CSAT 2021: every question, solved
80 questions from the official UPSC Prelims 2021 paper, in paper order. Tap an option; the answer and the reason appear instantly.
Read the passage
Researchers simulated street lighting on artificial grassland plots containing pea-aphids, sap-sucking insects, at night. These were exposed to two different types of light — a white light similar to newer commercial LED lights and an amber light similar to sodium street lamps. The low intensity amber light was shown to inhibit, rather than induce, flowering in a wild plant of the pea family which is a source of food for the pea-aphids in grasslands. The number of aphids was also significantly suppressed under the light treatment due to the limited amount of food available.
Which one of the following statements best reflects the most critical inference that can be made from the passage given above ?
Answer (b) & explanation
The critical inference is that light pollution can have a lasting harmful effect on an ecosystem (b). Step 1: the passage says night lighting cut flowering in plants, and through the food chain it cut aphid numbers. One change spread to other living things: a knock-on effect on the ecosystem. That is (b). Step 2: option (a) compares low and high intensity light. The passage reports no such comparison. Step 3: option (c) compares white light with other colours; also not reported. Option (d) talks of "proper intensity", which the passage does not discuss.
Tip: in science passages, the inference usually widens the finding one step (here, from plants to the ecosystem). Options adding new comparisons are traps.
Answer as per the official UPSC answer key.
Read the passage
Approximately 80 percent of all flowering plant species are pollinated by animals, including birds and mammals, but the main pollinators are insects. Pollination is responsible for providing us with a wide variety of food, as well as many plant-derived medicines. At least one-third of the world’s agricultural crops depend upon pollination. Bees are the most dominant taxa when it comes to pollination and they are crucial to more than four hundred crops. Pollination is an essential service that is the result of intricate relationships between plants and animals, and the reduction or loss of either affects the survival of both. Effective pollination requires resources, such as refuges of pristine natural vegetation.
On the basis of the passage given above, the following assumptions have been made :
- 1. Sustainable production of India’s cereal food grains is impossible without the diversity of pollinating animals.
- 2. Monoculture of horticultural crops hampers the survival of insects.
- 3. Pollinators become scarce in cultivated areas devoid of natural vegetation.
- 4. Diversity in insects induces diversity of plants.
Which of the above assumptions is/are valid ?
Answer (d) & explanation
Assumptions 3 and 4 are valid (d). Step 1: the passage says pollination needs "refuges of pristine natural vegetation". So pollinators become scarce in farms with no natural plants (3). Step 2: it says losing one partner affects the other, so the diversity of insects and plants go together (4). Step 3: assumption 1 is about cereal grains, and assumption 2 about monoculture of horticulture crops. Neither is mentioned. Also, most cereals like rice and wheat are wind- or self-pollinated. So options (a), (b) and (c) fail.
Tip: reject any statement whose key term (cereals, monoculture) never appears in the passage. Pick the ones you can trace to a line.
Answer as per the official UPSC answer key.
Read the passage
A study conducted on the impacts of climate change over the Cauvery basin of Tamil Nadu using regional climate models showed an increasing trend for maximum and minimum temperatures, and a decrease in the number of rainy days. These climatic shifts will have an impact on the hydrological cycles in the region, lead to more run-off and less recharge, and affect the groundwater tables. Further, there has been an increase in the frequency of droughts in the State. This has driven farmers to increase dependency on groundwater resources to secure their crops.
Which one of the following statements best reflects the crux of the passage given above ?
Answer (c) & explanation
The crux is that climate change makes water more critical while also threatening it (c). Step 1: the passage says climate change cuts groundwater recharge. At the same time, more droughts raise farmers' dependence on groundwater. So water becomes more important and more at risk together. That is (c). Step 2: options (a) and (b) bring in remedies: regional climate models and dry-land cropping. The passage's main point is the problem, not these fixes. Step 3: option (d), farmers adopting risky livelihoods, is a side detail, not the crux.
Tip: the crux captures the passage's central tension. When a passage shows a "double squeeze", choose the option that names both sides.
Answer as per the official UPSC answer key.
Read the passage
Researchers were able to use stem cells to gauge the neurotoxic effects of the environmental pollutant Bisphenol A (BPA). They used a combination of biochemical and cell-based assays to examine the gene expression profile during the differentiation of mouse embryonic stem cells upon treatment with BPA, a compound known to cause heart diseases, diabetes, and developmental abnormalities in humans. They were able to detect and measure BPA toxicity towards the proper specification of primary germ layers, such as endoderm and ectoderm, and the establishment of neural progenitor cells.
On the basis of the passage given above, the following assumptions have been made :
- 1. BPA may alter embryonic development in vivo.
- 2. Biochemical and cell-based assays are useful in finding out treatments for pollution-induced diseases.
- 3. Embryonic stem cells could serve as a model to evaluate the physiological effects of environmental pollutants.
Which of the above assumptions are valid ?
Answer (c) & explanation
Assumptions 1 and 3 are valid (c). Step 1: the passage says BPA (a chemical in some plastics) harmed the formation of germ layers in stem cells. Germ layers are the first steps of an embryo's growth. So BPA may alter embryo development in the body (1). Step 2: the study used embryonic stem cells as a test model. So they can serve as a model to study pollutants (3). Step 3: assumption 2 says the assays help find treatments. But the assays measured toxicity; treatments are not discussed. So options (a), (b) and (d) fail.
Tip: "in vivo" means in a living body; "in vitro" means in a lab dish. Separate what a study measured from what it might later lead to.
Answer as per the official UPSC answer key.
If 32019 is divided by 10, then what is the remainder ?
Answer (c) & explanation
The remainder is 7 (c). Step 1: the remainder on dividing by 10 is just the unit digit. Step 2: powers of 3 end in a repeating cycle: 3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81. The cycle is 3, 9, 7, 1, of length 4. Step 3: 2019 ÷ 4 leaves a remainder of 3 (2019 = 4 × 504 + 3). So take the 3rd term of the cycle: 7. Option (b), 3, is the first term. Options (a) and (d) are the 4th and 2nd terms.
Tip: unit digits of powers repeat every 4 (or fewer). Divide the power by 4 and use the remainder; a remainder of 0 means the 4th term.
Answer as per the official UPSC answer key.
The number 3798125P369 is divisible by 7. What is the value of the digit P ?
Answer (b) & explanation
P is 6 (b). Step 1: a test for 7 (it also works for 11 and 13): from the right, split the number into groups of three digits and add and subtract them in turn. 3798125P369 splits into 37 | 981 | 25P | 369. Step 2: 369 − 25P + 981 − 37 = 1313 − (250 + P) = 1063 − P. This must be divisible by 7. Step 3: 1063 = 7 × 151 + 6. So 1063 − P is divisible by 7 when P = 6. Options (a), (c) and (d) leave remainders.
Tip: the alternating three-digit sum works because 1001 = 7 × 11 × 13. It is the fastest check for large numbers.
Answer as per the official UPSC answer key.
From January 1, 2021, the price of petrol (in Rupees per litre) on mth day of the year is 80 + 0·1m, where m = 1, 2, 3, ..., 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on nth day of 2021 is 69 + 0·15n for any n. On which date in the year 2021 are the prices of these two fuels equal ?
Answer (b) & explanation
The prices are equal on 20th May (b). Step 1: in the first 100 days, petrol = 80 + 0·1m and diesel = 69 + 0·15n. Setting them equal gives 0·05n = 11, so n = 220. That is outside the first 100 days, so there is no match there. Step 2: after day 100, petrol stays at 80 + 10 = ₹ 90. Diesel = 90 when 69 + 0·15n = 90, so n = 140. Step 3: day 140 of 2021: January to April = 31 + 28 + 31 + 30 = 120 days. Day 140 is the 20th of May. Options (a), (c) and (d) are off by a day.
Tip: always check the range where a formula applies. 2021 is not a leap year, so February has 28 days.
the petrol formula stops at day 100. Using it beyond that gives a wrong day.
Answer as per the official UPSC answer key.
A biology class at high school predicted that a local population of animals will double in size every 12 years. The population at the beginning of the year 2021 was estimated to be 50 animals. If P represents the population after n years, then which one of the following equations represents the model of the class for the population ?
Answer (d) & explanation
The model is P = 50(2)^(n/12) (d). Step 1: doubling means multiplying, not adding. So the linear options (a) and (b) are out. Step 2: after 12 years, there should be exactly one doubling. Put n = 12: 2^(12/12) = 2¹ = 2, so P = 100. Correct. Step 3: option (c), 2^(12n), at n = 12 gives 2¹⁴⁴, which is absurdly large. So only (d) fits. After 24 years, (d) gives 50 × 4 = 200, again correct.
Tip: for growth that doubles every T years, use P = P₀ × 2^(n/T). Test an easy value of n to check any formula quickly.
Answer as per the official UPSC answer key.
In a class, 60% of students are from India and 50% of the students are girls. If 30% of the Indian students are girls, then what percentage of foreign students are boys ?
Answer (d) & explanation
20% of foreign students are boys (d). Step 1: take 100 students. 60 are Indian, and 30% of them, 18, are girls. Step 2: total girls = 50, so foreign girls = 50 − 18 = 32. Foreign students = 100 − 60 = 40. So foreign boys = 40 − 32 = 8. Step 3: the question asks for a share of foreign students: 8 ÷ 40 = 20%. Option (a), 45%, and the others fail. Note 8% of the whole class is also a trap if you forget to divide by 40.
Tip: always check the base of the percentage. "Percentage of foreign students" means divide by the foreign total, not the class total.
