CSAT Paper II of the 2024 Preliminary examination, held on 16 June 2024. 80 questions · 200 marks · qualifying at 33%. The questions broke down as Comprehension 27, Basic Numeracy 24, Data Interpretation 10, Mental Ability 9, Logical Reasoning 9.
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 of the following statements best reflect the most logical and rational inferences that can be made from the passage? 1. The current methods of food distribution are solely responsible for the loss and wastage of food. 2. Land productivity is adversely affected by the prevailing trend of food loss and wastage. 3. Reduction in the loss and wastage of food results in lesser carbon footprint. 4. Post-harvest technologies to prevent or reduce the loss and wastage of food are not available. Select the correct answer using the code given below.
UPSC's answer: (b) — Statement 1 is incorrect because the passage states food is lost or wasted 'throughout the supply chain, from initial agricultural production to final household consumption,' not solely due to distribution methods.
Based on the above passage, the following assumptions have been made : 1. The food distribution mechanism needs to be reimagined and made effective to reduce the loss and wastage of food. 2. Ensuring the reduction of wastage and loss of food is a social and moral responsibility of all citizens. Which of the assumptions given above is/are valid?
UPSC's answer: (c) — The passage states that food is lost or wasted throughout the supply chain, from initial agricultural production to final household consumption.
Which of the following statements best reflects/reflect the most logical and rational inference/inferences that can be made from the passage? 1. Central banks cannot bring down inflation without budgetary backing. 2. The effects of monetary policy depend on the fiscal policies pursued by the government. Select the correct answer using the code given below.
UPSC's answer: (c) — The passage states that without fiscal backup, monetary policy eventually loses traction, implying that central banks cannot effectively bring down inflation without budgetary support, which validates statement 1.
Based on the above passage, the following assumptions have been made : 1. Fiscal policies of governments are solely responsible for higher prices. 2. Higher prices do not affect the long-term government bonds. Which of the assumptions given above is/are valid?
UPSC's answer: (d) — Assumption 1 is not valid: the passage says higher prices come from a mix of forces — governments spending freely, central-bank interest rates and rising debt-service costs — so fiscal policy is not "solely" responsible.
What is the least possible number of cuts required to cut a cube into 64 identical pieces?
UPSC's answer: (b) — 64 = 4 x 4 x 4, so the cube is divided into 4 equal parts along length, 4 along breadth, and 4 along height. Dividing one edge into 4 equal parts requires 3 straight cuts. The same 3 cuts are needed in each of the three mutually perpendicular directions.
In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, -, × each at most two times. What is the smallest non-negative value of the expression?
UPSC's answer: (d) — There are four operator slots in 5 * 4 * 3 * 2 * 1, and each of +, −, × may be used at most twice. Try 5 − 4 − 3 + 2 × 1: − is used twice, + once and × once, which is allowed. By BODMAS, 2 × 1 = 2, so the value is 5 − 4 − 3 + 2 = 0.
A certain number of men can complete a piece of work in 6k days, where k is a natural number. By what percent should the number of men be increased so that the work can be completed in 5k days?
UPSC's answer: (c) — The total work is constant, so the product of the number of men and the number of days remains the same. Let the initial number of men be M, so the total work is M * 6k. To complete the same work in 5k days, let the new number of men be M'.
X, Y and Z can complete a piece of work individually in 6 hours, 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work?
UPSC's answer: (c) — Hourly work: X does 1/6, Y does 1/8 and Z does 1/8 of the job. To finish fastest, the fastest worker X should work as often as the rule allows — every alternate hour. Schedule X, Y, X, Z, X, Y for the first 6 hours: X works 3 hours (3/6 = 1/2) and Y and Z together 3 hours (3/8).
How many consecutive zeros are there at the end of the integer obtained in the product 1² × 2⁴ × 3⁶ × 4⁸ × … × 25⁵⁰?
UPSC's answer: (d) — The product is 1² × 2⁴ × 3⁶ × … × 25⁵⁰, i.e. each number k is raised to the power 2k. Trailing zeros come from pairs of 2 and 5; 2s are far more plentiful, so count the 5s. Only 5, 10, 15, 20 and 25 contain 5. Their powers are 10, 20, 30, 40 and 50.
