CSAT 2024: every question, solved
80 questions from the official UPSC Prelims 2024 paper, in paper order. Tap an option; the answer and the reason appear instantly.
Read the passage
According to the Food and Agriculture Organization, one-third of food produced for human consumption is lost or wasted globally. Food is lost or wasted throughout the supply chain, from initial agricultural production to final household consumption. The increasing wastage also results in land degradation by about 45%, mainly due to deforestation, unsustainable agricultural practices, and excessive groundwater extraction. The energy spent over wasted food results in about 3·5 billion tonnes of carbon dioxide production every year. Decay also leads to harmful emissions of other gases in the atmosphere. Addressing the loss and wastage of food in all forms is critical to complete the cycle of food sufficiency and food sustainability.
Which of the following statements best reflect the most logical and rational inferences that can be made from the passage?
- 1. The current methods of food distribution are solely responsible for the loss and wastage of food.
- 2. Land productivity is adversely affected by the prevailing trend of food loss and wastage.
- 3. Reduction in the loss and wastage of food results in lesser carbon footprint.
- 4. Post-harvest technologies to prevent or reduce the loss and wastage of food are not available.
Select the correct answer using the code given below.
Answer (b) & explanation
Statements 2 and 3 can be inferred (b). Step 1: the passage says food wastage causes land degradation of about 45%. Damaged land gives less output, so land productivity suffers (2). Step 2: the energy spent on wasted food produces about 3.5 billion tonnes of CO₂ a year. So cutting waste cuts the carbon footprint (3). Step 3: statement 1 fails on the word "solely": food is lost "throughout the supply chain", from farm to household, not only in distribution. Statement 4, about post-harvest technology, is never mentioned. So options (a), (c) and (d) fail.
Tip: words like "solely", "only" and "always" usually make a statement too strong. One-third of the world's food is lost or wasted, as per the FAO.
Answer as per the official UPSC answer key.
Read the passage
According to the Food and Agriculture Organization, one-third of food produced for human consumption is lost or wasted globally. Food is lost or wasted throughout the supply chain, from initial agricultural production to final household consumption. The increasing wastage also results in land degradation by about 45%, mainly due to deforestation, unsustainable agricultural practices, and excessive groundwater extraction. The energy spent over wasted food results in about 3·5 billion tonnes of carbon dioxide production every year. Decay also leads to harmful emissions of other gases in the atmosphere. Addressing the loss and wastage of food in all forms is critical to complete the cycle of food sufficiency and food sustainability.
Based on the above passage, the following assumptions have been made :
- 1. The food distribution mechanism needs to be reimagined and made effective to reduce the loss and wastage of food.
- 2. Ensuring the reduction of wastage and loss of food is a social and moral responsibility of all citizens.
Which of the assumptions given above is/are valid?
Answer (c) & explanation
Both assumptions are valid (c). Step 1: the passage says food is lost "from initial agricultural production to final household consumption". The supply side, including distribution, is part of the problem, so it must be made effective (1). Step 2: losses also happen at the household level, so every citizen has a role in cutting waste (2). Step 3: the last line calls tackling waste "critical" for food sufficiency and sustainability, which supports both. So options (a), (b) and (d) fail.
Tip: an assumption is what the author must believe for the argument to hold. If the problem spans the whole chain, action is needed at every link of the chain. Simple habits like cooking only what is needed reduce household waste.
Answer as per the official UPSC answer key.
Read the passage
As inflation rises, even governments previously committed to budget discipline are spending freely to help households. Higher interest rates announced by central banks are supposed to help produce modest fiscal austerity, because to maintain stable debts while paying more to borrow, governments must cut spending or raise taxes. Without the fiscal backup, monetary policy eventually loses traction. Higher interest rates become inflationary, not disinflationary, because they simply lead governments to borrow more to pay rising debt-service costs. The risk of monetary unmooring is greater when public debt rises, because interest rates become more important to budget deficits.
Which of the following statements best reflects/reflect the most logical and rational inference/inferences that can be made from the passage?
- 1. Central banks cannot bring down inflation without budgetary backing.
- 2. The effects of monetary policy depend on the fiscal policies pursued by the government.
Select the correct answer using the code given below.
Answer (c) & explanation
Both inferences follow (c). Step 1: the key line is "Without the fiscal backup, monetary policy eventually loses traction." Monetary policy means the central bank raising interest rates; fiscal policy means government spending and taxes. Step 2: so rate hikes alone cannot cure inflation if the government keeps spending; the central bank needs budgetary backing (1). Step 3: the passage also says high rates can even turn inflationary when governments simply borrow more. So the effect of monetary policy depends on fiscal choices (2). Options (a), (b) and (d) fail.
Tip: learn the two words: monetary policy = RBI (interest rates, money supply); fiscal policy = government (budget, taxes). In India the RBI's Monetary Policy Committee targets 4% inflation.
Answer as per the official UPSC answer key.
Read the passage
As inflation rises, even governments previously committed to budget discipline are spending freely to help households. Higher interest rates announced by central banks are supposed to help produce modest fiscal austerity, because to maintain stable debts while paying more to borrow, governments must cut spending or raise taxes. Without the fiscal backup, monetary policy eventually loses traction. Higher interest rates become inflationary, not disinflationary, because they simply lead governments to borrow more to pay rising debt-service costs. The risk of monetary unmooring is greater when public debt rises, because interest rates become more important to budget deficits.
Based on the above passage, the following assumptions have been made :
- 1. Fiscal policies of governments are solely responsible for higher prices.
- 2. Higher prices do not affect the long-term government bonds.
Which of the assumptions given above is/are valid?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: assumption 1 says fiscal policies are "solely" responsible for higher prices. The passage only says government spending can weaken the central bank's fight against inflation. It never says spending is the only cause; supply shocks, for example, are not ruled out. Step 2: assumption 2 talks about long-term government bonds. The passage mentions debt-service costs, but says nothing about how prices affect long-term bonds. Step 3: neither idea is needed for the argument to work. So options (a), (b) and (c) fail.
Tip: reject any assumption with "solely" unless the passage clearly names one single cause. Also reject statements about things the passage never discusses, however sensible they sound.
Answer as per the official UPSC answer key.
What is the least possible number of cuts required to cut a cube into 64 identical pieces?
Answer (b) & explanation
The least number of cuts is 9 (b). Step 1: 64 identical small cubes means 64 = 4 × 4 × 4. So each of the three directions (length, breadth, height) must be split into 4 parts. Step 2: to split one direction into 4 parts you need 3 cuts, since cuts are always one less than pieces. Step 3: three directions × 3 cuts = 3 + 3 + 3 = 9 cuts. Option (a), 8, is too few. Options (c), 12, and (d), 16, waste cuts.
Tip: for n × n × n identical pieces, the least cuts are 3(n − 1). For 27 pieces: 3 × 2 = 6 cuts. If the cuts are not equal in each direction, use (a − 1) + (b − 1) + (c − 1).
8 cuts can make at most 4 × 4 × 3 = 48 pieces, so 8 is not enough.
Answer as per the official UPSC answer key.
In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, −, × each at most two times. What is the smallest non-negative value of the expression?
Answer (d) & explanation
The smallest non-negative value is 0 (d). Step 1: zero is the smallest non-negative number, so first check whether 0 is possible. Step 2: try 5 − 4 − 3 + 2 × 1. Multiplication comes first (BODMAS): 2 × 1 = 2. Step 3: then 5 − 4 − 3 + 2 = 0. We used minus twice, plus once and times once, which the rule ("each at most two times") allows. Since 0 is reachable, options (a) 3, (b) 2 and (c) 1 cannot be the smallest.
Tip: when asked for the smallest or largest value, test the extreme option first. If it works, you are done. Always remember that × and ÷ are done before + and −.
always test the extreme option first. If 0 works, nothing smaller can be the answer.
Answer as per the official UPSC answer key.
A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days?
Answer (c) & explanation
The men must increase by 20% (c). Step 1: total work = men × days. So if M men take 6k days, M × 6k = M′ × 5k, where M′ is the new number of men. Step 2: M′ = 6M/5 = 1.2M. Step 3: the increase is 0.2M, that is 20%. Note that k cancels out, so its value does not matter. Option (b), 16.67%, is the fall in days (1k out of 6k), a common mix-up. Options (a) and (d) are wrong.
Tip: men and days are inversely related. If days go from 6 to 5, men go from 5 to 6, an increase of 1 on 5 = 20%. Always take the percentage on the old value.
(b) is the trap: 50/3% is the cut in days for the reverse change, not the rise in men.
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.
X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?
Answer (c) & explanation
The minimum time is 6 hours 45 minutes (c). Step 1: work done per hour: X = 1/6, Y = 1/8, Z = 1/8. To finish fast, use X, the fastest, as often as possible: every other hour, since no one can work two hours in a row. Step 2: order X, Y, X, Z, X, Y for 6 hours: 3 × 1/6 + 3 × 1/8 = 1/2 + 3/8 = 7/8 done. Step 3: 1/8 is left. Hour 7 can be X again: (1/8) ÷ (1/6) = 3/4 hour = 45 minutes. Total 6 h 45 min. Options (a) and (b) are too short; (d) wastes time.
Tip: in "one worker at a time" questions, give the fastest worker every slot the rule allows, and let the fastest finish the leftover bit.
Answer as per the official UPSC answer key.
How many consecutive zeros are there at the end of the integer obtained in the product 12 × 24 × 36 × 48 × … × 2550?
