counselling, expensive treatment and lack of adequate support from providers and family, coupled with torturous side-effects demotivate patients to continue treatment — with disastrous health consequences.
Which one of the following is the most logical, rational and crucial message conveyed by the above passage ?
Answer (b) & explanation
The message is that curing TB needs more than diagnosis and medicine (b). Step 1: the passage says nutrition, stigma, counselling and family support all decide whether patients finish their treatment. So medicine alone is not enough. That is (b). Step 2: option (a) says TB is not curable in India. That is extreme; TB is curable with full treatment. Step 3: option (c) blames surveillance, which the passage does not discuss. Option (d) says India will be free of TB only when poverty schemes succeed; "only when" overstates.
Tip: India runs the Ni-kshay Poshan Yojana, which gives TB patients money for nutrition, for exactly this reason. In CSAT, pick the balanced option and drop the extreme ones.
Answer as per the official UPSC answer key.
A five-storeyed building with floors from I to V is painted using four different colours and only one colour is used to paint a floor.
Consider the following statements :
- 1. The middle three floors are painted in different colours.
- 2. The second (II) and the fourth (IV) floors are painted in different colours.
- 3. The first (I) and the fifth (V) floors are painted red.
To ensure that any two consecutive floors have different colours
Answer (b) & explanation
Statement 3 alone is sufficient (b). Step 1: four colours are used on five floors, so exactly one colour repeats. Step 2: statement 3 says floors I and V are both red. That uses up the one repeat. So floors II, III and IV get the other three colours, all different and none red. Step 3: now every pair of neighbouring floors differs: I (red) and II, II and III, III and IV, IV and V (red). So statement 3 alone is enough. Statements 1 or 2 alone still allow, say, floors I and II to share a colour. So options (a), (c) and (d) fail.
Tip: in sufficiency questions, look for the statement that fixes the one repeat. Once the repeat is placed apart, the rest falls in line.
The key fact is hidden in the first line: four colours on five floors means only one repeat.
Answer as per the official UPSC answer key.
P, Q and R are three towns. The distance between P and Q is 60 km, whereas the distance between P and R is 80 km. Q is in the West of P and R is in the South of P. What is the distance between Q and R ?
Answer (d) & explanation
The distance between Q and R is 100 km (d). Step 1: Q is west of P and R is south of P. West and south are at right angles, so P is the right-angle corner of a triangle. Step 2: by Pythagoras, QR² = 60² + 80² = 3600 + 6400 = 10,000. Step 3: so QR = √10,000 = 100 km. Option (a), 140 km, simply adds 60 and 80, which would be true only if you travelled via P. Options (b) and (c) do not fit.
Tip: 60-80-100 is the 3-4-5 triangle multiplied by 20. Spotting such triples saves calculation. Direction questions with north-south and east-west legs almost always use Pythagoras.
Answer as per the official UPSC answer key.
All members of a club went to Mumbai and stayed in a hotel. On the first day, 80% went for shopping and 50% went for sightseeing, whereas 10% took rest in the hotel. Which of the following conclusion(s) can be drawn from the above data ?
- 1. 40% members went for shopping as well as sightseeing.
- 2. 20% members went for only shopping.
Select the correct answer using the code given below :
Answer (a) & explanation
Only conclusion 1 can be drawn (a). Step 1: 10% stayed in the hotel, so 90% went out. Step 2: both shopping and sightseeing = 80 + 50 − 90 = 40%. So conclusion 1 is correct. Step 3: only shopping = all shoppers − those who did both = 80 − 40 = 40%, not 20%. So conclusion 2 is wrong. Options (b), (c) and (d) fail.
Tip: always remove the "neither" group first. Then use: both = A + B − (those in at least one). A quick two-circle diagram makes "only A" and "both" easy to read off. Option (b) traps those who subtract 80 from 100 to get 20%.
Answer as per the official UPSC answer key.
In a school, 60% students play cricket. A student who does not play cricket, plays football. Every football player has got a two-wheeler. Which of the following conclusions cannot be drawn from the above data ?
- 1. 60% of the students do not have two-wheelers.
- 2. No cricketer has a two-wheeler.
- 3. Cricket players do not play football.
Select the correct answer using the code given below :
Answer (d) & explanation
None of the three conclusions can be drawn, so the answer is 1, 2 and 3 (d). Step 1: we know the 40% who do not play cricket play football, and every football player has a two-wheeler. Step 2: about cricketers we know nothing more. A cricketer may also play football, and may or may not own a two-wheeler. Step 3: so 1 (60% have no two-wheelers), 2 (no cricketer has one) and 3 (cricketers do not play football) are all unproven. Options (a), (b) and (c) fail.
Tip: "A student who does not play cricket plays football" does not mean cricketers never play football. A one-way rule cannot be reversed.
the question asks what cannot be drawn. Read 'cannot' twice.
UPSC repeats traps like this year after year. The PYQ Book gathers every trap in one place, so you see them coming. Try the free sample
Answer as per the official UPSC answer key.
The ratio of a two-digit natural number to a number formed by reversing its digits is 4 : 7. The number of such pairs is
Answer (b) & explanation
There are 4 such pairs (b). Step 1: let the number be 10a + b; reversed, it is 10b + a. Given (10a + b) : (10b + a) = 4 : 7, so 7(10a + b) = 4(10b + a). Step 2: 70a + 7b = 40b + 4a, so 66a = 33b, which gives b = 2a. Step 3: b must be a single digit, so a can be 1, 2, 3 or 4. The numbers are 12, 24, 36 and 48 (12 : 21 = 4 : 7, and so on). a = 5 would give b = 10, which is not a digit. Options (a), (c) and (d) fail.
Tip: write a two-digit number as 10a + b. Always check that the digits stay between 0 and 9.
Answer as per the official UPSC answer key.
In an examination, A has scored 20 marks more than B. If B has scored 5% less marks than A, how much has B scored?
Answer (b) & explanation
B scored 380 marks (b). Step 1: B scored 5% less than A. The gap of 20 marks is 5% of A's marks. Step 2: so A = 20 ÷ 0·05 = 400. Step 3: B = 400 − 20 = 380. Check: 5% of 400 is 20. It works. Option (c), 400, is A's score. Option (a), 360, subtracts twice. Option (d) does not fit.
Tip: "5% less than A" means the base is A. So the difference equals 5% of A. Finding A first is the key step. A quick check of each option against both facts also works: only 380 and 400 differ by 20 with a 5% gap based on the larger number.
400 is A's score, not B's.
Answer as per the official UPSC answer key.