On January 1st, 2023, a person saved ₹ 1. On January 2nd, 2023, he saved ₹ 2 more than that on the previous day. On January 3rd, 2023, he saved ₹ 2 more than that on the previous day and so on. At the end of which date was his total savings a perfect square as well a perfect cube?
UPSC's answer: (b) — Daily savings are ₹1, ₹3, ₹5, … — the odd numbers. The total after n days is 1 + 3 + … + (2n − 1) = n². So the total is always a perfect square. It is also a perfect cube when n² is a cube, i.e. when n itself is a cube. The first cube after 1 is n = 8: total = 8² = 64 = 4³.
Which one of the following statements best reflects the most logical and rational inference that can be made from the above passage?
UPSC's answer: (a) — The passage states that iconic cities like New York, London, and Paris succeeded because plans with a 'heavy systems approach' were imposed on them.
Based on the above passage, the following assumptions have been made : 1. India needs a new generation of urban professionals with knowledge relevant to modern urban practice. 2. Indian universities at present have no capacity or potential to impart training in systems approach. Which of the assumptions given above is/are correct?
UPSC's answer: (a) — The passage states that iconic cities like New York, London, and Paris succeeded because plans with a heavy systems approach were imposed on them.
Which one of the following statements best reflects the central idea of the above passage?
UPSC's answer: (b) — The passage argues that anonymous private entities with high capital can pay for more space, effectively 'buying a louder voice' on the internet.
Based on the above passage, the following assumptions have been made : 1. Internet is not inclusive enough. 2. Internet can adversely affect the quality of politics in a country. Which of the assumptions given above is/are valid?
UPSC's answer: (c) — The passage states that anonymous private entities with high capital can pay for more space, effectively buying a louder voice, which implies that the internet platform is not equally accessible or inclusive to all voices, validating Assumption 1.
222³³³ + 333²²² is divisible by which of the following numbers?
UPSC's answer: (b) — Divisibility by 2: 222³³³ is even and 333²²² is odd, so their sum is odd — not divisible by 2. Divisibility by 3: 222 and 333 are both multiples of 3, so both terms, and their sum, are divisible by 3.
What percent of water must be mixed with honey so as to gain 20% by selling the mixture at the cost price of honey?
UPSC's answer: (a) — Let the honey cost ₹1 per litre, and mix w litres of water with 1 litre of honey. Cost of the mixture = ₹1 (only the honey costs money). It is sold at the cost price of honey: (1 + w) litres × ₹1 = ₹(1 + w). A 20% gain needs 1 + w = 1.2, so w = 0.2 litre of water per litre of honey.
What is the rightmost digit preceding the zeros in the value of 30³⁰?
UPSC's answer: (d) — 30³⁰ = 3³⁰ × 10³⁰, so the number is 3³⁰ followed by 30 zeros. The digit just before the zeros is the unit digit of 3³⁰. Unit digits of powers of 3 repeat in the cycle 3, 9, 7, 1. 30 = 4 × 7 + 2, so 3³⁰ ends like 3², i.e. in 9. The digit is 9 — option (d).
421 and 427, when divided by the same number, leave the same remainder 1. How many numbers can be used as the divisor in order to get the same remainder 1?
UPSC's answer: (c) — If a number d leaves remainder 1 when dividing both 421 and 427, then d divides 420 and 426, and d must be greater than 1. The common divisors of 420 and 426 are the divisors of HCF(420, 426) = 6: 1, 2, 3, 6. 1 is excluded (it leaves remainder 0).
A can X contains 399 litres of petrol and a can Y contains 532 litres of diesel. They are to be bottled in bottles of equal size so that whole of petrol and diesel would be separately bottled. The bottle capacity in terms of litres is an integer. How many different bottle sizes are possible?
UPSC's answer: (b) — The problem requires finding the number of integer bottle sizes that can exactly divide both 399 litres of petrol and 532 litres of diesel. This is equivalent to finding the number of common divisors of 399 and 532, which is the number of divisors of their Greatest Common Divisor (GCD).
Consider the following statements in respect of the sum S = x + y + z, where x, y and z are distinct prime numbers each less than 10 : 1. The unit digit of S can be 0. 2. The unit digit of S can be 9. 3. The unit digit of S can be 5. Which of the statements given above are correct?
UPSC's answer: (c) — The distinct prime numbers less than 10 are 2, 3, 5, and 7. To check Statement 1 (unit digit 0), consider the set {2, 3, 5}; their sum is 10, which has a unit digit of 0, making this statement correct.