Answer (d) & explanation
There are 200 zeros at the end (d). Step 1: each trailing zero comes from one 2 and one 5. There are far more 2s than 5s, so just count the 5s. Step 2: the term k^(2k) gives 2k × (number of 5s in k). Only multiples of 5 matter: k = 5, 10, 15, 20 give 10 + 20 + 30 + 40 = 100. Step 3: k = 25 = 5 × 5 has two 5s, so it gives 2 × 25 × 2 = 100. Total = 200 fives, so 200 zeros. Options (a), (b) and (c) miss the extra 5s.
Tip: in zero-counting, numbers like 25, 125 hide extra 5s. Forgetting them is the most common trap.
(c) 100 is what you get if you forget that 25 carries two 5s.
Answer as per the official UPSC answer key.
On January 1st, 2023, a person saved ₹ 1. On January 2nd, 2023, he saved ₹ 2 more than that on the previous day. On January 3rd, 2023, he saved ₹ 2 more than that on the previous day and so on. At the end of which date was his total savings a perfect square as well a perfect cube?
Answer (b) & explanation
His total was a perfect square and cube on 8th January (b). Step 1: daily savings are 1, 3, 5, 7, … (odd numbers). The sum of the first n odd numbers = n². So after n days he has n² rupees. Step 2: n² is also a perfect cube only when n itself is a cube: n = 1, 8, 27, … Step 3: n = 8 gives 8² = 64 = 4³, both a square and a cube. So the 8th day, 8th January. Option (a) gives 49 (not a cube); (c) gives 81 (not a cube). Option (d) is wrong.
Tip: remember 1 + 3 + 5 + … (n terms) = n². A number that is both a square and a cube is a sixth power: 1, 64, 729.
Answer as per the official UPSC answer key.
Read the passage
Today, if we consider cities such as New York, London and Paris as some of the most iconic cities in the world, it is because plans carrying a heavy systems approach were imposed on their precincts. The backbone of the systems theory is the process of translating social, spatial and cultural desirables into mathematical models using computing, statistics, optimization and an algorithmic way of formulating and solving problems. The early universities of the West which began to train professionals in planning, spawned some of the most ingenious planners, who were experts in these domains. This was because these very subjects were absorbed into the planning curriculum that had its roots in the social sciences, geography and architecture. Planning in India, and its education differ from the West.
Which one of the following statements best reflects the most logical and rational inference that can be made from the above passage?
Answer (a) & explanation
The best inference is that urban planning courses need a diverse, interdisciplinary approach (a). Step 1: the passage says cities like New York, London and Paris became iconic through a systems approach: computing, statistics and maths. Step 2: Western universities produced great planners because these subjects were added to a curriculum rooted in social sciences, geography and architecture. That is a mix of fields, so (a). Step 3: options (b) bureaucracy, (c) funds and (d) population and poverty bring in outside facts the passage never mentions.
Tip: an inference must come from the passage itself. Reject options that may be true about India but are not in the text. "Interdisciplinary" means combining many subjects.
Answer as per the official UPSC answer key.
Read the passage
Today, if we consider cities such as New York, London and Paris as some of the most iconic cities in the world, it is because plans carrying a heavy systems approach were imposed on their precincts. The backbone of the systems theory is the process of translating social, spatial and cultural desirables into mathematical models using computing, statistics, optimization and an algorithmic way of formulating and solving problems. The early universities of the West which began to train professionals in planning, spawned some of the most ingenious planners, who were experts in these domains. This was because these very subjects were absorbed into the planning curriculum that had its roots in the social sciences, geography and architecture. Planning in India, and its education differ from the West.
Based on the above passage, the following assumptions have been made :
- 1. India needs a new generation of urban professionals with knowledge relevant to modern urban practice.
- 2. Indian universities at present have no capacity or potential to impart training in systems approach.
Which of the assumptions given above is/are correct?
Answer (a) & explanation
Only assumption 1 is valid (a). Step 1: the passage praises Western planning education and then says "Planning in India, and its education differ from the West." This implies India needs planners trained in modern methods, so assumption 1 holds. Step 2: assumption 2 says Indian universities have "no capacity or potential". The passage only says Indian education is different; it never says it is incapable. Step 3: so assumption 2 is far too strong. Options (b), (c) and (d) fail.
Tip: "different" is not "incapable". Extreme words like "no capacity", "never" and "impossible" usually make an assumption invalid. India's cities are growing fast, which raises the need for skilled planners.
Answer as per the official UPSC answer key.
Read the passage
Not every voice on the internet commands the same kind of audience. When anonymous private entities with high capital can pay for more space for their opinions, they are effectively buying a louder voice. If political discourse in the digital sphere is a matter of outshining one’s opponent till the election is won, then the quality of politics suffers. The focus of social media is restricted to the promotion of content that generates more user engagement, regardless of how inflammatory the content may be.
Which one of the following statements best reflects the central idea of the above passage?
Answer (b) & explanation
The central idea is that social media are profit-making products, not moral institutions (b). Step 1: the passage says rich entities can pay for space and buy "a louder voice". Step 2: it also says platforms push content that brings engagement, "regardless of how inflammatory" it is. Both show a business that seeks profit, not fairness. Step 3: options (a), (c) and (d) praise social media (instant information, stronger democracy, a necessary part of life). The passage is critical, so they fail.
Tip: first decide the tone of the passage: positive or critical. Then drop every option with the opposite tone. This one passage is critical throughout.
Answer as per the official UPSC answer key.
Read the passage
Not every voice on the internet commands the same kind of audience. When anonymous private entities with high capital can pay for more space for their opinions, they are effectively buying a louder voice. If political discourse in the digital sphere is a matter of outshining one’s opponent till the election is won, then the quality of politics suffers. The focus of social media is restricted to the promotion of content that generates more user engagement, regardless of how inflammatory the content may be.
Based on the above passage, the following assumptions have been made :
- 1. Internet is not inclusive enough.
- 2. Internet can adversely affect the quality of politics in a country.
Which of the assumptions given above is/are valid?
Answer (c) & explanation
Both assumptions are valid (c). Step 1: the passage opens: "Not every voice on the internet commands the same kind of audience." Rich players can buy a louder voice. So the internet is not equally open to all, that is, not inclusive enough (1). Step 2: it says that if online politics is just about outshining opponents, "the quality of politics suffers." So the internet can harm politics (2). Step 3: both ideas sit directly in the text, so options (a), (b) and (d) fail.
Tip: when a statement closely restates a line in the passage, it is valid. Underline key lines while reading. "Inclusive" means giving everyone a fair chance to be heard.
Answer as per the official UPSC answer key.
222333 + 333222 is divisible by which of the following numbers?
Answer (b) & explanation
The sum is divisible by 3 and 37 but not by 2 (b). Step 1: break the bases: 222 = 6 × 37 and 333 = 9 × 37. Both are multiples of 3 and 37, so both terms, and their sum, are divisible by 3 and 37. Step 2: check 2: 222 is even, so 222^333 is even. 333 is odd, so 333^222 is odd. Step 3: even + odd = odd, so the sum is not divisible by 2. Options (a), (c) and (d) wrongly include 2 or exclude 37 or 3.
Tip: for divisibility of a sum, check each term. Even + odd is always odd. Spotting a common factor (here 111 = 3 × 37) saves big calculations.
Answer as per the official UPSC answer key.
What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?
Answer (a) & explanation
Water equal to 20% of the honey must be added (a). Step 1: take 100 litres of honey costing ₹1 a litre, so ₹100 in all. Step 2: a 20% gain means selling for ₹120. Since the mixture is sold at the honey price of ₹1 a litre, we need 120 litres of mixture. Step 3: water added = 120 − 100 = 20 litres, which is 20% of the honey. Options (b), (c) and (d) are too small. (Water is free, so all the extra volume is profit.)
Tip: in "sell at cost price and still gain" questions, the gain comes entirely from the free item. Gain% = water added as a % of the original liquid.
read the base: UPSC asks for water as a percent of honey, not of the mixture.
Answer as per the official UPSC answer key.
What is the rightmost digit preceding the zeros in the value of 3030?
Answer (d) & explanation
The digit before the zeros is 9 (d). Step 1: 30^30 = 3^30 × 10^30. The 10^30 gives 30 zeros, so the digit just before them is the unit digit of 3^30. Step 2: unit digits of powers of 3 repeat in a cycle of four: 3, 9, 7, 1. Step 3: divide 30 by 4: remainder 2. So take the second digit in the cycle: 9. Options (a) 1, (b) 3 and (c) 7 are the other digits in the cycle.
Tip: for unit digits of powers, find the cycle (most digits repeat every 4). Divide the power by 4 and use the remainder; a remainder of 0 means the last digit of the cycle.
Answer as per the official UPSC answer key.
421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?
Answer (c) & explanation
Three numbers work as the divisor (c). Step 1: the divisor must leave remainder 1 for both, so it must divide 421 − 1 = 420 and 427 − 1 = 426. Step 2: it must divide their HCF. 426 − 420 = 6, and 6 divides both, so HCF = 6. Divisors of 6: 1, 2, 3, 6. Step 3: a remainder of 1 needs a divisor greater than 1 (dividing by 1 leaves 0). So only 2, 3 and 6 remain: three numbers. Option (d), 4, wrongly counts 1.