Seeta and Geeta go for a swim after a gap of every 2 days and every 3 days respectively. If on 1st January both of them went for a swim together, when will they go together next?
Answer (d) & explanation
They swim together next on 13th January (d). Step 1: a gap of 2 days means Seeta swims on day 1, rests 2 days, then swims on day 4, so every 3rd day. A gap of 3 days means Geeta swims every 4th day. Step 2: they meet again after LCM(3, 4) = 12 days. Step 3: 1st January + 12 days = 13th January. Option (a), 7th January, uses LCM(2, 3) = 6. Options (b) and (c) also misread the gap.
Tip: "after a gap of n days" means the event repeats every n + 1 days. This wording trap appears often in CSAT calendar sums.
LCM(2, 3) = 6 gives 7 January. The gap is not the cycle.
Answer as per the official UPSC answer key.
X, Y and Z are three contestants in a race of 1000 m. Assume that all run with different uniform speeds. X gives Y a start of 40 m and X gives Z a start of 64 m. If Y and Z were to compete in a race of 1000 m, how many metres start will Y give to Z?
Answer (b) & explanation
Y will give Z a start of 25 m (b). Step 1: X gives Y a 40 m start, so while X runs 1000 m, Y runs 960 m. X gives Z a 64 m start, so in the same time Z runs 936 m. Step 2: so Z : Y = 936 : 960 = 39 : 40. Step 3: when Y runs 1000 m, Z runs 1000 × 39/40 = 975 m. So Y can give Z a start of 1000 − 975 = 25 m. Options (a), (c) and (d) do not fit.
Tip: do not just subtract the two starts (64 − 40 = 24). Speeds are in ratio, so rescale to the new race length.
64 – 40 = 24 is close but wrong. The base is Y's 960 m, not 1000 m.
Answer as per the official UPSC answer key.
If x is greater than or equal to 25 and y is less than or equal to 40, then which one of the following is always correct?
Answer (c) & explanation
(y − x) ≤ 15 is always correct (c). Step 1: y − x is largest when y is as big as possible and x as small as possible: 40 − 25 = 15. So y − x can never be more than 15. Statement (c) always holds. Step 2: check the others. x = 25, y = 40 makes y bigger than x, so (a) fails. It also gives y − x = 15, not greater than 15, so (b) fails. Step 3: a very small y, like y = −100, gives x + y below 65, so (d) fails.
Tip: for "always true" questions with limits, test the extreme values. The edge case (here 25 and 40) usually breaks the wrong options.
Answer as per the official UPSC answer key.
Ena was born 4 years after her parents' marriage. Her mother is three years younger than her father and 24 years older than Ena, who is 13 years old. At what age did Ena's father get married?
Answer (b) & explanation
Ena's father married at 23 (b). Step 1: Ena is 13. Her mother is 24 years older, so 37. Her father is 3 years older than her mother, so 40. Step 2: Ena was born 4 years after the marriage. So the marriage was 13 + 4 = 17 years ago. Step 3: father's age then = 40 − 17 = 23 years. Option (d), 25, uses the mother's age plus a wrong step. Option (c), 24, confuses the age gap. Option (a) forgets the 3-year difference.
Tip: in age puzzles, first find everyone's present age, then move back in time. Write each step on a line to avoid mixing up who is older.
Answer as per the official UPSC answer key.
Rakesh had money to buy 8 mobile handsets of a specific company. But the retailer offered very good discount on that particular handset. Rakesh could buy 10 mobile handsets with the amount he had. What was the discount the retailer offered?
Answer (b) & explanation
The discount was 20% (b). Step 1: the same money buys 10 handsets instead of 8. So the new price is 8/10 of the old price. Step 2: the price fell by 2/10 = 20%. Step 3: check with numbers: say the money is ₹ 80,000. Old price = 10,000; new price = 8000. Discount = 2000 ÷ 10,000 = 20%. Option (c), 25%, divides by the new price (2000 ÷ 8000). Options (a) and (d) do not fit.
Tip: a discount is always measured on the original price. Buying 25% more items means a 20% price cut, not 25%. Remember: 1 − 8/10 = 20%.
25% is the rise in quantity, not the fall in price.
Fell for this one? Most aspirants do. The PYQ Book puts every UPSC trap side by side, so the pattern finally clicks. Try the free sample
Answer as per the official UPSC answer key.
The average marks of 100 students are given to be 40. It was found later that marks of one student were 53 which were misread as 83. The corrected mean marks are
Answer (b) & explanation
The corrected mean is 39·7 (b). Step 1: total marks as first counted = 100 × 40 = 4000. Step 2: one mark was read as 83 instead of 53, which is 30 too high. Correct total = 4000 − 30 = 3970. Step 3: correct average = 3970 ÷ 100 = 39·7. Option (d), 40·3, adds the 30 instead of subtracting it. Option (c) ignores the error. Option (a) takes off the whole 1 mark.
Tip: shortcut: the average changes by (error ÷ number of items). Here 30 ÷ 100 = 0·3 too high, so the true average is 40 − 0·3 = 39·7.
Answer as per the official UPSC answer key.
Read the passage
What stands in the way of the widespread and careful adoption of ‘Genetic Modification (GM)’ technology is an ‘Intellectual Property Rights’ regime that seeks to create private monopolies for such technologies. If GM technology is largely corporate driven, it seeks to maximize profits and that too in the short run. That is why corporations make major investments for herbicide-tolerant and pest-resistant crops. Such properties have only a short window, as soon enough, pests and weeds will evolve to overcome such resistance. This suits the corporations. The National Farmers Commission pointed out that priority must be given in genetic modification to the incorporation of genes that can help impart resistance to drought, salinity and other stresses.
Which one of the following is the most logical, rational and crucial message conveyed by the above passage ?
Answer (a) & explanation
The message is that public research institutions should lead GM technology and set its agenda (a). Step 1: the passage says corporate GM research chases short-term profit. It ignores farmers' real needs, like crops that resist drought or salinity. So public bodies should set the agenda. That is (a). Step 2: option (b), abolishing intellectual property rights, is extreme. Option (c), banning private firms from seed business, is also extreme. Step 3: option (d) says India should not grow GM crops at all. The passage wants GM used better, not dropped.
Tip: if a passage criticises who controls a technology, the answer usually shifts control, not bans the technology. In India, ICAR and state agricultural universities do such public research.
Answer as per the official UPSC answer key.