"30% of the Indian students" is not 30% of the whole class.
Answer as per the official UPSC answer key.
A Statement followed by Conclusion-I and Conclusion-II is given below. You have to take the Statement to be true even if it seems to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statement, disregarding the commonly known facts.
Statement : Some radios are mobiles. All mobiles are computers. Some computers are watches.
Conclusion-I : Certainly some radios are watches.
Conclusion-II : Certainly some mobiles are watches.
Which one of the following is correct ?
Answer (d) & explanation
Neither conclusion follows (d). Step 1: some radios are mobiles, and all mobiles are computers. The watches are linked only to "some computers". Step 2: those computers may be ones that are not mobiles and not radios. So we cannot be sure any radio or mobile is a watch. Step 3: conclusions I and II both say "certainly", so neither follows. Options (a), (b) and (c) fail.
Tip: "some A are B" and "some B are C" give no sure link between A and C. Draw the circles so that the watches touch computers away from mobiles. If such a drawing is possible, the "certain" conclusion fails.
The word 'certainly' needs a sure link; a 'some' link through a big group (computers) is not sure.
Answer as per the official UPSC answer key.
Read the passage
Fig trees (genus Ficus) are considered sacred in India, East Asia and Africa and are common in agricultural and urban landscapes where other large trees are absent. In natural forests, fig trees provide food for wildlife when other resources are scarce and support a high density and diversity of frugivores (fruit-eating animals). If frugivorous birds and bats continue to visit fig trees located in sites with high human disturbance, sacred fig trees may promote frugivore abundance. Under favourable microclimate, plenty of seedlings of other tree species would grow around fig trees.
On the basis of the passage given above, the following assumptions have been made :
- 1. Fig trees can often be keystone species in natural forests.
- 2. Fig trees can grow where other large woody species cannot grow.
- 3. Sacred trees can have a role in biodiversity conservation.
- 4. Fig trees have a role in the seed dispersal of other tree species.
Which of the above assumptions is/are valid ?
Answer (a) & explanation
Assumptions 1 and 2 are valid (a). Step 1: the passage says figs feed wildlife "when other resources are scarce". A plant that keeps many animals alive is a keystone species (1). Step 2: it says figs grow where other large trees are absent. So they can grow where other woody species cannot (2). Step 3: UPSC's key treats statement 3, sacred trees aiding conservation, as only conditional in the passage. Statement 4, seed dispersal of other trees, is unstated. So options (b), (c) and (d) fail.
Tip: a keystone species is one whose loss would collapse much of its ecosystem. Figs, which fruit all year, are a classic example in Indian forests.
Answer as per the official UPSC answer key.
Read the passage
At the heart of agroecology is the idea that agroecosystems should mimic the biodiversity levels and functioning of natural ecosystems. Such agricultural mimics, like their natural models, can be productive, pest-resistant, nutrient conserving, and resilient to shocks and stresses. In ecosystems there is no ‘waste’, nutrients are recycled indefinitely. Agroecology aims at closing nutrient loops, i.e., returning all nutrients that come out of the soil back to the soil such as through application of farmyard manure. It also harnesses natural processes to control pests and build soil fertility i.e., through intercropping. Agroecological practices include integrating trees with livestock and crops.
Consider the following :
- 1. Cover crops
- 2. Fertigation
- 3. Hydroponics
- 4. Mixed farming
- 5. Polyculture
- 6. Vertical farming
Which of the above farming practices can be compatible with agroecology, as implied by the passage ?
Answer (a) & explanation
Cover crops, mixed farming and polyculture fit agroecology (a). Step 1: agroecology works with natural soil and nutrient cycles. Cover crops return nutrients to the soil (1). Step 2: mixed farming joins crops and livestock, using dung as manure (4). Polyculture, growing many crops together, is intercropping (5). Step 3: fertigation (fertiliser through irrigation), hydroponics (plants in water) and vertical farming (indoor racks) bypass the soil cycle. So options (b), (c) and (d) fail.
Tip: agroecology means farming like an ecosystem. India's natural farming push, under the National Mission on Natural Farming (2024), follows these ideas.
Answer as per the official UPSC answer key.
Read the passage
Computers increasingly deal not just with abstract data like credit card details and databases, but also with the real world of physical objects and vulnerable human bodies. A modern car is a computer on wheels; an aeroplane is a computer on wings. The arrival of the “Internet of Things” will see computers baked into everything from road signs and MRI scanners to prosthetics and insulin pumps. There is little evidence that these gadgets will be any more trustworthy than their desktop counterparts. Hackers have already proved that they can take remote control of internet connected cars and pacemakers.
Which one of the following statements best reflects the most critical inference that can be made from the passage given above ?
Answer (a) & explanation
The critical inference is that computers are not completely safe (a). Step 1: the passage says hackers have taken control of connected cars and pacemakers. If such devices can be hacked, computers are not fully safe. That is (a). Step 2: option (b) blames companies for not taking security seriously; the passage does not say this. Option (c) asks for new laws; this also goes beyond the passage. Step 3: option (d), technology will affect our lives, is too vague to be the critical inference.
Tip: the safest inference stays closest to the facts given. Blame and remedies usually go beyond a passage that only reports events.
Answer as per the official UPSC answer key.
Read the passage
A social and physical environment riddled with poverty, inequities, unhygienic and insanitary conditions generates the risk of infectious diseases. Hygiene has different levels : personal, domestic and community hygiene. There is no doubt that personal cleanliness brings down the rate of infectious diseases. But the entry of the market into this domain has created a false sense of security that gets conditioned and reinforced by the onslaught of advertisements. Experience in Western Europe shows that along with personal hygiene, general improvements in environmental conditions and components like clean water, sanitation and food security have brought down infant/child death/infection rates considerably. The obsession with hand hygiene also brings in the persisting influence of the market on personal health, overriding or marginalising the negative impact on ecology and the emergence of resistant germs.
On the basis of the passage given above, the following assumptions have been made :
- 1. People who are obsessed with personal hygiene tend to ignore the community hygiene.
- 2. Emergence of multi-drug resistant germs can be prevented by personal cleanliness.
- 3. Entry of the market in the domain of hygiene increases the risk of infectious diseases.
- 4. Scientific and micro-level interventions are not sufficient to bring down the burden of infectious diseases.
- 5. It is community hygiene implemented through public health measures that is really effective in the battle against infectious diseases.
Which of the above assumptions are valid ?
Answer (c) & explanation
Assumptions 4 and 5 are valid (c). Step 1: the passage says Western Europe cut infections through clean water, sanitation, food security and hygiene for all. So small-scale, personal steps are not enough (4), and community hygiene through public health works (5). Step 2: assumption 3 says the market raises the risk. The passage says the market creates a false sense of security, not higher risk. Step 3: assumption 2 says personal cleanliness can prevent drug-resistant germs; not supported. Assumption 1 is also not stated. So options (a), (b) and (d) fail.
Tip: "false sense of security" is not the same as "increased risk". Check the exact claim, not just the topic.
Answer as per the official UPSC answer key.
A Statement followed by Conclusion-I and Conclusion-II is given below. You have to take the Statement to be true even if it seems to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statement, disregarding the commonly known facts.
Statement : Some cats are almirahs. Some almirahs are chairs. All chairs are tables.
Conclusion-I : Certainly some almirahs are tables.
Conclusion-II : Some cats may not be chairs.
Which one of the following is correct ?
Answer (c) & explanation
Both conclusions follow (c). Step 1: some almirahs are chairs, and all chairs are tables. So those almirahs are also tables. Conclusion I, "certainly some almirahs are tables", is true. Step 2: nothing links cats to chairs directly. So it is possible that some cats are not chairs. Conclusion II uses "may not", which only claims a possibility. Step 3: so both follow. Options (a), (b) and (d) fail.
Tip: "may" or "may not" conclusions follow whenever the case is possible and not ruled out. "Certainly" conclusions need a firm chain, like "some A are B, all B are C".
a 'may' conclusion follows whenever the statements leave that case open.
Answer as per the official UPSC answer key.
A boy plays with a ball and he drops it from a height of 1·5 m. Every time the ball hits the ground, it bounces back to attain a height 4/5th of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing ?
Answer (b) & explanation
The ball hits the ground 5 times (b). Step 1: each bounce reaches 4/5 of the previous height. It starts at 150 cm. Step 2: hit 1 → rises to 120 cm. Hit 2 → 96 cm. Hit 3 → about 77 cm. Hit 4 → about 61 cm. Hit 5 → about 49 cm. Step 3: after the fifth hit, the height is below 50 cm, so it does not bounce again. The ball hits the ground 5 times. Option (a), 4, stops too early. Options (c) and (d) go too far.
Tip: list each step in a small table. Converting metres to centimetres first (1·5 m = 150 cm) avoids decimal errors.
Some readers count one more landing after the last small bounce; the official answer is (b), as printed.
Answer as per the official UPSC answer key.
Images of consonants of the English alphabet (Capitals) are observed in a mirror. What is the number of images of these which do not look like their original shapes ?
Answer (b) & explanation
14 consonants look different in a mirror (b). Step 1: a capital letter looks the same in a mirror if it has a vertical line of symmetry. Step 2: among the 21 consonants, these have one: H, M, T, V, W, X, Y. That is 7 letters. Step 3: the rest look different: 21 − 7 = 14. Option (a), 13, wrongly includes another letter. Options (c) and (d) miss some symmetric letters.