Based on the above passage, the following assumptions have been made : 1. For effective school education, parents have greater role than the governments. 2. School curriculum that conforms to today's requirements and is uniform for the entire country may address the issues brought out. Which of the assumptions given above is/are valid?
UPSC's answer: (d) — Assumption 1 is invalid because the passage attributes the low academic competencies to systemic issues like curriculum expectations and the transition gap, not to a lack of parental effort or a comparison of roles between parents and government.
Which one of the following statements best reflects the central idea conveyed by the passage?
UPSC's answer: (c) — The passage highlights a critical gap: while parents and children expect 'graduates' from class 8 to proceed to higher education and avoid agriculture, their actual academic competencies (reading and arithmetic) are far below curricular standards.
Which one of the following statements best reflects the thinking of the author about the science?
UPSC's answer: (d) — The passage contrasts the views of Newton and Galileo, who saw science solely as an account of the world and a duty to tell the truth, with the modern view that science is a social enterprise.
Two persons P and Q enter into a business. P puts ₹ 14,000 more than Q, but P has invested for 8 months and Q has invested for 10 months. If P's share is ₹ 400 more than Q's share out of the total profit of ₹ 2,000, what is the capital contributed by P?
UPSC's answer: (a) — Let Q's capital be x, so P's capital is x + 14,000. The profit sharing ratio is determined by the product of capital and time: P's share is proportional to 8(x + 14,000) and Q's share is proportional to 10x.
P's salary is 20% lower than Q's salary which is 20% lower than R's salary. By how much percent is R's salary more than P's salary?
UPSC's answer: (b) — Let R's salary be 100 units. Q's salary is 20% lower than R's, so Q = 100 - 20 = 80 units. P's salary is 20% lower than Q's, so P = 80 - (20% of 80) = 80 - 16 = 64 units. The difference between R's and P's salary is 100 - 64 = 36 units.
A number is mistakenly divided by 4 instead of multiplying by 4. What is the percentage change in the result due to this mistake?
UPSC's answer: (d) — Let the number be x. The correct result is 4x; the mistaken result is x/4. The result falls by 4x − x/4 = 15x/4. As a percentage of the correct result: (15x/4) ÷ 4x × 100 = 15/16 × 100 = 93.75%. Option (d).
In an examination, 80% of students passed in English, 70% of students passed in Hindi and 15% failed in both the subjects. What is the percentage of students who failed in only one subject?
UPSC's answer: (b) — Let the total number of students be 100. The number of students who passed in English is 80, so those who failed in English are 100 - 80 = 20. The number of students who passed in Hindi is 70, so those who failed in Hindi are 100 - 70 = 30.
A father said to his son, "n years back I was as old as you are now. My present age is four times your age n years back". If the sum of the present ages of the father and the son is 130 years, what is the difference of their ages?
UPSC's answer: (a) — Let the son be S and the father F years old now. "n years back I was as old as you are now": F − n = S, so n = F − S. "My present age is four times your age n years back": F = 4(S − n) = 4(S − F + S) = 4(2S − F), so 5F = 8S. With F + S = 130: S = 50 and F = 80.
Consider the following : 1. 1000 litres = 1 m³ 2. 1 metric ton = 1000 kg 3. 1 hectare = 10000 m² Which of the above are correct?
UPSC's answer: (d) — 1 m³ = 100 cm × 100 cm × 100 cm = 1,000,000 cm³, and since 1 litre = 1000 cm³, 1,000,000 ÷ 1000 = 1000 litres, so statement 1 is correct. 1 metric ton is defined as 1000 kg, so statement 2 is correct. 1 hectare is defined as 10000 m², so statement 3 is correct.
Which of the following is/are emphatically conveyed by the author of the passage? 1. Without science, mankind could not have continued to exist till today. 2. It is the science that will ultimately determine the destiny of mankind. Select the correct answer using the code given below.
UPSC's answer: (d) — The passage argues that science and mankind are inextricably linked, stating that 'Science and mankind cannot be divorced from time to time at men’s convenience.' The author explicitly rejects the idea of treating science as an 'abstract third party' that is independently praised or blamed…
Based on the above passage, the following assumptions have been made : 1. The horrors of modern life are the inevitable result of the progress of science. 2. The aspect of truth likely to be overlooked is that science is what man has made it. Which of the assumptions given above is/are correct?