Tip: the remainder must always be smaller than the divisor. That rule quietly removes small divisors in such questions.
counting 1 as a divisor gives (d). Dividing by 1 leaves remainder 0, not 1.
Answer as per the official UPSC answer key.
A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?
Answer (b) & explanation
Four bottle sizes are possible (b). Step 1: the bottle size must divide both 399 and 532 exactly, so it must be a divisor of their HCF. Step 2: 399 = 3 × 7 × 19 and 532 = 4 × 7 × 19. HCF = 7 × 19 = 133. Step 3: divisors of 133 are 1, 7, 19 and 133: four sizes. Options (a), (c) and (d) miscount.
Tip: "how many sizes" means count the divisors of the HCF; "the largest size" means the HCF itself. To count divisors quickly, write the number as primes: 7¹ × 19¹ gives (1 + 1)(1 + 1) = 4.
Answer as per the official UPSC answer key.
Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers each less than 10:
- 1. The unit digit of S can be 0.
- 2. The unit digit of S can be 9.
- 3. The unit digit of S can be 5.
Which of the statements given above are correct?
Answer (c) & explanation
Statements 1 and 3 are correct (c). Step 1: the primes below 10 are 2, 3, 5 and 7. We must pick three different ones, so there are only four possible sets. Step 2: list the sums: 2 + 3 + 5 = 10, 2 + 3 + 7 = 12, 2 + 5 + 7 = 14, 3 + 5 + 7 = 15. Step 3: unit digit 0 occurs (10), so 1 is true. Unit digit 5 occurs (15), so 3 is true. Unit digit 9 never occurs, so 2 is false. Options (a), (b) and (d) fail.
Tip: when the cases are few, simply list them all. Remember 1 is not a prime and 2 is the only even prime.
Answer as per the official UPSC answer key.
Read the passage
By the time children reach class 8, the bulk of them tend to be in the age range of 13 years to 15 years. But in our country, about a quarter of all children in class 8 struggle with reading simple texts and more than half are still unable to do basic arithmetic operations like division. Every year about 25 million young boys and girls from elementary school move into the life that lies for them beyond compulsory schooling. They cannot enter the workforce at least in the organized sector till they are 18. For many families, these children are the first from their families ever to get this far in school. Parents and children expect that such ‘graduates’ from school will go on to high school and college. Hardly anyone wants to go back to agriculture. On the other hand, abilities in terms of academic competencies are far lower than they should be even based on curricular expectations of class 8.
Based on the above passage, the following assumptions have been made :
- 1. For effective school education, parents have greater role than the governments.
- 2. School curriculum that conforms to today’s requirements and is uniform for the entire country may address the issues brought out.
Which of the assumptions given above is/are valid?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: assumption 1 says parents have a bigger role than governments. The passage mentions parents' expectations, but never compares their role with the government's. Step 2: assumption 2 suggests a uniform national curriculum. The passage says children fall short even of the existing class 8 curriculum. So the problem is learning, not the curriculum design; the passage proposes no uniform syllabus. Step 3: so options (a), (b) and (c) fail.
Tip: an assumption must be needed by the passage. Solutions the author never suggests are not assumptions. Surveys like ASER report similar gaps in basic reading and arithmetic.
Answer as per the official UPSC answer key.
Read the passage
By the time children reach class 8, the bulk of them tend to be in the age range of 13 years to 15 years. But in our country, about a quarter of all children in class 8 struggle with reading simple texts and more than half are still unable to do basic arithmetic operations like division. Every year about 25 million young boys and girls from elementary school move into the life that lies for them beyond compulsory schooling. They cannot enter the workforce at least in the organized sector till they are 18. For many families, these children are the first from their families ever to get this far in school. Parents and children expect that such ‘graduates’ from school will go on to high school and college. Hardly anyone wants to go back to agriculture. On the other hand, abilities in terms of academic competencies are far lower than they should be even based on curricular expectations of class 8.
Which one of the following statements best reflects the central idea conveyed by the passage?
Answer (c) & explanation
The central idea is that policy should align young people's skills with their expectations (c). Step 1: the passage says families expect class 8 "graduates" to go to high school and college, and hardly anyone wants to return to farming. Step 2: but their actual abilities are far below even class 8 level. This gap between expectations and competence is the core problem; fixing it is (c). Step 3: options (a) poverty and (b) money incentives are never discussed. Option (d) wants pass-outs to go back to farming, the opposite of the passage's mood.
Tip: the central idea usually ties together the two halves of a passage. Here: high hopes versus low skills.
Answer as per the official UPSC answer key.
Read the passage
We take it for granted now that science has a social responsibility. The idea would not have occurred to Newton or Galileo. They thought of science as an account of the world as it is, and the only responsibility that they acknowledged was to tell the truth. The idea that science is a social enterprise is modern, and it begins at the industrial revolution. We are surprised that we cannot trace a social sense further back, because we nurse the illusion that the industrial revolution ended a golden age.
Which one of the following statements best reflects the thinking of the author about the science?
Answer (d) & explanation
The author thinks science must pursue truth and also serve society (d). Step 1: the passage says Newton and Galileo saw science's only duty as "to tell the truth". Step 2: it adds that today "we take it for granted" that science has a social responsibility, an idea that began with the industrial revolution. Joining both gives (d). Step 3: option (c) reverses the link: the passage says the social sense began at the industrial revolution, not that science caused it. Options (a), scientists' commitment, and (b), scientific awareness, are not discussed.
Tip: when a passage moves from an old view to a new one, the best answer often joins both. India's Constitution (Article 51A) lists developing scientific temper as a fundamental duty.
Answer as per the official UPSC answer key.
Consider the sequence
A _ BCD _ BBCDABC _ DABC _ D
that follows a certain pattern. Which one of the following completes the sequence?
Answer (c) & explanation
The blanks are A, A, C, D (c). Step 1: break the sequence into blocks of five letters: A_BCD, _BBCD, ABC_D, ABC_D. Step 2: look for the rule: each block is ABCD with one letter doubled, and the doubled letter moves along: AABCD, ABBCD, ABCCD, ABCDD. Step 3: so the blanks are A, A, C, D. Option (d), A, A, D, C, swaps the last two. Options (a) and (b) break the first blocks.
Tip: in letter-series blanks, try splitting the line into equal blocks of 4, 5 or 6. A pattern usually shows up once the blocks line up.
Answer as per the official UPSC answer key.
Two persons P and Q enter into a business. P puts ₹ 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P’s share is ₹ 400 more than Q’s share out of the total profit of ₹ 2,000, what is the capital contributed by P?
Answer (a) & explanation
P contributed ₹30,000 (a). Step 1: profit shares: P + Q = 2,000 and P − Q = 400. So P gets 1,200 and Q gets 800, a ratio of 3 : 2. Step 2: profit is shared by capital × months: 8p : 10q = 3 : 2. So 16p = 30q, and p : q = 15 : 8. Step 3: the gap of 7 parts is ₹14,000, so one part = ₹2,000 and P's capital = 15 × 2,000 = ₹30,000 (Q's is ₹16,000; check: 30,000 − 16,000 = 14,000). Options (b), (c) and (d) fail the check.
Tip: in partnership questions, profit ratio = capital × time. Always check your answer against every given fact.
Answer as per the official UPSC answer key.
P’s salary is 20% lower than Q’s salary which is 20% lower than R’s salary. By how much percent is R’s salary more than P’s salary?
Answer (b) & explanation
R's salary is 56.25% more than P's (b). Step 1: let R = 100. Q is 20% lower: 80. P is 20% lower than Q: 80 − 16 = 64. Step 2: R is more than P by 100 − 64 = 36. Step 3: "more than P" means the base is P: 36/64 × 100 = 56.25%. Option (a) and the others use the wrong base or add the two 20% cuts as 40%. Two 20% cuts do not make 40%.
Tip: "X is how much more than Y" always divides by Y. Taking 100 for the top value makes chained percentages easy. Two successive cuts of 20% give a total cut of 36%, not 40%.
"more than P's salary" means divide by P, not by R.
Answer as per the official UPSC answer key.
A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?
Answer (d) & explanation
The result changes by 93.75% (d). Step 1: take an easy number, 4. The correct result is 4 × 4 = 16. The wrong result is 4 ÷ 4 = 1. Step 2: the change is 16 − 1 = 15. Step 3: as a percentage of the correct result: 15/16 × 100 = 93.75% (a fall). In general: correct = 4x, wrong = x/4, so the change is (4x − x/4)/4x = 15/16, whatever x is. Options (a), (b) and (c) are wrong.
Tip: percentage change is always measured on the correct (original) value. Picking a friendly number such as the divisor itself makes the arithmetic quick.
Answer as per the official UPSC answer key.
In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?
Answer (b) & explanation
20% failed in only one subject (b). Step 1: 15% failed both, so 85% passed in at least one subject. Step 2: passed both = 80 + 70 − 85 = 65% (adding English and Hindi counts the "both" group twice). Step 3: everyone is in one of three groups: passed both (65%), failed both (15%) or failed exactly one. So failed only one = 100 − 65 − 15 = 20%. Check: passed only English = 15%, only Hindi = 5%; total 20%. Options (a), (c) and (d) fail.
Tip: for two-subject pass/fail questions use: at least one = A + B − both. Draw two circles if you get confused.
Answer as per the official UPSC answer key.
A father said to his son, “n years back I was as old as you are now. My present age is four times your age n years back”. If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?