Tip: the vowels A, I, O and U are also symmetric, but the question asks only about consonants. There are 26 letters, 5 vowels, so 21 consonants. Memorise "AHIMOTUVWXY" as the mirror-same capitals.
Answer as per the official UPSC answer key.
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
Answer (b) & explanation
The shortest distance is 25 km (b). Step 1: trace the path. South 10 km. Facing South, left is East: 20 km. Facing East, left is North: 40 km. Facing North, right is East: 5 km. Facing East, right is South: 30 km. Step 2: north-south: −10 + 40 − 30 = 0. She ends on the same level as her house. East: 20 + 5 = 25 km. Step 3: so the bank is 25 km due East of the house. Options (a), (c) and (d) fail.
Tip: add up all north-south moves and all east-west moves separately. If one adds to zero, the answer is simply the other total.
Answer as per the official UPSC answer key.
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?
Answer (d) & explanation
9 integers have a digit sum of 10 (d). Step 1: numbers from 700 to 799 are written 7ab. We need a + b = 3: 703, 712, 721, 730. That is 4. Step 2: 8ab needs a + b = 2: 802, 811, 820. That is 3. 9ab needs a + b = 1: 901, 910. That is 2. Step 3: 1000 has digit sum 1, so it does not count. Total = 4 + 3 + 2 = 9. Options (a), (b) and (c) miss some.
Tip: two digits adding to k (with k ≤ 9) can be arranged in k + 1 ways. So 3 gives 4, 2 gives 3, 1 gives 2.
Answer as per the official UPSC answer key.
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
Answer (b) & explanation
She is at an angle less than 45° North of East (b). Step 1: 12 km North, then 6 km South, leaves her 6 km North. Then 8 km East. Step 2: so her net position is 6 km North and 8 km East. Step 3: the north part (6) is less than the east part (8). So the direction is closer to East: tan θ = 6/8, giving about 37° North of East, less than 45°. Options (a) and (c) wrongly say South. Option (d) says more than 45°.
Tip: if the two parts are equal, the angle is exactly 45°. The bigger part decides which direction the line leans towards.
Answer as per the official UPSC answer key.
Read the passage
India faces a challenging immediate future in energy and climate policy-making. The problems are multiple : sputtering fossil fuel production capabilities; limited access to electricity and modern cooking fuel for the poorest; rising fuel imports in an unstable global energy context; continued electricity pricing and governance challenges leading to its costly deficits or surplus supply; and not least, growing environmental contestation around land, water and air. But all is not bleak: growing energy efficiency programmes; integrated urbanisation and transport policy discussions; inroads to enhancing energy access and security; and bold renewable energy initiatives, even if not fully conceptualised, suggest the promise of transformation.
Which one of the following statements best reflects the critical message conveyed by the passage given above ?
Answer (a) & explanation
The critical message is that India's energy decisions are becoming more complex and interlinked (a). Step 1: the passage lists many linked problems: supply, access, imports, pricing and environment. It also lists linked responses. So decision-making is complex. That is (a). Step 2: options (c) and (d) are too negative. The passage speaks of a "promise of transformation", not failure or a narrow supply focus. Step 3: option (b), policy heavily tuned to sustainable development goals, overstates what the passage says.
Tip: if a passage piles up many connected issues, the message is usually "complexity". Check the passage's tone before choosing a negative option.
Answer as per the official UPSC answer key.
Read the passage
There are reports that some of the antibiotics sold in the market are fed to poultry and other livestock as growth promoters. Overusing these substances can create superbugs, pathogens that are resistant to multiple drugs and could be passed along humans. Mindful of that, some farming companies have stopped using the drugs to make chickens gain weight faster. Since Denmark banned antibiotic growth promoters in the 1990s, the major pork exporter says it is producing more pigs — and the animals get fewer diseases.
Which one of the following statements best reflects the critical message conveyed by the passage given above ?
Answer (d) & explanation
The critical message is that antibiotics should only be used to treat diseases (d). Step 1: the passage objects to antibiotics used as growth promoters in farm animals. Denmark banned that use, not all use. So antibiotics should be kept for treating illness. That is (d). Step 2: option (c), banning antibiotics on animals completely, would stop treatment of sick animals too. Step 3: options (a) and (b), avoiding animal products or replacing them with plant foods, are not discussed.
Tip: overuse of antibiotics breeds drug-resistant germs (antimicrobial resistance). India's Kerala launched a state action plan against it in 2018. Choose the option matching the passage's exact objection.
Answer as per the official UPSC answer key.
Read the passage
Policy makers and media have placed the blame for skyrocketing food prices on a variety of factors, including high fuel prices, bad weather in key food producing countries, and the diversion of land to non-food production. Increased emphasis, however, has been placed on a surge in demand for food from the most populous emerging economies. It seems highly probable that mass consumption in these countries could be well poised to create a food crisis.
With reference to the above passage, the following assumptions have been made :
- 1. Oil producing countries are one of the reasons for high food prices.
- 2. If there is a food crisis in the world in the near future, it will be in the emerging economies.
Which of the above assumptions is/are valid ?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: assumption 1 blames oil-producing countries. But the passage blames high fuel prices, not the countries that produce oil. So 1 fails. Step 2: assumption 2 says a food crisis will be in emerging economies. The passage says demand from emerging economies may cause a crisis, but it does not say where it will strike. So 2 fails. Step 3: so options (a), (b) and (c) fail.
Tip: separate cause from location. "Emerging economies may create a crisis" is not "the crisis will happen in emerging economies". Small word shifts like this decide many CSAT answers.
Answer as per the official UPSC answer key.
Read the passage
A central message of modern development economics is the importance of income growth, by which is meant growth in Gross Domestic Product (GDP). In theory, rising GDP creates employment and investment opportunities. As incomes grow in a country where the level of GDP was once low, households, communities, and governments are increasingly able to set aside some funds for the production of things that make for a good life. Today GDP has assumed such a significant place in the development lexicon, that if someone mentions “economic growth”, we know they mean growth in GDP.
With reference to the above passage, the following assumptions have been made :
- 1. Rising GDP is essential for a country to be a developed country.
- 2. Rising GDP guarantees a reasonable distribution of income to all households.
Which of the above assumptions is/are valid ?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: the passage reports what development economics says "in theory" about GDP. It does not call GDP growth essential for becoming developed. So assumption 1 fails. Step 2: assumption 2 says rising GDP guarantees fair income for all households. The passage says nothing about distribution. So 2 fails. Step 3: options (a), (b) and (c) fail.
Tip: reporting a theory is not endorsing it. Also, "guarantees" is a very strong word. GDP measures total output; it can rise even while inequality grows, which is why measures like the Human Development Index exist.
Answer as per the official UPSC answer key.
Seven books P, Q, R, S, T, U and V are placed side by side. R, Q and T have blue covers and other books have red covers. Only S and U are new books and the rest are old. P, R and S are law reports; the rest are Gazetteers. Books of old Gazetteers with blue covers are
Answer (c) & explanation
The old Gazetteers with blue covers are Q and T (c). Step 1: list each group. Gazetteers: all except the law reports P, R and S, so Q, T, U, V. Step 2: old books: all except the new ones S and U, so P, Q, R, T, V. Blue covers: Q, R, T. Step 3: books in all three groups: Q and T. Option (a) includes R, a law report. Options (b) and (d) include U, a new book.
Tip: in grouping puzzles, write each list and find the common members. Using "all except" lists helps avoid errors when a group is described by what it is not.
Answer as per the official UPSC answer key.
Replace the incorrect term by the correct term in the given sequence
3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40
where odd terms and even terms follow the same pattern.
Answer (a) & explanation
The incorrect term 2 should be replaced by 0 (a). Step 1: odd places: 3, 7, 13, 21, 31, 43. The gaps are 4, 6, 8, 10, 12. Step 2: even places: 2, 4, 10, 18, 28, 40. The gaps from 4 on are 6, 8, 10, 12, matching the odd places. So the first gap must also be 4. Step 3: the first even term should be 4 − 4 = 0, not 2. Options (b), (c) and (d) give a wrong first gap.
Tip: when a question says two sub-series follow the same pattern, find the pattern in the clean one, then fix the other. Each even term here is 3 less than its odd partner.
Answer as per the official UPSC answer key.
| 7B | 10A | 3C |
|---|---|---|
| 3C | 9B | 6A |
| 10A | 13C | ? |
Following is a matrix of certain entries. The entries follow a certain trend row-wise. Choose the missing entry (?) accordingly.
Answer (c) & explanation
The missing entry is 3B (c). Step 1: look at the numbers in each row. The third number is the second minus the first: 10 − 7 = 3 and 9 − 3 = 6. So in the last row, 13 − 10 = 3. Step 2: look at the letters. Each row uses A, B and C once each. The last row already has A and C, so the missing letter is B. Step 3: put them together: 3B. Option (a), 9B, gets the number wrong. Options (b) 3A and (d) 3C repeat a letter already in the row.
Tip: in matrix puzzles, split the entry into parts (number and letter) and solve each part on its own. Check your rule on every row before trusting it.
Answer as per the official UPSC answer key.
You are given two identical sequences in two rows :
| Sequence-I : | 8 | 4 | 6 | 15 | 52.5 | 236.25 |
|---|---|---|---|---|---|---|
| Sequence-II : | 5 | A | B | C | D | E |
What is the entry in the place of C for the Sequence-II ?