Read the passage
What stands in the way of the widespread and careful adoption of ‘Genetic Modification (GM)’ technology is an ‘Intellectual Property Rights’ regime that seeks to create private monopolies for such technologies. If GM technology is largely corporate driven, it seeks to maximize profits and that too in the short run. That is why corporations make major investments for herbicide-tolerant and pest-resistant crops. Such properties have only a short window, as soon enough, pests and weeds will evolve to overcome such resistance. This suits the corporations. The National Farmers Commission pointed out that priority must be given in genetic modification to the incorporation of genes that can help impart resistance to drought, salinity and other stresses.
On the basis of the above passage, the following assumptions have been made :
- 1. The issue of effects of natural calamities on agriculture is not given due consideration by GM technology companies.
- 2. In the long run, GM technology will not be able to solve agricultural problems arising due to global warming.
Which of the above assumptions is/are valid ?
Answer (a) & explanation
Only assumption 1 is valid (a). Step 1: the passage says GM companies invest in herbicide and pest traits. Traits for drought and salinity, which matter for natural calamities, are left for a Commission to urge. So companies neglect this issue. Assumption 1 holds. Step 2: assumption 2 says GM will not solve climate-related farm problems in the long run. But the passage wants GM to be used for these stresses, so it believes GM can help. Assumption 2 contradicts the passage. Step 3: options (b), (c) and (d) fail.
Tip: an assumption that goes against the author's hope cannot be valid. Check whether the passage sees a tool as useless or just badly used.
Answer as per the official UPSC answer key.
Read the passage
Most invasive species are neither terribly successful nor very harmful. Britain’s invasive plants are not widespread, not spreading especially quickly, and often less of a nuisance than vigorous natives such as bracken. The arrival of new species almost always increases biological diversity in a region; in many cases, a flood of newcomers drives no native species to extinction. One reason is that invaders tend to colonise disturbed habitats like polluted lakes and post-industrial wasteland, where little else lives. They are nature’s opportunists.
Which one of the following is the most logical and rational inference that can be made from the above passage ?
Answer (c) & explanation
The inference is that campaigns against foreign plants are sometimes pointless (c). Step 1: the passage says most invading plants are "neither terribly successful nor very harmful". So fighting all of them can be a waste. "Sometimes" matches this. That is (c). Step 2: option (b) calls laws unnecessary. But "most" means some invaders are harmful, so some laws are needed. Step 3: options (a) and (d) ask us to deliberately use foreign plants for deserts or biodiversity. The passage never recommends this.
Tip: "most" supports "sometimes", but not "always" or "never". India's Lantana and Parthenium (congress grass) show that a few invaders do great harm.
Answer as per the official UPSC answer key.
Read the passage
Diarrhoeal deaths among Indian children are mostly due to food and water contamination. Use of contaminated groundwater and unsafe chemicals in agriculture, poor hygiene in storage and handling of food items to food cooked and distributed in unhygienic surroundings; there are myriad factors that need regulation and monitoring. People need to have awareness of adulteration and ways of complaining to the relevant authorities. Surveillance of food-borne diseases involves a number of government agencies and entails a good training of inspection staff. Considering the proportion of the urban population that depends on street food for its daily meals, investing in training and education of street vendors is of great significance.
On the basis of the above passage, the following assumptions have been made :
- 1. Food safety is a complex issue that calls for a multipronged solution.
- 2. Great investments need to be made in developing the manpower for surveillance and training.
- 3. India needs to make sufficient legislation for governing food processing industry.
Which of the above assumptions is/are valid ?
Answer (a) & explanation
Assumptions 1 and 2 are valid (a). Step 1: the passage says "myriad factors" affect food safety and call for regulation, awareness and surveillance. So it is a complex issue needing many fixes. Assumption 1 holds. Step 2: it says food inspectors and vendors need training. So investment in manpower for surveillance and training is needed. Assumption 2 holds. Step 3: assumption 3 is about laws for the food processing industry. That industry is not discussed. So 3 fails, and options (b), (c) and (d) fail.
Tip: India's food regulator is FSSAI, set up under the Food Safety and Standards Act, 2006. But in CSAT, use only what the passage says.
Answer as per the official UPSC answer key.
Read the passage
The interests of working and poor people have historically been neglected in the planning of our cities. Our cities are increasingly intolerant, unsafe and unlivable places for large numbers of citizens and yet we continue to plan via the old ways — the static Development Plan — that draws exclusively from technical expertise, distanced from people’s live experiences and needs, and actively excluding large number of people, places, activities and practices that are an integral part of the city.
The passage seems to argue
Answer (d) & explanation
The passage argues for people's groups taking part in city planning (d). Step 1: it says the flaw is planning "exclusively from technical expertise, distanced from people's lived experiences". The fix is to involve people. That is (d). Step 2: option (c) wants cities planned mainly for the poor. That would just swap one exclusion for another; the passage wants everyone included. Step 3: option (a), against builders and elites, and option (b), against smart cities, are not the passage's argument; it does not oppose these outright.
Tip: when a passage names a flaw ("exclusively experts"), the answer is the opposite: inclusion. India's 74th Amendment (1992) set up ward committees to give citizens a say.
Answer as per the official UPSC answer key.
Read the passage
A vast majority of Indians are poor, with barely 10 percent employed in the organised sector. We are being convinced that vigorous economic growth is generating substantial employment. But this is not so. When our economy was growing at 3 percent per year, employment in the organised sector was growing at 2 percent per year. As the economy began to grow at 7 — 8 percent per year, the rate of growth of employment in the organised sector actually declined to 1 percent per year.
The above passage seems to imply that
- 1. most of modern economic growth is based on technological progress.
- 2. much of modern Indian economy does not nurture sufficient symbiotic relationship with labour-intensive, natural resource-based livelihoods.
- 3. service sector in India is not very labour-intensive.
- 4. literate rural population is not willing to enter organised sector.
Which of the statements given above are correct ?
Answer (c) & explanation
Statements 1, 2 and 3 are implied (c). Step 1: the passage says India's growth has been faster but has made fewer jobs. UPSC's key reads this as growth driven by technology and capital (1). Step 2: it also implies the modern economy is cut off from labour-intensive, natural resource-based livelihoods like farming and crafts (2). And the fast-growing services sector does not use much labour (3). Step 3: statement 4 says literate rural people are unwilling to join the organised sector. Nothing in the passage blames workers' attitude. So options (a), (b) and (d) fail.
Tip: "jobless growth" is the theme here. Statements about people's motives need direct support in the passage.
Answer as per the official UPSC answer key.