Answer (a) & explanation
The age difference is 30 years (a). Step 1: let the father be F and the son S. "n years back I was as old as you are now" means F − n = S, so n = F − S. Step 2: "my age is four times your age n years back": F = 4(S − n) = 4(S − F + S) = 4(2S − F). So 5F = 8S, giving F : S = 8 : 5. Step 3: 8 + 5 = 13 parts = 130 years, so one part = 10. F = 80, S = 50, difference = 30 years. Check: n = 30; the son 30 years back was 20, and 4 × 20 = 80. Options (b), (c) and (d) fail.
Tip: in age puzzles, note that the age difference never changes. Turn each sentence into one equation.
Answer as per the official UPSC answer key.
Consider the following :
- 1. 1000 litres = 1 m3
- 2. 1 metric ton = 1000 kg
- 3. 1 hectare = 10000 m2
Which of the above are correct?
Answer (d) & explanation
All three statements are correct (d). Step 1: a cube 1 m on each side holds 1000 litres. So 1 m³ = 1000 L (1 is right). Step 2: a metric ton, also called a tonne, is 1000 kg (2 is right). Step 3: a hectare is a square field 100 m × 100 m, so 1 hectare = 10,000 m² (3 is right). So options (a), (b) and (c), which leave one out, are wrong.
Tip: learn these everyday conversions: 1 litre = 1000 cm³; 1 hectare is about 2.47 acres; 1 km² = 100 hectares. Land records and farm questions use hectares often.
Answer as per the official UPSC answer key.
Read the passage
“The history of science is the real history of mankind.” In this striking epigram, a nineteenth-century writer links science with its background. Like most epigrams, its power lies in emphasizing by contrast an aspect of truth which may be easily overlooked. In this case, it is easy to overlook the relations between science and mankind, and to treat the former as some abstract third party, which can sometimes be praised for its beneficial influences, but frequently and conveniently blamed for the horrors of war. Science and mankind cannot be divorced from time to time at men’s convenience. Yet we have seen that, in spite of countless opportunities of improvement, the opening years of the present period of civilization have been dominated by international conflict. Is this the inevitable result of the progress of science or does the fault lie elsewhere?
Which of the following is/are emphatically conveyed by the author of the passage?
- 1. Without science, mankind could not have continued to exist till today.
- 2. It is the science that will ultimately determine the destiny of mankind.
Select the correct answer using the code given below.
Answer (d) & explanation
Neither statement is conveyed (d). Step 1: the author's main point is that science and mankind "cannot be divorced"; science is part of human history, not a separate "third party". Step 2: statement 1 says mankind could not have survived without science. The passage never says this. Statement 2 says science will decide mankind's destiny. The passage does not say this either. Step 3: in fact, the last question, "does the fault lie elsewhere?", hints that people, not science, may be to blame for wars. So options (a), (b) and (c) fail.
Tip: "emphatically conveyed" means the author clearly says it. Big claims like survival or destiny must be in the text, not just possible.
Answer as per the official UPSC answer key.
Read the passage
“The history of science is the real history of mankind.” In this striking epigram, a nineteenth-century writer links science with its background. Like most epigrams, its power lies in emphasizing by contrast an aspect of truth which may be easily overlooked. In this case, it is easy to overlook the relations between science and mankind, and to treat the former as some abstract third party, which can sometimes be praised for its beneficial influences, but frequently and conveniently blamed for the horrors of war. Science and mankind cannot be divorced from time to time at men’s convenience. Yet we have seen that, in spite of countless opportunities of improvement, the opening years of the present period of civilization have been dominated by international conflict. Is this the inevitable result of the progress of science or does the fault lie elsewhere?
Based on the above passage, the following assumptions have been made :
- 1. The horrors of modern life are the inevitable result of the progress of science.
- 2. The aspect of truth likely to be overlooked is that science is what man has made it.
Which of the assumptions given above is/are correct?
Answer (b) & explanation
Only assumption 2 is correct (b). Step 1: the passage says people wrongly treat science as an "abstract third party" that can be praised or blamed. The overlooked truth is that science belongs to mankind; it is what man makes of it (2). Step 2: assumption 1 says the horrors of modern life are the inevitable result of science. The author only asks this as a question ("Is this the inevitable result...?") and hints the fault may lie elsewhere. Step 3: so 1 is not assumed. Options (a), (c) and (d) fail.
Tip: a question asked by the author is not the author's belief. Read the closing question as a doubt, not a claim.
Answer as per the official UPSC answer key.
Read the passage
Only with long experience and opening of his wares on many a beach where his language is not spoken, will the merchant come to know the worth of what he carries, and what is parochial and what is universal in his choice. Such delicate goods as justice, love and honour, courtesy, and indeed all the things we care for, are valid everywhere but they are variously moulded and often differently handled, and sometimes nearly unrecognizable if you meet them in a foreign land, and the art of learning fundamental common values is perhaps the greatest gain of travel to those who wish to live at ease among their fellows.
When we meet other people while we travel, we learn to differentiate between
Answer (c) & explanation
Travel teaches us to tell local values from universal values (c). Step 1: the passage says the merchant, after opening his wares on many foreign beaches, learns "what is parochial and what is universal". Step 2: "parochial" means local or narrow. The goods are values like justice, love, honour and courtesy, valid everywhere but shaped differently in each land. So (c). Step 3: option (a), imagination and understanding, (b), communities and nationalities, and (d), friends and foes, are not in the passage.
Tip: when a passage uses a hard word, the answer often uses its simple meaning. Parochial = local; universal = common to all. The "merchant" here is a metaphor for the traveller.
Answer as per the official UPSC answer key.
Read the passage
Only with long experience and opening of his wares on many a beach where his language is not spoken, will the merchant come to know the worth of what he carries, and what is parochial and what is universal in his choice. Such delicate goods as justice, love and honour, courtesy, and indeed all the things we care for, are valid everywhere but they are variously moulded and often differently handled, and sometimes nearly unrecognizable if you meet them in a foreign land, and the art of learning fundamental common values is perhaps the greatest gain of travel to those who wish to live at ease among their fellows.
With reference to the above passage, the following assumptions have been made :
- 1. Travel leads to an understanding of humans.
- 2. Travel helps those who wish to learn fundamental common values.
- 3. A person with long experience in travel can resolve differences amongst people.
Which of the assumptions given above are valid?
Answer (a) & explanation
Assumptions 1 and 2 are valid (a). Step 1: the passage calls "the art of learning fundamental common values" the greatest gain of travel (2). Step 2: it adds this helps those "who wish to live at ease among their fellows", so travel helps us understand people (1). Step 3: assumption 3 says a well-travelled person can resolve differences among others. The passage talks only about the traveller's own understanding, not settling disputes. So options (b), (c) and (d) fail.
Tip: watch for statements that stretch a personal benefit into a social power. Understanding others is not the same as resolving their quarrels.
Answer as per the official UPSC answer key.
Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X + Y) is the greatest two-digit number, then what is the number of possible values of X?
Answer (d) & explanation
There are 8 possible values of X (d). Step 1: let X = 10a + b, so Y = 10b + a. Then X + Y = 11(a + b). The greatest two-digit number is 99, so 11(a + b) = 99, giving a + b = 9. Step 2: Y must also be a two-digit number, so b cannot be 0. That removes 90. Step 3: X can be 18, 27, 36, 45, 54, 63, 72, 81: 8 values. Option (c), 6, and the others miscount.
Tip: a number plus its reverse is always a multiple of 11; the difference is always a multiple of 9. Watch for hidden conditions like "Y is also two-digit", which rule out a zero digit.
90 looks valid, but its reverse, 09, is not a two-digit number.
Answer as per the official UPSC answer key.
Consider the following :
Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women
If the average weight of the women is 63 kg, then what is the average weight of the boys?
Answer (b) & explanation
The average weight of the boys is 42 kg (b). Step 1: the average weight of women is 63 kg, so 4 women weigh 4 × 63 = 252 kg. Step 2: 6 boys weigh the same as 4 women: 252 kg. Step 3: one boy, on average, weighs 252 ÷ 6 = 42 kg. The girls and men are extra information and can be ignored. Option (d), 63 kg, just repeats the women's figure. Options (a) and (c) are wrong.
Tip: CSAT often adds data you do not need. Find the shortest link between what is given and what is asked; here women to boys directly.
Answer as per the official UPSC answer key.
How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)?
Answer (a) & explanation
The hands coincide 3 times (a). Step 1: the hands meet every 12/11 hours, about 1 hour 5 minutes. In 12 hours they meet only 11 times, because between 11 and 1 they meet just once, at 12:00. Step 2: after 10:00 a.m., they meet at about 10:54, then at 12:00, then at about 1:05. Step 3: the next meeting is about 2:11, after the window. So 3 times. Option (b), 4, wrongly assumes once every hour.
Tip: hands meet 11 times in 12 hours and 22 times in a day. The 11-to-1 gap holds only one meeting, at 12 o'clock.
four hours does not mean four meetings. The 11 to 1 stretch has only one.
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Answer as per the official UPSC answer key.
The calendar for the year 2025 is same for
Answer (c) & explanation
2031 has the same calendar as 2025 (c). Step 1: an ordinary year moves the weekday forward by 1 day; a leap year by 2. Step 2: add the shifts from 2025: 2025 (1) + 2026 (1) + 2027 (1) + 2028 (2, leap) + 2029 (1) + 2030 (1) = 7, which is 0 extra days. So 2031 starts on the same weekday as 2025. Step 3: 2031 is also not a leap year, like 2025, so the whole calendar matches. Options (a) 2029, (b) 2030 and (d) 2033 do not add up to a multiple of 7.