Answer (c) & explanation
The entry at C is 9.375 (c). Step 1: find the rule in Sequence-I. Each term is the one before multiplied by 0.5, 1.5, 2.5, 3.5, 4.5 in turn. The multiplier grows by 1 each step. Step 2: the two sequences are "identical", so Sequence-II follows the same rule, only starting from 5. Step 3: 5 × 0.5 = 2.5, then 2.5 × 1.5 = 3.75, then 3.75 × 2.5 = 9.375. Option (a), 2.5, is the first step and option (b), 5, is the start. Option (d), 32.8125, is a later term.
Tip: when a sequence grows unevenly, divide each term by the one before it. The pattern often hides in these ratios.
Answer as per the official UPSC answer key.
A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1·5 km/hr and Y walks with a uniform speed of 1 km/hr in the first hour, with a uniform speed of 1·25 km/hr in the second hour and with a uniform speed of 1·5 km/hr in the third hour and so on. Which of the following is/are correct ?
- 1. They take 5 hours to meet.
- 2. They meet midway between A and B.
Select the correct answer using the code given below :
Answer (c) & explanation
Both statements are correct (c). Step 1: X walks at a steady 1.5 km/hr. In 5 hours X covers 1.5 × 5 = 7.5 km. Step 2: Y's speed rises by 0.25 each hour: 1, 1.25, 1.5, 1.75, 2. In 5 hours Y covers 1 + 1.25 + 1.5 + 1.75 + 2 = 7.5 km. Step 3: together they cover 7.5 + 7.5 = 15 km, the full distance. So they meet after 5 hours (statement 1). Each has walked 7.5 km, which is exactly midway (statement 2). So options (a), (b) and (d) fail.
Tip: Y's speeds average 1.5 km/hr over those 5 hours, the same as X. Equal average speeds for equal time mean equal distance.
Answer as per the official UPSC answer key.
A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5 : 6 : 7 : 8 : 9 : 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks ?
Answer (b) & explanation
He scored below 60% in 3 papers (b). Step 1: the marks are in the ratio 5 : 6 : 7 : 8 : 9 : 10. Their average is 45 ÷ 6 = 7.5. Step 2: his overall score is 60%, and every paper has the same maximum. So the average share, 7.5, stands for 60%. Step 3: any paper with a ratio term below 7.5 is below 60%. Those are 5, 6 and 7, which is 3 papers. Options (a), (c) and (d) count wrongly. The papers with 8, 9 and 10 are above 60%.
Tip: when all papers carry the same maximum, the overall percentage equals the average paper. Simply compare each term with the average.
Answer as per the official UPSC answer key.
Read the passage
With respect to what are called denominations of religion, if everyone is left to be a judge of his own religion, there is no such thing as religion that is wrong; but if they are to be a judge of each other’s religion, there is no such thing as a religion that is right, and therefore all the world is right or all the world is wrong in the matter of religion.
What is the most logical assumption that can be made from the passage given above ?
Answer (c) & explanation
The most logical assumption is that religious denominations tend to ignore the unity of man (c). Step 1: the passage says if each judges his own religion, all are right. But if each judges the others', none is right. Each group sees only its own view, so they divide people instead of seeing what they share. That is (c). Step 2: option (a) says no one can live without a religion; the passage does not say this. Option (b), a duty to spread one's religion, is also not stated. Step 3: option (d) says men do not understand their own religion; the passage never doubts that.
Tip: an assumption must sit underneath the author's argument. Reject options that bring in duties or needs the passage never mentions.
Answer as per the official UPSC answer key.
Read the passage
It is certain, that seditions, wars, and contempt or breach of the laws are not so much to be imputed to the wickedness of the subjects, as to the bad state of a dominion. For men are not born fit for citizenship, but must be made so. Besides, men’s natural passions are everywhere the same; and if wickedness more prevails, and more offences are committed in one commonwealth than in another, it is certain that the former has neither enough pursued the end of unity, nor framed its laws with sufficient forethought; and that, therefore, it has failed in making quite good its right as a commonwealth.
Which among the following is the most logical and rational inference that can be made from the passage given above ?
Answer (c) & explanation
The best inference is that the best dominion pursues unity and has laws for good citizenship (c). Step 1: the passage says trouble comes from a state that has not pursued the end of unity nor framed laws with forethought. So a good state does both. That is (c). Step 2: option (b) says the sovereign is responsible for all problems. But the passage says "not so much" the subjects, which is softer. Step 3: option (a) calls wars inevitable, and option (d) calls a good state impossible. The passage says the opposite: men can be "made" fit for citizenship.
Tip: watch for absolute words like "all", "inevitable" and "impossible". The passage's mild wording ("not so much") rarely supports them.
Answer as per the official UPSC answer key.
Read the passage
Inequality violates a basic democratic norm : the equal standing of citizens. Equality is a relation that obtains between persons in respect of some fundamental characteristic that they share in common. Equality is, morally speaking, a default principle. Therefore, persons should not be discriminated on grounds such as race, caste, gender, ethnicity, disability, or class. These features of human condition are morally irrelevant. The idea that one should treat persons with respect not only because some of these persons possess some special features or talent, for example skilled cricketers, gifted musicians, or literary giants, but because persons are human beings, is by now part of commonsense morality.
With reference to the above passage, the following assumptions have been made :
- 1. Equality is a prerequisite for people to participate in the multiple transactions of society from a position of confidence.
- 2. Occurrence of inequality is detrimental to the survival of democracy.
- 3. Equal standing of all citizens is an idea that cannot actually be realised even in a democracy.
- 4. Right to equality should be incorporated into our values and day-to-day political vocabulary.
Which of the above assumptions are valid ?
Answer (c) & explanation
Assumptions 1 and 4 are valid (c). Step 1: the passage calls the equal standing of citizens a basic democratic norm. People need it to take part in society with confidence (1). Step 2: it says respecting persons as human beings is now part of "commonsense morality". So equality should be in our values and everyday vocabulary (4). Step 3: assumption 2 talks of the survival of democracy; the passage only says inequality violates a norm. Assumption 3 says equality cannot be realised, which goes against the passage. So options (a), (b) and (d) fail.
Tip: "violates a norm" is not the same as "destroys the system". Do not let an option exaggerate the passage's claim.
Answer as per the official UPSC answer key.
Read the passage
Aristocratic government ruins itself by limiting too narrowly the circle within which power is confined; oligarchic government ruins itself by the incautious scramble for immediate wealth. But even democracy ruins itself by excess of democracy. Its basic principle is the equal right of all to hold office and determine public policy. This is, at first glance, a delightful arrangement; it becomes disastrous because the people are not properly equipped by education to select the best rulers and the wisest courses. The people have no understanding and only repeat what their rulers are pleased to tell them. Such a democracy is tyranny or autocracy. — Plato
Which one of the following statements best reflects the crux of the passage given above ?
Answer (b) & explanation
The crux is that any form of government tends to decay through an excess of its basic principle (b). Step 1: the passage shows aristocracy ruins itself by keeping power too narrow, oligarchy by greed for wealth, and democracy by "excess of democracy". Each fails by pushing its own principle too far. That is (b). Step 2: option (a), societies trying different governments, is only background. Step 3: option (c) says education ensures a perfect democracy, which overpromises. Option (d) calls government a "necessary evil"; Plato does not argue this.
Tip: when a passage gives several examples of one pattern, the crux is the pattern itself, not any single example.
Answer as per the official UPSC answer key.
In a group of 120 persons, 80 are Indians and rest are foreigners. Further, 70 persons in the group can speak English. The number of Indians who can speak English is
Answer (d) & explanation
The number of Indians who speak English is 30 or more (d). Step 1: there are 120 people: 80 Indians and 40 foreigners. Step 2: 70 people speak English. Even if all 40 foreigners speak English, at least 70 − 40 = 30 speakers must be Indian. Step 3: if fewer foreigners speak English, more Indians must. It can go up to all 70. So the answer is "30 or more". Option (a), exactly 20, is impossible, and option (b), exactly 30, is only the least case. Option (c), 30 or less, gets the direction wrong.
Tip: for "at least" questions, give the other group the most it can take. What is left is the minimum for your group.
the question asks for what must be true. Find the smallest overlap, not an exact number.
Answer as per the official UPSC answer key.
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum. Which of the following is/are correct ?
- 1. S is always divisible by 74.
- 2. S is always divisible by 9.
Select the correct answer using the code given below :
Answer (c) & explanation
Both statements are correct (c). Step 1: the non-zero digits that are multiples of 3 are 3, 6 and 9. Without repeating digits, they make 3 × 2 × 1 = 6 numbers. Step 2: each digit appears in each place (hundreds, tens, units) twice. So S = 2 × (3 + 6 + 9) × 111 = 36 × 111 = 3996. Step 3: 3996 = 74 × 54, so it is divisible by 74 (statement 1). Its digits add up to 27, so it is divisible by 9 (statement 2). So options (a), (b) and (d) fail.
Tip: for the sum of all numbers made from given digits, use (number of times each digit sits in a place) × (sum of digits) × 111.
Answer as per the official UPSC answer key.
There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B. Consider the following statements :
- 1. The average score of Class-B will definitely decrease.
- 2. The average score of Class-A will definitely increase.
Which of the above statements is/are correct ?
Answer (a) & explanation
Only statement 1 is correct (a). Step 1: every student in Class A scores between 17 and 21. Every student in Class B scores 22 or more. Step 2: the four new students in B all score less than anyone already in B. So B's average must fall (statement 1). Step 3: Class A's average depends on who leaves. If the four toppers leave, A's average falls. If the four lowest leave, it rises. So it does not "definitely" increase (statement 2 fails). Options (b), (c) and (d) fail.