Read the passage
India has banking correspondents, who help bring people in the hinterland into the banking fold. For them to succeed, banks cannot crimp on costs. They also cannot afford to ignore investing in financial education and literacy. Banking correspondents are way too small to be viewed as a systemic risk. Yet India’s banking regulator has restricted them to serving only one bank, perhaps to prevent arbitrage. Efforts at banking outreach may succeed only if there are better incentives at work for such last-mile workers and also those providers who ensure not just basic bank accounts but also products such as accident and life insurance and micro pension schemes.
Which one of the following is the most logical, rational and crucial inference that can be derived from the above passage ?
Answer (c) & explanation
The inference is that meaningful financial inclusion needs banking correspondents with diverse skills (c). Step 1: the passage says correspondents must give financial education and sell insurance and pensions, not just open accounts. That needs varied skills. That is (c). Step 2: option (b) asks for more correspondents. The passage asks for better incentives, not more workers. Step 3: option (a) says efforts have failed, which the passage does not say. Option (d), each correspondent serving many banks, goes beyond the passage, and "impossible unless" is extreme.
Tip: banking correspondents are local agents who offer bank services in villages without branches. They were key to Jan Dhan Yojana, launched in 2014.
Answer as per the official UPSC answer key.
What is X in the sequence
132, 129, 124, 117, 106, 93, X?
Answer (c) & explanation
X is 76 (c). Step 1: find the drops: 132 − 129 = 3, 129 − 124 = 5, 124 − 117 = 7, 117 − 106 = 11, 106 − 93 = 13. Step 2: 3, 5, 7, 11, 13 are prime numbers in order. The next prime is 17. Step 3: X = 93 − 17 = 76. Option (b), 75, and option (d), 77, use the wrong drop. Option (a), 74, subtracts 19, skipping a prime.
Tip: when gaps are 2, 3, 5, 7, 11, 13 or similar, think of primes. Note that 9 is skipped because it is not prime. Always write out the differences first in number series.
Answer as per the official UPSC answer key.
A wall clock moves 10 minutes fast in every 24 hours. The clock was set right to show the correct time at 8:00 a.m. on Monday. When the clock shows the time 6:00 p.m. on Wednesday, what is the correct time?
Answer (a) & explanation
The correct time is 5:36 p.m. (a). Step 1: the clock gains 10 minutes every 24 hours. So it shows 1450 minutes for every 1440 true minutes. Step 2: from 8:00 a.m. Monday to 6:00 p.m. Wednesday, the clock shows 58 hours = 3480 minutes. True time = 3480 × 1440/1450 = 3456 minutes = 57 hours 36 minutes. Step 3: 8:00 a.m. Monday + 57 h 36 min = 5:36 p.m. Wednesday. Option (b), 5:30 p.m., and the others use the wrong base.
Tip: a fast clock's shown time includes its gain. Convert using the ratio true : shown = 1440 : 1450, not by subtracting a fixed amount.
the clock is fast, so the true time is behind the clock. Adding the 24 minutes instead gives a time not in the options.
Answer as per the official UPSC answer key.
If the numerator and denominator of a proper fraction are increased by the same positive quantity which is greater than zero, the resulting fraction is
Answer (b) & explanation
The new fraction is always greater than the original (b). Step 1: take a proper fraction a/b, where a < b. Add k to both: (a + k)/(b + k). Step 2: the difference = (a + k)/(b + k) − a/b = k(b − a) / [b(b + k)]. Since b > a and k > 0, this is positive. Step 3: check: 1/2 becomes 2/3 when 1 is added. 2/3 is bigger. So (a), (c) and (d) fail.
Tip: adding the same amount to top and bottom pulls any fraction towards 1. A proper fraction (below 1) rises; an improper fraction (above 1) falls. This one rule answers many CSAT fraction questions instantly.
Answer as per the official UPSC answer key.
What is X in the sequence
4, 196, 16, 144, 36, 100, 64, X?
Answer (b) & explanation
X is 64 (b). Step 1: split the series into two. Odd places: 4, 16, 36, 64 = 2², 4², 6², 8². Step 2: even places: 196, 144, 100 = 14², 12², 10². They fall by 2 each time. Step 3: X is in an even place, so X = 8² = 64. Option (d), 256, continues the odd-place series (16²) by mistake. Options (a) and (c) do not fit.
Tip: when a series jumps up and down, it is often two series mixed together. Separate the odd and even places. Knowing squares up to 25² and cubes up to 15³ makes such questions quick.
Answer as per the official UPSC answer key.
In a group of 15 people, 7 can read French, 8 can read English while 3 of them can read neither of these two languages. The number of people who can read exactly one language is
Answer (b) & explanation
9 people can read exactly one language (b). Step 1: 3 read neither, so 15 − 3 = 12 read at least one. Step 2: both = 7 + 8 − 12 = 3. Step 3: exactly one = those who read at least one − those who read both = 12 − 3 = 9. Check: French only = 7 − 3 = 4; English only = 8 − 3 = 5; 4 + 5 = 9. Option (a), 10, forgets to subtract correctly. Option (c), 5, and (d), 4, give only one language's "only" group.
Tip: "exactly one" = (A only) + (B only). Always remove the "neither" group before using the overlap formula.
Answer as per the official UPSC answer key.
A printer numbers the pages of a book starting with 1 and uses 3089 digits in all. How many pages does the book have?
Answer (c) & explanation
The book has 1049 pages (c). Step 1: count digits used. Pages 1 to 9: 9 digits. Pages 10 to 99: 90 pages × 2 = 180. Pages 100 to 999: 900 × 3 = 2700. Total so far = 2889. Step 2: digits left = 3089 − 2889 = 200. Each page from 1000 on uses 4 digits, so 200 ÷ 4 = 50 pages. Step 3: last page = 999 + 50 = 1049. Option (d), 1050, adds one too many. Options (a) and (b) undercount.
Tip: remember the block totals: 9, 189 (to 99) and 2889 (to 999). Then divide the remainder by the digits per page.
Answer as per the official UPSC answer key.
Consider the following sequence that follows some arrangement :
c_accaa_aa_bc_b
The letters that appear in the gaps are
Answer (b) & explanation
The letters in the gaps are c, b, b, b (b). Step 1: split the series into blocks of five: c_acc | aa_aa | _bc_b. Step 2: each block has the pattern XXYXX: two of one letter, one different letter, then two of the first. Filling in: ccacc, aabaa, bbcbb. Step 3: the gaps, in order, are c, b, b, b. That is option (b). Options (a), (c) and (d) break the XXYXX pattern.
Tip: in letter series, count the total letters and try splitting them into equal blocks (of 4, 5 or 6). A repeating block usually becomes clear at once.
Answer as per the official UPSC answer key.