Tip: keep adding odd days until you reach a multiple of 7, and check that both years are the same type (leap or ordinary).
Answer as per the official UPSC answer key.
Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements :
- 1. (p − r)2(qs) is even.
- 2. (q − s)q2s is even.
- 3. (q + r)2(p + s) is odd.
Which of the statements given above are correct?
Answer (d) & explanation
All three statements are correct (d). Step 1: rule: a product is even if any factor is even; it is odd only if all factors are odd. p, q are odd; r, s are even. Step 2: statement 1: (p − r)² × q × s. s is even, so the product is even. Statement 2: (q − s) × q² × s: again s makes it even. Step 3: statement 3: q + r = odd + even = odd, so its square is odd. p + s = odd + even = odd. Odd × odd = odd. So all three are true, and options (a), (b) and (c) fail.
Tip: odd ± even = odd; odd ± odd = even. One even factor makes a whole product even.
Answer as per the official UPSC answer key.
What is the angle between the minute hand and hour hand when the clock shows 4:25 hours?
Answer (c) & explanation
The angle is 17.5° (c). Step 1: the minute hand moves 6° a minute. At 25 minutes it is 25 × 6 = 150° from 12. Step 2: the hour hand moves 30° each hour and 0.5° each minute. At 4:25 it is 4 × 30 + 25 × 0.5 = 120 + 12.5 = 132.5°. Step 3: the gap is 150 − 132.5 = 17.5°. Option (a), 12.5°, is just the hour hand's extra movement. Options (b) and (d) are wrong.
Tip: use the formula angle = |30H − 5.5M|. Here |120 − 137.5| = 17.5°. If the answer is above 180°, subtract it from 360°.
(b) 15° forgets that the hour hand also moves during the 25 minutes.
Answer as per the official UPSC answer key.
Read the passage
Conventional classrooms, by emphasizing fixed duration over learning effectiveness, resign themselves to variable outcomes. The tyranny of the classroom is that every learner is subjected to the same set of lectures in the same way for the same duration. In the end, a few learners shine, some survive, and the rest are left behind. After the fixed duration, the classroom model moves on, with not a thought spared for those left behind. This is how we end up with 10 percent employability in our graduates after a decade and half of formal education. Repeating the same ineffectual script in the realm of skill education will not produce different results.
Which of the following statements best reflects/reflect the most logical and rational inference/inferences that can be made from the passage?
- 1. In conventional classroom learning, the central goal is duration of learning rather than attainment of competency.
- 2. Conventional classrooms encourage one-size-fits-all approach and stamp out all differentiation.
Select the correct answer using the code given below.
Answer (c) & explanation
Both inferences follow (c). Step 1: the passage says conventional classrooms emphasise "fixed duration over learning effectiveness". So the goal is time spent, not skill gained (1). Step 2: it calls it "the tyranny of the classroom" that every learner gets "the same set of lectures in the same way for the same duration". That is a one-size-fits-all approach that ignores differences among learners (2). Step 3: both ideas come straight from the text, so options (a), (b) and (d) fail.
Tip: when a statement paraphrases a key line, accept it. The passage's remedy is competency-based learning, where each learner moves on only after mastering a skill.
Answer as per the official UPSC answer key.
Read the passage
Conventional classrooms, by emphasizing fixed duration over learning effectiveness, resign themselves to variable outcomes. The tyranny of the classroom is that every learner is subjected to the same set of lectures in the same way for the same duration. In the end, a few learners shine, some survive, and the rest are left behind. After the fixed duration, the classroom model moves on, with not a thought spared for those left behind. This is how we end up with 10 percent employability in our graduates after a decade and half of formal education. Repeating the same ineffectual script in the realm of skill education will not produce different results.
Based on the above passage, the following assumptions have been made :
- 1. As a large number of workers in our country are employed in unorganized sector, India does not need to change its present conventional classroom system of education.
- 2. Even with its present conventional classroom system of education, India produces sufficient number of skilled workers to fully realize the benefits of demographic dividend.
Which of the assumptions given above is/are valid?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: the passage attacks the classroom system: some learners are left behind and only 10 percent of graduates are employable. It warns that copying this model in skill education will fail. Step 2: assumption 1 says India need not change its system. Assumption 2 says the present system produces enough skilled workers. Both defend the current system, the exact opposite of the passage. Step 3: the unorganised sector is not even mentioned. So options (a), (b) and (c) fail.
Tip: an assumption must agree with the author's line of argument. If a statement contradicts the author's conclusion, reject it at once.
Answer as per the official UPSC answer key.
Read the passage
When a child reaches adolescence, there is apt to be a conflict between the parents and the child, since the latter considers himself to be by now quite capable of managing his own affairs, while the former are filled with parental solicitude, which is often a disguise for love of power. Parents consider, usually, that the various moral problems which arise in adolescence are peculiarly their province. The options they express, however, are so dogmatic that the young seldom confide in them, and usually go their own way in secret.
Based on the above passage, the following assumptions have been made :
- 1. The adolescent does not feel comfortable with his parents because they tend to be dominating and assertive.
- 2. The adolescent of modern times does not have much respect for parents.
Which of the assumptions given above is/are valid?
Answer (a) & explanation
Only assumption 1 is valid (a). Step 1: the passage says parental care is "often a disguise for love of power" and parents' opinions are "so dogmatic" that the young seldom confide in them. So the adolescent is uneasy because parents are dominating (1). Step 2: assumption 2 says adolescents lack respect for parents. The passage speaks of not confiding, not of disrespect. Step 3: it also never mentions "modern times". So 2 adds new ideas, and options (b), (c) and (d) fail.
Tip: not confiding in someone is different from not respecting them. Watch for options that swap one feeling for another.
Answer as per the official UPSC answer key.
Read the passage
When a child reaches adolescence, there is apt to be a conflict between the parents and the child, since the latter considers himself to be by now quite capable of managing his own affairs, while the former are filled with parental solicitude, which is often a disguise for love of power. Parents consider, usually, that the various moral problems which arise in adolescence are peculiarly their province. The options they express, however, are so dogmatic that the young seldom confide in them, and usually go their own way in secret.
Which one of the following statements best reflects the central idea of the above passage?
Answer (a) & explanation
The central idea is that parents may not be of much help as children grow into adults (a). Step 1: the passage shows adolescents feel able to manage their own lives, while parents are dogmatic. Step 2: so the young "seldom confide" in parents and go their own way in secret. Parents end up of little help, which is (a). The word "may" keeps it suitably mild. Step 3: option (b) says parents' involvement is "unnecessary", which is too absolute. Options (c) nuclear families and (d) stubborn adolescents are not discussed.
Tip: prefer moderate words ("may", "often") over absolute ones ("unnecessary", "never") in central-idea questions.
Answer as per the official UPSC answer key.
What is the number of fives used in numbering a 260-page book?
Answer (b) & explanation
There are 56 fives (b). Step 1: count fives in the units place: 5, 15, 25, …, 255. That is one in every 10 pages: 26 fives. Step 2: count fives in the tens place: 50–59, 150–159 and 250–259, ten each: 30 fives. (Pages 55, 155, 255 get counted in both places, which is right, since they each have two fives.) Step 3: the hundreds place has no 5, because pages stop at 260. Total = 26 + 30 = 56. Options (a), (c) and (d) miscount.
Tip: count digit by digit, place by place. Do not try to list numbers; count the units, tens and hundreds places separately.
55 and 155 have two fives each; the place-by-place count handles them without double counting.
Answer as per the official UPSC answer key.
What is the sum of the first 28 terms in the following sequence?
1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, …
Answer (b) & explanation
The sum of the first 28 terms is 84 (b). Step 1: group the terms: (1), (1, 2), (1, 3, 2), (1, 4, 3, 2), (1, 5, 4, 3, 2) … Group n has n terms and its sum is 1 + 2 + … + n. Step 2: 1 + 2 + … + 7 = 28 terms, so the first 28 terms are exactly groups 1 to 7. Step 3: sum = 1 + 3 + 6 + 10 + 15 + 21 + 28 = 84. Options (a), (c) and (d) are off by one.
Tip: odd-looking sequences often break into groups. Find where each group starts (here, every new 1) and the pattern becomes clear.
Answer as per the official UPSC answer key.
A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?
Answer (d) & explanation
P costs ₹1,350 (d). Step 1: start with the smallest item. Let Q = 100. R is 20% more: 120. P is 25% more than R: 120 + 30 = 150. Total = 370 parts. Step 2: 370 parts = ₹3,330, so one part = ₹9. Step 3: P = 150 × 9 = ₹1,350 (R = ₹1,080, Q = ₹900; total ₹3,330). Options (a), (b) and (c) do not fit the total.
Tip: take 100 for the item everything else is based on. Then convert parts to rupees in one step. Check with the total.
Answer as per the official UPSC answer key.
If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?
Answer (a) & explanation
A must be 9 (a). Step 1: AB + CD = 1CE. Two two-digit numbers add to at most 198, so the hundreds digit 1 comes from a carry. Step 2: in the tens column, A + C + (carry from units) gives a result ending in C, with a carry of 1. So A + carry = 10. Step 3: A is a single digit, so the carry from units must be 1 and A = 9. (Example: 97 + 25 = 122 fails distinctness, but 98 + 27 = 125 works: A = 9, C = 2, E = 5.) Option (d) is wrong, since A is fixed.