Tip: adding values below the average always lowers it. Removing values changes the average only according to which ones are removed; "definitely" needs every case to agree.
the word "definitely". 2 can happen, but it does not have to.
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.
Consider two Statements and a Question :
Statement-1 : Priya is 4 ranks below Seema and is 31st from the bottom.
Statement-2 : Ena is 2 ranks above Seema and is 37th from the bottom.
Question : What is Seema's rank from the top in the class of 40 students ?
Which one of the following is correct in respect of the Statements and the Question ?
Answer (c) & explanation
Either statement alone is enough (c). Step 1: in a class of 40, rank from top = 40 − rank from bottom + 1. Step 2: Statement-1: Priya is 31st from the bottom, so she is 40 − 31 + 1 = 10th from the top. Seema is 4 ranks above her, so 6th. Step 3: Statement-2: Ena is 37th from the bottom, so 4th from the top. Seema is 2 ranks below her, so again 6th. Each statement alone gives the answer. Options (a) and (b) wrongly say one is not enough. Option (d) wrongly says both are needed.
Tip: in data sufficiency, test each statement on its own first. Only combine them if neither works alone.
Answer as per the official UPSC answer key.
Consider two Statements and a Question :
Statement-1 : Each of A and D is heavier than each of B, E and F, but none of them is the heaviest.
Statement-2 : A is heavier than D, but is lighter than C.
Question : Who is the heaviest among A, B, C, D and E ?
Which one of the following is correct in respect of the Statements and the Question ?
Answer (c) & explanation
1. Statement-1 alone: A and D beat B, E and F, but we are not told who beats A and D. C is never mentioned, so we cannot name the heaviest.
2. Statement-2 alone: C > A > D. We know nothing about B and E, so again we cannot say.
3. Together: C > A > D, and A, D are heavier than B and E. So C is the heaviest, and both statements are needed (c).
4. A different reading of Statement-1 makes the data unclear, which is why (d) is also accepted.
The words 'none of them' can be read two ways, so UPSC's final key accepts both (c) and (d).
Answer as per the official UPSC answer key.
In the English alphabet, the first 4 letters are written in opposite order; and the next 4 letters are written in opposite order and so on; and at the end Y and Z are interchanged. Which will be the fourth letter to the right of the 13th letter ?
Answer (b) & explanation
The letter is T (b). Step 1: reverse the alphabet in blocks of four: DCBA HGFE LKJI PONM TSRQ XWVU. Then Y and Z swap, giving ZY at the end. Step 2: count to the 13th letter. The first three blocks have 12 letters, so the 13th is the first letter of the 4th block: P. Step 3: the fourth letter to the right of the 13th is the 17th letter. That is the first letter of the 5th block: T. Option (a), N, comes from the normal alphabet. Options (c) and (d) are other miscounts.
Tip: write out the new order fully before counting. "Fourth to the right of the 13th" simply means position 13 + 4 = 17.
Answer as per the official UPSC answer key.
Read the passage
Nothing can exist in a natural state which can be called good or bad by common assent, since every man who is in a natural state consults only his own advantage, and determines what is good or bad according to his own fancy and insofar as he has regard for his own advantage alone, and holds himself responsible to no one save himself by any law; and therefore sin cannot be conceived in a natural state, but only in a civil state, which is decreed by common consent what is good or bad, and each one holds himself responsible to the state.
Which one of the following statements best reflects the central idea of the passage given above ?
Answer (a) & explanation
The central idea is that ideas of right and wrong come from the formation of a state (a). Step 1: the passage says in a natural state each man judges good and bad by his own advantage. Nothing is good or bad "by common assent". Step 2: right and wrong are fixed by common consent "only in a civil state". That is (a). Step 3: option (b) says no man would be morally right without a ruler, which goes too far. Option (c) calls man immoral; but the passage says morality cannot even exist in a natural state. Option (d), survival of the species, is not discussed.
Tip: this is Spinoza's social-contract view. "Immoral" needs a moral standard; the passage says no shared standard exists before the state.
Answer as per the official UPSC answer key.
Read the passage
In the immediate future, we will see the increasing commodification of many new technologies — artificial intelligence and robotics, 3D manufacturing, custom made biological and pharmaceutical products, lethal autonomous weapons and driverless cars. This will pose conundrums. The moral question of how a driverless car will decide between hitting a jaywalker and swerving and damaging the car has often been debated. The answer is both simple — save the human life — and complex. At which angle should the car swerve — just enough to save the jaywalker or more than enough ? If the driverless car is in Dublin, who would take the decision ? The Irish Government, or the car’s original code writer in California, or a software programmer in Hyderabad to whom maintenance is outsourced ? If different national jurisdictions have different fine print on prioritising a human life, how will it affect insurance and investment decisions, including transnational ones ?
Which of the following statements best reflect the rational, plausible and practical implications that can be derived from the passage given above ?
- 1. Too much globalization is not in the best interests of any country.
- 2. Modern technologies are increasingly blurring the economic borders.
- 3. Innovation and capital have impinged on the domain of the State.
- 4. Public policy of every country should focus on developing its own supply chains.
- 5. Geopolitics will have to reconcile to many ambiguities and uncertainties.
Select the correct answer using the code given below :
Answer (c) & explanation
Implications 2, 3 and 5 are valid (c). Step 1: one driverless car involves Dublin, a code writer in California and a programmer in Hyderabad. Technology is blurring economic borders (2). Step 2: a code writer, not a government, may decide how the car swerves. Innovation and capital have entered the domain of the state (3). Step 3: different countries have different rules, which creates uncertainty for geopolitics, insurance and investment (5). Statements 1 (too much globalisation is bad) and 4 (build your own supply chains) are policy opinions the passage never gives. So options (a), (b) and (d) fail.
Tip: an implication follows from facts in the passage. Advice about what countries "should" do needs the author to argue it.
Answer as per the official UPSC answer key.
Read the passage
The resolution of bankruptcy cases of Indian banks under the Insolvency and Bankruptcy Code should help bring non-performing assets (NPA) situation under some control. Despite the slow pace of resolutions by the National Company Law Tribunal, the Code can be helpful in cleaning up bank books in future credit cycles. The recapitalisation of public sector banks too can help increase the capital cushion of banks and induce them to lend more and boost economic activity. But bad debt resolution and recapitalisation are only a part of the solution as they, by themselves, can do very little to rein in reckless lending that has pushed the Indian banking system to its current sorry state. Unless there are systemic reforms that address the problem of unsustainable lending, future credit cycles will continue to stress the banking system.
Which one of the following statements best reflects the most logical, rational and practical suggestion implied by the passage given above ?
Answer (d) & explanation
The suggestion is that Indian banking needs structural reforms as the long-term answer to bad loans (d). Step 1: the passage says bad-debt resolution and recapitalisation are "only a part of the solution". Step 2: it ends: unless there are "systemic reforms" to stop unsustainable lending, future credit cycles will stress banks. That is (d). Step 3: option (a), government monitoring of lending, and option (c), mergers, are specific steps the passage never proposes. Option (b), low interest rates to boost lending, goes against the passage's worry about reckless lending.
Tip: the last line of a passage often carries its suggestion. Here "unless there are systemic reforms" points straight to (d).
Answer as per the official UPSC answer key.
Read the passage
In India, the objective of macroeconomic policy is to enhance the economic welfare of the people, and any one wing of such macro policy, monetary or fiscal, cannot independently work without active support of another.
Which one of the following statements best reflects the corollary to the passage given above ?
Answer (a) & explanation
The corollary is that the central bank cannot work independently of the government (a). Step 1: the passage says monetary policy and fiscal policy cannot work "without active support of another". Step 2: monetary policy is run by the central bank (the RBI in India). Fiscal policy (taxes and spending) is run by the government. So the RBI cannot work fully on its own. That is (a). Step 3: options (b) close regulation, (c) socialist policies and (d) financial sector reforms all bring in new ideas that the single sentence does not contain.
Tip: a corollary is a direct, small step from the passage. Translate the key terms (monetary = central bank, fiscal = government) and the answer appears.
Answer as per the official UPSC answer key.
Consider the following Table :
| Player | Runs scored in the First Innings | Balls faced in the First Innings | Runs scored in the Second Innings | Balls faced in the Second Innings |
|---|---|---|---|---|
| A | 61 | 99 | 14 | 76 |
| B | 05 | 12 | 50 | 85 |
| C | 15 | 75 | 20 | 50 |
| D | 13 | 55 | 12 | 50 |
Who is the fastest run scorer in the Test Match ?
Answer (b) & explanation
B is the fastest scorer (b). Step 1: "fastest" means the most runs per ball over the whole match, not in one innings. So add both innings for each player. Step 2: A scored 75 in 175 balls, about 0.43 runs per ball. B scored 55 in 97 balls, about 0.57. Step 3: C scored 35 in 125 balls (0.28) and D scored 25 in 105 balls (0.24). B has the highest rate, so (b). Option (a), A, has the most runs, but took many more balls.
Tip: speed means a rate, not a total. Divide runs by balls; in cricket, strike rate = runs per 100 balls.
A's first innings looks the most striking, but you have to add both innings before you compare.
Answer as per the official UPSC answer key.
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?
Answer (b) & explanation
The statement certainly correct is that some villagers under 25 are literate (b). Step 1: four-fifths are under 25 and one-third are literate. Add them: 4/5 + 1/3 = 17/15, which is more than the whole village. Step 2: two groups that together exceed the total must overlap. So some literate villagers must be under 25. That is (b). Step 3: options (a), (c) and (d) link houses, paddy and age in exact ways. The data give no such link, so none is certain.
