CSAT 2020: every question, solved
80 questions from the official UPSC Prelims 2020 paper, in paper order. Tap an option; the answer and the reason appear instantly.
Read the passage
In India, over the last decade or so, labour has been departing agriculture, but is only going to construction and unregistered manufacturing which are not markedly better jobs. Services, where labour tends to be most productive, are not generating the additional jobs the country needs. India will need 24 million or so jobs over the next decade. The new sector, e-commerce, can at best close only half the jobs gap. Only those sectors that drive domestic demand such as health and education can comfortably fill the other half.
Which one of the following is best implied in the passage?
Answer (d) & explanation
The passage best implies that more social-sector spending is vital for large-scale job creation (d). Step 1: it says only health and education "can comfortably fill the other half" of the jobs gap. So spending on these sectors is key to creating jobs. That is (d). Step 2: option (c) says services are reducing unemployment. The passage says they are not generating enough jobs, so (c) is false. Step 3: option (a), stopping rural-urban migration, and option (b), better working conditions in construction, are not the passage's point.
Tip: look for the line that offers a solution; it usually holds the implication. Health and education are labour-intensive, so they create many jobs per rupee spent.
Answer as per the official UPSC answer key.
Read the passage
In India, the current focus on the right to privacy is based on some new realities of the digital age. A right is a substantive right only if it works in all situations, and for everyone. A right to free expression for an individual about her exploitation, for instance, is meaningless without actual availability of security that guarantees that private force cannot be used to thwart this right. The role of the State, therefore, is not just to abstain from preventing rightful free expression, but also to actively ensure that private parties are not able to block it.
On the basis of the above passage, the following assumptions have been made :
- 1. State should have some institutions to ensure its appropriate role in a digital society.
- 2. State should ensure that private parties do not violate the citizens’ right to privacy.
- 3. Digital economy is not compatible with the idea of not violating the citizens’ privacy.
Which of the above assumptions is/are valid?
Answer (a) & explanation
Assumptions 1 and 2 are valid (a). Step 1: the passage says the State must "actively ensure that private parties are not able to block" citizens' rights. So the State should stop private firms from violating privacy (2). Step 2: doing this needs proper institutions, such as regulators (1). Step 3: assumption 3 says a digital economy cannot respect privacy. That contradicts the passage, which wants the right to work "in all situations". So options (b), (c) and (d) fail.
Tip: privacy was declared a fundamental right in the Puttaswamy case (2017). The Digital Personal Data Protection Act, 2023 set up a Data Protection Board to enforce it. In CSAT, though, rely on the passage.
Answer as per the official UPSC answer key.
Read the passage
One of the biggest ironies around water is that it comes from rivers and other wetlands. Yet it is seen as divorced from them. While water is used as a resource, public policy does not always grasp that it is a part of the natural ecosystem. Efforts at engineering water systems are thus efforts at augmenting water supply rather than strengthening the capacities of ecological systems.
Which one of the following is the most logical and rational inference that can be made from the above passage?
Answer (c) & explanation
The inference is that wetlands must be seen as more than just open sources of water (c). Step 1: the passage says policy treats water as a resource "divorced" from wetlands. It ignores the wetland as a living ecosystem. So wetlands should be valued for more than water. That is (c). Step 2: option (b) asks to expand engineered water systems. That repeats the very approach the passage criticises. Step 3: option (a), the Ramsar Convention, is outside knowledge not in the passage. Option (d), charging for water, is not discussed.
Tip: avoid options that rely on facts the passage never gives, even if true. India has 90+ Ramsar sites, but that does not make (a) the inference here.
Answer as per the official UPSC answer key.
Read the passage
Asset allocation is the most important investment decision we will ever make, and sadly, most of us do not give that decision the importance it deserves. We are adamant about seeking predictability with our future. We tend to think of investing in risky assets as extremely volatile and value eroding. We also dislike fluctuating returns and the loss of control of investment. We think our money is best left idle, unproductive but safe. There is no asset that is risk-free. We could lose our jobs, our homes can lose value, our banks can go bankrupt, our bonds can default, the government can collapse and companies we chose fondly may cease to exist. But we cannot live life assuming that all these extreme events are waiting to happen, and all at the same time. All these extreme forms of risks we know will not manifest at the same time.
Which one of the following statements best implies the suggestion given by the author of the passage?
Answer (a) & explanation
The author suggests spreading wealth across different assets to cut risk (a). Step 1: the passage says no asset is risk-free, but all risks "will not manifest at the same time". So holding many kinds of assets means losses in one are offset by gains in another. That is diversification, option (a). Step 2: option (d), investing is risky, just restates a fact; it is not a suggestion. Step 3: option (b) makes risk-taking a necessary part of personality, which overstates. Option (c), hiring an asset manager, is not mentioned.
Tip: "don't put all your eggs in one basket" is the core idea. When asked for a suggestion, pick an action that solves the problem the passage describes.
Answer as per the official UPSC answer key.
Read the passage
Although most of the Genetically Modified (GM) crops cultivated now are genetically engineered for a single trait, in future, crops genetically engineered for more than one trait will be the norm. Thus, biotechnology’s role in agriculture and the regulation of the same cannot be understood solely in the context of the current generation of GM crops. Instead, there is a need to take a comprehensive look, taking into account various aspects, including socio-economic impacts, so that the potential of the technology can be harnessed while minimizing negative impacts. Given the importance of biotechnology in developing varieties that can help in climate change mitigation and adaptation, not using biotechnology as a part of the climate change action plan cannot be an option. Domestic regulation of biotechnology cannot be viewed in isolation of trade policy and obligations under various international treaties and conventions.
With reference to the above passage, the following assumptions have been made :
- 1. Biotechnology regulation is an evolving process.
- 2. Participation of people is needed in policy decisions regarding biotechnology regulation.
- 3. Biotechnology regulation should take into account socio-economic aspects in decision-making.
- 4. Wider involvement of political executive in biotechnology regulation improves its effectiveness in dealing with the country’s trade policies and international obligations.
Which of the above assumptions are valid?
Answer (b) & explanation
Assumptions 1 and 3 are valid (b). Step 1: the passage says regulation must look beyond "the current generation" of GM crops. So biotech regulation keeps evolving (1). Step 2: it says regulation must include "socio-economic impacts". So social and economic aspects count (3). Step 3: assumption 2, public participation, and assumption 4, a wider role for the political executive in trade policy, are not mentioned in the passage. So options (a), (c) and (d) fail.
Tip: check each statement against a line in the passage. If you cannot point to a line, the statement is not a valid assumption, however sensible it sounds. India's GM crop approvals are made by the Genetic Engineering Appraisal Committee (GEAC).
Answer as per the official UPSC answer key.
Read the passage
Although most of the Genetically Modified (GM) crops cultivated now are genetically engineered for a single trait, in future, crops genetically engineered for more than one trait will be the norm. Thus, biotechnology’s role in agriculture and the regulation of the same cannot be understood solely in the context of the current generation of GM crops. Instead, there is a need to take a comprehensive look, taking into account various aspects, including socio-economic impacts, so that the potential of the technology can be harnessed while minimizing negative impacts. Given the importance of biotechnology in developing varieties that can help in climate change mitigation and adaptation, not using biotechnology as a part of the climate change action plan cannot be an option. Domestic regulation of biotechnology cannot be viewed in isolation of trade policy and obligations under various international treaties and conventions.
Which one of the following statements best implies the crux of the passage?
Answer (c) & explanation
The crux is that biotechnology's role is not limited to current GM crop priorities (c). Step 1: the passage says its role "cannot be understood solely in the context of the current generation of GM crops". That is (c), almost word for word. Step 2: option (a) is about the precautionary principle, and option (b) about biotech's present use in climate work. Neither is discussed. Step 3: option (d), that negative impacts are not understood, is not the main point.
Tip: the crux is the central claim, often stated directly. When an option repeats a key sentence in plain words, it is usually right. Options that bring in new topics are traps.
Answer as per the official UPSC answer key.
How many zeroes are there at the end of the following product? 1 × 5 × 10 × 15 × 20 × 25 × 30 × 35 × 40 × 45 × 50 × 55 × 60
Answer (a) & explanation
The product ends in 10 zeros (a). Step 1: each zero needs one 2 and one 5. Step 2: count the 5s. The 12 numbers from 5 to 60 each give one 5. 25 and 50 give one extra each. Total = 14 fives. Step 3: count the 2s. Only the even numbers give 2s: 10 (one), 20 (two), 30 (one), 40 (three), 50 (one), 60 (two). Total = 10 twos. Zeros = the smaller count = 10. Option (c), 14, counts only the 5s. Options (b) and (d) are also wrong.
Tip: usually 2s are plentiful and 5s are scarce. Here most numbers are odd multiples of 5, so the 2s run out first. Always count both.
here the 2s run out first. Counting only the 5s gives 14, which is a trap option.
Answer as per the official UPSC answer key.
Let XYZ be a three-digit number, where (X + Y + Z) is not a multiple of 3. Then (XYZ + YZX + ZXY) is not divisible by
Answer (b) & explanation
The sum is not divisible by 9 (b). Step 1: in XYZ + YZX + ZXY, each digit appears once in every place (hundreds, tens, units). So the sum = 111X + 111Y + 111Z = 111(X + Y + Z). Step 2: 111 = 3 × 37. So the sum is divisible by 3 (a), by 37 (c) and by (X + Y + Z) (d). Step 3: to be divisible by 9, we need a second factor of 3. That would have to come from X + Y + Z, but the question says it is not a multiple of 3. So the sum is not divisible by 9.
Tip: check with numbers: 124 + 241 + 412 = 777 = 111 × 7. 777 ÷ 9 is not whole.
Answer as per the official UPSC answer key.
Let p, q, r and s be natural numbers such that p – 2016 = q + 2017 = r – 2018 = s + 2019. Which one of the following is the largest natural number?