UPSC's answer: (b) — The passage explicitly states that it is easy to overlook the relations between science and mankind, treating science as an abstract third party rather than a human creation. This supports Assumption 2, which identifies the overlooked truth as the fact that science is what man has made it.
When we meet other people while we travel, we learn to differentiate between
UPSC's answer: (c) — The passage states that a merchant learns the worth of his goods and distinguishes between what is 'parochial' and what is 'universal' through travel and experience.
With reference to the above passage, the following assumptions have been made : 1. Travel leads to an understanding of humans. 2. Travel helps those who wish to learn fundamental common values. 3. A person with long experience in travel can resolve differences amongst people. Which of the assumptions given above are valid?
UPSC's answer: (a) — Assumption 1 is valid because the passage states that travel allows one to learn 'fundamental common values' and live at ease among 'fellows,' implying an understanding of human nature and shared values.
Let X be a two-digit number and Y be another two-digit number formed by interchanging the digits of X. If (X + Y) is the greatest two-digit number, then what is the number of possible values of X?
UPSC's answer: (d) — Write X = 10a + b; then Y = 10b + a, and X + Y = 11(a + b). The greatest two-digit number is 99, so a + b = 9. Both X and Y must be two-digit numbers, so neither digit can be 0 — this rules out 90 (whose reverse, 09, is not two-digit).
Consider the following : Weight of 6 boys = Weight of 7 girls = Weight of 3 men = Weight of 4 women If the average weight of the women is 63 kg, then what is the average weight of the boys?
UPSC's answer: (b) — Let the total weight of the group be W. The problem states that the weight of 4 women is equal to W, so 4 * (Average Weight of Women) = W. Given the average weight of women is 63 kg, W = 4 * 63 = 252 kg. The weight of 6 boys is also equal to W, so 6 * (Average Weight of Boys) = 252 kg.
How many times the hour hand and the minute hand coincide in a clock between 10:00 a.m. and 2:00 p.m. (same day)?
UPSC's answer: (a) — The hour and minute hands coincide 11 times in a 12-hour period, approximately every 65 minutes and 27 seconds. The first coincidence after 10:00 a.m. occurs at approximately 10:54:33 a.m. The next coincidence occurs at approximately 12:00:00 p.m. (exactly 12:00).
The calendar for the year 2025 is same for
UPSC's answer: (c) — A year's calendar repeats only when the next year begins on the same weekday AND is of the same type (common or leap). January 1, 2025 falls on a Wednesday, and 2025 is a common year (365 days). Each common year shifts the starting weekday forward by 1; each leap year shifts it forward by 2.
Let p, q, r and s be distinct positive integers. Let p, q be odd and r, s be even. Consider the following statements : 1. (p - r)²(qs) is even. 2. (q - s)q²s is even. 3. (q + r)²(p + s) is odd. Which of the statements given above are correct?
UPSC's answer: (d) — Let p and q be odd integers, and r and s be even integers. Statement 1: (p - r) is (odd - even) = odd. (qs) is (odd * even) = even. The product of an odd and an even number is even, so Statement 1 is correct. Statement 2: (q - s) is (odd - even) = odd. q² is (odd * odd) = odd. s is even.
What is the angle between the minute hand and hour hand when the clock shows 4:25 hours?
UPSC's answer: (c) — The hour hand moves 0.5° per minute, so at 4:25 it is at 4 * 30° + 25 * 0.5° = 132.5° from the 12 o'clock position. The minute hand moves 6° per minute, so at 25 minutes it is at 25 * 6° = 150° from the 12 o'clock position.
Which of the following statements best reflects/reflect the most logical and rational inference/inferences that can be made from the passage? 1. In conventional classroom learning, the central goal is duration of learning rather than attainment of competency. 2. Conventional classrooms encourage one-size-fits-all approach and stamp out all differentiation. Select the correct answer using the code given below.
UPSC's answer: (c) — Statement 1 is supported by the passage's opening line, which states that conventional classrooms emphasize 'fixed duration over learning effectiveness,' implying the central goal is time spent rather than competency attained.
Based on the above passage, the following assumptions have been made : 1. As a large number of workers in our country are employed in unorganized sector, India does not need to change its present conventional classroom system of education. 2. Even with its present conventional classroom system of education, India produces sufficient number of skilled workers to fully realize the benefits of demographic dividend. Which of the assumptions given above is/are valid?