Tip: if two fractions of the same group add up to more than 1, the groups must share members. The overlap is at least the excess (here 2/15).
Answer as per the official UPSC answer key.
Consider two Statements and a Question :
Statement-1 : The last day of the month is a Wednesday.
Statement-2 : The third Saturday of the month was the seventeenth day.
Question : What day is the fourteenth of the given month ?
Which one of the following is correct in respect of the Statements and the Question ?
Answer (b) & explanation
Statement-2 alone is sufficient (b). Step 1: Statement-2 says the third Saturday was the 17th. The 14th is 3 days earlier. Three days before Saturday is Wednesday. So Statement-2 alone answers it. Step 2: Statement-1 says the last day is a Wednesday. But we do not know whether the month has 28, 29, 30 or 31 days. So the 14th could fall on different days. Step 3: so (a) fails, and since Statement-2 works alone, (c) and (d) fail too.
Tip: a fixed date with a known weekday is the best anchor. A clue about "the last day" fails when the month's length is unknown.
Answer as per the official UPSC answer key.
Which day is 10th October, 2027 ?
Answer (a) & explanation
10 October 2027 is a Sunday (a). Step 1: use an anchor date: 10 October 2021 was a Sunday (the CSAT exam was held that day). Step 2: count odd days from 10 Oct 2021 to 10 Oct 2027. That is 6 years, and each normal year adds 1 odd day. Only one 29 February falls in between (2024), adding 1 more. Total = 6 + 1 = 7 odd days = 0 extra. Step 3: so the weekday stays the same: Sunday. Options (b), (c) and (d) come from missing or adding the leap day.
Tip: a normal year shifts the weekday by 1, a leap year by 2. Count only the 29 Februarys that fall inside your range.
Answer as per the official UPSC answer key.
Consider two Statements and four Conclusions given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statements, disregarding the commonly known facts.
Statement-1 : Some greens are blues.
Statement-2 : Some blues are blacks.
Conclusion-1 : Some greens are blacks.
Conclusion-2 : No green is black.
Conclusion-3 : All greens are blacks.
Conclusion-4 : All blacks are greens.
Which one of the following is correct ?
Answer (d) & explanation
None of the four conclusions follows (d). Step 1: "some greens are blues" and "some blues are blacks" give no sure link between greens and blacks. The blues that are black may not be the green ones. Step 2: so "some greens are blacks" (1), "no green is black" (2), "all greens are blacks" (3) and "all blacks are greens" (4) are each possible, but none is certain. Step 3: options (a), (b) and (c) pair conclusions that do not follow. Conclusions 1 and 2 do form an "either-or" pair, but no option offers "either 1 or 2".
Tip: two "some" statements never give a definite conclusion. Draw the circles in two ways; if the answer changes, nothing follows.
1 and 2 form an 'either–or' pair, but no option offers 'either 1 or 2'.
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.
What is the value of 'X' in the sequence 2, 7, 22, 67, 202, X, 1822 ?
Answer (c) & explanation
X is 607 (c). Step 1: look at how each term is made from the one before. 2 × 3 + 1 = 7; 7 × 3 + 1 = 22; 22 × 3 + 1 = 67; 67 × 3 + 1 = 202. The rule is × 3, then + 1. Step 2: so X = 202 × 3 + 1 = 607. Step 3: check with the next term: 607 × 3 + 1 = 1822. It matches. Options (a) 603, (b) 605 and (d) 608 fail this check.
Tip: when terms grow about three times each step, try "× 3 ± a small number". Always confirm using the term after the blank.
Answer as per the official UPSC answer key.
Read the passage
The best universities like Harvard and MIT, despite having the luxury of having some truly excellent teachers on their payroll, are increasingly embracing the “flipped classroom” format, where students listen to video lectures at home, and spend class time applying their knowledge, solving problems, discussing examples, etc. Professors guide that discussion and fill in wherever necessary, explaining those bits that seem to be eluding the students and throwing in advanced ideas that happen to be topical. These universities have made their video lectures available free for anyone in the world. They are also encouraging colleges and universities all over the world to integrate these online courses into their own pedagogy, picking the pieces that are appropriate for their needs and building a package around them.
Which one of the following statements best reflects the central idea of the passage given above ?
Answer (b) & explanation
The central idea is that higher education can be made easier to access and cheaper without diluting content (b). Step 1: top universities like Harvard and MIT put their video lectures online free for anyone. Other colleges can build these into their teaching. So good content reaches more people at low cost. That is (b). Step 2: option (a) says online mode is better than classroom. But the flipped classroom mixes both: videos at home, discussion in class. Step 3: option (c), no need for infrastructure, and option (d), coaching institutes thriving, are not in the passage.
Tip: a "flipped classroom" means lectures at home and problem-solving in class. Don't confuse blended learning with fully online learning.
Answer as per the official UPSC answer key.
Read the passage
Our cities are extremely vulnerable to climate change because of large concentrations of populations and poor infrastructure. Moreover, population densities are increasing in them but we have not yet developed the systems to address climate change impacts. Our cities contribute to 65 per cent of the GDP, but there are not enough facilities to cater to the needs of the people. It is important to address the issues of air quality, transport, etc., that are vital to identifying sustainable solutions. We need to involve citizens in city planning and create an ecosystem that meets the needs of the people.
Which among the following is the most logical and rational inference that can be made from the passage given above ?
Answer (c) & explanation
The best inference is that our cities need sustainability-related interventions to be maintained and developed (c). Step 1: the passage says cities are vulnerable to climate change. It says air quality, transport and citizen planning are "vital to identifying sustainable solutions". That is (c). Step 2: option (a), administrative autonomy, and option (d), PPP mode, are never mentioned. Step 3: option (b) calls rising density a hindrance to sustainable development. The passage mentions density only as one cause of vulnerability; it does not make it the main barrier.
Tip: pick the option that uses the passage's own keywords and conclusion. Options naming specific models (PPP, autonomy) are usually outside the text.
Answer as per the official UPSC answer key.
Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store. If Jay bought 3 pens and 5 pencils, and Vijay bought 2 pens and 7 pencils, then which one of the following is correct ?
Answer (c) & explanation
A pen costs twice as much as a pencil (c). Step 1: both spent the same amount. So 3 pens + 5 pencils = 2 pens + 7 pencils. Step 2: take away 2 pens and 5 pencils from both sides. What is left: 1 pen = 2 pencils. Step 3: so a pen costs two times a pencil. Option (a) reverses it; option (b), equal prices, and option (d), three times, do not fit the equation.
Tip: when two purchases cost the same, cancel the common items. What remains is a direct price comparison, with no need for algebra.
Answer as per the official UPSC answer key.
P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score ?
Answer (a) & explanation
Q scored 360 (a). Step 1: Q scored 10% less than P. So the gap between them is 10% of P's marks. Step 2: the gap is 40 marks. So 10% of P = 40, which gives P = 400. Step 3: Q = 400 − 40 = 360. Option (c), 400, is P's score, not Q's. Options (b) 380 and (d) 420 come from using Q as the base of the percentage.
Tip: always ask "10% of whom?". Here "less than P" means P is the base. Check: 10% of 400 is 40, and 400 − 40 = 360.
10% less than P, so the base is P, not Q.
Answer as per the official UPSC answer key.
A person P asks one of his three friends X as to how much money he had. X replied, "If Y gives me ₹ 40, then Y will have half of as much as Z, but if Z gives me ₹ 40, then three of us will have equal amount." What is the total amount of money that X, Y and Z have ?
Answer (b) & explanation
The total is ₹ 360 (b). Step 1: use the second condition first. If Z gives X ₹ 40, all three are equal. So X + 40 = Y = Z − 40. Step 2: the first condition: if Y gives X ₹ 40, Y has half of Z. So Y − 40 = Z ÷ 2. Put Y = Z − 40: Z − 80 = Z ÷ 2, so Z = 160. Step 3: then Y = 120 and X = 80. Total = 160 + 120 + 80 = ₹ 360. Options (a), (c) and (d) do not satisfy both conditions.
Tip: start with the condition that gives the simplest link ("all equal"). Then plug the answer options back in to check quickly.
Answer as per the official UPSC answer key.
In a code language 'MATHEMATICS' is written as 'LBSIDNZUHDR'. How is 'CHEMISTRY' written in that code language ?
Answer (b) & explanation
CHEMISTRY is written BIDNHTSSX (b). Step 1: compare MATHEMATICS with LBSIDNZUHDR letter by letter. M → L (−1), A → B (+1), T → S (−1), H → I (+1). The moves alternate −1, +1. Step 2: apply this to CHEMISTRY: C−1 = B, H+1 = I, E−1 = D, M+1 = N, I−1 = H, S+1 = T, T−1 = S, R+1 = S, Y−1 = X. Step 3: the code is BIDNHTSSX. Option (c) has L and T, getting M wrong. Options (a) and (d) start with the wrong move.
Tip: in coding questions, check the first four letters to find the pattern. Then look at only the letters where the options differ.
Answer as per the official UPSC answer key.
At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other ?
Answer (d) & explanation
The hands are opposite between 7:05 and 7:10 (d). Step 1: the angle between the hands is |30H − 5.5M|, where H is the hour and M the minutes. At 7:00 it is 30 × 7 = 210°, so (a) fails. Step 2: as minutes pass, the minute hand closes the gap at 5.5° per minute. We need 210 − 5.5M = 180, so M = 30 ÷ 5.5 ≈ 5.45 minutes. Step 3: so the hands are 180° apart at about 7:05:27. That is just after 7:05, so (b) and (c) fail.
