CSAT Paper II of the 2021 Preliminary examination, held on 10 October 2021. 80 questions · 200 marks · qualifying at 33%. The questions broke down as Comprehension 27, Basic Numeracy 26, Mental Ability 14, Logical Reasoning 8, Data Interpretation 4.
The answer under each question is UPSC's official key. The note beside it is the first line of our explanation; the full reasoning, option by option, is one click away.
Which one of the following statements best reflects the most critical inference that can be made from the passage given above ?
UPSC's answer: (b) — The passage describes a simulation where street lighting (light pollution) affected pea-aphids and their food source, a wild plant. The amber light inhibited flowering in the plant, which reduced the food supply for the aphids.
On the basis of the passage given above, the following assumptions have been made : 1. Sustainable production of India’s cereal food grains is impossible without the diversity of pollinating animals. 2. Monoculture of horticultural crops hampers the survival of insects. 3. Pollinators become scarce in cultivated areas devoid of natural vegetation. 4. Diversity in insects induces diversity of plants. Which of the above assumptions is/are valid ?
UPSC's answer: (d) — Assumption 3 is valid because the passage states that effective pollination requires resources like 'refuges of pristine natural vegetation,' implying that cultivated areas lacking this vegetation will have scarce pollinators.
Which one of the following statements best reflects the crux of the passage given above ?
UPSC's answer: (c) — The passage states that climate change leads to rising temperatures and fewer rainy days, which alters hydrological cycles by increasing runoff and decreasing groundwater recharge.
On the basis of the passage given above, the following assumptions have been made : 1. BPA may alter embryonic development in vivo. 2. Biochemical and cell-based assays are useful in finding out treatments for pollution-induced diseases. 3. Embryonic stem cells could serve as a model to evaluate the physiological effects of environmental pollutants. Which of the above assumptions are valid ?
UPSC's answer: (c) — Assumption 1 is valid because the passage states BPA causes developmental abnormalities in humans and affects germ layer specification in stem cells, implying it can alter embryonic development in vivo.
If 3²⁰¹⁹ is divided by 10, then what is the remainder ?
UPSC's answer: (c) — The last digit of powers of 3 repeats in a cycle of 4: 3¹ = 3, 3² = 9, 3³ = 27, 3⁴ = 81, then 3, 9, 7, 1 again. 2019 = 4 × 504 + 3, so 3²⁰¹⁹ ends in the same digit as 3³, which is 7. The remainder on division by 10 is the last digit, 7 — option (c).
The number 3798125P369 is divisible by 7. What is the value of the digit P ?
UPSC's answer: (b) — A quick test for 7 (valid because 1001 = 7 × 11 × 13): split the number into groups of three digits from the right and take the alternating sum; the number is divisible by 7 if that sum is. From the right, 3798125P369 splits into the groups 369, 25P, 981 and 37, i.e. 369, (250 + P), 981, 37.
From January 1, 2021, the price of petrol (in Rupees per litre) on mᵗʰ day of the year is 80 + 0·1m, where m = 1, 2, 3, ..., 100 and thereafter remains constant. On the other hand, the price of diesel (in Rupees per litre) on nᵗʰ day of 2021 is 69 + 0·15n for any n. On which date in the year 2021 are the prices of these two fuels equal ?
UPSC's answer: (b) — Petrol rises to 80 + 0·1 × 100 = ₹90 on day 100 and then stays at ₹90. Before day 100 the prices never meet: 80 + 0·1n = 69 + 0·15n gives n = 220, which is beyond 100. After day 100, petrol is ₹90, so 69 + 0·15n = 90 gives n = 140.
A biology class at high school predicted that a local population of animals will double in size every 12 years. The population at the beginning of the year 2021 was estimated to be 50 animals. If P represents the population after n years, then which one of the following equations represents the model of the class for the population ?
UPSC's answer: (d) — Doubling every 12 years means that after n years the population has doubled n/12 times. Starting from 50, the population after n years is P = 50 × 2ⁿᐟ¹². Check: at n = 12, P = 50 × 2 = 100; at n = 24, P = 50 × 4 = 200. Hence P = 50 (2)ⁿᐟ¹², option (d).
In a class, 60% of students are from India and 50% of the students are girls. If 30% of the Indian students are girls, then what percentage of foreign students are boys ?
UPSC's answer: (d) — Assume the total number of students is 100 for easy calculation. 60% are Indian students, so there are 60 Indian students and 40 foreign students. 30% of the Indian students are girls, which means 0.30 * 60 = 18 Indian girls. 50% of the total students are girls, so there are 50 girls in total.