A family has two children along with their parents. The average of the weights of the children and their mother is 50 kg. The average of the weights of the children and their father is 52 kg. If the weight of the father is 60 kg, then what is the weight of the mother?
Answer (d) & explanation
The mother weighs 54 kg (d). Step 1: the average of the two children and the mother is 50, so their total = 150 kg. The average of the children and the father is 52, so that total = 156 kg. Step 2: both totals include the same two children. So the difference, 156 − 150 = 6 kg, is the father's weight minus the mother's. Step 3: mother = 60 − 6 = 54 kg. Option (b), 50 kg, is just the first average. Options (a) and (c) do not fit.
Tip: when two groups share members, subtract their totals. The shared part cancels, leaving only the difference you need. You never have to find the children's weights.
Answer as per the official UPSC answer key.
Suppose you have sufficient amount of rupee currency in three denominations : ₹ 1, ₹ 10 and ₹ 50. In how many different ways can you pay a bill of ₹ 107 ?
Answer (c) & explanation
There are 18 ways to pay ₹ 107 (c). Step 1: count by the number of ₹ 50 notes. Two ₹ 50 notes leave ₹ 7, which can only be paid in ₹ 1 coins: 1 way. Step 2: one ₹ 50 note leaves ₹ 57. You can use 0 to 5 ₹ 10 notes, with ₹ 1 coins for the rest: 6 ways. Step 3: no ₹ 50 note leaves ₹ 107. You can use 0 to 10 ₹ 10 notes: 11 ways. Total = 1 + 6 + 11 = 18. Options (a), (b) and (d) miss or add a case.
Tip: in coin-counting questions, fix the biggest note first, then count the choices for the next one. The smallest coin always fills the rest in exactly one way.
Answer as per the official UPSC answer key.
'A' started from his house and walked 20 m towards East, where his friend 'B' joined him. They together walked 10 m in the same direction. Then 'A' turned left while 'B' turned right and travelled 2 m and 8 m respectively. Again 'B' turned left to travel 4 m followed by 5 m to his right to reach his office. 'A' turned right and travelled 12 m to reach his office. What is the shortest distance between the two offices ?
Answer (b) & explanation
1. Draw it. Both reach a point 30 m east of A's house.
2. A: 2 m north, then 12 m east. B: 8 m south, 4 m east, then 5 m south.
3. Gap east–west: A went 12 m east, B 4 m east: 8 m. Gap north–south: A is 2 m north, B is 13 m south: 15 m.
4. 8 and 15 make a right-angled triangle: 8 × 8 + 15 × 15 = 64 + 225 = 289 = 17 × 17. Distance = 17 m.
Answer as per the official UPSC answer key.
Consider two statements S1 and S2 followed by a question :
S1 : p and q both are prime numbers.
S2 : p + q is an odd integer.
Question : Is pq an odd integer?
Which one of the following is correct?
Answer (b) & explanation
S2 alone is sufficient (b). Step 1: test S1. p and q are primes. p = 3, q = 5 gives pq = 15, odd. But p = 2, q = 3 gives pq = 6, even. So S1 gives no fixed answer. Step 2: test S2. p + q is odd. For whole numbers, an odd sum means one number is even and the other odd. Any product with an even number is even. So pq is never odd. Step 3: S2 gives a definite answer: "No". That counts as sufficient. Options (a), (c) and (d) fail.
Tip: in data sufficiency, a firm "No" is as good as a firm "Yes". Remember: even × anything = even; odd + odd = even.
a firm No is also an answer. Sufficiency does not need a "Yes".
One trap spotted is one mark saved. The PYQ Book lines up every trap UPSC has set, so you walk in prepared. Try the free sample
Answer as per the official UPSC answer key.
Which year has the same calendar as that of 2009?
Answer (d) & explanation
2015 has the same calendar as 2009 (d). Step 1: two years share a calendar if they start on the same day and are both leap or both non-leap. Step 2: add odd days (days beyond full weeks). A normal year has 1 odd day; a leap year has 2. 2009, 2010 and 2011 give 1 each. 2012 (leap) gives 2. 2013 and 2014 give 1 each. Total = 7 = 0 odd days. Step 3: so 2015 starts on the same day as 2009, and both are non-leap. Options (a), (b) and (c) do not total a multiple of 7.
Tip: a non-leap year's calendar usually repeats after 6 or 11 years. Counting odd days settles it quickly.
Answer as per the official UPSC answer key.
Number 136 is added to 5B7 and the sum obtained is 7A3, where A and B are integers. It is given that 7A3 is exactly divisible by 3. The only possible value of B is
Answer (d) & explanation
1. Try each value of B in the sum 5B7 + 136.
2. B = 2: 527 + 136 = 663. It must start with 7. Fails. B = 5: 557 + 136 = 693. Fails.
3. B = 7: 577 + 136 = 713. Digit sum 7 + 1 + 3 = 11 is not divisible by 3. Fails.
4. B = 8: 587 + 136 = 723. Digit sum 12 is divisible by 3. Works, so B = 8.
Answer as per the official UPSC answer key.
Read the passage
India’s economic footprint, given its population, still remains small compared to the US, the European Union or China. It has much to learn from other economies, yet must implement solutions that fit its unique circumstances. India especially needs an effective long-term regulatory system based on collaboration rather than the current top-down approach. Regulations seek desirable outcomes yet are repeatedly used as political tools to push one agenda or another. Often, regulations fail to consider impacts on jobs and economic growth — or less restrictive alternatives. Regulations may be used to protect local markets at the expense of more widely shared prosperity in the future. Additionally, regulations inevitably result in numerous unintended consequences. In today’s hyper competitive global economy, regulations need to be viewed as “weapons” that seek cost-justified social and environmental benefits while improving the economic well-being of most citizens.
Which one of the following is the most logical, rational and crucial inference that can be derived from the above passage ?
Answer (b) & explanation
The inference is that India must use regulations strategically in a competitive global economy (b). Step 1: the passage says regulations "need to be viewed as 'weapons'" that must be cost-justified in a "hyper competitive global economy". That means using them strategically. That is (b). Step 2: option (d) makes jobs and growth the dominant concern. The passage also values social and environmental gains, so (d) overstates. Step 3: option (a) links regulation to the size of the economy, which the passage does not say. Option (c) claims India's rules block integration, also unsupported.
Tip: a key metaphor ("weapons") often carries the main message. Choose the option closest to it.
Answer as per the official UPSC answer key.