Tip: the minute hand gains 5.5° per minute on the hour hand. This one fact solves most clock-angle questions.
at 7:00 the angle is 210°, not 180°. The minute hand has to catch up 30°.
Answer as per the official UPSC answer key.
In an objective type test of 90 questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attempting all the 90 questions, a student got a total of 387 marks. What is the number of incorrect responses ?
Answer (a) & explanation
The student gave 9 wrong answers (a). Step 1: if all 90 were right, the score would be 90 × 5 = 450. Step 2: each wrong answer loses the 5 marks it would have earned and costs 2 more. So each wrong answer reduces the score by 7. Step 3: the score fell by 450 − 387 = 63. So wrong answers = 63 ÷ 7 = 9. Check: 81 × 5 − 9 × 2 = 405 − 18 = 387. Options (b), (c) and (d) fail this check.
Tip: in negative-marking questions, assume all are correct, then divide the shortfall by (marks for right + penalty for wrong).
Answer as per the official UPSC answer key.
Consider the following addition problem : 3P + 4P + PP + PP = RQ2; where P, Q and R are different digits. What is the arithmetic mean of all such possible sums ?
Answer (c) & explanation
The mean of the possible sums is 202 (c). Step 1: write out the sum: 3P + 4P + PP + PP = (30 + P) + (40 + P) + 11P + 11P = 70 + 24P. Step 2: the sum RQ2 ends in 2. So 24P must end in 2, which happens when P = 3 (sum 142) or P = 8 (sum 262). In both, P, Q and R are different digits. Step 3: the mean is (142 + 262) ÷ 2 = 202. Options (a), (b) and (d) do not match.
Tip: in digit puzzles, start with the units place. The last digit of a sum usually narrows the choices to one or two.
Answer as per the official UPSC answer key.
Consider the following multiplication problem :
(PQ) × 3 = RQQ, where P, Q and R are different digits and R ≠ 0.
What is the value of (P + R) ÷ Q ?
Answer (b) & explanation
(P + R) ÷ Q is 2 (b). Step 1: Q × 3 must end in Q. Only Q = 0 (0 × 3 = 0) and Q = 5 (5 × 3 = 15) work. Step 2: if Q = 0, then P0 × 3 = R00, which no single digit P can give. So Q = 5. Step 3: try P5 × 3 until the result ends in 55: 85 × 3 = 255. So P = 8 and R = 2. Then (P + R) ÷ Q = 10 ÷ 5 = 2. Option (d) is wrong because the data do fix the answer.
Tip: look for digits that repeat themselves when multiplied (0, 1, 5, 6). They often unlock such puzzles quickly.
Answer as per the official UPSC answer key.
Read the passage
Can a democracy avoid being a welfare state for long ? Why cannot mass welfare be left entirely to the markets ? There is a built-in tension between markets and democracy. Markets do not work on a one-person-one-vote principle as democracies do. What one gets out of the market place depends on one’s endowments, skills, purchasing power and the forces of demand and supply. Markets reward individual initiative and skill, and may also lift many from the bottom rungs of society, but some people never get the opportunity to develop skills that markets demand; they are simply too poor and too handicapped; or skill formation takes too long. By creating jobs, markets may be able to help even unskilled people, but capitalism has always witnessed bursts of unemployment.
With reference to the above passage, the following assumptions have been made :
- 1. Modern democracies rely on the market forces to enable them to be welfare states.
- 2. Markets ensure sufficient economic growth necessary for democracies to be effective.
- 3. Government programmes are needed for those left behind in economic growth.
Which of the above assumptions is/are valid ?
Answer (b) & explanation
Only assumption 3 is valid (b). Step 1: the passage asks why welfare cannot be "left entirely to the markets". It says some people never get to build the skills markets reward, and capitalism sees bursts of unemployment. So government programmes are needed for those left behind (3). Step 2: assumption 1 says democracies rely on markets to be welfare states. The passage says the opposite. Step 3: assumption 2 says markets ensure enough growth for democracy. The passage only says markets may lift some people. So options (a), (c) and (d) fail.
Tip: the tension between markets and democracy is a key idea. Markets work on "one rupee, one vote"; democracy works on "one person, one vote".
Answer as per the official UPSC answer key.
Read the passage
In our schools, we teach our children all that is there to know about physics, maths and history and what-have-you. But do we teach them about the bitter caste divide that plagues the country, about the spectre of famine that stalks large parts of our land, about gender sensitivity, about the possibility of atheism as a choice, etc. ? Equally important, do we teach them to ask questions, or do we teach them only to passively receive our wisdom ? From the cocooned world of school, suddenly, the adolescent finds himself/herself in the unfettered world of university. Here he/she is swept up in a turmoil of ideas, influences and ideologies. For someone who has been discouraged from asking questions and forming an opinion, this transition can be painful.
Which one of the following statements best reflects the central idea of the passage given above ?
Answer (d) & explanation
The central idea is that good citizens need social and life skills besides academic content (d). Step 1: the passage says schools teach physics, maths and history, but not caste, famine, gender or how to ask questions. Step 2: so the jump to university is painful. Schools must add life and social skills to subjects. That is (d). Step 3: option (a), curriculum versus parents' expectations, is not discussed. Option (b) contradicts the passage. Option (c) is too general; it misses the key point "in addition to academic content".
Tip: between a broad option and a specific one that matches the passage, choose the specific one. The best answer captures the passage's exact concern.
Answer as per the official UPSC answer key.
There are three points P, Q and R on a straight line such that PQ : QR = 3 : 5. If n is the number of possible values of PQ : PR, then what is n equal to ?
Answer (b) & explanation
There are 2 possible values of PQ : PR (b). Step 1: take PQ = 3 and QR = 5. Draw the possible orders. Step 2: if Q lies between P and R, then PR = 3 + 5 = 8, giving 3 : 8. If P lies between Q and R, then PR = 5 − 3 = 2, giving 3 : 2. Step 3: R cannot lie between P and Q, because QR (5) is longer than PQ (3). So n = 2. Options (a), (c) and (d) miscount the cases.
Tip: for points on a line, list every possible order and test each one. A case is possible only if the lengths fit.
Answer as per the official UPSC answer key.
On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?
Answer (b) & explanation
There are 6 ways (b). Step 1: a chess board has two main diagonals with 8 squares each. Step 2: a straight run of 6 squares on a diagonal of 8 can start at square 1, 2 or 3. That gives 3 ways on each diagonal. Step 3: two diagonals × 3 = 6. Option (a), 4, and the bigger options (c) 8 and (d) 12 do not match this count. UPSC's key counts only the two main diagonals here.
Tip: the number of runs of length k in a line of n squares is n − k + 1. Here 8 − 6 + 1 = 3.
Answer as per the official UPSC answer key.
In the series _b_a_ba_b_abab_aab; fill in the six blanks ( _ ) using one of the following given four choices such that the series follows a specific order.
Answer (d) & explanation
The blanks are filled by ababab (d). Step 1: put the letters a, b, a, b, a, b into the six blanks in order. Step 2: the series becomes abbaab abbaab abbaab. Step 3: the block "abbaab" repeats three times, so the series has a clear order. Options (a) bababa, (b) baabba and (c) bbaabb break this repeating pattern.
Tip: in letter-series questions, try each option and look for a block that repeats. The series length (18 here) often hints at the block size (6).
Answer as per the official UPSC answer key.
Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?
Answer (b) & explanation
Six numbers can be formed (b). Step 1: all numbers use all five digits, so they are 5-digit numbers. To be above 30000, the first digit must be 3. Step 2: the remaining digits are 2, 2, 3, 3. The number of ways to arrange them is 4! ÷ (2! × 2!) = 6. Step 3: they are 2233, 2323, 2332, 3223, 3232 and 3322. Options (a), (c) and (d) miscount by ignoring or double-counting the repeated digits.
Tip: when digits repeat, divide by the factorial of each repeat count. Without this, you would count the same number many times.
Answer as per the official UPSC answer key.
Consider the following statements :
- 1. The sum of 5 consecutive integers can be 100.
- 2. The product of three consecutive natural numbers can be equal to their sum.
Which of the above statements is/are correct ?
Answer (c) & explanation
Both statements are correct (c). Step 1: the sum of 5 consecutive integers is 5 × the middle one. 100 = 5 × 20, so 18 + 19 + 20 + 21 + 22 = 100. Statement 1 is true. Step 2: for statement 2, try small natural numbers: 1 × 2 × 3 = 6, and 1 + 2 + 3 = 6. They are equal, so statement 2 is true. Step 3: so options (a), (b) and (d) fail.
Tip: for consecutive numbers, the sum = count × middle value (with an odd count). For "can be" statements, one example is enough to prove it true.
Answer as per the official UPSC answer key.
A cubical vessel of side 1 m is filled completely with water. How many millilitres of water is contained in it (neglect thickness of the vessel) ?
Answer (d) & explanation
The vessel holds 10,00,000 ml (d). Step 1: the vessel is a cube of side 1 m, so its volume is 1 m³. Step 2: 1 m³ = 1000 litres. Step 3: 1 litre = 1000 ml. So 1000 × 1000 = 10,00,000 ml (one million). Option (a), 1000, is the number of litres, not millilitres. Options (b) and (c) drop zeroes.