A Statement followed by Conclusion-I and Conclusion-II is given below. You have to take the Statement to be true even if it seems to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statement, disregarding the commonly known facts. Statement : Some radios are mobiles. All mobiles are computers. Some computers are watches. Conclusion-I : Certainly some radios are watches. Conclusion-II : Certainly some mobiles are watches. Which one of the following is correct ?
UPSC's answer: (d) — The statement 'Some radios are mobiles' establishes a partial overlap between radios and mobiles, but does not imply all radios are mobiles. The statement 'All mobiles are computers' means the set of mobiles is entirely contained within the set of computers.
On the basis of the passage given above, the following assumptions have been made : 1. Fig trees can often be keystone species in natural forests. 2. Fig trees can grow where other large woody species cannot grow. 3. Sacred trees can have a role in biodiversity conservation. 4. Fig trees have a role in the seed dispersal of other tree species. Which of the above assumptions is/are valid ?
UPSC's answer: (d) — Assumption 1 is valid because the passage states fig trees provide food when other resources are scarce and support high density/diversity of frugivores, fitting the definition of a keystone species.
Consider the following : 1. Cover crops 2. Fertigation 3. Hydroponics 4. Mixed farming 5. Polyculture 6. Vertical farming Which of the above farming practices can be compatible with agroecology, as implied by the passage ?
UPSC's answer: (a) — The passage defines agroecology as mimicking natural ecosystems, closing nutrient loops, and harnessing natural processes for pest control and soil fertility. Cover crops (1) are compatible because they protect soil, fix nitrogen, and mimic natural ground cover, aligning with nutrient conservation.
Which one of the following statements best reflects the most critical inference that can be made from the passage given above ?
UPSC's answer: (a) — The passage highlights that computers are increasingly integrated into physical objects and vulnerable human bodies, such as cars, pacemakers, and insulin pumps. It explicitly states there is little evidence that these gadgets will be more trustworthy than desktop counterparts.
On the basis of the passage given above, the following assumptions have been made : 1. People who are obsessed with personal hygiene tend to ignore the community hygiene. 2. Emergence of multi-drug resistant germs can be prevented by personal cleanliness. 3. Entry of the market in the domain of hygiene increases the risk of infectious diseases. 4. Scientific and micro-level interventions are not sufficient to bring down the burden of infectious diseases. 5. It is community hygiene implemented through public health measures that is really effective in the battle against infectious diseases. Which of the above assumptions are valid ?
UPSC's answer: (c) — Assumption 4 is valid because the passage states that personal hygiene alone is insufficient and that 'general improvements in environmental conditions' (community level) are required to considerably reduce infection rates, implying micro-level interventions alone are not enough.
A Statement followed by Conclusion-I and Conclusion-II is given below. You have to take the Statement to be true even if it seems to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statement, disregarding the commonly known facts. Statement : Some cats are almirahs. Some almirahs are chairs. All chairs are tables. Conclusion-I : Certainly some almirahs are tables. Conclusion-II : Some cats may not be chairs. Which one of the following is correct ?
UPSC's answer: (c) — The statement 'All chairs are tables' implies that the set of chairs is a subset of the set of tables. The statement 'Some almirahs are chairs' means there is an intersection between almirahs and chairs.
A boy plays with a ball and he drops it from a height of 1·5 m. Every time the ball hits the ground, it bounces back to attain a height 4/5ᵗʰ of the previous height. The ball does not bounce further if the previous height is less than 50 cm. What is the number of times the ball hits the ground before the ball stops bouncing ?
UPSC's answer: (b) — The ball is dropped from 1.5 m, which is 150 cm, and it hits the ground for the 1st time from 150 cm. After each hit, the next bounce height is 4/5 of the previous height: 120 cm, 96 cm, 76.8 cm, 61.44 cm, and 49.152 cm.
Images of consonants of the English alphabet (Capitals) are observed in a mirror. What is the number of images of these which do not look like their original shapes ?
UPSC's answer: (b) — The English alphabet has 21 consonants: B, C, D, F, G, H, J, K, L, M, N, P, Q, R, S, T, V, W, X, Y, Z. A letter looks the same in a mirror if it has vertical symmetry (left-right symmetry).
A bank employee drives 10 km towards South from her house and turns to her left and drives another 20 km. She again turns left and drives 40 km, then she turns to her right and drives for another 5 km. She again turns to her right and drives another 30 km to reach her bank where she works. What is the shortest distance between her bank and her house ?
UPSC's answer: (b) — Take the house as (0,0), with east as +x and north as +y. 10 km south gives (0,-10); a left turn while facing south means east, so 20 km east gives (20,-10). A left turn while facing east means north, so 40 km north gives (20,30).
Integers are listed from 700 to 1000. In how many integers is the sum of the digits 10 ?