UPSC's answer: (d) — The passage explicitly states that the conventional classroom model leads to variable outcomes and leaves many learners behind, resulting in only 10 percent employability among graduates.
Based on the above passage, the following assumptions have been made : 1. The adolescent does not feel comfortable with his parents because they tend to be dominating and assertive. 2. The adolescent of modern times does not have much respect for parents. Which of the assumptions given above is/are valid?
UPSC's answer: (a) — The passage states that parents' 'parental solicitude' is often a 'disguise for love of power,' which directly supports the assumption that parents are dominating and assertive.
Which one of the following statements best reflects the central idea of the above passage?
UPSC's answer: (a) — The passage highlights a conflict during adolescence where parents, driven by 'parental solicitude' and a 'love of power,' insist on managing moral problems. It notes that the options parents express are often inadequate or ineffective in resolving these specific adolescent issues.
What is the number of fives used in numbering a 260-page book?
UPSC's answer: (b) — Count the digit 5 in the units place from 1 to 260: 5, 15, ..., 255, giving 26 occurrences. Count the digit 5 in the tens place: 50-59, 150-159, and 250-259, giving 10 + 10 + 10 = 30 occurrences. There is no hundreds-place 5 because the book ends at page 260.
What is the sum of the first 28 terms in the following sequence? 1, 1, 2, 1, 3, 2, 1, 4, 3, 2, 1, 5, 4, 3, 2, …
UPSC's answer: (b) — The sequence is made of blocks that count down: (1), (2, 1), (3, 2, 1), (4, 3, 2, 1), … Block n has n terms, so the first 7 blocks contain 1 + 2 + … + 7 = 28 terms — exactly the first 28 terms. Each block sums to 1 + 2 + … + n: the block sums are 1, 3, 6, 10, 15, 21, 28.
A person buys three articles P, Q and R for ₹ 3,330. If P costs 25% more than R and R costs 20% more than Q, then what is the cost of P?
UPSC's answer: (d) — Let the cost of article Q be x. Since R costs 20% more than Q, the cost of R is 1.20x. Since P costs 25% more than R, the cost of P is 1.25 * 1.20x = 1.50x. The total cost is the sum of P, Q, and R: 1.50x + x + 1.20x = 3.70x.
If the sum of the two-digit numbers AB and CD is the three-digit number 1CE, where the letters A, B, C, D, E denote distinct digits, then what is the value of A?
UPSC's answer: (a) — The equation is AB + CD = 1CE, which translates to (10A + B) + (10C + D) = 100 + 10C + E. Simplifying the equation gives 10A + B + D = 100 + E.
Three numbers x, y, z are selected from the set of the first seven natural numbers such that x > 2y > 3z. How many such distinct triplets (x, y, z) are possible?
UPSC's answer: (d) — The numbers come from {1, 2, …, 7} and must satisfy x > 2y > 3z. z = 1: 2y > 3 means y ≥ 2. y = 2: x > 4, so x = 5, 6, 7 → (5, 2, 1), (6, 2, 1), (7, 2, 1). y = 3: x > 6, so x = 7 → (7, 3, 1). y ≥ 4 needs x > 8 — impossible. z = 2: 2y > 6 means y ≥ 4, which again needs x > 8 — impossible.
The total cost of 4 oranges, 6 mangoes and 8 apples is equal to twice the total cost of 1 orange, 2 mangoes and 5 apples. Consider the following statements : 1. The total cost of 3 oranges, 5 mangoes and 9 apples is equal to the total cost of 4 oranges, 6 mangoes and 8 apples. 2. The total cost of one orange and one mango is equal to the cost of one apple. Which of the statements given above is/are correct?
UPSC's answer: (c) — Let one orange, mango and apple cost O, M and A. The condition 4O + 6M + 8A = 2(O + 2M + 5A) = 2O + 4M + 10A simplifies to 2O + 2M = 2A, i.e. O + M = A. So Statement 2 is correct. Statement 1: (3O + 5M + 9A) − (4O + 6M + 8A) = A − O − M = 0, so the two totals are equal. Statement 1 is correct.
Which one of the following statements best reflects the most logical, rational and practical suggestion implied by the passage?
UPSC's answer: (b) — The passage describes a process where carbon dioxide (CO2) is injected into underground basalt rocks, causing it to react with calcium and magnesium to form limestone.