Read the passage
India’s economic footprint, given its population, still remains small compared to the US, the European Union or China. It has much to learn from other economies, yet must implement solutions that fit its unique circumstances. India especially needs an effective long-term regulatory system based on collaboration rather than the current top-down approach. Regulations seek desirable outcomes yet are repeatedly used as political tools to push one agenda or another. Often, regulations fail to consider impacts on jobs and economic growth — or less restrictive alternatives. Regulations may be used to protect local markets at the expense of more widely shared prosperity in the future. Additionally, regulations inevitably result in numerous unintended consequences. In today’s hyper competitive global economy, regulations need to be viewed as “weapons” that seek cost-justified social and environmental benefits while improving the economic well-being of most citizens.
On the basis of the above passage, the following assumptions have been made : In today’s global economy,
- 1. regulations are not effectively used to protect local markets.
- 2. social and environmental concerns are generally ignored by the governments across the world while implementing the regulations.
Which of the above assumptions is/are valid ?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: the passage says regulations "may be used to protect local markets". Assumption 1 says they are not effectively used for this. That is the opposite of what the passage suggests, so 1 fails. Step 2: assumption 2 says governments generally ignore social and environmental concerns. The passage never says this. Step 3: so options (a), (b) and (c) fail.
Tip: an assumption must agree with the passage, not contradict it. Also beware of sweeping words like "generally ignored by governments across the world"; such broad claims need clear support, which passages rarely give.
Answer as per the official UPSC answer key.
Read the passage
In a study, scientists compared the microbiomes of poorly nourished and well nourished infants and young children. Gut microbes were isolated from faecal samples of malnourished and healthy children. The microbiome was “immature” and less diverse in malnourished children compared to the better developed “mature” microbiome found in healthy children of the same age. According to some studies, the chemical composition of mother’s milk has shown the presence of a modified sugar (sialylated oligosaccharides). This is not utilized by the baby for its own nutrition. However, the bacteria constituting the infant’s microbiome thrive on this sugar which serves as their food. Malnourished mothers have low levels of this sugar in their milk. Consequently, the microbiomes of their infants fail to mature. That in turn, leads to malnourished babies.
Which one of the following is the most logical, rational and crucial inference that can be derived from the above passage ?
Answer (d) & explanation
The inference is that research on gut bacteria and nutrition has policy implications (d). Step 1: the study links mothers' milk, gut bacteria and malnutrition in babies. Such findings can shape nutrition policy. That is (d). Step 2: options (b) and (c) suggest specific treatments: putting mature microbiomes into babies' guts, or replacing mother's milk with fortified dairy milk. The passage never tests these, and (c) even goes against breastfeeding. Step 3: option (a) says the condition cannot be treated; that is defeatist and not stated.
Tip: when a passage reports early research, the safe inference is that it "has implications". Specific cures go beyond the evidence.
Answer as per the official UPSC answer key.
Read the passage
In a study, scientists compared the microbiomes of poorly nourished and well nourished infants and young children. Gut microbes were isolated from faecal samples of malnourished and healthy children. The microbiome was “immature” and less diverse in malnourished children compared to the better developed “mature” microbiome found in healthy children of the same age. According to some studies, the chemical composition of mother’s milk has shown the presence of a modified sugar (sialylated oligosaccharides). This is not utilized by the baby for its own nutrition. However, the bacteria constituting the infant’s microbiome thrive on this sugar which serves as their food. Malnourished mothers have low levels of this sugar in their milk. Consequently, the microbiomes of their infants fail to mature. That in turn, leads to malnourished babies.
On the basis of the above passage, the following assumptions have been made :
- 1. Processed probiotic foods are a solution to treat the children suffering from malnutrition due to immature gut bacteria composition.
- 2. The babies of malnourished mothers generally tend to be malnourished.
Which of the above assumptions is/are valid ?
Answer (b) & explanation
Only assumption 2 is valid (b). Step 1: the passage says malnourished mothers' milk has less of certain sugars. This keeps their babies' gut bacteria immature, which "leads to malnourished babies". So babies of malnourished mothers tend to be malnourished. Assumption 2 holds. Step 2: assumption 1 offers processed probiotic foods as a cure. Probiotic foods are not mentioned in the passage. Step 3: so options (a), (c) and (d) fail.
Tip: this is part of the cycle of malnutrition: an underfed mother often has an underweight baby. India's POSHAN Abhiyaan targets mothers and young children together for this reason.
Answer as per the official UPSC answer key.
Read the passage
Temperatures have risen nearly five times as rapidly on the Western Antarctic Peninsula than the global average over the past five decades. Researchers have now found that melting glaciers are causing a loss of species diversity among benthos in the coastal waters off the Antarctic Peninsula, impacting an entire seafloor ecosystem. They believe increased levels of suspended sediment in water to be the cause of the dwindling biodiversity in the coastal region.
On the basis of the above passage, the following assumptions have been made :
- 1. Regions of glaciers warm faster than other regions due to global warming.
- 2. Global warming can lead to seafloor sedimentation in some areas.
- 3. Melting glaciers can reduce marine biodiversity in some areas.
Which of the above assumptions is/are valid ?
Answer (c) & explanation
Assumptions 2 and 3 are valid (c). Step 1: the passage says warming melts glaciers, which raises the amount of suspended sediment in the sea. So warming can cause seafloor sedimentation in some areas (2). Step 2: it says this sediment cuts the diversity of benthic (seafloor) life. So melting glaciers can reduce marine biodiversity (3). Step 3: assumption 1 says all glacier regions warm faster than others. The passage speaks of one peninsula warming fast. One case does not prove a general rule. So options (a), (b) and (d) fail.
Tip: "in some areas" makes 2 and 3 safe. A single example cannot support a claim about every region.
Answer as per the official UPSC answer key.
Read the passage
A research team examined a long-term owl roost. Owls prey on small mammals and the excreted remains of those meals that accumulated over the time, provide us an insight into the composition and structure of small mammals over the past millennia. The research suggested that when the Earth went through a period of rapid warming about 13,000 years ago, the small mammal community was stable and resilient. But, from the last quarter of the nineteenth century, human-made changes to the environment had caused an enormous drop in biomass and energy flow. This dramatic decline in energy flow means modern ecosystems are not adapting as easily as they did in the past.
On the basis of the above passage, the following assumptions have been made :
- 1. Global warming is a frequently occurring natural phenomenon.
- 2. The impending global warming will not adversely affect small mammals.
- 3. Humans are responsible for the loss of the Earth’s natural resilience.
Which of the above assumptions is/are valid ?