UPSC's answer: (d) — Integers from 700 to 1000 include 700–999 and 1000; 1000 has digit sum 1, so it is not counted. For 700–799, hundreds digit is 7, so tens + units must be 3; the pairs are (0,3), (1,2), (2,1), (3,0), giving 703, 712, 721, 730: 4 numbers.
A woman runs 12 km towards her North, then 6 km towards her South and then 8 km towards her East. In which direction is she from her starting point ?
UPSC's answer: (b) — The woman runs 12 km North and then 6 km South, resulting in a net displacement of 6 km North from the starting point. She then runs 8 km East, so her final position is 6 km North and 8 km East of the start.
Which one of the following statements best reflects the critical message conveyed by the passage given above ?
UPSC's answer: (a) — The passage opens by stating that India faces a 'challenging immediate future' in energy and climate policy-making due to 'multiple' problems.
Which one of the following statements best reflects the critical message conveyed by the passage given above ?
UPSC's answer: (d) — The passage highlights that using antibiotics as growth promoters in livestock leads to the creation of drug-resistant superbugs that can be transmitted to humans.
With reference to the above passage, the following assumptions have been made : 1. Oil producing countries are one of the reasons for high food prices. 2. If there is a food crisis in the world in the near future, it will be in the emerging economies. Which of the above assumptions is/are valid ?
UPSC's answer: (d) — Assumption 1 is not valid: the passage lists 'high fuel prices' as one factor blamed for food prices; it does not blame oil-producing countries.
With reference to the above passage, the following assumptions have been made : 1. Rising GDP is essential for a country to be a developed country. 2. Rising GDP guarantees a reasonable distribution of income to all households. Which of the above assumptions is/are valid ?
UPSC's answer: (d) — The passage states that rising GDP creates employment and investment opportunities and allows funds to be set aside for a good life, but it does not claim that GDP growth is the sole or essential criterion for a country to be classified as 'developed'.
Seven books P, Q, R, S, T, U and V are placed side by side. R, Q and T have blue covers and other books have red covers. Only S and U are new books and the rest are old. P, R and S are law reports; the rest are Gazetteers. Books of old Gazetteers with blue covers are
UPSC's answer: (c) — Identify the cover color of each book: R, Q, and T have blue covers, while P, S, U, and V have red covers. Determine the age of each book: S and U are new, so P, Q, R, T, and V are old. Classify the book type: P, R, and S are law reports, so Q, T, U, and V are Gazetteers.
Replace the incorrect term by the correct term in the given sequence 3, 2, 7, 4, 13, 10, 21, 18, 31, 28, 43, 40 where odd terms and even terms follow the same pattern.
UPSC's answer: (a) — Odd-position terms: 3, 7, 13, 21, 31, 43 — differences 4, 6, 8, 10, 12. Even-position terms: 2, 4, 10, 18, 28, 40 — differences 2, 6, 8, 10, 12. To follow the same pattern the first difference must be 4, so the first even term should be 4 − 4 = 0.
Following is a matrix of certain entries. The entries follow a certain trend row-wise. Choose the missing entry (?) accordingly. 7B | 10A | 3C 3C | 9B | 6A 10A | 13C | ?
UPSC's answer: (c) — In each row, the third number is the difference between the second and first numbers: 10 - 7 = 3, 9 - 3 = 6, 13 - 10 = 3. In each row, the letters are A, B and C in some order, and the third letter is the one not present in the first two entries: B and A give C, C and B give A, A and C give B.
You are given two identical sequences in two rows : Sequence-I : 8, 4, 6, 15, 52·5, 236·25 Sequence-II : 5, A, B, C, D, E What is the entry in the place of C for the Sequence-II ?
UPSC's answer: (c) — Identify the pattern in Sequence-I: 8 × 0.5 = 4; 4 × 1.5 = 6; 6 × 2.5 = 15; 15 × 3.5 = 52.5; 52.5 × 4.5 = 236.25. The multipliers follow the arithmetic progression: 0.5, 1.5, 2.5, 3.5, 4.5 (increasing by 1 each step). Apply the first multiplier to Sequence-II: 5 × 0.5 = 2.5 (This is A).
A person X from a place A and another person Y from a place B set out at the same time to walk towards each other. The places are separated by a distance of 15 km. X walks with a uniform speed of 1·5 km/hr and Y walks with a uniform speed of 1 km/hr in the first hour, with a uniform speed of 1·25 km/hr in the second hour and with a uniform speed of 1·5 km/hr in the third hour and so on. Which of the following is/are correct ? 1. They take 5 hours to meet. 2. They meet midway between A and B. Select the correct answer using the code given below :
UPSC's answer: (c) — X walks at a constant speed of 1.5 km/hr, so in 5 hours, X covers 1.5 × 5 = 7.5 km. Y's speed increases by 0.25 km/hr every hour: 1.0 km/hr (1st hr), 1.25 km/hr (2nd hr), 1.5 km/hr (3rd hr), 1.75 km/hr (4th hr), and 2.0 km/hr (5th hr).