Based on the above passage, the following assumptions have been made : 1. Giant icebergs have a bearing on primary productivity and food chains of the Southern Ocean. 2. Melting of giant icebergs can produce climate change effects and impact world fisheries. Which of the assumptions given above is/are valid?
UPSC's answer: (c) — The passage states that giant icebergs store up to 20 percent of carbon in the Southern Ocean, directly linking them to primary productivity, which validates Assumption 1.
Which one of the following statements best reflects the most logical, rational and practical message conveyed by the passage?
UPSC's answer: (c) — The passage states that caterpillar frass induces corn plants to turn off their defense mechanisms against insect predators. This specific biological mechanism allows caterpillars to feed more efficiently and grow faster by suppressing the host plant's natural resistance.
32⁵ + 2²⁷ is divisible by
UPSC's answer: (c) — 32⁵ = (2⁵)⁵ = 2²⁵. 2²⁵ + 2²⁷ = 2²⁵(1 + 2²) = 5 × 2²⁵. The number has both 2 and 5 as factors, so it is divisible by 10 — option (c).
Let p and q be positive integers satisfying p < q and p + q = k. What is the smallest value of k that does not determine p and q uniquely?
UPSC's answer: (c) — List the pairs with p < q and p + q = k: k = 3: (1, 2) only — unique. k = 4: (1, 3) only — unique. k = 5: (1, 4) and (2, 3) — two pairs, so p and q are not determined. The smallest such k is 5 — option (c).
A person walks 100 m straight from his house, turns left and walks 100 m, again turns left and walks 300 m, then turns right and walks 100 m to reach his office. In which direction does he walk initially from his house if his office is exactly in the North-East direction?
UPSC's answer: (c) — Headings: first walk in direction h; turn left; turn left again (now opposite to h); turn right (back to the first left-turn direction). Net displacement = 100 along h + 100 left of h − 300 along h + 100 left of h = 200 opposite to h + 200 to the left of h.
A person walks 100 m Westward, then turns left and walks 100 m. He then takes 225° turn clockwise. In which direction is he walking now?
UPSC's answer: (d) — The person starts by walking 100 m Westward, so his initial direction of travel is West. He turns left (90° counter-clockwise) from West, which changes his direction to South. He then walks 100 m South, maintaining the Southward direction.
A Statement is given followed by two Conclusions numbered I and II. Consider the Statement and the Conclusions. Statement : India is the world's largest producer of milk. Conclusion-I : India is the world's largest exporter of milk. Conclusion-II : India does not import milk. Which one of the following is correct?
UPSC's answer: (d) — The statement establishes that India is the world's largest producer of milk, which refers to total domestic output. Being the largest producer does not logically imply that India is the largest exporter, as a significant portion of production may be consumed domestically.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : What are the values of m and n, where m and n are natural numbers? Statement-I : m + n > mn and m > n. Statement-II : The product of m and n is 24. Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (c) — Statement I provides the inequalities m + n > mn and m > n. For natural numbers, if m ≥ 2 and n ≥ 2, then mn ≥ m + n, which contradicts the first inequality. Therefore, one of the numbers must be 1. Since m > n, n must be 1, and m can be any natural number greater than 1.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : What is the time required to download the software? Statement-I : The size of the software is 12 megabytes. Statement-II : The transfer rate is 2·4 kilobytes per second. Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (c) — To calculate the time required for download, the formula Time = Size / Transfer Rate is necessary. Statement I provides the size of the software as 12 megabytes, but without the transfer rate, the time cannot be determined.
Which one of the following statements best reflects the crux of the above passage?
UPSC's answer: (a) — The passage defines a robust democracy as one where reality is transparently expressed through political speech and media. It explicitly states that a 'normatively responsible media' has the responsibility to circulate the content of reality without distortion.
Which one of the following statements best reflects the most logical, rational and practical message implied by the passage?
UPSC's answer: (d) — The passage highlights that manufacturers and service providers use interconnected home devices to gather personal data to overcome thin profit margins. It explicitly states that this data collection happens 'with or without our agreement,' indicating a lack of user consent.
Which one of the following statements best reflects the crux of the above passage?