Answer (c) & explanation
r is the largest (c). Step 1: call the common value k. Then p − 2016 = k gives p = k + 2016. q + 2017 = k gives q = k − 2017. Step 2: r − 2018 = k gives r = k + 2018. s + 2019 = k gives s = k − 2019. Step 3: compare: r has the biggest number added, so r is the largest. p is second. q and s are smaller. Options (a), (b) and (d) fail.
Tip: setting a chain of equal expressions to one letter, k, makes comparison easy. Watch the signs: "p minus 2016" means p is bigger than k, while "q plus 2017" means q is smaller than k.
Answer as per the official UPSC answer key.
How many five-digit prime numbers can be obtained by using all the digits 1, 2, 3, 4 and 5 without repetition of digits?
Answer (a) & explanation
No such prime exists, so the answer is zero (a). Step 1: any number made from all of 1, 2, 3, 4 and 5 has a digit sum of 1 + 2 + 3 + 4 + 5 = 15. Step 2: 15 is divisible by 3, so every such number is divisible by 3. Step 3: a number divisible by 3 (and bigger than 3) is not prime. So there are zero such primes. Options (b), (c) and (d) fail.
Tip: before counting arrangements, check the digit sum. If it is divisible by 3, no arrangement can be prime. This trick saves you from listing 120 numbers.
Answer as per the official UPSC answer key.
In the sum
⊗ + 1⊗ + 5⊗ + ⊗⊗ + ⊗1 = 1⊗⊗
for which digit does the symbol ⊗ stand?
Answer (b) & explanation
The symbol stands for 3 (b). Step 1: test the options. Put ⊗ = 3. Step 2: left side: 3 + 13 + 53 + 33 + 31 = 133. Step 3: right side: 1⊗⊗ = 133. Both sides match, so ⊗ = 3. Check another: ⊗ = 2 gives 2 + 12 + 52 + 22 + 21 = 109, but 1⊗⊗ = 122. No match. Options (a), (c) and (d) fail.
Tip: when an equation has one unknown digit and four options, plugging in is quickest. Algebra also works: the left side is 24⊗ + 61 and the right side is 100 + 11⊗, so 13⊗ = 39 and ⊗ = 3.
Trying the four options is quicker than any algebra here.
Answer as per the official UPSC answer key.
If you have two straight sticks of length 7·5 feet and 3·25 feet, what is the minimum length can you measure?
Answer (b) & explanation
The minimum length you can measure is 0·25 foot (b). Step 1: by adding and subtracting the two sticks, you can measure any multiple of their HCF, and nothing smaller. Step 2: write both in quarter-feet: 7·5 feet = 30 quarters; 3·25 feet = 13 quarters. Step 3: HCF(30, 13) = 1 quarter, which is 0·25 foot. For example, 30 − 2 × 13 = 4 quarters, and 13 − 3 × 4 = 1 quarter. Option (a), 0·05, is too small. Options (c) and (d) are not the minimum.
Tip: the smallest measurable length with two rods is their HCF. Convert decimals to whole units first to find it easily.
Answer as per the official UPSC answer key.
A simple mathematical operation in each number of the sequence 14, 18, 20, 24, 30, 32, ... results in a sequence with respect to prime numbers. Which one of the following is the next number in the sequence?
Answer (c) & explanation
The next number is 38 (c). Step 1: subtract 1 from each term: 14 − 1 = 13, 18 − 1 = 17, 20 − 1 = 19, 24 − 1 = 23, 30 − 1 = 29, 32 − 1 = 31. Step 2: these are prime numbers in order: 13, 17, 19, 23, 29, 31. Step 3: the next prime after 31 is 37. Add 1 back: 38. Option (a), 34, would need 33, not prime. Option (b), 36, needs 35, not prime. Option (d), 40, skips 37.
Tip: when a question hints at primes, try adding or subtracting 1 from each term. Know the primes up to 100 by heart.
Answer as per the official UPSC answer key.
One page is torn from a booklet whose pages are numbered in the usual manner starting from the first page as 1. The sum of the numbers on the remaining pages is 195. The torn page contains which of the following numbers?
Answer (b) & explanation
The torn page has 7 and 8 (b). Step 1: find the total before tearing. 1 + 2 + … + 20 = 20 × 21 ÷ 2 = 210. 1 to 19 gives only 190, which is less than 195, so the booklet had 20 pages. Step 2: missing sum = 210 − 195 = 15. Step 3: a torn leaf has two consecutive numbers that add to 15: 7 + 8. Option (a), 5 + 6 = 11. Option (c), 9 + 10 = 19. Option (d), 11 + 12 = 23. None of these is 15.
Tip: use n(n + 1) ÷ 2 for the sum of 1 to n. Find the smallest total just above the given sum; the difference is the torn page.
Answer as per the official UPSC answer key.
Consider the following arrangement that has some missing letters :
abab_b_bcb_dcdcded_d
The missing letters which complete the arrangement are
Answer (c) & explanation
The missing letters are a, c, c, e (c). Step 1: there are 20 letters. Split them into blocks of five: abab_ | b_bcb | _dcdc | ded_d. Step 2: each block alternates two letters: ababa, bcbcb, cdcdc, deded. Each new block moves one letter forward. Step 3: the blanks are a, c, c, e. That is option (c). Options (a), (b) and (d) break the alternating pattern.
Tip: count the total letters, then try equal blocks. A clean split (here 4 blocks of 5) usually shows the rule at once.
Answer as per the official UPSC answer key.
Let A3BC and DE2F be four-digit numbers where each letter represents a different digit greater than 3. If the sum of the numbers is 15902, then what is the difference between the values of A and D?
Answer (c) & explanation
1. Units: C + F ends in 2 and both digits are at least 4, so C + F = 12, carry 1. Tens: B + 2 + 1 ends in 0, so B = 7, carry 1.
2. Hundreds: 3 + E + 1 ends in 9, so E = 5. Thousands: A + D = 15.
3. Digits left (greater than 3, not 5 or 7): C, F = 4, 8 and A, D = 6, 9. Difference = 3.
Answer as per the official UPSC answer key.
Two Statements S1 and S2 are given below followed by a Question :
S1 : There are not more than two figures on any page of a 51-page book.
S2 : There is at least one figure on every page.
Question : Are there more than 100 figures in that book?
Which one of the following is correct in respect of the above Statements and the Question?
Answer (c) & explanation
S1 and S2 together are not sufficient (c). Step 1: S1 says at most 2 figures per page. S2 says at least 1 figure per page. Step 2: with 51 pages, the total lies between 51 × 1 = 51 and 51 × 2 = 102. Step 3: 102 is above 100, but 51 is not. So the answer could be "yes" or "no". Even together, the statements do not settle it. Options (a), (b) and (d) fail.
Tip: in data sufficiency, find the full possible range. If the range crosses the question's line (here 100), the data are not enough. S1 alone gives 0 to 102; S2 alone gives 51 or more; neither settles it.
Answer as per the official UPSC answer key.
Consider the following data :
| Average marks in English | Average marks in Hindi | |
|---|---|---|
| Girls | 9 | 8 |
| Boys | 8 | 7 |
| Overall average marks | 8·8 | x |
What is the value of x in the above table?
Answer (a) & explanation
x is 7·8 (a). Step 1: in English, girls average 9 and boys 8. The class average of 8·8 is much nearer 9. So most of the class are girls. Step 2: try 10 students: 8 girls and 2 boys. (8 × 9 + 2 × 8) ÷ 10 = 88 ÷ 10 = 8·8. It fits. So the ratio is 4 : 1. Step 3: Hindi, same class: (8 × 8 + 2 × 7) ÷ 10 = 78 ÷ 10 = 7·8. Options (b), (c) and (d) do not fit this ratio.
Tip: a weighted average sits closer to the bigger group. Use the alligation idea: distances 0·2 and 0·8 give the ratio 4 : 1.
Answer as per the official UPSC answer key.
A family of two generations consisting of six members P, Q, R, S, T and U has three males and three females. There are two married couples and two unmarried siblings. U is P's daughter and Q is R's mother-in-law. T is an unmarried male and S is a male. Which one of the following is correct?
Answer (b) & explanation
R is S's wife (b). Step 1: Q is R's mother-in-law. So Q is in the older generation, and R married Q's child. Step 2: the two unmarried siblings must be T (unmarried male) and U (P's daughter). So R's spouse is the remaining child, S, a male. The couples are P–Q and S–R. Step 3: males: P, S, T. Females: Q, R, U. So R is S's wife. Option (a) fails because U is unmarried. Option (c) fails because S is married. So (d) fails too.
Tip: in family puzzles, first count generations and couples. Then place unmarried people; the married pairs follow.
Answer as per the official UPSC answer key.
If in a particular year 12th January is a Sunday, then which one of the following is correct?
Answer (c) & explanation
12th July is a Sunday if the year is a leap year (c). Step 1: days from 12 January to 12 July = 31 (Jan) + 28 (Feb) + 31 (Mar) + 30 (Apr) + 31 (May) + 30 (Jun) = 181 days. In a leap year, February has 29, so it is 182. Step 2: 182 = 7 × 26, an exact number of weeks. So in a leap year, 12 July falls on the same day, Sunday. Step 3: option (d) says the opposite, so it fails. Options (a) and (b) about 15 July do not work: 15 July would be Wednesday (leap) or Tuesday (non-leap).
Tip: count days between dates and divide by 7. The remainder tells how many days the weekday moves forward.
Answer as per the official UPSC answer key.
Read the passage
Private investment in general is volatile. Foreign private investment is more volatile because the available investment avenues are significantly greater (i.e., the entire world). Therefore, the responsibility of providing employment cannot be left to Foreign Direct Investment (FDI). The current FDI inflows are volatile over time and, across sectors and regions, which is a necessary consequence of their search for the highest returns. The adverse consequences are unstable employment and an accentuation of income and regional inequalities. A probable positive consequence of foreign investment is the inflow of new technology and its subsequent diffusion. However, the technology diffusion is not at all certain because the existing state of physical and human capital in India may prove inadequate for the diffusion.