Answer (b) & explanation
Only assumption 3 is valid (b). Step 1: the passage says human-made changes caused "an enormous drop in biomass and energy flow". So ecosystems now recover less easily. Humans have weakened Earth's natural resilience. Assumption 3 holds. Step 2: assumption 1 calls warming a frequent natural event. The passage describes one past warming episode, not frequent ones. So 1 fails. Step 3: assumption 2 says coming warming will not harm small mammals. Even if small mammals coped in the past, today's ecosystems are weaker. So 2 fails. Options (a), (c) and (d) fail.
Tip: a past event does not guarantee the same result today, especially when the passage says conditions have changed.
Answer as per the official UPSC answer key.
Read the passage
Food varieties extinction is happening all over the world — and it is happening fast. For example, of the 7,000 apple varieties that were grown during the nineteenth century, fewer than a hundred remain. In the Philippines, thousands of varieties of rice once thrived; now only up to a hundred are grown there. In China, 90 percent of the wheat varieties cultivated just a century ago have disappeared. Farmers in the past painstakingly bred and developed crops well suited to the peculiarities of their local climate and environment. In the recent past, our heavy dependence on a few high yielding varieties and technology-driven production and distribution of food is causing the dwindling of diversity in food crops. If some mutating crop disease or future climate change decimates the few crop plants we have come to depend on to feed our growing population, we might desperately need some of those varieties we have let go extinct.
On the basis of the above passage, the following assumptions have been made :
- 1. Humans have been the main reason for the large scale extinction of plant species.
- 2. Consumption of food mainly from locally cultivated crops ensures crop diversity.
- 3. The present style of production and distribution of food will finally lead to the problem of food scarcity in the near future.
- 4. Our food security may depend on our ability to preserve the locally cultivated varieties of crops.
Which of the above assumptions are valid ?
Answer (b) & explanation
Assumptions 2 and 4 are valid (b). Step 1: the passage says growing local varieties keeps crop diversity alive. So eating mainly local crops supports diversity (2). Step 2: it says we "might desperately need" these varieties in future. So food security may depend on saving them (4). Step 3: assumption 1 is about all plant species, but the passage covers only food crops. Assumption 3 is a firm forecast of scarcity ("will finally lead"), which the passage does not make. So options (a), (c) and (d) fail.
Tip: "may depend" matches "might need". A cautious passage supports cautious statements, not firm predictions. India's seed banks and traditional seed savers help protect such varieties.
Answer as per the official UPSC answer key.
If every alternative letter of the English alphabet from B onwards (including B) is written in lower case (small letters) and the remaining letters are capitalized, then how is the first month of the second half of the year written ?
Answer (d) & explanation
July is written jUlY (d). Step 1: from B onwards, every alternate letter, B, D, F, H and so on, is written small. These are the letters at even places in the alphabet (B = 2, D = 4). The odd-place letters stay capital. Step 2: the first month of the second half of the year is JULY. Step 3: J is the 10th letter (even) → j. U is 21st (odd) → U. L is 12th (even) → l. Y is 25th (odd) → Y. So it is jUlY. Options (a), (b) and (c) get at least one letter wrong.
Tip: memorise letter positions with "EJOTY": E = 5, J = 10, O = 15, T = 20, Y = 25. It speeds up all alphabet questions.
Answer as per the official UPSC answer key.
Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is
Answer (d) & explanation
The sheet is 30 units long (d). Step 1: single-digit odd primes are 3, 5 and 7. Their average is 15 ÷ 3 = 5. So the first piece = 5. Step 2: let the third piece be t. The second piece = 5 + t/3. The third equals the other two together: t = 5 + (5 + t/3), so t − t/3 = 10, giving t = 15. The second piece = 5 + 5 = 10. Step 3: sheet = 5 + 10 + 15 = 30 units. Option (b), 15, is only the third piece. Options (a) and (c) do not fit.
Tip: 2 is the only even prime, so "odd primes" leaves out 2. Shortcut: the third piece is half the sheet, so the sheet is twice 15.
15 is the third piece. The question asks for the whole sheet.
Answer as per the official UPSC answer key.
In the sequence 1, 5, 7, 3, 5, 7, 4, 3, 5, 7, how many such 5s are there which are not immediately preceded by 3 but are immediately followed by 7 ?
Answer (a) & explanation
Only one 5 fits the rule (a). Step 1: list each 5 with its neighbours. The sequence is 1, 5, 7, 3, 5, 7, 4, 3, 5, 7. First 5: before it is 1, after it is 7. Second 5: before it is 3, after it is 7. Third 5: before it is 3, after it is 7. Step 2: we need a 5 not after 3 but followed by 7. Step 3: the second and third 5s come right after a 3, so they fail. Only the first 5 qualifies. The answer is 1. Options (b), (c) and (d) miscount.
Tip: in such questions, mark each target number and check both sides one by one. Rushing leads to missed or extra counts.
Answer as per the official UPSC answer key.
A joint family consists of seven members A, B, C, D, E, F and G with three females. G is a widow and sister-in-law of D's father F. B and D are siblings and A is daughter of B. C is cousin of B. Who is E ?
- 1. Wife of F
- 2. Grandmother of A
- 3. Aunt of C
Select the correct answer using the code given below :
Answer (d) & explanation
E is F's wife, A's grandmother and C's aunt, so all three are right (d). Step 1: G is a widow and F's sister-in-law, so she is the wife of F's late brother. C, a cousin of B, is G's child. Step 2: there are three females: G, A (B's daughter) and one more. B and D's mother must be in the family, so E is F's wife. Step 3: then E is the grandmother of A, B's daughter. And E is C's aunt, as the wife of C's uncle F. Options (a), (b) and (c) leave out one true link.
Tip: draw a family tree with symbols (+ for male, − for female). Fix the widowed or married pairs first; the rest falls in place.
Answer as per the official UPSC answer key.
Each face of a cube can be painted in black or white colours. In how many different ways can the cube be painted ?
Answer (b) & explanation
A cube can be painted in 10 different ways (b). Step 1: count by the number of black faces. 0 black: 1 way. 1 black: 1 way (any face looks the same after turning). Step 2: 2 black: 2 ways, either next to each other or opposite. 3 black: 2 ways, either all three meeting at a corner, or in a row like a band. Step 3: 4 black is the same as 2 white: 2 ways. 5 black: 1 way. 6 black: 1 way. Total = 1 + 1 + 2 + 2 + 2 + 1 + 1 = 10. Options (a), (c) and (d) miscount.
Tip: two cube colourings are the same if one can be turned to look like the other. Count patterns, not face labels.
a cube can be turned, so two paintings that match after turning are the same.
Answer as per the official UPSC answer key.