UPSC's answer: (c) — The passage defines green growth as rethinking strategies to balance environmental sustainability with the needs of poor and vulnerable groups.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : What are the unique values of x and y, where x, y are distinct natural numbers? Statement-I : x / y is odd. Statement-II : xy = 12 Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (c) — Statement I alone: x/y odd allows endless pairs (3, 1), (5, 1), (6, 2), … — not enough. Statement II alone: xy = 12 allows (1, 12), (2, 6), (3, 4), (4, 3), (6, 2), (12, 1) — not enough.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. A certain amount was distributed among X, Y and Z. Question : Who received the least amount? Statement-I : X received 4/5 of what Y and Z together received. Statement-II : Y received 2/7 of what X and Z together received. Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (c) — Let the total amount be T, so X + Y + Z = T. From Statement I: X = (4/5)(Y + Z). Since Y + Z = T - X, we get X = (4/5)(T - X), which simplifies to 5X = 4T - 4X, or 9X = 4T, so X = (4/9)T. From Statement II: Y = (2/7)(X + Z).
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : If the average marks in a class are 60, then what is the number of students in the class? Statement-I : The highest marks in the class are 70 and the lowest marks are 50. Statement-II : Exclusion of highest and lowest marks from the class does not change the average. Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (d) — Statement I gives only the highest (70) and lowest (50) marks; the number of students cannot be found. Statement II: removing 70 and 50 leaves the average at 60. Since 70 + 50 = 120 = 2 × 60, this is true for any class size — it gives no equation for n.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. There are three distinct prime numbers whose sum is a prime number. Question : What are those three numbers? Statement-I : Their sum is less than 23. Statement-II : One of the numbers is 5. Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (a) — If 2 were one of the three primes, the sum would be 2 + odd + odd = even and greater than 2 — not prime. So all three primes are odd. Statement I (sum < 23): the odd triples are {3, 5, 7} = 15, {3, 5, 11} = 19, {3, 5, 13} = 21, {3, 7, 11} = 21 (others reach 23 or more).
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Question : Is (x + y) an integer? Statement-I : (2x + y) is an integer. Statement-II : (x + 2y) is an integer. Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (d) — Let 2x + y = m and x + 2y = n. Adding: 3(x + y) = m + n, so x + y = (m + n)/3. Even when m and n are integers, (m + n)/3 need not be one. Example: x = y = 1/3 gives 2x + y = 1 and x + 2y = 1, but x + y = 2/3. With x = y = 1, all three are integers.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. A person buys three articles p, q and r for ₹ 50. The price of the article q is ₹ 16 which is the least. Question : What is the price of the article p? Statement-I : The cost of p is not more than that of r. Statement-II : The cost of r is not more than that of p. Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (c) — The total cost of articles p, q, and r is ₹50, and the cost of q is given as ₹16. Subtracting the cost of q from the total gives the combined cost of p and r as ₹34 (50 - 16 = 34).
A Question is given followed by two Statements I and II. Consider the Question and the Statements. P, Q, R and S appeared in a test. Question : Has P scored more marks than Q? Statement-I : The sum of the marks scored by P and Q is equal to the sum of the marks scored by R and S. Statement-II : The sum of the marks scored by P and S is more than the sum of the marks scored by Q and R. Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (d) — Let the marks of P, Q, R and S be p, q, r and s. Statement I gives p + q = r + s, so r = p + q - s. Statement II gives p + s > q + r; substituting r gives p + s > q + p + q - s, i.e. 2s > 2q, so s > q.
Which one of the following statements best reflects the most logical and rational message conveyed by the above passage?
UPSC's answer: (d) — The passage contrasts the 'unitarian' and 'dictatorial' nature of absolute truths (associated with religion and science) with the 'plural' and 'contradictory' nature of reality embraced by poetry.
Based on the above passage, the following assumptions have been made : 1. The author of the passage believes that flowers are creations of Nature's luxury. 2. The author of the passage does not believe in the usefulness of flowers except as things of beauty. Which of the assumptions given above is/are valid?
UPSC's answer: (d) — The passage explicitly states that flowers evolved to attract insects for pollination, not to please humans or as a 'luxury'. It defines beauty and perfume as by-products of this biological function, not as the primary purpose.
A Question is given followed by two Statements I and II. Consider the Question and the Statements. Age of each of P and Q is less than 100 years but more than 10 years. If you interchange the digits of the age of P, the number represents the age of Q. Question : What is the difference of their ages? Statement-I : The age of P is greater than the age of Q. Statement-II : The sum of their ages is 11/6 times their difference. Which one of the following is correct in respect of the above Question and the Statements?