A student appeared in 6 papers. The maximum marks are the same for each paper. His marks in these papers are in the proportion of 5 : 6 : 7 : 8 : 9 : 10. Overall he scored 60%. In how many number of papers did he score less than 60% of the maximum marks ?
UPSC's answer: (b) — Let the marks be 5k, 6k, 7k, 8k, 9k and 10k, a total of 45k, and let the maximum in each paper be M. Overall 60% means 45k = 0·6 × 6M = 3·6M, so M = 12·5k and 60% of M = 7·5k. Papers with less than 7·5k: 5k, 6k and 7k — three papers. Hence option (b).
What is the most logical assumption that can be made from the passage given above ?
UPSC's answer: (c) — The passage argues that if individuals judge their own religion, all are right; if they judge each other, all are wrong or right collectively, creating a logical paradox.
Which among the following is the most logical and rational inference that can be made from the passage given above ?
UPSC's answer: (c) — The passage argues that seditions, wars, and law breaches are attributed to the 'bad state of a dominion' rather than the inherent wickedness of subjects.
With reference to the above passage, the following assumptions have been made : 1. Equality is a prerequisite for people to participate in the multiple transactions of society from a position of confidence. 2. Occurrence of inequality is detrimental to the survival of democracy. 3. Equal standing of all citizens is an idea that cannot actually be realised even in a democracy. 4. Right to equality should be incorporated into our values and day-to-day political vocabulary. Which of the above assumptions are valid ?
UPSC's answer: (c) — Assumption 1 is valid because the passage states that inequality violates the democratic norm of equal standing, implying that equality is necessary for citizens to participate in society with confidence and without discrimination.
Which one of the following statements best reflects the crux of the passage given above ?
UPSC's answer: (b) — The passage begins by stating that aristocratic government ruins itself by limiting power too narrowly, which is an excess of its defining characteristic. It continues by noting that oligarchic government ruins itself through an incautious scramble for wealth, which is an excess of its basic drive.
In a group of 120 persons, 80 are Indians and rest are foreigners. Further, 70 persons in the group can speak English. The number of Indians who can speak English is
UPSC's answer: (d) — Total persons = 120; Indians = 80, so foreigners = 120 - 80 = 40. Total English speakers = 70; let Indian English speakers = x and foreign English speakers = y, so x + y = 70. Since only 40 foreigners exist, y cannot exceed 40. Therefore x = 70 - y is at least 70 - 40 = 30.
Consider all 3-digit numbers (without repetition of digits) obtained using three non-zero digits which are multiples of 3. Let S be their sum. Which of the following is/are correct ? 1. S is always divisible by 74. 2. S is always divisible by 9. Select the correct answer using the code given below :
UPSC's answer: (c) — A 3-digit number is a multiple of 3 if and only if the sum of its digits is a multiple of 3. The set of all such numbers is formed by permuting all valid combinations of three distinct non-zero digits whose sum is divisible by 3.
There are two Classes A and B having 25 and 30 students respectively. In Class-A the highest score is 21 and lowest score is 17. In Class-B the highest score is 30 and lowest score is 22. Four students are shifted from Class-A to Class-B. Consider the following statements : 1. The average score of Class-B will definitely decrease. 2. The average score of Class-A will definitely increase. Which of the above statements is/are correct ?
UPSC's answer: (a) — Every Class-A score (17 to 21) is below every Class-B score (22 to 30). Statement 1 is correct: the four students added to Class B all score less than anyone already in B, so B's average must fall. Statement 2 is not correct: whether A's average rises depends on which four students leave.
Consider two Statements and a Question : Statement-1 : Priya is 4 ranks below Seema and is 31st from the bottom. Statement-2 : Ena is 2 ranks above Seema and is 37th from the bottom. Question : What is Seema's rank from the top in the class of 40 students ? Which one of the following is correct in respect of the Statements and the Question ?
UPSC's answer: (c) — Statement-1: Priya is 31st from the bottom in 40 students, so Priya is 40 - 31 + 1 = 10th from the top. Priya is 4 ranks below Seema, so Seema is 10 - 4 = 6th from the top. Statement-2: Ena is 37th from the bottom in 40 students, so Ena is 40 - 37 + 1 = 4th from the top.