How many triplets (x, y, z) satisfy the equation x + y + z = 6, where x, y and z are natural numbers ?
Answer (d) & explanation
10 triplets satisfy the equation (d). Step 1: natural numbers start at 1, so zero is not allowed. List the sets of three numbers that add to 6: 1, 1, 4; 1, 2, 3; 2, 2, 2. Step 2: count the orders. 1, 1, 4 can be arranged in 3 ways. 1, 2, 3 in 6 ways. 2, 2, 2 in 1 way. Step 3: total = 3 + 6 + 1 = 10. Option (b), 5, and option (c), 9, miss some orders. Option (a) counts only the sets.
Tip: formula: the number of ways to write n as a sum of k natural numbers (order counts) is (n − 1)C(k − 1). Here 5C2 = 10.
Answer as per the official UPSC answer key.
If $ means 'divided by'; @ means 'multiplied by'; # means 'minus', then the value of 10#5@1$5 is
Answer (d) & explanation
The value is 9 (d). Step 1: replace the symbols: # is minus, @ is times, $ is divided by. So 10#5@1$5 becomes 10 − 5 × 1 ÷ 5. Step 2: by BODMAS, do multiplication and division first, left to right: 5 × 1 = 5, then 5 ÷ 5 = 1. Step 3: then subtract: 10 − 1 = 9. Option (b), 1, works left to right without BODMAS: (10 − 5) × 1 ÷ 5 = 1. Options (a) and (c) are also wrong.
Tip: after swapping symbols, always apply BODMAS: Brackets, Orders, Division and Multiplication, then Addition and Subtraction. The trap answer usually comes from working left to right.
Answer as per the official UPSC answer key.
An 8-digit number 4252746B leaves remainder 0 when divided by 3. How many values of B are possible?
Answer (c) & explanation
B can take 4 values (c). Step 1: a number is divisible by 3 if the sum of its digits is divisible by 3. Step 2: digits without B: 4 + 2 + 5 + 2 + 7 + 4 + 6 = 30. That is already a multiple of 3. Step 3: so B itself must be a multiple of 3: 0, 3, 6 or 9. That is 4 values. Option (b), 3, forgets 0. Options (a) and (d) miscount.
Tip: remember divisibility rules: by 3 or 9, use the digit sum; by 4, the last two digits; by 8, the last three; by 11, the difference of alternate digit sums. And 0 is a valid digit, so do not skip it.
don't forget B = 0.
Answer as per the official UPSC answer key.
Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least. Whenever F scores the highest, B scores the least. In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A.
If F stands second in the ranking, then the position of B is
Answer (c) & explanation
B is fifth (c). Step 1: F is second, so F is not first. So C is first. When C is first, E is last (sixth). Step 2: the remaining places 3, 4 and 5 go to D, A and B. We know D > A and A > B. Step 3: so D is 3rd, A is 4th and B is 5th. Option (d), sixth, belongs to E. Options (a) and (b) break D > A > B.
Tip: in ranking puzzles, apply the "if" condition first, then the fixed rules ("whenever C is highest, E is least"). Fill the remaining spots using the chain of comparisons.
Answer as per the official UPSC answer key.
Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least. Whenever F scores the highest, B scores the least. In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A.
If B scores the least, the rank of C will be
Answer (d) & explanation
C can be second or third (d). Step 1: if C were first, E would be last. But B is last, so C is not first. So F is first. Step 2: "close competitors" puts D just above A. C must be above A, and A above B. Step 3: two orders work: F, C, E, D, A, B and F, E, C, D, A, B. In the first, C is 2nd; in the second, C is 3rd. So C is second or third. Options (a), (b) and (c) give only one possibility.
Tip: when clues leave two valid orders, the answer must cover both. "Second or third" type options exist for exactly this case.
Answer as per the official UPSC answer key.
Six students A, B, C, D, E and F appeared in several tests. Either C or F scores the highest. Whenever C scores the highest, then E scores the least. Whenever F scores the highest, B scores the least. In all the tests they got different marks; D scores higher than A, but they are close competitors; A scores higher than B; C scores higher than A.
If E is ranked third, then which one of the following is correct ?
Answer (b) & explanation
C gets more marks than E (b). Step 1: E is 3rd, so E is not last. So C is not first (since C first would make E last). So F is first and B is last. Step 2: C, D and A take places 2, 4 and 5. D must be just above A (close competitors). So D is 4th, A is 5th and C is 2nd. Step 3: C (2nd) is above E (3rd), so C gets more marks. Option (a) reverses this. Option (c), A fourth, and option (d), D fifth, are wrong.
Tip: use each "whenever" rule in reverse too: if E is not last, C cannot be first. Contrapositives unlock many ranking puzzles.
'close competitors' means next to each other in rank. Without it, D could be second.
Answer as per the official UPSC answer key.
Read the following statements S1 and S2 and answer the item that follows :
S1 : Twice the weight of Sohan is less than the weight of Mohan or that of Rohan.
S2 : Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.
Which one of the following statements is correct ?
Answer (d) & explanation
Whose weight is greatest cannot be determined (d). Step 1: S1 says 2S < M and 2S < R. So Sohan is lighter than half of each of the others. Sohan is the lightest. Step 2: S2 says 2R > M and 2R > S. This tells us R is more than half of M. But M could be above or below R. Step 3: for example, M = 10, R = 8 fits, and so does M = 8, R = 10. So we cannot tell who is heaviest. Options (a), (b) and (c) fail.
Tip: "twice R is greater than M" does not mean R is greater than M. Test two sets of numbers to see whether an order is fixed.
Answer as per the official UPSC answer key.
Read the following statements S1 and S2 and answer the item that follows :
S1 : Twice the weight of Sohan is less than the weight of Mohan or that of Rohan.
S2 : Twice the weight of Rohan is greater than the weight of Mohan or that of Sohan.
Which one of the following statements is correct ?
Answer (b) & explanation
Sohan's weight is the least (b). Step 1: S1 says 2S < M and 2S < R. Step 2: so S < M/2, which is less than M. And S < R/2, which is less than R. So Sohan is lighter than both Mohan and Rohan. Step 3: therefore Sohan is the lightest. Options (a) and (c) name the wrong person. Option (d) fails because S1 alone fixes the lightest.
Tip: "twice A is less than B" means A is less than half of B, so A is certainly below B. This item and the previous one use the same data: one ordering (least) is fixed, the other (greatest) is not.
Answer as per the official UPSC answer key.
All years by topic
Every question from 2011 to 2026, grouped by syllabus topic, with year-wise trends.