UPSC's answer: (a) — Let P = 10a + b and Q = 10b + a, with digits a, b from 1 to 9 (both ages are between 10 and 100). The difference is 9|a − b| and the sum is 11(a + b). Statement I (P older) only says a > b; the difference could be 9, 18, 27, … — not enough.
A Main Statement is followed by four Statements labelled P, Q, R and S. Choose the ordered pair of the Statements where the first Statement implies the second, and the two Statements are logically consistent with the Main Statement. Main Statement : Pradeep becomes either a Director or a Producer. Statement P : Pradeep is a Director. Statement Q : Pradeep is a Producer. Statement R : Pradeep is not a Director. Statement S : Pradeep is not a Producer. Select the correct answer.
UPSC's answer: (c) — The main statement says Pradeep becomes a Director or a Producer — at least one of the two. S → P: if he is not a Producer, he must be a Director. S implies P, and both fit the main statement. R → Q: if he is not a Director, he must be a Producer. R implies Q, and both fit the main statement.
If a + b means a - b; a - b means a × b; a × b means a ÷ b; a ÷ b means a + b, then what is the value of 10 + 30 - 100 × 50 ÷ 25? (Operations are to be replaced simultaneously)
UPSC's answer: (d) — The problem states that operations are to be replaced simultaneously, which means we must first substitute the symbols in the expression with their defined meanings before applying the standard order of operations (BODMAS/PEMDAS). The given expression is 10 + 30 - 100 × 50 ÷ 25.
If P means 'greater than (>)'; Q means 'less than (<)'; R means 'not greater than (≯)'; S means 'not less than (≮)' and T means 'equal to (=)', then consider the following statements : 1. If 2x(S)3y and 3x(T)4z, then 9y(P)8z. 2. If x(Q)2y and y(R)z, then x(R)z. Which of the statements given above is/are correct?
UPSC's answer: (d) — S means ≥ and T means =, so statement 1 gives 2x ≥ 3y and 3x = 4z. From 3x = 4z, x = 4z/3, so 2x = 8z/3. Substituting in 2x ≥ 3y gives 8z/3 ≥ 3y, i.e. 8z ≥ 9y, which is the opposite of 9y > 8z, so statement 1 is false. Q means < and R means ≤, so statement 2 gives x < 2y and y ≤ z.
If in a certain code, 'ABCD' is written as 24 and 'EFGH' is written as 1680, then how is 'IJKL' written in that code?
UPSC's answer: (a) — Identify the position of each letter in the English alphabet: A=1, B=2, C=3, D=4; E=5, F=6, G=7, H=8; I=9, J=10, K=11, L=12. Verify the coding pattern using the first example: The code for 'ABCD' is the product of their positions, 1 × 2 × 3 × 4 = 24.
If in a certain code, 'POT' is written as ATOP and 'TRAP' is written as APART, then how is 'ARENA' written in that code?
UPSC's answer: (d) — Analyze the first example: 'POT' becomes 'ATOP'. The original letters are P, O, T. The code is A, T, O, P. This indicates the original string is reversed to T, O, P, and then 'A' is prepended to the front. Verify with the second example: 'TRAP' becomes 'APART'. The original letters are T, R, A, P.
What will come in place of * in the sequence 3, 14, 39, 84, *, 258?
UPSC's answer: (b) — Calculate the first differences between consecutive terms: 14 - 3 = 11, 39 - 14 = 25, 84 - 39 = 45. Calculate the second differences between the first differences: 25 - 11 = 14, 45 - 25 = 20. Calculate the third differences between the second differences: 20 - 14 = 6.
In some code, letters P, Q, R, S, T represent numbers 4, 5, 10, 12, 15. It is not known which letter represents which number. If Q - S = 2S and T = R + S + 3, then what is the value of P + R - T?
UPSC's answer: (b) — The equation Q - S = 2S simplifies to Q = 3S. From the set {4, 5, 10, 12, 15}, the only pair where one number is three times the other is S = 5 and Q = 15. Substituting S = 5 into T = R + S + 3 gives T = R + 8. The remaining numbers are {4, 10, 12}.
Question paper and answer key: Union Public Service Commission. Explanations: UPSC Answer Check. Practise this paper with a timer →
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