In the English alphabet, the first 4 letters are written in opposite order; and the next 4 letters are written in opposite order and so on; and at the end Y and Z are interchanged. Which will be the fourth letter to the right of the 13th letter ?
UPSC's answer: (b) — The alphabet is rearranged in blocks of four in reverse order: A-D becomes D-C-B-A, E-H becomes H-G-F-E, I-L becomes L-K-J-I, M-P becomes P-O-N-M, Q-T becomes T-S-R-Q, U-X becomes X-W-V-U, and Y-Z becomes Z-Y.
Which one of the following statements best reflects the central idea of the passage given above ?
UPSC's answer: (a) — The passage states that in a natural state, individuals determine good and bad solely based on their own advantage, meaning no common moral standard exists. It explicitly argues that 'sin cannot be conceived in a natural state' because there is no external authority to which one is responsible.
Which of the following statements best reflect the rational, plausible and practical implications that can be derived from the passage given above ? 1. Too much globalization is not in the best interests of any country. 2. Modern technologies are increasingly blurring the economic borders. 3. Innovation and capital have impinged on the domain of the State. 4. Public policy of every country should focus on developing its own supply chains. 5. Geopolitics will have to reconcile to many ambiguities and uncertainties. Select the correct answer using the code given below :
UPSC's answer: (c) — The passage links a driverless car in Dublin to a code writer in California and a maintenance programmer in Hyderabad, showing that modern technology decisions cross national economic borders.
Which one of the following statements best reflects the most logical, rational and practical suggestion implied by the passage given above ?
UPSC's answer: (d) — The passage explicitly states that bad debt resolution and recapitalisation are only partial solutions and cannot rein in reckless lending on their own.
Which one of the following statements best reflects the corollary to the passage given above ?
UPSC's answer: (a) — The passage states that the objective of macroeconomic policy is to enhance economic welfare. It asserts that neither the monetary wing nor the fiscal wing can work independently without the active support of the other.
Consider the following Table : Player | Runs scored in the First Innings | Balls faced in the First Innings | Runs scored in the Second Innings | Balls faced in the Second Innings A | 61 | 99 | 14 | 76 B | 05 | 12 | 50 | 85 C | 15 | 75 | 20 | 50 D | 13 | 55 | 12 | 50 Who is the fastest run scorer in the Test Match ?
UPSC's answer: (b) — Fastest run scorer means highest strike rate: total runs divided by total balls faced, multiplied by 100. A: (61+14)/(99+76) = 75/175 = 42.86. B: (5+50)/(12+85) = 55/97 = 56.70. C: (15+20)/(75+50) = 35/125 = 28.00. D: (13+12)/(55+50) = 25/105 = 23.81.
Half of the villagers of a certain village have their own houses. One-fifth of the villagers cultivate paddy. One-third of the villagers are literate. Four-fifth of the villagers are under 25 years of age. Which one of the following statements is certainly correct ?
UPSC's answer: (b) — Let the total number of villagers be 100 for ease of calculation. The number of villagers under 25 years of age is 4/5 of 100, which equals 80. The number of literate villagers is 1/3 of 100, which is approximately 33.33.
Consider two Statements and a Question : Statement-1 : The last day of the month is a Wednesday. Statement-2 : The third Saturday of the month was the seventeenth day. Question : What day is the fourteenth of the given month ? Which one of the following is correct in respect of the Statements and the Question ?
UPSC's answer: (b) — Statement-2 states that the third Saturday of the month is the 17th. If the 17th is a Saturday, the 10th and 3rd are also Saturdays. The 14th is three days after the 11th (which is a Sunday, as 17th is Saturday) or simply count back: 17th (Sat) -> 16th (Fri) -> 15th (Thu) -> 14th (Wed).
Which day is 10th October, 2027 ?
UPSC's answer: (a) — 1 January 2000 was a Saturday. From 1 January 2000 to 1 January 2027 there are 27 years, of which 7 are leap years (2000, 2004, 2008, 2012, 2016, 2020, 2024), giving 27 × 365 + 7 = 9 862 days, i.e. 1 408 weeks and 6 odd days, so 1 January 2027 falls on a Friday.
Consider two Statements and four Conclusions given below. You have to take the Statements to be true even if they seem to be at variance from the commonly known facts. Read all Conclusions and then decide which of the given Conclusion(s) logically follows/follow from the Statements, disregarding the commonly known facts. Statement-1 : Some greens are blues. Statement-2 : Some blues are blacks. Conclusion-1 : Some greens are blacks. Conclusion-2 : No green is black. Conclusion-3 : All greens are blacks. Conclusion-4 : All blacks are greens. Which one of the following is correct ?