With reference to the above passage, the following assumptions have been made :
- 1. Relying on foreign investment in the long run is not an economically sound policy.
- 2. Policies must be undertaken to reduce volatility in foreign private investment.
- 3. Policies must be undertaken to strengthen domestic private investment.
- 4. Public investment should be given priority over private investment.
- 5. Substantial public investment in education and health should be undertaken.
Which of the above assumptions is/are valid?
Answer (b) & explanation
Assumptions 1, 3 and 5 are valid (b). Step 1: the passage says jobs "cannot be left to FDI". So relying on foreign investment in the long run is unwise (1), and domestic private investment must be strengthened (3). Step 2: it says weak human capital blocks the spread of technology. So spending on education and health is needed (5). Step 3: assumption 2 fails because the passage calls FDI volatility a "necessary consequence", which policy cannot remove. Assumption 4, putting public over private investment, is not argued. So options (a), (c) and (d) fail.
Tip: if a passage calls something unavoidable, reject options that ask policy to prevent it.
Answer as per the official UPSC answer key.
Read the passage
Many opportunities to harness the highly skewed, seasonal and spatial distribution of monsoon flows, which occur in a four-month period from June to September annually, have been lost. Since these few months account for most of the rainfall and consequent freshwater availability, the need for holding rainwater in reservoirs, for subsequently releasing it for use over the year, is a necessity nobody can afford to overlook. Climate change will continue to affect weather conditions and create water shortages and excesses. While millions suffer from droughts and floods, waters in the country’s many rivers flow unutilized, and are discharged into the sea every year.
With reference to the above passage, which of the following could be the most rational and practical implications for India?
- 1. Inter-linking of rivers should be undertaken.
- 2. A network of dams and canals should be built across the country for proper distribution of water.
- 3. Farmers should be provided easy loans for digging borewells.
- 4. Usage of water for agriculture should be regulated by law.
- 5. Distribution of river water among regions should be regulated by the Union Government.
Select the correct answer using the code given below.
Answer (a) & explanation
Implications 1 and 2 are rational and practical (a). Step 1: the passage says monsoon water should be stored in reservoirs and moved from flood-hit to drought-hit areas, instead of flowing into the sea. This points to inter-linking rivers (1) and a network of dams and canals (2). Step 2: statement 3, loans for borewells, would pull more groundwater; the passage does not suggest it. Step 3: statement 4, a law on farm water use, and statement 5, Union control of river sharing, are not discussed. So options (b), (c) and (d) fail.
Tip: India's Ken–Betwa link, whose foundation stone was laid in December 2024, is the first project under the national river-linking plan.
Answer as per the official UPSC answer key.
Read the passage
People will invest in education whenever they are granted the economic freedom to fully enjoy its benefits. Again, this is for the obvious reason that the return on education increases as the level of economic freedom rises. When people, thanks to lower tax rates, are allowed to retain most of the higher income that they gain from each incremental level of education, it makes eminent sense to invest in education. On the other hand, when the government decides to tax the higher income of educated individuals at even higher rates, it makes very little sense to invest in educating oneself further. The same incentives apply to parents who decide on whether to invest in their children’s education.
With reference to the above passage, the following assumptions have been made :
- 1. Lower tax rates in a country invariably translate into greater investments in higher education.
- 2. Investment in the education of children ensures their economic freedom.
- 3. Economic freedom has a positive impact on building up human capital.
Which of the above assumptions is/are valid?
Answer (c) & explanation
Only assumption 3 is valid (c). Step 1: the passage says when people are free to keep the returns on their efforts, they invest in education. That builds human capital. So economic freedom helps human capital (3). Step 2: assumption 1 says lower taxes invariably lead to more investment in higher education. "Invariably" (always) overstates. Step 3: assumption 2 reverses the cause. The passage says freedom drives education, not that education ensures freedom. So options (a), (b) and (d) fail.
Tip: watch for reversed cause and effect. "A leads to B" does not mean "B leads to A". Also, "invariably" and "always" need very strong support.
Answer as per the official UPSC answer key.
Read the passage
Our urban bodies cannot possibly ensure sustainable delivery of water in our cities unless financing mechanisms are put in place. Water delivery requires heavy investment in collecting it from a natural source, treating it to make it potable, and laying a distribution network of pipes for delivery to the users. It also requires investments in sewerage infrastructure and sewage treatment plants so that the sewers can carry the wastewater to these plants to ensure that no untreated sewage is discharged back into natural water bodies. If our cities were rich enough to meet the entire cost, water could be delivered free. They are not.
What is the most logical and crucial message conveyed by the passage?
Answer (a) & explanation
The message is that urban local bodies must recover costs through user charges (a). Step 1: the passage says water delivery needs heavy investment, and cities cannot meet "the entire cost" themselves. So water cannot be free; users must pay. That is (a). Step 2: option (b), that local bodies are inefficient, is not raised. Option (d), capping city population, is also not raised. Step 3: option (c) says the shortage cannot be solved. That is defeatist; the passage offers a way, user charges.
Tip: when a passage stresses cost, the message usually concerns who pays. Choose the option that offers the passage's own solution, not an extreme one.
Answer as per the official UPSC answer key.
Read the passage
Our urban bodies cannot possibly ensure sustainable delivery of water in our cities unless financing mechanisms are put in place. Water delivery requires heavy investment in collecting it from a natural source, treating it to make it potable, and laying a distribution network of pipes for delivery to the users. It also requires investments in sewerage infrastructure and sewage treatment plants so that the sewers can carry the wastewater to these plants to ensure that no untreated sewage is discharged back into natural water bodies. If our cities were rich enough to meet the entire cost, water could be delivered free. They are not.
With reference to the above passage, the following assumptions have been made :
- 1. Rich cities only can ensure sustainable delivery of water.
- 2. Sustainable delivery of water in cities means much more than supplying water to households.
Which of the above assumptions is/are valid?
Answer (b) & explanation
Only assumption 2 is valid (b). Step 1: the passage says water delivery includes treatment, pipes, sewers and sewage plants. So sustainable delivery means much more than supplying water to homes (2). Step 2: assumption 1 says only rich cities can do this. But the passage says poorer cities can also deliver with "financing mechanisms". So 1 fails. Step 3: so options (a), (c) and (d) fail.
Tip: "only" claims fail if the passage shows another way. India's AMRUT 2.0 mission funds water supply and sewerage in cities that cannot pay alone.
Answer as per the official UPSC answer key.
Read the passage
In India, agriculture still engages about half of its workforce, and about 85 per cent of its farms are small and marginal. Compared to China and Vietnam, which have experienced fast structural and rural transformation, India’s story is of slow transformation. As a result, poverty reduction in India was at a much slower pace during 1988–2014, compared to China and Vietnam. India’s poverty reduction was slow during 1988–2005, but during 2005–2012, it accelerated dramatically—almost three times faster than during the earlier period. What did India do during this period? Research reveals that the relative price scenario changed significantly (by more than 50%) in favour of agriculture in the wake of rising global prices. This boosted private investments in agriculture by more than 50%. As a result, agri-GDP growth touched 4·1% during 2007–2012 as against 2·4% during 2002–2007. The net surplus of agri-trade touched $25 billion in 2013–2014; real farm wages rose by 7% per annum. All this led to unprecedented fall in poverty.
With reference to the above passage, the following assumptions have been made :
- 1. Structural and rural transformation is impossible when farms are mainly small and marginal.
- 2. A good price incentive can trigger investments in agriculture.
- 3. India needs to build value chains for high-value agri-products like livestock and horticulture.
- 4. Higher global prices of agricultural commodities are essential for India’s poverty reduction.
Which of the above assumptions are valid?
Answer (c) & explanation
Assumptions 2 and 3 are valid (c). Step 1: the passage says better relative prices raised private farm investment by over 50%. So a good price incentive triggers investment (2). Step 2: UPSC's key also reads into the price-led gains a need to build value chains for high-value products like livestock and horticulture (3). Step 3: assumption 1 says transformation is impossible with small farms; that is too strong. Assumption 4 says high global prices are essential for poverty reduction; also too strong. So options (a), (b) and (d) fail.
Tip: "impossible" and "essential" are absolute words. Unless the passage uses them, reject such statements.
Answer as per the official UPSC answer key.
Read the passage
In India, agriculture still engages about half of its workforce, and about 85 per cent of its farms are small and marginal. Compared to China and Vietnam, which have experienced fast structural and rural transformation, India’s story is of slow transformation. As a result, poverty reduction in India was at a much slower pace during 1988–2014, compared to China and Vietnam. India’s poverty reduction was slow during 1988–2005, but during 2005–2012, it accelerated dramatically—almost three times faster than during the earlier period. What did India do during this period? Research reveals that the relative price scenario changed significantly (by more than 50%) in favour of agriculture in the wake of rising global prices. This boosted private investments in agriculture by more than 50%. As a result, agri-GDP growth touched 4·1% during 2007–2012 as against 2·4% during 2002–2007. The net surplus of agri-trade touched $25 billion in 2013–2014; real farm wages rose by 7% per annum. All this led to unprecedented fall in poverty.
Which one of the following statements best reflects the critical message of the passage?
Answer (d) & explanation
The critical message is that inclusive agricultural growth is key to reducing poverty soon (d). Step 1: the passage says faster farm growth, higher wages and a farm trade surplus "led to unprecedented fall in poverty". So farm growth that reaches many people cuts poverty. That is (d). Step 2: option (a), large-scale off-farm jobs, and option (b), farmer producer companies, are not discussed. Step 3: option (c), putting private over public investment, is not the passage's point.
Tip: the critical message ties together the passage's evidence. Here every fact points to farm growth reducing poverty. Pick the option that names that link, not a side topic.
Answer as per the official UPSC answer key.