Tip: in letter-sum puzzles, start with the carries. A sum of two two-digit numbers can carry only 1 into the hundreds.
Answer as per the official UPSC answer key.
Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible?
Answer (d) & explanation
1. Start with z. If z = 2, then 2y > 6 means y ≥ 4 and x > 8: impossible. So z = 1.
2. With z = 1, 2y > 3 gives y ≥ 2. y = 2 needs x > 4: x = 5, 6, 7. y = 3 needs x > 6: x = 7. y = 4 needs x > 8: none.
3. Four triplets: (5, 2, 1), (6, 2, 1), (7, 2, 1), (7, 3, 1).
Answer as per the official UPSC answer key.
The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples. Consider the following statements :
- 1. The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples.
- 2. The total cost of one orange and one mango is equal to the cost of one apple.
Which of the statements given above is/are correct?
Answer (c) & explanation
Both statements are correct (c). Step 1: write o, m, a for the prices. 4o + 6m + 8a = 2(o + 2m + 5a) = 2o + 4m + 10a. Step 2: simplify: 2o + 2m = 2a, so o + m = a. One orange and one mango cost the same as one apple: statement 2 is right. Step 3: statement 1: (3o + 5m + 9a) − (4o + 6m + 8a) = a − o − m = 0. The two totals are equal, so statement 1 is right too. Options (a), (b) and (d) fail.
Tip: form one equation and simplify it first. Then test each statement by subtracting the two sides and checking for zero.
Answer as per the official UPSC answer key.
Read the passage
When an international team of scientists pumped a carbon dioxide and water mix into underground basalt rocks, basic chemistry took over. The acidic mixture dissolved rocks’ calcium and magnesium and formed limestone. Basically carbon dioxide is converted into stone, exclaimed the scientists.
Which one of the following statements best reflects the most logical, rational and practical suggestion implied by the passage?
Answer (b) & explanation
The best suggestion is that this can be a method of carbon sequestration (b). Step 1: scientists pumped CO₂ and water into basalt rocks. The acid dissolved calcium and magnesium and formed limestone. Step 2: the key line is "carbon dioxide is converted into stone". Turning CO₂ into rock locks it away for good, which is carbon sequestration (capture and storage). So (b). Step 3: option (a), making commercial limestone, and (c), sourcing minerals, are side effects, not the point. Option (d) misreads the chemistry as an aim.
Tip: ask why the experiment matters, not just what happened. This idea, called mineral carbonation, is being tested in Iceland. It helps reach net-zero by removing CO₂ from the air.
Answer as per the official UPSC answer key.
Read the passage
Geographers analyzed 175 satellite images of ocean colour, which is an indicator of phytoplankton productivity at the ocean’s surface, and found that giant icebergs are responsible for storing up to 20 percent of carbon in the Southern Ocean. The researchers discovered that melting water from giant icebergs which contains iron and other nutrients, supports hitherto unexpectedly high levels of phytoplankton growth.
Based on the above passage, the following assumptions have been made :
- 1. Giant icebergs have a bearing on primary productivity and food chains of the Southern Ocean.
- 2. Melting of giant icebergs can produce climate change effects and impact world fisheries.
Which of the assumptions given above is/are valid?
Answer (c) & explanation
Both assumptions are valid (c). Step 1: meltwater from giant icebergs carries iron and nutrients that boost phytoplankton. Phytoplankton are the base of the ocean food chain, so icebergs affect primary productivity and food chains (1). Step 2: icebergs help store up to 20 percent of the Southern Ocean's carbon. So changes in iceberg melting can affect the climate, and more or less plankton affects fish stocks (2). Step 3: both follow from the passage, so options (a), (b) and (d) fail.
Tip: remember the chain: nutrients → phytoplankton → fish. Phytoplankton also absorb CO₂ through photosynthesis, which is why oceans are a major carbon sink. Iron is often the missing nutrient in the Southern Ocean.
Answer as per the official UPSC answer key.
Read the passage
Evolution has endowed caterpillars that feed on corn with a unique ability, they can induce the plant to turn off its defence against insect predators. This helps caterpillars to eat more and grow faster. The agent that causes this effect is the caterpillar’s faeces or frass. The find could throw new light on compounds associated with plant response to pathogens like fungi or bacteria.
Which one of the following statements best reflects the most logical, rational and practical message conveyed by the passage?
Answer (c) & explanation
The practical message is that this can help develop organic, eco-friendly pesticides (c). Step 1: caterpillars make the corn plant switch off its defences through a natural compound in their droppings (frass). Step 2: once we understand how this switch works, we can find ways to keep plant defences on, a natural, chemical-free way to protect crops. That points to sustainable pest control, as UPSC's key takes it. Step 3: option (a), using caterpillars on weeds, is not suggested. Option (b), medical antimicrobials, goes beyond plants. Option (d), genetically modified caterpillars, is far-fetched.
Tip: in "practical message" questions, choose the option closest to the field of the passage, here crops and pests, not medicine. Biological pest control is part of integrated pest management.
Answer as per the official UPSC answer key.
325 + 227 is divisible by
Answer (c) & explanation
The number is divisible by 10 (c). Step 1: write everything as powers of 2. 32 = 2⁵, so 32⁵ = 2²⁵. Step 2: 2²⁵ + 2²⁷ = 2²⁵ × (1 + 2²) = 2²⁵ × (1 + 4) = 5 × 2²⁵. Step 3: it has a factor 5 and a factor 2, so it is divisible by 10. It has no factor 3, 7 or 11, so options (a), (b) and (d) fail.
Tip: when the bases are powers of the same number, convert them to one base. Then take out the smaller power as a common factor. This turns a huge sum into a simple product.
when the bases differ, check if they are powers of the same number.
Answer as per the official UPSC answer key.
Let p and q be positive integers satisfying p < q and p + q = k. What is the smallest value of k that does not determine p and q uniquely?
Answer (c) & explanation
The smallest such k is 5 (c). Step 1: p and q are positive whole numbers with p < q. Step 2: k = 3: only 1 + 2, so unique. k = 4: only 1 + 3, because 2 + 2 is not allowed (p must be less than q). Unique again. Step 3: k = 5: both 1 + 4 and 2 + 3 work. Two answers, so k = 5 is the first value that does not fix p and q. Option (b), 4, forgets the p < q rule. Options (a) and (d) are wrong.
Tip: test the smallest cases one by one. Read the conditions carefully: "p < q" rules out equal numbers.
Answer as per the official UPSC answer key.
A person walks 100 m straight from his house, turns left and walks 100 m, again turns left and walks 300 m, then turns right and walks 100 m to reach his office. In which direction does he walk initially from his house if his office is exactly in the North-East direction?
Answer (c) & explanation
He first walked South (c). Step 1: test the options. Suppose he starts walking South 100 m. A left turn while facing South points East: 100 m East. Another left points North: 300 m North. A right turn points East: 100 m East. Step 2: net movement: East = 100 + 100 = 200 m; North = 300 − 100 = 200 m. Step 3: equal East and North means exactly North-East. Options (a), (b) and (d) do not give equal East and North parts.
Tip: in direction questions, testing each option is often faster than working backwards. Remember: facing South, your left is East and your right is West.
'left' depends on the way he faces. Facing South, his left is East, not West.
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.
A person walks 100 m Westward, then turns left and walks 100 m. He then takes 225° turn clockwise. In which direction is he walking now?
Answer (d) & explanation
He is now walking North-East (d). Step 1: he walks West. A left turn while facing West points South. Step 2: now turn 225° clockwise from South: 90° brings him to West, 180° to North, and 45° more (total 225°) to North-East. Step 3: so he faces North-East. Options (a), (b) and (c) come from turning the wrong way or miscounting the angle.
Tip: break big turns into 90° steps plus a remainder. Clockwise goes N → E → S → W; anticlockwise goes N → W → S → E. A 45° step lands on the corner directions (NE, SE, SW, NW).
the distances walked do not matter; only the facing direction does.
Answer as per the official UPSC answer key.
A Statement is given followed by two Conclusions numbered I and II. Consider the Statement and the Conclusions.
Statement : India is the world's largest producer of milk.
Conclusion-I : India is the world's largest exporter of milk.
Conclusion-II : India does not import milk.
Which one of the following is correct?
Answer (d) & explanation
Neither conclusion follows (d). Step 1: the statement only says India produces the most milk. Step 2: conclusion 1, largest exporter, does not follow. A country can be the biggest producer and also the biggest consumer, exporting very little. That is actually India's case. Step 3: conclusion 2, India does not import milk, does not follow either. A big producer may still import some milk products. Production says nothing about trade either way. So options (a), (b) and (c) fail.
Tip: producing, consuming, exporting and importing are four different things; do not jump from one to another. India has been the world's top milk producer since 1998, thanks to the White Revolution (Operation Flood).
don't bring in outside facts; judge only from the statement.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Question : What are the values of m and n, where m and n are natural numbers?
Statement-I : m + n > mn and m > n.
Statement-II : The product of m and n is 24.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (c) & explanation
Both statements together are needed (c). Step 1: statement I: m + n > mn can be rewritten as (m − 1)(n − 1) < 1. With natural numbers, this means one of them is 1. Since m > n, n = 1, but m could be anything. Not enough. Step 2: statement II: mn = 24 allows 1 × 24, 2 × 12, 3 × 8 and 4 × 6. Not enough. Step 3: together: n = 1, so m = 24. A single answer. Options (a), (b) and (d) fail.