UPSC's answer: (d) — Statement 1 states that some Greens are Blues, establishing an overlap between the Green and Blue sets. Statement 2 states that some Blues are Blacks, establishing an overlap between the Blue and Black sets.
What is the value of 'X' in the sequence 2, 7, 22, 67, 202, X, 1822 ?
UPSC's answer: (c) — Observe the relationship between consecutive terms: each term is obtained by multiplying the previous term by 3 and adding 1. Verify with the first step: 2 × 3 + 1 = 7. Verify with the second step: 7 × 3 + 1 = 22. Verify with the third step: 22 × 3 + 1 = 67.
Which one of the following statements best reflects the central idea of the passage given above ?
UPSC's answer: (b) — The passage highlights that top universities like Harvard and MIT are adopting the 'flipped classroom' model, where video lectures are done at home and class time is used for application and discussion.
Which among the following is the most logical and rational inference that can be made from the passage given above ?
UPSC's answer: (c) — The passage explicitly states that cities are vulnerable to climate change and lack the systems to address these impacts despite high population densities and GDP contribution. It highlights the necessity to address critical issues like air quality and transport to identify 'sustainable solutions'.
Jay and Vijay spent an equal amount of money to buy some pens and special pencils of the same quality from the same store. If Jay bought 3 pens and 5 pencils, and Vijay bought 2 pens and 7 pencils, then which one of the following is correct ?
UPSC's answer: (c) — Let the price of a pen be P and the price of a pencil be C. Jay's total expenditure is 3P + 5C. Vijay's total expenditure is 2P + 7C. Since they spent equal amounts, equate the expressions: 3P + 5C = 2P + 7C. Subtract 2P from both sides to get P + 5C = 7C.
P scored 40 marks more than Q in an examination. If Q scored 10% less marks than P, then how much did Q score ?
UPSC's answer: (a) — Let P's score be P and Q's score be Q. The problem states P scored 40 marks more than Q, so P = Q + 40. It also states Q scored 10% less than P, which means Q = P - 0.10P = 0.90P. Substitute P = Q + 40 into the second equation: Q = 0.90(Q + 40). Expanding gives Q = 0.90Q + 36.
A person P asks one of his three friends X as to how much money he had. X replied, "If Y gives me ₹ 40, then Y will have half of as much as Z, but if Z gives me ₹ 40, then three of us will have equal amount." What is the total amount of money that X, Y and Z have ?
UPSC's answer: (b) — If Z gives X ₹40, all three have equal amounts: X + 40 = Y = Z − 40. So Y = X + 40 and Z = X + 80. If Y gives X ₹40, Y has half of Z: Y − 40 = Z ÷ 2, i.e. X = (X + 80) ÷ 2, so X = 80. Then Y = 120 and Z = 160, and the total is 80 + 120 + 160 = ₹360 — option (b).
In a code language 'MATHEMATICS' is written as 'LBSIDNZUHDR'. How is 'CHEMISTRY' written in that code language ?
UPSC's answer: (b) — MATHEMATICS → LBSIDNZUHDR: the letters are shifted alternately −1 and +1 (M→L, A→B, T→S, H→I, E→D, M→N, …). Apply the same to CHEMISTRY: C→B, H→I, E→D, M→N, I→H, S→T, T→S, R→S, Y→X. CHEMISTRY is written BIDNHTSSX — option (b).
At which one of the following times, do the hour hand and the minute hand of the clock make an angle of 180° with each other ?
UPSC's answer: (d) — At 7:00, the hour hand is at 210° and the minute hand is at 0°, creating an initial angle of 150°. The minute hand moves at 6° per minute, while the hour hand moves at 0.5° per minute, resulting in a relative speed of 5.5° per minute.
In an objective type test of 90 questions, 5 marks are allotted for every correct answer and 2 marks are deducted for every wrong answer. After attempting all the 90 questions, a student got a total of 387 marks. What is the number of incorrect responses ?
UPSC's answer: (a) — Let the number of correct answers be C and the number of incorrect answers be I. Since all 90 questions were attempted, C + I = 90. The total score is calculated as 5C - 2I = 387. Substituting C = 90 - I into the score equation gives 5(90 - I) - 2I = 387.
Consider the following addition problem : 3P + 4P + PP + PP = RQ2; where P, Q and R are different digits. What is the arithmetic mean of all such possible sums ?
UPSC's answer: (c) — 3P + 4P + PP + PP = (30 + P) + (40 + P) + 11P + 11P = 70 + 24P. The sum RQ2 ends in 2, so 24P must end in 2: P = 3 (24 × 3 = 72) or P = 8 (24 × 8 = 192). P = 3 gives 142 (R = 1, Q = 4) and P = 8 gives 262 (R = 2, Q = 6); in both, P, Q and R are different digits.