Two Statements S1 and S2 are given below with regard to four numbers P, Q, R and S followed by a Question :
S1 : R is greater than P as well as Q.
S2 : S is not the largest one.
Question : Among four numbers P, Q, R and S, which one is the largest?
Which one of the following is correct in respect of the above Statements and the Question?
Answer (c) & explanation
S1 and S2 together are sufficient, but neither alone (c). Step 1: S1 says R is greater than P and Q. So the largest is either R or S; we know nothing about S. S1 alone is not enough. Step 2: S2 says S is not the largest. Alone, it leaves P, Q or R, so it is not enough. Step 3: together, S1 rules out P and Q, and S2 rules out S. So R is the largest. Options (a), (b) and (d) fail.
Tip: in data sufficiency, test each statement alone first, then together. Mark what each one rules out. If the two together leave exactly one answer, choose "together sufficient".
Answer as per the official UPSC answer key.
Two Statements S1 and S2 are given below followed by a Question :
S1 : n is a prime number.
S2 : n leaves a remainder of 1 when divided by 4.
Question : If n is a unique natural number between 10 and 20, then what is n?
Which one of the following is correct in respect of the above Statements and the Question?
Answer (d) & explanation
Even together, S1 and S2 are not sufficient (d). Step 1: S1: n is prime and between 10 and 20. That leaves 11, 13, 17 and 19. Not unique. Step 2: S2: n leaves remainder 1 when divided by 4. Between 10 and 20 that gives 13 and 17. Not unique either. Step 3: together, both 13 and 17 are prime and leave remainder 1 (13 = 12 + 1, 17 = 16 + 1). Still two values. So the data are not enough. Options (a), (b) and (c) fail.
Tip: "unique" means exactly one answer. If two values still survive, the statements are insufficient. Listing the candidates is the safest method here.
Answer as per the official UPSC answer key.
Two Statements S1 and S2 are given below with regard to two numbers followed by a Question :
S1 : Their product is 21.
S2 : Their sum is 10.
Question : What are the two numbers?
Which one of the following is correct in respect of the above Statements and the Question?
Answer (c) & explanation
S1 and S2 together are sufficient, but neither alone (c). Step 1: S1 alone: two numbers with product 21 could be 1 and 21 or 3 and 7 (or even fractions). Not enough. Step 2: S2 alone: many pairs add to 10: 1 and 9, 2 and 8, and so on. Not enough. Step 3: together: among pairs with product 21, only 3 and 7 add to 10. Algebra agrees: x + y = 10 and xy = 21 give x² − 10x + 21 = 0, so x = 3 or 7. The numbers are fixed. Options (a), (b) and (d) fail.
Tip: a sum and a product together fix two numbers, since they make a quadratic with one pair of roots.
Answer as per the official UPSC answer key.
A man walks down the backside of his house straight 25 metres, then turns to the right and walks 50 metres again; then he turns towards left and again walks 25 metres. If his house faces to the East, what is his direction from the starting point?
Answer (d) & explanation
He is North-West of his starting point (d). Step 1: the house faces East, so its back side faces West. He walks 25 m West. Step 2: facing West, a right turn points him North. He walks 50 m North. Facing North, a left turn points him West. He walks 25 m West. Step 3: net movement: 25 + 25 = 50 m West and 50 m North. Equal amounts of West and North give North-West. Options (a), (b) and (c) fail.
Tip: draw a quick sketch with N at the top. Remember: facing West, right is North and left is South. Equal moves in two directions give the in-between direction.
Answer as per the official UPSC answer key.
Two Statements are given followed by two Conclusions :
Statements : All numbers are divisible by 2. All numbers are divisible by 3.
Conclusion-I : All numbers are divisible by 6.
Conclusion-II : All numbers are divisible by 4.
Which of the above Conclusions logically follows/follow from the two given Statements?
Answer (a) & explanation
Only Conclusion I follows (a). Step 1: all numbers are divisible by 2 and by 3. Since 2 and 3 share no common factor, a number divisible by both is divisible by 2 × 3 = 6. So Conclusion I follows. Step 2: Conclusion II says all are divisible by 4. But being divisible by 2 does not mean divisible by 4. For example, 6 is divisible by 2 and 3, but not by 4. Step 3: so II does not follow. Options (b), (c) and (d) fail.
Tip: if a number is divisible by two co-prime numbers (no shared factor), it is divisible by their product. This does not work for 2 and 4, which share a factor.
Answer as per the official UPSC answer key.
Two Statements are given followed by two Conclusions :
Statements : All cats are dogs. All cats are black.
Conclusion-I : All dogs are black.
Conclusion-II : Some dogs are not black.
Which of the above Conclusions logically follows/follow from the two given Statements, disregarding commonly known facts?
Answer (c) & explanation
Neither conclusion follows (c). Step 1: "All cats are dogs" puts the cats inside the dogs group. "All cats are black" says the cats are black. Step 2: so we know the cat part of the dogs is black. The other dogs may or may not be black. Step 3: so "all dogs are black" (I) is not certain, and "some dogs are not black" (II) is not certain either. Neither follows. Options (a), (b) and (d) fail.
Tip: draw circles: a small "cats" circle inside "dogs", also inside "black". The rest of "dogs" is unknown. When I and II are opposites, check if they form an either-or pair; here they do not, because "all dogs are black" is only possible, not certain.
I and II are opposites, so one of them must be true. But neither follows by itself, and no option says 'either I or II'.
Answer as per the official UPSC answer key.
Consider the following sequence of numbers :
5 1 4 7 3 9 8 5 7 2 6 3 1 5 8 6 3 8 5 2 2 4 3 4 9 6
How many odd numbers are followed by the odd number in the above sequence?
Answer (b) & explanation
6 odd numbers are followed by an odd number (b). Step 1: go through the sequence and mark each pair of neighbours where both are odd. Step 2: the pairs are: 5 1, 7 3, 3 9, 5 7, 3 1 and 1 5. Step 3: that is 6 pairs. Each pair counts one odd number followed by an odd number. Options (a), (c) and (d) miscount.
Tip: in such counting questions, move through the list once, slowly, and tick each pair. Counting in a hurry is the main source of error. Odd digits are 1, 3, 5, 7 and 9.
7 3 9 gives two pairs (7 3 and 3 9). Count overlapping pairs separately.
Answer as per the official UPSC answer key.
A is 16th from the left end in a row of boys and V is 18th from the right end. G is 11th from A towards the right and 3rd from V towards the right end. How many boys are there in the row?
Answer (b) & explanation
There are 41 boys in the row (b). Step 1: A is 16th from the left. G is 11 places to A's right, so G is 16 + 11 = 27th from the left. Step 2: G is 3rd from V towards the right, so V is 3 places to G's left: 24th from the left. Step 3: V is also 18th from the right. Total = 24 + 18 − 1 = 41. We subtract 1 because V is counted twice. Option (c), 42, forgets to subtract 1. Options (a) and (d) fail.
Tip: total in a row = position from left + position from right − 1. Fix one person's position from both ends to use this formula.
Answer as per the official UPSC answer key.
Three Statements S1, S2 and S3 are given below followed by a Question :
S1 : C is younger than D, but older than A and B.
S2 : D is the oldest.
S3 : A is older than B.
Question : Who among A, B, C and D is the youngest?
Which one of the following is correct in respect of the above Statements and the Question?
Answer (d) & explanation
S1 and S3 together are sufficient (d). Step 1: S1 says C is younger than D but older than A and B. So D and C are above A and B. The youngest is A or B. S1 alone is not enough. Step 2: S3 says A is older than B. Combined with S1, B is the youngest. Step 3: S2 (D is oldest) adds nothing new, since S1 already places D above C, A and B. So options (a), (b) and (c) fail.
Tip: in such questions, look for the statement that breaks the final tie. Here S1 narrows it to two people, and S3 decides between them.
Answer as per the official UPSC answer key.
How many integers are there between 1 and 100 which have 4 as a digit but are not divisible by 4?
Answer (c) & explanation
12 such integers exist (c). Step 1: list the numbers from 1 to 100 with a 4 as a digit: 4, 14, 24, 34, 40 to 49 (ten numbers), 54, 64, 74, 84, 94. That is 19 numbers. Step 2: among them, those divisible by 4: 4, 24, 40, 44, 48, 64, 84. That is 7. Step 3: 19 − 7 = 12. Option (b), 11, and option (d), 13, miscount by one. Option (a) misses the 40s.
Tip: count the 40s block separately; it is easy to miss that 44 has two 4s but counts once. A number is divisible by 4 if its last two digits are divisible by 4.
Answer as per the official UPSC answer key.
Let x, y be the volumes; m, n be the masses of two metallic cubes P and Q respectively. Each side of Q is two times that of P and mass of Q is two times that of P. Let u = m/x and v = n/y. Which one of the following is correct?
Answer (a) & explanation
u = 4v (a). Step 1: Q's sides are twice P's. Volume grows by the cube: 2 × 2 × 2 = 8. So y = 8x. Step 2: Q's mass is only twice P's: n = 2m. Step 3: v = n ÷ y = 2m ÷ 8x = ¼ × (m ÷ x) = ¼u. So u = 4v. P is four times as dense as Q. Option (b), u = 2v, wrongly doubles the volume instead of multiplying by 8. Options (c) and (d) fail.
Tip: doubling the side multiplies area by 4 and volume by 8. Here u and v are densities (mass ÷ volume). Remember the square and cube rules for scaling.
Doubling the side does not double the volume; it makes it 8 times.
Answer as per the official UPSC answer key.
The average age of a teacher and three students is 20 years. If all the three students are of same age and the difference between the age of the teacher and each student is 20 years, then what is the age of the teacher?
Answer (c) & explanation
The teacher is 35 years old (c). Step 1: the average of 4 people is 20, so their total = 80 years. Step 2: let each student be s years. The teacher is s + 20. So 3s + (s + 20) = 80, which gives 4s = 60 and s = 15. Step 3: teacher = 15 + 20 = 35 years. Check: 15 + 15 + 15 + 35 = 80. Option (d), 45, and options (a) and (b) fail this check.