Tip: rearrange inequalities into a product form like (m − 1)(n − 1). It quickly shows which values are possible.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Question : What is the time required to download the software?
Statement-I : The size of the software is 12 megabytes.
Statement-II : The transfer rate is 2·4 kilobytes per second.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (c) & explanation
Both statements together are needed (c). Step 1: download time = size ÷ transfer rate. Step 2: statement I gives only the size (12 MB). Statement II gives only the rate (2.4 KB per second). Neither alone gives a time. Step 3: together they give one definite time (about 12 × 1024 ÷ 2.4 seconds, roughly 85 minutes). So (c). Options (a), (b) and (d) fail.
Tip: in data sufficiency you only need to know that one answer is fixed; you need not calculate it. Watch units: MB and KB differ by 1024 (or 1000).
Answer as per the official UPSC answer key.
Read the passage
In a robust democracy, reality, howsoever inconvenient it may be, finds its expression both in the speech of political leaders and the other social forms of assertion. The existence of the real has to be transparent, both through its circulation in and by the media as well as its argumentative articulation in deliberative democracy. A normatively responsible media through its communication effect has the responsibility to circulate the content of reality without distortion.
Which one of the following statements best reflects the crux of the above passage?
Answer (a) & explanation
The crux is that responsible media should not distort reality in an ideal democracy (a). Step 1: the passage says in a robust democracy, reality, "howsoever inconvenient", must be expressed openly by leaders and society. Step 2: its last sentence says a responsible media must "circulate the content of reality without distortion". That is (a). Step 3: option (b) calls fake news inherent, and (d) says media and leaders cannot be controlled: both are negative and unsupported. Option (c), no restrictions at all on speech, is too broad; the passage talks about truthful reporting, not unlimited freedom.
Tip: the last sentence of a short passage often states its crux. In India, Article 19(1)(a) protects free speech, with reasonable limits under Article 19(2).
Answer as per the official UPSC answer key.
Read the passage
Now-a-days there is a growing trend to use interconnected home devices. As consumers increasingly network their homes, the connected home device manufacturers and service providers will seek to overcome “thin profit margins by gathering more of our personal data—with or without our agreement—turning the home into a corporate storefront”. Corporate marketers will have powerful incentives to observe consumer behaviour to understand the buying needs and preferences of the device owners.
Which one of the following statements best reflects the most logical, rational and practical message implied by the passage?
Answer (d) & explanation
The message is that connected home devices can bring security and privacy risks (d). Step 1: the passage says device makers will gather "more of our personal data—with or without our agreement". Step 2: it says homes may become a "corporate storefront", with marketers watching consumer behaviour. That is a clear warning about privacy. So (d). Step 3: options (a) and (b) praise data use for industry and growth; the passage does not. Option (c), comfort and quality of life, is also not the passage's point.
Tip: catch the tone. Phrases like "with or without our agreement" signal a warning. India's Digital Personal Data Protection Act, 2023, requires consent for most data use.
Answer as per the official UPSC answer key.
Read the passage
Green growth involves rethinking growth strategies with regard to the impacts on environmental sustainability and the environmental resources available to poor and vulnerable groups. In rethinking growth, we need to focus on the current reality of a resource-constrained world. Resource intensive and, in particular energy intensive processes will need to make way for more efficient and resource frugal development strategies if we are to avoid an economic dead end or a world in which only a small elite is able to enjoy affluence in the midst of a sea of poverty.
Which one of the following statements best reflects the crux of the above passage?
Answer (c) & explanation
The crux is that high environmental standards are now needed for steady, inclusive growth (c). Step 1: the passage says we live in a resource-constrained world. Energy-heavy processes must give way to efficient, frugal strategies. Step 2: otherwise we face "an economic dead end" (no steady growth) or a world where only "a small elite" is rich (no inclusive growth). So green growth is a must for good growth: (c). Step 3: options (a), (b) and (d) treat the environment and growth as enemies, or call degradation unavoidable. The passage argues the opposite.
Tip: "green growth" means growth and the environment going together. Reject options that set them against each other.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Question : What are the unique values of x and y, where x, y are distinct natural numbers?
Statement-I : x/y is odd.
Statement-II : xy = 12
Which one of the following is correct in respect of the above Question and the Statements?
Answer (c) & explanation
Both statements together are needed (c). Step 1: statement I: x/y is odd. Endless pairs work, like (3, 1), (5, 1), (6, 2). Not enough. Step 2: statement II: xy = 12 with distinct numbers: (1, 12), (2, 6), (3, 4) and their reverses. Not enough. Step 3: together, check x/y for each pair: 12/1 = 12 (even), 6/2 = 3 (odd), 4/3 is not whole. Only x = 6, y = 2 works. Unique. Options (a), (b) and (d) fail.
Tip: list all cases from the more limited statement, then filter them with the other. If exactly one survives, both are needed together.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
A certain amount was distributed among X, Y and Z.
Question : Who received the least amount?
Statement-I : X received 4/5 of what Y and Z together received.
Statement-II : Y received 2/7 of what X and Z together received.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (c) & explanation
Both statements together are needed (c). Step 1: statement I: X = 4/5 of (Y + Z). So X gets 4/9 of the total, but how Y and Z split the rest is unknown. Not enough. Step 2: statement II: Y = 2/7 of (X + Z). So Y gets 2/9 of the total, but X and Z's split is unknown. Not enough. Step 3: together: X = 4/9, Y = 2/9, so Z = 3/9. Y received the least. Options (a), (b) and (d) fail.
Tip: "A gets a/b of what the others get" means A's share = a/(a + b) of the total. This turns ratios into fractions of the whole quickly.
"4/5 of what Y and Z received" is not 4/5 of the total. Convert it: 4 parts against 5 parts means 4/9.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Question : If the average marks in a class are 60, then what is the number of students in the class?
Statement-I : The highest marks in the class are 70 and the lowest marks are 50.
Statement-II : Exclusion of highest and lowest marks from the class does not change the average.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (d) & explanation
Even both statements together are not enough (d). Step 1: we need the number of students, given the average is 60. Step 2: statement I gives the highest (70) and lowest (50) marks. Statement II says removing them does not change the average. But 70 and 50 themselves average 60, so removing them keeps the average at 60 for any class size. Step 3: so the statements are always consistent but never fix the number. Options (a), (b) and (c) fail.
Tip: when a statement is true for every possible value, it gives no information. Check whether a fact actually narrows the answer.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
There are three distinct prime numbers whose sum is a prime number.
Question : What are those three numbers?
Statement-I : Their sum is less than 23.
Statement-II : One of the numbers is 5.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (a) & explanation
Statement I alone is enough; Statement II alone is not (a). Step 1: if 2 were one of the numbers, the sum of 2 + two odd primes is even and bigger than 2, so not prime. So all three are odd primes. Step 2: statement I (sum < 23): possible odd sums are 15 (3, 5, 7), 19 (3, 5, 11) and 21 (3, 7, 11). Only 19 is prime, so the numbers are 3, 5, 11. Enough. Step 3: statement II (one number is 5): 3 + 5 + 11 = 19 and 5 + 7 + 11 = 23 both work. Not enough. So (a); options (b), (c) and (d) fail.
Tip: rule out the even prime 2 first in prime-sum questions; it changes odd/even results.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Question : Is (x + y) an integer?
Statement-I : (2x + y) is an integer.
Statement-II : (x + 2y) is an integer.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (d) & explanation
Even both statements together are not enough (d). Step 1: adding them: (2x + y) + (x + 2y) = 3(x + y) is an integer. So x + y is an integer divided by 3, which may or may not be whole. Step 2: test x = y = 1/3: 2x + y = 1 and x + 2y = 1 (integers), but x + y = 2/3, not an integer. Step 3: test x = y = 1: both statements hold and x + y = 2, an integer. Two different answers, so the question cannot be settled. Options (a), (b) and (c) fail.
Tip: in data sufficiency, try fractions. Many traps assume x and y must be whole numbers when the question never says so.
adding the two statements looks like it settles it. Always test a fraction before you accept "integer" claims.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
A person buys three articles p, q and r for ₹ 50. The price of the article q is ₹ 16 which is the least.
Question : What is the price of the article p?
Statement-I : The cost of p is not more than that of r.
Statement-II : The cost of r is not more than that of p.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (c) & explanation
Both statements together are needed (c). Step 1: p + q + r = 50 and q = 16, so p + r = 34. Step 2: statement I says p ≤ r, so p could be 17 or less. Statement II says r ≤ p, so p could be 17 or more. Each alone leaves many values. Step 3: together, p ≤ r and r ≤ p force p = r = 17. A single answer. (q = 16 is still the least, as stated.) Options (a), (b) and (d) fail.
Tip: "not more than" (≤) and "not less than" (≥) together mean "equal to". Look for two statements that squeeze a value from both sides.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
P, Q, R and S appeared in a test.
Question : Has P scored more marks than Q?
Statement-I : The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S.
Statement-II : The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (d) & explanation
1. Test with numbers that obey both statements.
2. P = 1, Q = 3, R = 0, S = 4. Statement I: 1 + 3 = 0 + 4. Statement II: 1 + 4 = 5 is more than 3 + 0 = 3. Both hold, and P is less than Q.