Consider the following multiplication problem : (PQ) × 3 = RQQ, where P, Q and R are different digits and R ≠ 0. What is the value of (P + R) ÷ Q ?
UPSC's answer: (b) — (10P + Q) × 3 = 100R + 11Q, so 30P + 3Q = 100R + 11Q, i.e. 30P = 100R + 8Q. The product RQQ is at most 99 × 3 = 297, so R is 1 or 2. Dividing by 2: 15P = 50R + 4Q, so 4Q must be a multiple of 5, giving Q = 0 or 5. Q = 0 gives 15P = 50R, so P = 10 (R = 3) — not a digit.
With reference to the above passage, the following assumptions have been made : 1. Modern democracies rely on the market forces to enable them to be welfare states. 2. Markets ensure sufficient economic growth necessary for democracies to be effective. 3. Government programmes are needed for those left behind in economic growth. Which of the above assumptions is/are valid ?
UPSC's answer: (b) — The passage states that markets do not work on a one-person-one-vote principle and that outcomes depend on endowments, skills, and purchasing power, which contradicts the assumption that democracies rely on market forces to be welfare states.
Which one of the following statements best reflects the central idea of the passage given above ?
UPSC's answer: (d) — The passage argues that schools focus exclusively on academic subjects like physics, maths, and history, neglecting critical social issues such as caste, famine, and gender sensitivity.
There are three points P, Q and R on a straight line such that PQ : QR = 3 : 5. If n is the number of possible values of PQ : PR, then what is n equal to ?
UPSC's answer: (b) — Let the length of PQ be 3x and QR be 5x, based on the given ratio PQ : QR = 3 : 5. Since P, Q, and R are on a straight line, there are two possible relative positions for the points: Q lies between P and R, or P lies between Q and R (R cannot lie between P and Q because PQ < QR).
On a chess board, in how many different ways can 6 consecutive squares be chosen on the diagonals along a straight path ?
UPSC's answer: (b) — The official answer (b) takes 'the diagonals' to mean the two main diagonals of the chessboard, each running corner to corner through 8 squares. On a line of 8 squares, a run of 6 consecutive squares can start at square 1, 2 or 3 — 3 ways. Two main diagonals give 3 + 3 = 6 ways — option (b).
In the series _b_a_ba_b_abab_aab; fill in the six blanks ( _ ) using one of the following given four choices such that the series follows a specific order.
UPSC's answer: (d) — Fill the six blanks in order with a, b, a, b, a, b (option d): the series becomes abbaab abbaab abbaab. It is the block 'abbaab' repeated three times, a clear pattern. The other choices give strings with no repeating block (for example, option (a) gives bbaabbaabbababaaab). Hence option (d).
Using 2, 2, 3, 3, 3 as digits, how many distinct numbers greater than 30000 can be formed ?
UPSC's answer: (b) — The digits available are 2, 2, 3, 3, 3. To form a number greater than 30000, the first digit must be 3. After placing 3 in the first position, the remaining digits to arrange are 2, 2, 3, 3.
Consider the following statements : 1. The sum of 5 consecutive integers can be 100. 2. The product of three consecutive natural numbers can be equal to their sum. Which of the above statements is/are correct ?
UPSC's answer: (c) — Let the five consecutive integers be n-2, n-1, n, n+1, n+2; their sum is 5n, so 5n = 100 implies n = 20, which is an integer, making Statement 1 correct. Let the three consecutive natural numbers be n, n+1, n+2; the equation for their product equaling their sum is n(n+1)(n+2) = 3n + 3.
A cubical vessel of side 1 m is filled completely with water. How many millilitres of water is contained in it (neglect thickness of the vessel) ?
UPSC's answer: (d) — The vessel is a cube with side 1 m, so its volume is 1 m × 1 m × 1 m = 1 m³. 1 m = 100 cm, therefore 1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³. 1 cm³ of water equals 1 millilitre. Hence the water contained is 1,000,000 millilitres, which is option (d).
There are 6 persons arranged in a row. Another person has to shake hands with 3 of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place ?
UPSC's answer: (b) — Label the 6 persons in the row as 1, 2, 3, 4, 5, and 6. The condition requires selecting 3 persons such that no two selected persons are adjacent (consecutive). If person 1 is selected, person 2 cannot be selected. The remaining 2 must be chosen from {3, 4, 5, 6} with no adjacency.
An amount of money was distributed among A, B and C in the ratio p : q : r. Consider the following statements : 1. A gets the maximum share if p is greater than (q + r). 2. C gets the minimum share if r is less than (p + q). Which of the above statements is/are correct ?