Tip: turn the average into a total first (average × number). Then use one letter for the unknown and build a simple equation. Always check by adding back.
Answer as per the official UPSC answer key.
A person bought a car and sold it for ₹ 3,00,000. If he incurred a loss of 20%, then how much did he spend to buy the car?
Answer (d) & explanation
He spent ₹ 3,75,000 on the car (d). Step 1: a 20% loss means he got back 80% of what he paid. Step 2: 80% = ₹ 3,00,000, so 1% = 3,00,000 ÷ 80 = ₹ 3,750. Step 3: 100% = ₹ 3,75,000. Check: 20% of 3,75,000 is 75,000, and 3,75,000 − 75,000 = 3,00,000. Option (a), ₹ 3,60,000, wrongly adds 20% of the selling price. Options (b) and (c) fail.
Tip: loss and profit % are always on the cost price. So cost = selling price ÷ (1 − loss%). Adding 20% to the selling price is the classic trap.
(a) adds 20% to 3,00,000. The 20% is of the buying price, not the selling price.
Answer as per the official UPSC answer key.
Read the passage
Spanish ships in the late 16th century first brought the potato tuber from South America to Europe whereby in the early 19th century, it had become a reliable backup to cereal crops, particularly in the cold, rain-soaked soils of Ireland. The Irish were soon almost wholly dependent on the potato as their staple food. And they were planting primarily one prodigious variety, the ‘Lumper’ potato, whose genetic frailty would be cruelly exposed by the fungus ‘Phytophthora infestans’. In 1845, spores of the deadly fungus began spreading across the country, destroying nearly all the Lumpers in its path. The resulting famine killed or displaced millions.
Which one of the following statements best reflects the critical message of the passage?
Answer (d) & explanation
The critical message is that relying on one uniform food source is unwise (d). Step 1: the passage says the Irish depended almost wholly on one potato variety, and one fungus wiped it out, causing famine. So depending on a single, uniform food is risky. That is (d). Step 2: option (a), suitable soil and climate, misses the point; the potato grew well in Ireland. Step 3: option (c), some fungal infections cannot be stopped, is too general. Option (b), tubers cannot replace cereals, is not the message.
Tip: this is the Irish Potato Famine of the 1840s. It is the classic warning against monoculture and a reason to keep crop diversity.
Answer as per the official UPSC answer key.
Read the passage
India is at once among the fastest growing global economies and home to the largest number of malnourished children in the world. There are regions where malnutrition is not the exception but the norm. And across the country, malnutrition is the cause of death for roughly half the 1·3 million children who die before their fifth birthday each year. Even those children who survive suffer permanently from the damage that has already been done to their bodies and minds from not getting enough of the right foods and nutrients. Around 44 million children under 5 are stunted. That makes it harder for them to learn in school and subsequently earn a living as adults. Their lifetime earnings potential is almost a quarter less than that of their healthy peers.
With reference to the above passage, which of the following is/are the most rational and practical implication/implications?
- 1. India’s Public Distribution System should be monitored by the Union Government.
- 2. Girls should be encouraged to delay marriage and first pregnancy.
- 3. Mothers should be encouraged to breastfeed their children immediately after birth.
- 4. The supply of safe drinking water and proper sanitation facilities to all should be ensured.
- 5. Authorities should ensure the vaccination as prescribed.
Select the correct answer using the code given below.
Answer (b) & explanation
Implications 2, 3, 4 and 5 are rational and practical (b). Step 1: the passage says most damage from malnutrition happens before age five. So steps should target mothers and young children. Step 2: delaying marriage and first pregnancy (2), early breastfeeding (3), safe water and sanitation (4) and proper vaccination (5) all protect young children. Step 3: statement 1, Union monitoring of the PDS, is an administrative change the passage does not imply. So options (a), (c) and (d) fail.
Tip: India's legal minimum marriage age for women is 18. Breastfeeding within the first hour of birth is a key WHO advice point. Link each option to the passage's focus: early childhood.
Answer as per the official UPSC answer key.
Read the passage
The pulse variety ‘Pusa Arhar 16’ has the potential to be grown in the paddy-growing regions of Punjab, Haryana and Uttar Pradesh and eventually in all of India. Its yield (about 2000 kg/hectare) will be significantly greater than those of the existing varieties and because its size will be uniform, it will be amenable to mechanical harvesting, an attractive feature for farmers in northern India who currently use this technology for paddy. Most important, Arhar straw, unlike paddy straw, is green and can be ploughed back into the soil. In paddy straw, the problem is the high silica content, which does not allow for easy decomposition. In the case of Arhar, the farmer, even after combine harvesting, just needs to run a rotovator to cut the leftover straw into pieces, which can be ploughed back and will decompose very fast. All this is difficult with leftover paddy stalks that cannot be easily salvaged or ploughed back. Farmers, therefore, choose the easiest option of simply burning it.
Which of the following are the most rational inferences that can be made from the passage?
- 1. Farmers’ income will be higher with pulse cultivation than with paddy cultivation.
- 2. Pulse cultivation causes less pollution as compared to paddy cultivation.
- 3. Pulse straw can be used to improve soil quality.
- 4. In the context of northern Indian agriculture, paddy straw has no usefulness.
- 5. Mechanized agriculture is the main cause for stubble burning.
Select the correct answer using the code given below.
Answer (c) & explanation
Inferences 2 and 3 only (c). Step 1: the passage says arhar (pulse) straw is ploughed back into the soil and decomposes. So pulse straw improves soil (3). Step 2: paddy straw is burnt, causing smoke. So pulses cause less pollution than paddy (2). Step 3: statement 1, farmers' income, is not compared. Statement 4, paddy straw has no use, is too absolute. Statement 5 fails: the passage says paddy straw is burnt because of its high silica, not because of mechanisation. So options (a), (b) and (d) fail.
Tip: stubble burning in Punjab and Haryana adds to Delhi's winter smog. In CSAT, though, use the passage's stated reason, here silica.
Answer as per the official UPSC answer key.
Read the passage
In India, authorities always look to store the maximum amount of water in reservoirs during the monsoon season, which is then used for irrigation and generation of electricity during the summer months. It is an internationally accepted practice that the water level of a reservoir should be kept below a certain level before the onset of monsoon season. This is so that when monsoon rains come, there is space to store the excess rainwater and also so that water can be released in a regulated manner. But the authorities store the maximum amount of water in reservoirs even before the close of the monsoon, only to ensure greater electricity generation and irrigation.
With reference to the above passage, the following assumptions have been made :
- 1. High risks involved in holding maximum water in reservoirs are due to our over-dependence on hydropower projects.
- 2. Storage capacity of dams should not be fully used before or during monsoon season.
- 3. Role of dams in flood control is underestimated in India.
Which of the above assumptions is/are valid?
Answer (d) & explanation
All three assumptions are valid (d). Step 1: the passage says reservoirs are filled early "only to ensure greater electricity generation and irrigation". So the risk comes from over-reliance on hydropower and storage (1). Step 2: it says space must be kept free for monsoon inflows. So dams should not be full before or during the monsoon (2). Step 3: by filling dams early, their flood-control role is ignored (3). So options (a), (b) and (c) fail.
Tip: Kerala's 2018 floods raised this debate: dams full before heavy rain had to release water suddenly. A dam's empty space is itself a flood shield.
Answer as per the official UPSC answer key.
Read the passage
Economic liberalization in India was shaped largely by the economic problems of the government than by the economic priorities of the people or by the long-term development objectives. Thus, there were limitations in conception and design which have been subsequently validated by experience. Jobless growth, persistent poverty and rising inequality have mounted as problems since economic liberalization began. And all these years later, four quiet crises confront the economy; agriculture, infrastructure, industrialization and education as constraints on the country’s future prospects. These problems must be resolved if economic growth has to be sustained and transformed into meaningful development.
Which of the following is/are the most rational and logical inference/inferences that can be made from the passage?
- 1. It is essential to rethink and redefine the economic role of the State in the quest for development.
- 2. India has not made effective implementation of its policies in social sectors nor made sufficient investments in them.
Select the correct answer using the code given below.
Answer (c) & explanation
Both inferences are valid (c). Step 1: the passage says reform was shaped by the government's problems, not the people's priorities. So the State's economic role needs rethinking (1). Step 2: it points to persistent poverty and a crisis in education. These show weak effort and spending in social sectors (2). Step 3: so options (a), (b) and (d) fail.
Tip: when a passage lists outcomes like poverty and poor schooling, it implies weak social-sector policy. "Rethink the role of the State" is a moderate claim that a critical passage can easily support.
Answer as per the official UPSC answer key.
Read the passage
Economic liberalization in India was shaped largely by the economic problems of the government than by the economic priorities of the people or by the long-term development objectives. Thus, there were limitations in conception and design which have been subsequently validated by experience. Jobless growth, persistent poverty and rising inequality have mounted as problems since economic liberalization began. And all these years later, four quiet crises confront the economy; agriculture, infrastructure, industrialization and education as constraints on the country’s future prospects. These problems must be resolved if economic growth has to be sustained and transformed into meaningful development.
With reference to the above passage, the following assumptions have been made :
- 1. India’s economy needs to be greatly integrated with global economy so as to create large number of jobs and to sustain its growth momentum.
- 2. Economic liberalization would cause large economic growth which would reduce poverty and create sufficient employment in the long run.
Which of the above assumptions is/are valid?
Answer (d) & explanation
Neither assumption is valid (d). Step 1: the passage blames liberalisation for "jobless growth, persistent poverty and rising inequality". Step 2: assumption 1 says India needs more integration with the global economy to create jobs. That praises integration, against the passage's tone. Step 3: assumption 2 says liberalisation will cut poverty and create jobs in the long run. That also praises it. Both go against the passage. So options (a), (b) and (c) fail.