3. P = 5, Q = 1, R = 2, S = 4. Statement I: 6 = 6. Statement II: 9 is more than 3. Both hold, and now P is more than Q.
4. Same statements, different answers: even together they are not enough. (d).
Answer as per the official UPSC answer key.
Read the passage
Unlike religion and science, poetry does not posit or expect any belief in absolute truths. Those forces or individuals who claim to have absolute truths in their grasp tend to turn dictatorial and tyrannical. Truth usually does not admit any contradictions or imperfections. It is unitarian. It is, therefore, not of much use for poetry. Poetry abides by the plurality of life and existence. Perhaps poetry follows reality which is plural, anachronistic, full of contradictions. Against the tyranny of truth, poetry remains a partisan of democratic reality. Against the arrogance of power, wealth and hierarchy, poetry proposes both humility and defiance.
Which one of the following statements best reflects the most logical and rational message conveyed by the above passage?
Answer (d) & explanation
The message is that poetry is a form of dynamic resistance against tyranny and bigotry (d). Step 1: the passage says those who claim absolute truth turn "dictatorial and tyrannical". Step 2: poetry stands "against the tyranny of truth" and, against power and hierarchy, offers "humility and defiance". Defiance against power is resistance: (d). Step 3: option (a) narrows the idea to human imperfection. Option (b), poetry is "anathema to truth", and (c), poetry is only feeling, misstate it; the passage says poetry follows plural reality, not that it hates truth.
Tip: the closing lines often carry the main message. Words like "against" and "defiance" point to resistance.
Answer as per the official UPSC answer key.
Read the passage
The flower was not invented to please us. It flaunted its petals and spread its perfume to attract an insect. The insect carries the pollen from flower to flower so that pollen is not carried away by wind and thus not wasted. What we call a flower’s beauty is merely a by-product and a human invention. The perfume is not there to please us, it pleases us because it is there and we have been conditioned to it.
Based on the above passage, the following assumptions have been made :
- 1. The author of the passage believes that flowers are creations of Nature’s luxury.
- 2. The author of the passage does not believe in the usefulness of flowers except as things of beauty.
Which of the assumptions given above is/are valid?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: the author says the flower's petals and perfume have a purpose: to attract insects that carry pollen, so it is not wasted. Step 2: assumption 1 calls flowers a "luxury" of Nature. But the author sees them as useful, not as luxury. Step 3: assumption 2 says the author sees flowers as useful only for beauty. The author says beauty is "merely a by-product" and a human idea. Both statements reverse the author's view, so options (a), (b) and (c) fail.
Tip: when a passage argues "X is not for Y but for Z", reject options that say X is for Y. Pollination by insects is a classic example of mutual benefit in nature.
Answer as per the official UPSC answer key.
A Question is given followed by two Statements I and II. Consider the Question and the Statements.
Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q.
Question : What is the difference of their ages?
Statement-I : The age of P is greater than the age of Q.
Statement-II : The sum of their ages is 11/6 times their difference.
Which one of the following is correct in respect of the above Question and the Statements?
Answer (a) & explanation
Statement II alone is enough; Statement I alone is not (a). Step 1: let P's age be 10a + b and Q's be 10b + a. Sum = 11(a + b); difference = 9(a − b). Step 2: statement II: 11(a + b) = (11/6) × 9(a − b). So 2(a + b) = 3(a − b), giving a = 5b. Only b = 1, a = 5 works: ages 51 and 15, difference 36. Enough. Step 3: statement I only says P is older; many pairs fit (like 21 and 12, or 93 and 39). Not enough. So (a).
Tip: for reversed-digit numbers, remember: sum = 11 × (digit sum); difference = 9 × (digit gap). These two facts solve most such puzzles.
Answer as per the official UPSC answer key.
A Main Statement is followed by four Statements labelled P, Q, R and S. Choose the ordered pair of the Statements where the first Statement implies the second, and the two Statements are logically consistent with the Main Statement.
Main Statement : Pradeep becomes either a Director or a Producer.
Statement P : Pradeep is a Director.
Statement Q : Pradeep is a Producer.
Statement R : Pradeep is not a Director.
Statement S : Pradeep is not a Producer.
Select the correct answer.
Answer (c) & explanation
Both SP and RQ are valid pairs (c). Step 1: the main statement says Pradeep becomes either a Director or a Producer. So if one is false, the other must be true. Step 2: S, "not a Producer", implies P, "a Director". So SP works. Step 3: R, "not a Director", implies Q, "a Producer". So RQ works too. Both pairs are consistent with the main statement. Options (a), (b) and (d) leave one out.
Tip: for "either A or B", the valid pairs are always "not A → B" and "not B → A". The pairs "A → not B" are not safe, because both might be true.
the pair must start with a negative (not X) and end with the other choice (Y), never the other way round.
Answer as per the official UPSC answer key.
If a + b means a − b; a − b means a × b; a × b means a ÷ b; a ÷ b means a + b, then what is the value of 10 + 30 − 100 × 50 ÷ 25? (Operations are to be replaced simultaneously)
Answer (d) & explanation
The value is −25 (d). Step 1: replace every sign at the same time: + becomes −, − becomes ×, × becomes ÷, ÷ becomes +. So 10 + 30 − 100 × 50 ÷ 25 becomes 10 − 30 × 100 ÷ 50 + 25. Step 2: do × and ÷ first (BODMAS): 30 × 100 = 3000, ÷ 50 = 60. Step 3: 10 − 60 + 25 = −25. Options (a), (b) and (c) come from changing signs one at a time or ignoring the order of operations.
Tip: rewrite the whole expression with new signs before calculating. Then apply BODMAS: division and multiplication before addition and subtraction.
replacing one sign at a time changes signs you have already replaced. Swap all of them together.
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.
If P means 'greater than (>)'; Q means 'less than (<)'; R means 'not greater than (≯)'; S means 'not less than (≮)' and T means 'equal to (=)', then consider the following statements :
- 1. If 2x(S)3y and 3x(T)4z, then 9y(P)8z.
- 2. If x(Q)2y and y(R)z, then x(R)z.
Which of the statements given above is/are correct?
Answer (d) & explanation
Neither statement is correct (d). Step 1: decode: P = >, Q = <, R = ≤ (not greater), S = ≥ (not less), T = =. Step 2: statement 1: 2x ≥ 3y and 3x = 4z, so x = 4z/3. Then 8z/3 ≥ 3y, that is 8z ≥ 9y. The claim 9y > 8z is the opposite, so 1 is wrong. Step 3: statement 2: x < 2y and y ≤ z give only x < 2z. Try y = z = 5, x = 8: x < 10 holds, but x > z. So x ≤ z need not hold; 2 is wrong. Options (a), (b) and (c) fail.
Tip: decode symbols first, then test a counter-example. One case that breaks a statement is enough to reject it.
Answer as per the official UPSC answer key.
If in a certain code, 'ABCD' is written as 24 and 'EFGH' is written as 1680, then how is 'IJKL' written in that code?
Answer (a) & explanation
IJKL is written as 11880 (a). Step 1: use alphabet positions: A = 1, B = 2, C = 3, D = 4. ABCD = 1 × 2 × 3 × 4 = 24. Step 2: check: E, F, G, H = 5, 6, 7, 8. 5 × 6 × 7 × 8 = 1680. The rule is the product of positions. Step 3: I, J, K, L = 9, 10, 11, 12. 9 × 10 × 11 × 12 = 90 × 132 = 11880. Options (b), (c) and (d) are wrong products.
Tip: in number codes for letters, first try the sum of positions, then the product. Learn the positions: E = 5, J = 10, O = 15, T = 20 (remember "EJOT").
Answer as per the official UPSC answer key.
If in a certain code, 'POT' is written as ATOP and 'TRAP' is written as APART, then how is 'ARENA' written in that code?
Answer (d) & explanation
ARENA is written as AANERA (d). Step 1: look at the first example: POT reversed is TOP; adding A in front gives ATOP. Step 2: check the second: TRAP reversed is PART; with A in front: APART. So the rule is: reverse the word, then put A in front. Step 3: ARENA reversed is ANERA. With A in front: AANERA. Options (a), (b) and (c) do not follow the rule.
Tip: in coding questions, test your rule on every example before applying it. Reversal plus a fixed added letter is a common pattern.
Answer as per the official UPSC answer key.
What will come in place of * in the sequence 3, 14, 39, 84, *, 258?
Answer (b) & explanation
The missing number is 155 (b). Step 1: take the differences: 14 − 3 = 11, 39 − 14 = 25, 84 − 39 = 45. Step 2: take the differences again: 25 − 11 = 14, 45 − 25 = 20. These rise by 6, so the next ones are 26 and 32. Step 3: next first differences: 45 + 26 = 71, then 71 + 32 = 103. So * = 84 + 71 = 155, and 155 + 103 = 258 checks out. Options (a), (c) and (d) fail the check.
Tip: if the first differences show no pattern, take differences of differences. Always confirm with the last given term.
Answer as per the official UPSC answer key.
In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q − S = 2S and T = R + S + 3, then what is the value of P + R − T?
Answer (b) & explanation
1. Q − S = 2S means Q = 3S. From the list, (S, Q) is (4, 12) or (5, 15).
2. If S = 4, Q = 12: T = R + 7 must come from 5, 10, 15. No pair works. So S = 5, Q = 15.
3. Then T = R + 8 from 4, 10, 12: R = 4, T = 12, and P = 10. P + R − T = 10 + 4 − 12 = 2.
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.