UPSC's answer: (a) — The shares of A, B and C are proportional to p, q and r, so the largest ratio gives the largest share and the smallest ratio gives the smallest share. If p > q + r, then p is greater than q and also greater than r, because q and r are positive parts of the ratio.
Which one of the following statements best sums up the passage given above ?
UPSC's answer: (c) — The passage explicitly states that historically, the driver for opening frontiers has always been the search for resources, citing medieval merchants and Portuguese caravels as examples. It argues that science and curiosity are weaker drivers compared to the economic need for resources.
The idea which the first part of the passage mentions is
UPSC's answer: (d) — The first part of the passage states that 'most people would agree that telling deliberate lies is wrong'. It immediately adds an exception: 'except perhaps in certain special situations where more harm will be done by telling the truth'.
Which one of the following habits is found more often in good people ?
UPSC's answer: (b) — The passage states that even the most truthful people tell many 'semantic lies'. It defines these semantic lies as the use of words containing 'some measure of falsehood'. Crucially, the passage specifies that this falsehood is 'more or less deliberate'.
A pie diagram shows the percentage distribution of proteins, water and other dry elements in the human body. Given that proteins correspond to 16% and water corresponds to 70%. If both proteins and the other dry elements correspond to p%, then what is the central angle of the sector representing p on the pie diagram ?
UPSC's answer: (c) — The total percentage of all components in the human body is 100%. Water corresponds to 70% and proteins correspond to 16%. The percentage of 'other dry elements' is calculated as 100% - 70% - 16% = 14%.
Joseph visits the club on every 5th day, Harsh visits on every 24th day, while Sumit visits on every 9th day. If all three of them met at the club on a Sunday, then on which day will all three of them meet again ?
UPSC's answer: (b) — Calculate the Least Common Multiple (LCM) of the visit intervals: 5, 24, and 9. The prime factorization of 5 is 5, of 24 is 2³ × 3, and of 9 is 3². The LCM is 2³ × 3² × 5 = 8 × 9 × 5 = 360 days. Determine the number of weeks in 360 days by dividing by 7: 360 ÷ 7 = 51 weeks and 3 days remainder.
The difference between a 2-digit number and the number obtained by interchanging the positions of the digits is 54. Consider the following statements : 1. The sum of the two digits of the number can be determined only if the product of the two digits is known. 2. The difference between the two digits of the number can be determined. Which of the above statements is/are correct ?
UPSC's answer: (b) — Let the number be 10a + b. Then (10a + b) − (10b + a) = 9(a − b) = 54, so the digits differ by 6. Statement 2 is correct: the difference between the digits is always 6. The possible numbers are 60, 71, 82 and 93 (or their reverses), with digit sums 6, 8, 10 and 12.
X said to Y, "At the time of your birth I was twice as old as you are at present." If the present age of X is 42 years, then consider the following statements : 1. 8 years ago, the age of X was five times the age of Y. 2. After 14 years, the age of X would be two times the age of Y. Which of the above statements is/are correct ?
UPSC's answer: (b) — When Y was born, X's age was X − Y. We are told X − Y = 2Y, so 42 − Y = 2Y and Y = 14. Statement 1: 8 years ago X was 34 and Y was 6; 34 is not 5 × 6 = 30, so it is not correct. Statement 2: after 14 years X will be 56 and Y will be 28; 56 = 2 × 28, so it is correct. Hence 2 only, option (b).
If the price of an article is decreased by 20% and then the new price is increased by 25%, then what is the net change in the price ?
UPSC's answer: (a) — Let the original price of the article be 100. A 20% decrease reduces the price to 100 - 20 = 80. A subsequent 25% increase on the new price of 80 is calculated as 25% of 80, which equals 20. The final price becomes 80 + 20 = 100.
When a certain number is multiplied by 7, the product entirely comprises ones only (1111...). What is the smallest such number ?
UPSC's answer: (d) — We need the smallest number N such that 7 × N is a repunit (a number made up entirely of the digit 1, e.g. 111, 1111, 11111, 111111, …). This is equivalent to finding the smallest repunit that is exactly divisible by 7, since N = (repunit) ÷ 7.
A man completes 7/8 of a job in 21 days. How many more days will it take him to finish the job if quantum of work is further increased by 50% ?
UPSC's answer: (d) — The man completes 7/8 of a job in 21 days, so his rate of work is (7/8) ÷ 21 = 1/24 of the job per day. The quantum of work is increased by 50%, making the total work 1.5 times the original, but he has already completed 7/8 of the original job.
Question paper and answer key: Union Public Service Commission. Explanations: UPSC Answer Check. Practise this paper with a timer →
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