Tip: check the author's attitude. If the passage is critical of a policy, statements praising that policy cannot be its assumptions.
Answer as per the official UPSC answer key.
A shop owner offers the following discount options on an article to a customer :
- 1. Successive discounts of 10% and 20%, and then pay a service tax of 10%
- 2. Successive discounts of 20% and 10%, and then pay a service tax of 10%
- 3. Pay a service tax of 10% first, then successive discounts of 20% and 10%
Which one of the following is correct?
Answer (d) & explanation
All three options are equally good (d). Step 1: each option multiplies the price by the same three numbers: 0·9 (10% off), 0·8 (20% off) and 1·1 (10% tax). Step 2: multiplication can be done in any order: 0·9 × 0·8 × 1·1 = 0·8 × 0·9 × 1·1 = 1·1 × 0·8 × 0·9 = 0·792. Step 3: so the final price is the same in all three. Options (a), (b) and (c) fail.
Tip: successive percentage changes multiply, so their order never matters. Two successive discounts of 20% and 10% equal a single 28% discount, not 30%.
Answer as per the official UPSC answer key.
The letters from A to Z are numbered from 1 to 26 respectively. If GHI = 1578 and DEF = 912, then what is ABC equal to?
Answer (d) & explanation
ABC equals 246 (d). Step 1: GHI → DEF → ABC: each letter moves back 3 places at each step. So the code should change by the same amount each step. Step 2: 1578 − 912 = 666. Step 3: ABC = 912 − 666 = 246. Options (a), (b) and (c) do not fit.
Tip: if letter groups shift by a fixed step, their codes often shift by a fixed amount too. Find the gap between two known codes and apply it once more.
Answer as per the official UPSC answer key.
What is the missing term @ in the following?
ACPQ : BESU :: MNGI : @
Answer (d) & explanation
The missing term is NPJM (d). Step 1: find the rule from ACPQ to BESU. A → B (+1), C → E (+2), P → S (+3), Q → U (+4). Step 2: apply it to MNGI. M + 1 = N, N + 2 = P, G + 3 = J, I + 4 = M. Step 3: so the answer is NPJM. Option (a), NPJL, ends with +3 instead of +4. Option (b), NOJM, uses +1 for the second letter. Option (c), NPIL, gets the last two wrong.
Tip: in letter analogies, write the shift for each position. A growing pattern (+1, +2, +3, +4) is very common.
Answer as per the official UPSC answer key.
What is the largest number among the following?
Answer (c) & explanation
(1/3)⁻⁴ is the largest (c). Step 1: a negative power flips the fraction: (1/a)⁻ⁿ = aⁿ. Step 2: so (1/2)⁻⁶ = 2⁶ = 64; (1/4)⁻³ = 4³ = 64; (1/3)⁻⁴ = 3⁴ = 81; (1/6)⁻² = 6² = 36. Step 3: the largest is 81, option (c). Options (a) and (b) tie at 64. Option (d) is the smallest.
Tip: remember x⁻ⁿ = 1/xⁿ. Flipping first turns the question into simple powers. Know powers of 2 up to 2¹⁰ = 1024 and of 3 up to 3⁶ = 729.
Answer as per the official UPSC answer key.
What is the greatest length x such that 3½ m and 8¾ m are integral multiples of x?
Answer (d) & explanation
The greatest length is 1¾ m (d). Step 1: write both in quarter-metres: 3½ m = 14/4 and 8¾ m = 35/4. Step 2: HCF(14, 35) = 7. So x = 7/4 = 1¾ m. Step 3: check: 3½ = 2 × 1¾ and 8¾ = 5 × 1¾. Both are whole multiples. Option (c), 1¼, divides 8¾ (7 times) but not 3½. Options (a) and (b) fail too.
Tip: for the HCF of fractions, put them over a common denominator and take the HCF of the numerators. Or use HCF of numerators ÷ LCM of denominators.
Answer as per the official UPSC answer key.
Consider the following data :
| Year | Birthrate | Death rate |
|---|---|---|
| 1911–1921 | 48·1 | 35·5 |
| 1921–1931 | 46·4 | 36·3 |
| 1931–1941 | 45·2 | 31·2 |
| 1941–1951 | 39·9 | 27·4 |
| 1951–1961 | 41·7 | 22·8 |
| 1961–1971 | 41·1 | 18·9 |
| 1971–1981 | 37·1 | 14·8 |
For which period was the natural growth rate maximum?
Answer (d) & explanation
Natural growth rate was highest in 1971–1981 (d). Step 1: natural growth = birth rate − death rate. Step 2: from the table: 1911–21: 12·6; 1941–51: 12·5; 1961–71: 22·2; 1971–81: 22·3. Step 3: the biggest is 22·3, in 1971–1981. Option (c), 1961–71, is very close but slightly lower. Options (a) and (b) are much lower.
Tip: when two values are close, calculate carefully; UPSC often places a near-miss option. Historically, India's growth peaked around 1961–81 as death rates fell faster than birth rates.
1961–71 (22·2) is very close; subtract carefully.
Answer as per the official UPSC answer key.
The recurring decimal representation 1·272727... is equivalent to
Answer (b) & explanation
1·272727... equals 14/11 (b). Step 1: split it: 1 + 0·2727... Step 2: a two-digit repeating block over 99: 0·2727... = 27/99 = 3/11. Step 3: 1 + 3/11 = 14/11. Check: 14 ÷ 11 = 1·2727... Option (a), 13/11 = 1·1818... Option (c), 127/99 = 1·2828... Option (d), 137/99 = 1·3838... All fail.
Tip: for pure recurring decimals, put the repeating digits over as many 9s as there are digits: 0·ab ab... = ab/99. Then simplify. If one digit does not repeat, like 1·2333..., use 9s for repeating digits and 0s for the rest.
Answer as per the official UPSC answer key.
What is the least four-digit number when divided by 3, 4, 5 and 6 leaves a remainder 2 in each case?
Answer (b) & explanation
The least such number is 1022 (b). Step 1: a number leaving remainder 2 when divided by 3, 4, 5 and 6 has the form LCM × k + 2. LCM(3, 4, 5, 6) = 60. Step 2: the smallest four-digit multiple of 60: 60 × 17 = 1020. Step 3: add 2: 1022. Option (a), 1012, is 60 × 16·8 + 2, not valid. Option (c), 1122 = 60 × 18·67 + 2, fails. Option (d) also fails.
Tip: same remainder for all divisors → number = LCM × k + remainder. Find the LCM, then the first suitable multiple.
Answer as per the official UPSC answer key.
In adult population of a city, 40% men and 30% women are married. What is the percentage of married adult population if no man marries more than one woman and no woman marries more than one man; and there are no widows and widowers?
Answer (c) & explanation
34 2/7% of adults are married (c). Step 1: each married man has one wife, so married men = married women. So 0·4M = 0·3W, which gives M : W = 3 : 4. Step 2: take M = 300 and W = 400. Married men = 40% of 300 = 120; married women = 30% of 400 = 120. Total married = 240 out of 700. Step 3: 240 ÷ 700 = 24/70 = 34 2/7%. Option (d), 35%, simply averages 40 and 30. Options (a) and (b) fail.
Tip: never average percentages of groups of different sizes. Find the group ratio first, then use real numbers.
Answer as per the official UPSC answer key.
What is the remainder when 51 × 27 × 35 × 62 × 75 is divided by 100?
Answer (a) & explanation
The remainder is 50 (a). Step 1: the remainder on dividing by 100 is just the last two digits. So keep only the last two digits at each step. Step 2: 35 × 62 = 2170 → 70. 70 × 75 = 5250 → 50. 50 × 27 = 1350 → 50. 50 × 51 = 2550 → 50. Step 3: the remainder is 50. Option (b), 25, and option (c), 5, come from multiplying only the 5-ending numbers. Option (d) fails.
Tip: an even number times a multiple of 25 gives a multiple of 50. Here 62 is even and 75 is a multiple of 25, and the other factors are odd, so the product ends in 50.
Answer as per the official UPSC answer key.
A sum of ₹ 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6. What is the difference between the maximum share and the minimum share?
Answer (c) & explanation
The difference is ₹ 400 (c). Step 1: clear the fractions by multiplying each by 12 (the LCM of 2, 4 and 6): ½ × 12 = 6, ¾ × 12 = 9, ⅚ × 12 = 10. So the ratio is 6 : 9 : 10. Step 2: total parts = 25. One part = 2500 ÷ 25 = ₹ 100. Step 3: maximum − minimum = (10 − 6) × 100 = ₹ 400. So X gets ₹ 600, Y ₹ 900 and Z ₹ 1000. Options (a), (b) and (d) do not fit.
Tip: to simplify a ratio of fractions, multiply all terms by the LCM of the denominators. Then share the total by parts.
Answer as per the official UPSC answer key.
For what value of n, the sum of digits in the number (10n + 1) is 2?
Answer (b) & explanation
The digit sum is 2 for any whole number n (b). Step 1: for n ≥ 1, 10ⁿ + 1 looks like 100…01: one 1, some zeros, then another 1. Digit sum = 2. Step 2: for n = 0, 10⁰ = 1, so 10⁰ + 1 = 2. Digit sum is also 2. Step 3: so it works for every whole number (0, 1, 2, …). Option (c) leaves out 0. Option (a) is too narrow. Option (d) fails because a fractional n, like 0·5, gives a non-whole number.
Tip: whole numbers include 0; natural (positive) numbers start at 1. CSAT often tests this difference, so always check n = 0 separately.
don't forget n = 0. That is the difference between (b) and (c).
Answer as per the official UPSC answer key.
In a class, there are three groups A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight of the students of the class?
Answer (c) & explanation
The class average stays the same (c). Step 1: moving students from groups A and B into group C changes the groups, but not the class. Step 2: the total weight of the class is unchanged, and so is the number of students. Step 3: average = total ÷ number, so the class average stays the same. The group averages may change, but the question asks about the whole class. Options (a), (b) and (d) fail.