Tip: remember 1 m³ = 1000 litres and 1 cm³ = 1 ml. So 1 m³ = 100 × 100 × 100 cm³ = 10,00,000 ml.
1000 is the answer in litres. The question asks for millilitres.
Answer as per the official UPSC answer key.
There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place ?
Answer (b) & explanation
There are 4 ways (b). Step 1: number the people 1 to 6 in the row. We must choose 3 of them, with no two standing side by side. Step 2: list the choices: (1, 3, 5), (1, 3, 6), (1, 4, 6) and (2, 4, 6). Step 3: that is 4 ways. Options (a) 3, (c) 5 and (d) 6 miss or add cases.
Tip: a quick formula for choosing k items from n in a row with no two adjacent is C(n − k + 1, k). Here C(4, 3) = 4.
Answer as per the official UPSC answer key.
An amount of money was distributed among A, B and C in the ratio p : q : r. Consider the following statements :
- 1. A gets the maximum share if p is greater than (q + r).
- 2. C gets the minimum share if r is less than (p + q).
Which of the above statements is/are correct ?
Answer (a) & explanation
Only statement 1 is correct (a). Step 1: if p is greater than q + r, then p is more than half the total. So p is bigger than both q and r, and A gets the maximum share. Statement 1 is true. Step 2: r less than p + q only means r is less than half. That does not make r the smallest. Step 3: try 1 : 5 : 4. Here r = 4 is less than 6, but A gets the least, not C. So statement 2 is false, and options (b), (c) and (d) fail.
Tip: to disprove a "general" statement, find one counter-example with small numbers.
Answer as per the official UPSC answer key.
Read the passage
Medieval merchants risked the hazards of the Silk Road to reach the markets of China; Portuguese caravels in the 15 century sailed beyond the bounds of the known world, searching less for knowledge than for gold and spices. Historically, the driver for opening frontiers has always been the search for resources. Science and curiosity are weaker drivers. The only way to open up space, whether the space of solar system or interstellar space is to create an economic engine and that engine is resource extraction.
Which one of the following statements best sums up the passage given above ?
Answer (c) & explanation
The passage is best summed up as: humans explore new frontiers mainly for economic reasons (c). Step 1: it gives examples: medieval merchants on the Silk Road and Portuguese ships seeking gold and spices. Step 2: it says "the driver for opening frontiers has always been the search for resources", and space too needs an economic engine. That is (c). Step 3: option (a) widens it to any human endeavour, but the passage talks only of frontiers. Option (b) predicts space will govern the economy, which is not said. Option (d), risk-taking, is not the main point.
Tip: watch the scope. An option that stretches "frontiers" to "every human activity" goes beyond the passage.
Answer as per the official UPSC answer key.
Read the passage
“...... most people would agree that telling deliberate lies is wrong, except perhaps in certain special situations where more harm will be done by telling the truth. Even the most truthful people probably tell a good many more lies that might be regarded as semantic lies; their use of words contains some measure of falsehood, more or less deliberate.”
The idea which the first part of the passage mentions is
Answer (d) & explanation
UPSC's key gives (d): disagreement about the harm in telling the truth. Step 1: the first part says most people agree deliberate lies are wrong, "except perhaps in certain special situations where more harm will be done by telling the truth". Step 2: UPSC reads the key idea as this exception: people differ on when telling the truth does harm. That is (d). Step 3: option (a), agreement about telling lies, also looks close because of "most people would agree". But UPSC picked the exception as the idea. Options (b) and (c) do not match the wording.
Tip: in short quotes, UPSC often tests the qualifier ("except", "unless"). The exception usually carries the idea being examined.
Answer as per the official UPSC answer key.
Read the passage
“...... most people would agree that telling deliberate lies is wrong, except perhaps in certain special situations where more harm will be done by telling the truth. Even the most truthful people probably tell a good many more lies that might be regarded as semantic lies; their use of words contains some measure of falsehood, more or less deliberate.”
Which one of the following habits is found more often in good people ?
Answer (b) & explanation
The habit found more often in good people is intentional mixing of truth with falsehood (b). Step 1: the passage says even the most truthful people tell "semantic lies". Their words contain "some measure of falsehood, more or less deliberate". Step 2: "deliberate" means intentional. So truth mixed with falsehood on purpose is (b). Step 3: option (a) leaves out the deliberate part. Options (c), falsifying facts, and (d), complete concealment, are much stronger than the passage's mild claim.
Tip: when two options look alike, find the word that separates them. Here "intentional" matches "deliberate" in the passage.
Answer as per the official UPSC answer key.
A pie diagram shows the percentage distribution of proteins, water and other dry elements in the human body. Given that proteins correspond to 16% and water corresponds to 70%. If both proteins and the other dry elements correspond to p%, then what is the central angle of the sector representing p on the pie diagram ?
Answer (c) & explanation
The central angle is 108° (c). Step 1: proteins are 16% and water is 70%. Everything else is the "other dry elements". Step 2: p% is proteins plus other dry elements, which is everything except water: 100 − 70 = 30%. Step 3: a full pie is 360°. So 30% of 360° = 108°. Option (a), 54°, uses only part of it. Options (b) and (d) use wrong percentages.
Tip: in a pie chart, 1% = 3.6°. Often the quickest route is to subtract the parts you don't need from 100%.
Answer as per the official UPSC answer key.
Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again ?
Answer (b) & explanation
They meet again on a Wednesday (b). Step 1: they meet again after the LCM of 5, 24 and 9. 24 = 2³ × 3 and 9 = 3², so the LCM = 2³ × 3² × 5 = 360 days. Step 2: find the weekday shift: 360 ÷ 7 = 51 weeks and 3 days left over. Step 3: Sunday + 3 days = Wednesday. Option (d), Sunday, ignores the extra days. Options (a) and (c) miscount.
Tip: "every nth day" problems use the LCM. Then divide by 7 and use the remainder to move the weekday forward.
Answer as per the official UPSC answer key.
The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54.
Consider the following statements :
- 1. The sum of the two digits of the number can be determined only if the product of the two digits is known.
- 2. The difference between the two digits of the number can be determined.
Which of the above statements is/are correct ?
Answer (b) & explanation
1. Swapping the two digits of a number always changes it by 9 × (the gap between the digits). Example: 71 − 17 = 54 = 9 × 6.
2. So 54 ÷ 9 = 6: the digits differ by 6. Statement 2 is correct.
3. The number could be 71, 82 or 93, with digit sums 8, 10 and 12. The sum is not fixed.
4. Statement 1 says the sum can be found 'only if' the product is known. Other facts could also fix it, so 'only if' is wrong. Statement 1 is incorrect.
Answer as per the official UPSC answer key.
X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements :
- 1. 8 years ago, the age of X was five times the age of Y.
- 2. After 14 years, the age of X would be two times the age of Y.
Which of the above statements is/are correct ?
Answer (b) & explanation
Only statement 2 is correct (b). Step 1: when Y was born, X's age equalled the age gap. That gap is twice Y's present age. So X − Y = 2Y, which means X = 3Y. With X = 42, Y = 14. Step 2: statement 1: 8 years ago, X was 34 and Y was 6. 34 is not 5 × 6 = 30, so it is false. Step 3: statement 2: after 14 years, X will be 56 and Y 28. 56 = 2 × 28, so it is true. Options (a), (c) and (d) fail.
Tip: the age gap between two people never changes. "At your birth I was ..." gives you that gap directly.
Answer as per the official UPSC answer key.
If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price ?
Answer (a) & explanation
There is no net change, 0% (a). Step 1: a 20% cut means multiplying by 0.8. Step 2: a 25% rise on the new price means multiplying by 1.25. Step 3: 0.8 × 1.25 = 1. So the final price equals the starting price. Options (b) and (c) wrongly add or subtract the percentages (25 − 20 = 5). Option (d) is wrong because the multipliers settle it without knowing the price.
Tip: for successive percentage changes, multiply the factors. A shortcut is a + b + ab/100: −20 + 25 − 500/100 = 0.
don't just add –20 and +25. The 25% is taken on the reduced price.
Answer as per the official UPSC answer key.
When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such number ?
Answer (d) & explanation
The smallest number is 15873 (d). Step 1: multiply each option by 7 and look for an answer made only of ones. Step 2: 15873 × 7 = 111111. That works. Step 3: the others fail: 15713 × 7 = 109991, 15723 × 7 = 110061 and 15783 × 7 = 110481. Also, 111111 is the smallest all-ones number divisible by 7 (1, 11, 111, 1111 and 11111 are not). So (d).
Tip: 111111 = 3 × 7 × 11 × 13 × 37. It is a handy number: divisible by 7, 11 and 13 together.
Answer as per the official UPSC answer key.
A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increased by 50% ?
Answer (d) & explanation
He needs 15 more days (d). Step 1: he does 7/8 of the job in 21 days. So the whole job takes 21 ÷ 7/8 = 24 days. Step 2: the work is raised by 50%, so the total is now 1.5 jobs. Work left = 1.5 − 7/8 = 12/8 − 7/8 = 5/8 of a job. Step 3: 5/8 of a job takes 5/8 × 24 = 15 days. Option (a), 24, is the time for one full job. Options (b) and (c) miscalculate the remaining work.
Tip: first find the time for one full job. Then any amount of work is just that fraction of the time.
the 50% is added to the whole job, not to the remaining 1/8.
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Answer as per the official UPSC answer key.
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Every question from 2011 to 2026, grouped by syllabus topic, with year-wise trends.