Tip: read what the question asks. Shifting people inside a group never changes the overall average. Only adding or removing people from outside can change it.
the groups' averages may change, but the question asks about the class.
Answer as per the official UPSC answer key.
How many different sums can be formed with the denominations ₹ 50, ₹ 100, ₹ 200, ₹ 500 and ₹ 2,000 taking at least three denominations at a time?
Answer (a) & explanation
16 different sums can be formed (a). Step 1: we take at least three notes, each a different denomination. Choose 3 out of 5: 5C3 = 10 ways. Choose 4: 5C4 = 5 ways. Choose all 5: 1 way. Step 2: total = 10 + 5 + 1 = 16. Step 3: no two choices give the same total, because these notes (50, 100, 200, 500, 2000) never add up to each other's sums. So all 16 sums are different. Options (b), (c) and (d) miscount.
Tip: total selections of 5 items = 2⁵ = 32. Minus those with 0, 1 or 2 items (1 + 5 + 10 = 16) gives 16. Both routes agree.
Answer as per the official UPSC answer key.
Read the passage
Bank credit to the industrial sector has started shrinking. Its decline has been a serious concern as credit growth is essential to revive investment. The problem’s origins lie in the incomplete reforms of the last 25 years. An institutional change that should have followed the 1991 reforms should have been setting up of a resolution corporation for banks. In a market economy with booms and busts, banks should be allowed to be set up and to fail. Today, we cannot shut down banks because there is no proper system to shut them down. Weak loss-making banks continue to need more capital.
Which one of the following is the most logical and rational inference that can be made from the above passage?
Answer (c) & explanation
The inference is that India lacks a system to deal with failed banks (c). Step 1: the passage says "we cannot shut down banks because there is no proper system to shut them down". So India lacks an institutional way to handle bank failure. That is (c). Step 2: options (a) and (b) say banks cannot help growth and that 1991 reforms failed. Both are too sweeping. Step 3: option (d), foreign investment as an alternative, is not discussed.
Tip: when a passage states a problem in one clear line, the inference usually restates it. Note: the Insolvency and Bankruptcy Code, 2016 covers firms; banks still lack a separate resolution law. But answer only from the passage.
Answer as per the official UPSC answer key.
Read the passage
India has tremendous potential for solar energy. We all realize that we have to stop burning fossil fuels to meet our energy needs. But certain renewable resources are still going through their cost curves and learning curves to get the required amount of output. The Indian Government has strongly committed to its targets of reducing emissions by 33 per cent by 2030, and towards this it has initiated a strong push towards a gas-based economy and has also invested heavily in renewable energy. However, business houses are wary of investing too heavily in renewable energy at a time when the technology is not yet ready.
Which one of the following is the most logical and rational inference that can be made from the above passage?
Answer (c) & explanation
The inference is that rushing renewables to market too soon may be costly (c). Step 1: the passage says renewables are "still going through their cost curves", meaning their prices are still falling. Business is wary while "the technology is not yet ready". So pushing them early is costly. That is (c). Step 2: option (a) predicts India will miss its 33% target. The passage does not predict this. Step 3: option (b), import gas instead of renewables, and option (d), more gas exploration, are not suggested.
Tip: a cost curve shows prices falling as technology matures. Solar power costs in India fell sharply over the last decade for this reason.
Answer as per the official UPSC answer key.
Read the passage
India has tremendous potential for solar energy. We all realize that we have to stop burning fossil fuels to meet our energy needs. But certain renewable resources are still going through their cost curves and learning curves to get the required amount of output. The Indian Government has strongly committed to its targets of reducing emissions by 33 per cent by 2030, and towards this it has initiated a strong push towards a gas-based economy and has also invested heavily in renewable energy. However, business houses are wary of investing too heavily in renewable energy at a time when the technology is not yet ready.
With reference to the above passage, the following assumptions have been made :
- 1. Governments often provide inefficient and costly subsidies for technologies that may not be ready in the near future.
- 2. India’s commitment of reducing emissions by 33% by 2030 shall be on the basis of gas-based economy.
Which of the above assumptions is/are valid?
Answer (a) & explanation
Only assumption 1 is valid (a). Step 1: UPSC's key reads the passage's point about heavy state support for a technology that is "not yet ready" as costly and inefficient subsidy (1). Step 2: assumption 2 says the 33% emissions target will rest on a gas-based economy. But the passage says the target depends on gas and renewables, not gas alone. So 2 fails. Step 3: so options (b), (c) and (d) fail.
Tip: watch for an option that keeps one part of a pair and drops the other. "Gas and renewables" does not mean "gas-based". India later updated its Paris goal to 45% lower emissions intensity by 2030 (from 2005 levels).
Answer as per the official UPSC answer key.
Read the passage
Genome editing is different from genome modification. Genome editing typically involves finding the part of a plant genome that could be changed to render it less vulnerable to disease, or resistant to certain herbicides, or to increase yields. Researchers use ‘molecular scissors’ to dissect the genome and repair it, which is a process that occurs naturally when plants are under attack from diseases and can throw up new mutations that enable the plant to survive future attacks. This evolutionary process can effectively be speeded up now that it is possible to examine plant genomes in detail in laboratories, and create mechanisms through which the relevant genes can be altered very precisely.
With reference to the above passage, the following assumptions have been made :
- 1. Genome editing does not require the transfer of genes from one plant to another.
- 2. Through genome editing, the chosen genes can be altered precisely in a manner akin to the natural process that helps plants to adapt to the environmental factors.
Which of the above assumptions is/are valid?
Answer (c) & explanation
Both assumptions are valid (c). Step 1: the passage says genome editing changes a plant's own genes, unlike genetic modification, which moves genes from another organism. So editing does not need gene transfer (1). Step 2: it says editing speeds up a natural repair process and works "very precisely". So chosen genes can be changed precisely, much like nature's own way of adapting (2). Step 3: so options (a), (b) and (d) fail.
Tip: CRISPR is the best-known gene-editing tool. In May 2025, India released two genome-edited rice varieties, DRR Dhan 100 (Kamala) and Pusa DST Rice 1, the world's first such rice varieties.
Answer as per the official UPSC answer key.
Read the passage
Many people understand the connection between solid waste management and health in terms of the consequences of unattended heaps of dry garbage which become home for flies and other vermin. However, there is another aspect that is not well-understood, that is, what happens when unscientific solid waste management combines with poor drainage and dumping of untreated sewage into drains which are meant to carry storm water during rains. The result is choked drains which are full of stagnant water breeding mosquitoes, resulting in the spread of water-borne diseases.
In the context of India, which one of the following statements best reflects the critical message of the passage?
Answer (c) & explanation
The message is that solid waste management must be integrated with drainage and sewerage upkeep (c). Step 1: the passage says disease spreads when poor waste handling "combines with poor drainage" and sewage. So these must be managed together. That is (c). Step 2: option (a), drains not separated for sewage and storm water, is only a detail. Step 3: option (b), local bodies lack money and power, is not the main point. Option (d), drinking water shortage, is not discussed.
Tip: the message usually ties the passage's facts together. Here every fact links waste and drainage. Swachh Bharat Mission (Urban) 2.0 covers both solid waste and used-water management.
Answer as per the official UPSC answer key.
Read the passage
In Part III of the Constitution, which assures people certain fundamental rights, Article 25 proclaims that “all persons are equally entitled to freedom of conscience and the right freely to profess, practise and propagate religion”. What people fail to notice is that this proclamation is prefixed with the words “subject to public order, morality, health and to the other provisions of this Part”, which set conditions precedent for the legal protection of religious practices of any community. The closing words of this prefatory rider in Article 25 virtually constitute a subordination clause placing other fundamental rights mentioned in Part III over and above the right to religious freedom. Among those other fundamental rights is the right to equality before law and equal protection of laws—assured at the outset and elaborated in later articles to mean, inter alia, that the State shall not deny equal protection of laws to any person or group of persons on the basis of religion alone.
What is the most logical inference from the above passage?
Answer (b) & explanation
The inference is that religious freedom under the Constitution is open to State intervention (b). Step 1: the passage says Article 25 is "subject to public order, morality, health" and to other fundamental rights. So the State can step in. That is (b). Step 2: options (a) and (d) say the State cannot interfere and that practices are immune to law. Both reverse the passage. Step 3: option (c) says religious freedom is not a fundamental right. That ignores Part III, where Articles 25–28 sit.
Tip: Article 25(2) also lets the State regulate secular activity linked to religion and open Hindu temples to all classes. Freedoms in India are rarely absolute.
Answer as per the official UPSC answer key.
How many different 5-letter words (with or without meaning) can be constructed using all the letters of the word 'DELHI' so that each word has to start with D and end with I?
Answer (d) & explanation
6 such words can be made (d). Step 1: the word must start with D and end with I. So the first and last letters are fixed. Step 2: the middle three places are filled by E, L and H. Step 3: three letters can be arranged in 3 × 2 × 1 = 6 ways: ELH, EHL, LEH, LHE, HEL, HLE. Option (a), 24, fixes only one end (4! = 24). Options (b) and (c) do not follow any rule.
Tip: fix the letters whose places are given, then arrange the rest. n different letters can be arranged in n! ways. 3! = 6, 4! = 24, 5! = 120.
Answer as per the official UPSC answer key.
A bottle contains 20 litres of liquid A. 4 litres of liquid A is taken out of it and replaced by same quantity of liquid B. Again 4 litres of the mixture is taken out and replaced by same quantity of liquid B. What is the ratio of quantity of liquid A to that of liquid B in the final mixture?
Answer (c) & explanation
The final ratio of A to B is 16 : 9 (c). Step 1: each round removes 4 of 20 litres, so it keeps 16/20 = 4/5 of liquid A. Step 2: after two rounds: A = 20 × (4/5) × (4/5) = 20 × 16/25 = 12·8 litres. Step 3: B = 20 − 12·8 = 7·2 litres. Ratio 12·8 : 7·2 = 128 : 72 = 16 : 9. Option (a), 4 : 1, is the ratio after only one round (16 : 4). Options (b) and (d) fail.
Tip: for repeated replacement, use: remaining = original × (1 − removed/total)ⁿ. This formula saves step-by-step work.
Answer as per the official UPSC answer key.
The average score of a batsman after his 50th innings was 46·4. After 60th innings, his average score increases by 2·6. What was his average score in the last ten innings?
Answer (c) & explanation
His average in the last ten innings was 62 (c). Step 1: total after 50 innings = 50 × 46·4 = 2320. Step 2: the new average after 60 innings = 46·4 + 2·6 = 49. Total = 60 × 49 = 2940. Step 3: runs in the last 10 innings = 2940 − 2320 = 620. Average = 620 ÷ 10 = 62. Option (d), 49, is the new overall average. Options (a) and (b) fail.
Tip: always convert averages to totals before subtracting. Shortcut: the last 10 innings must lift 60 innings by 2·6 each and also match the old average: 46·4 + (60 × 2·6) ÷ 10 = 46·4 + 15·6 = 62.
Answer as per the official UPSC answer key.
As a result of 25% hike in the price of rice per kg, a person is able to purchase 6 kg less rice for ₹ 1,200. What was the original price of rice per kg?
Answer (b) & explanation
The original price was ₹ 40 per kg (b). Step 1: a 25% price rise means the same money buys 4/5 as much. So quantity falls by 1/5. Step 2: that 1/5 equals 6 kg. So the old quantity = 6 × 5 = 30 kg. Step 3: old price = 1200 ÷ 30 = ₹ 40. Check: new price = ₹ 50; 1200 ÷ 50 = 24 kg, which is 6 kg less. Options (a), (c) and (d) fail this check.
Tip: price up by 1/4 means quantity down by 1/5 (for fixed spending). Price up by 1/n means quantity down by 1/(n + 1).
Answer as per the official UPSC answer key.
A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?
Answer (a) & explanation
40% of the work takes 6 days (a). Step 1: X does 20% in 8 days, so the full job takes 40 days. Y does 25% in 6 days, so the full job takes 24 days. Step 2: together, per day: 1/40 + 1/24 = 3/120 + 5/120 = 8/120 = 1/15. So together they finish in 15 days. Step 3: 40% of the job takes 0·4 × 15 = 6 days. Option (b), 8, and the others fail.
Tip: convert each person's partial work into full-job time. Then add daily rates (1/days), not days. Using LCM units (here 120 units of work) also makes it quick.
Answer as per the official UPSC answer key.
A car travels from a place X to place Y at an average speed of v km/hr, from Y to X at an average speed of 2v km/hr, again from X to Y at an average speed of 3v km/hr and again from Y to X at an average speed of 4v km/hr. Then the average speed of the car for the entire journey
Answer (b) & explanation
The average speed lies between v and 2v (b). Step 1: each trip covers the same distance d. Average speed = total distance ÷ total time, not the average of the speeds. Step 2: total time = d/v + d/2v + d/3v + d/4v = (d/v)(1 + ½ + ⅓ + ¼) = 25d/12v. Step 3: average speed = 4d ÷ 25d/12v = 48v/25 = 1·92v. That is between v and 2v. Option (c) is the trap from averaging the speeds (2·5v).
Tip: for equal distances, the average speed is the harmonic mean, always less than the simple average. Slow legs take more time, so they pull the average down.
the plain average of v, 2v, 3v, 4v is 2·5v. The car spends more time at low speed.
Answer as per the official UPSC answer key.
Consider the following statements :
- 1. The minimum number of points of intersection of a square and a circle is 2.
- 2. The maximum number of points of intersection of a square and a circle is 8.
Which of the above statements is/are correct?
Answer (b) & explanation
Only statement 2 is correct (b). Step 1: statement 1 says the minimum number of meeting points is 2. But a circle can lie completely away from the square, or fully inside without touching it. Then there are 0 points. So 1 is false. Step 2: statement 2: a circle can cut each of the 4 sides twice, when it is a bit larger than the inscribed circle. That gives 8 points. So 2 is true. Step 3: so options (a), (c) and (d) fail.
Tip: a straight line can meet a circle at most twice. Multiply by the number of sides to get the maximum for any polygon: a triangle gives 6, a square 8.
Answer as per the official UPSC answer key.
A man takes half time in rowing a certain distance downstream than upstream. What is the ratio of the speed in still water to the speed of current?
Answer (d) & explanation
The ratio of speed in still water to current is 3 : 1 (d). Step 1: the same distance takes half the time downstream, so the downstream speed is double the upstream speed. Step 2: let the boat's speed be b and the current c. Downstream = b + c; upstream = b − c. So b + c = 2(b − c). Step 3: this gives b + c = 2b − 2c, so b = 3c. Ratio = 3 : 1. Option (b), 2 : 1, is the ratio of the speeds, not of boat to current. Options (a) and (c) fail.
Tip: downstream adds the current, upstream subtracts it. Half the time means double the speed for the same distance.
Answer as per the official UPSC answer key.
How many pairs of natural numbers are there such that the difference of whose squares is 63?
Answer (a) & explanation
There are 3 such pairs (a). Step 1: x² − y² = (x − y)(x + y) = 63. Both factors must be odd, because 63 is odd, and x + y is the larger factor. Step 2: factor pairs of 63: 1 × 63, 3 × 21, 7 × 9. Step 3: solve each. 1 and 63: x = 32, y = 31. 3 and 21: x = 12, y = 9. 7 and 9: x = 8, y = 1. That is 3 pairs. Check: 64 − 1 = 63. Options (b), (c) and (d) miscount.
Tip: for x² − y² = N, count the factor pairs of N with the same parity (both odd or both even). Each gives one solution.
Answer as per the official UPSC answer key.
Which one of the following will have minimum change in its value if 5 is added to both numerator and the denominator of the fractions 2/3, 3/4, 4/5 and 5/6?
Answer (d) & explanation
5/6 changes the least (d). Step 1: adding the same number to the top and bottom pulls a fraction towards 1. The fraction already closest to 1 moves the least. Step 2: among 2/3, 3/4, 4/5 and 5/6, the closest to 1 is 5/6. Step 3: check: 5/6 → 10/11, a change of 5/66 (about 0·076). 2/3 → 7/8, a change of 5/24 (about 0·21). So 5/6 changes least. Options (a), (b) and (c) change more.
Tip: the change for a/b with k added is k(b − a) ÷ [b(b + k)]. A bigger b means a smaller change, which favours 5/6.
Answer as per the official UPSC answer key.
A digit n > 3 is divisible by 3 but not divisible by 6. Which one of the following is divisible by 4?
Answer (d) & explanation
3n + 1 is divisible by 4 (d). Step 1: n is a single digit above 3, divisible by 3 but not by 6. Digits divisible by 3 above 3 are 6 and 9. 6 is divisible by 6, so n = 9. Step 2: test each option. 2n = 18; 3n = 27; 2n + 4 = 22; 3n + 1 = 28. Step 3: only 28 is divisible by 4. So the answer is (d). Options (a), (b) and (c) fail.
Tip: "digit" means 0 to 9. That small range lets you find n directly, then test options. Divisible by 3 but not 6 means an odd multiple of 3.
Answer as per the official UPSC answer key.
If 1 litre of water weighs 1 kg, then how many cubic millimetres of water will weigh 0·1 gm?
Answer (c) & explanation
100 cubic millimetres of water weigh 0·1 gm (c). Step 1: 1 litre weighs 1 kg, so 1 ml weighs 1 g. And 1 ml = 1 cm³. Step 2: 1 cm = 10 mm, so 1 cm³ = 10 × 10 × 10 = 1000 mm³. So 1 g of water = 1000 mm³. Step 3: 0·1 g = 0·1 × 1000 = 100 mm³. Option (d), 1000, is the volume for 1 g. Options (a) and (b) fail.
Tip: water facts to remember: 1 ml = 1 cm³ = 1 g; 1 litre = 1000 cm³ = 1 kg. When converting cubic units, cube the length factor: (10)³ = 1000.
Answer as per the official UPSC answer key.
A vessel full of water weighs 40 kg. If it is one-third filled, its weight becomes 20 kg. What is the weight of the empty vessel?
Answer (a) & explanation
The empty vessel weighs 10 kg (a). Step 1: full weighs 40 kg; one-third full weighs 20 kg. Going from full to one-third full removes 2/3 of the water, and the weight drops by 40 − 20 = 20 kg. Step 2: so 2/3 of the water = 20 kg, and all the water = 30 kg. Step 3: vessel = 40 − 30 = 10 kg. Check: one-third water = 10 kg, plus vessel 10 kg = 20 kg. Options (b), (c) and (d) fail.
Tip: the difference between two states removes the vessel's weight. Use it to find the contents first, then subtract from the total.
Answer as per the official UPSC answer key.
A frog tries to come out of a dried well 4·5 m deep with slippery walls. Every time the frog jumps 30 cm, slides down 15 cm. What is the number of jumps required for the frog to come out of the well?
Answer (b) & explanation
The frog needs 29 jumps (b). Step 1: each jump gives a net gain of 30 − 15 = 15 cm. But on the last jump, the frog gets out and does not slide back. Step 2: so before its final jump, the frog must reach 450 − 30 = 420 cm. That takes 420 ÷ 15 = 28 jumps. Step 3: one more jump of 30 cm takes it out: 28 + 1 = 29. Option (c), 30, uses 450 ÷ 15 without the last-jump rule. Options (a) and (d) fail.
Tip: in climbing puzzles, subtract the final full jump from the height first. Then divide the rest by the net gain, and add 1.
450/15 = 30 ignores the last jump, after which it does not slide back.
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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.