UPSC Insta–DART (Daily Aptitude and Reasoning Test) 6 Sep 2025

Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too.We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.

Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).

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• Question 1 of 5 1. Question A container has 144 litres of oil and another has 180 litres of vinegar. They must be packed in tins of equal capacity so that each contains only one type. The tin capacity in litres is an integer. How many different tin sizes are possible? a) 5 b) 6 c) 9 d) 10 Correct Answer: c Exp) Option c is the correct answer. Tin size must be a common factor of 144 and 180. 144 = 2⁴ × 3² 180 = 2² × 3² × 5 GCD = 2² × 3² = 4 × 9 = 36. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Number of factors = 9 → hence 9 possible sizes. Incorrect Answer: c Exp) Option c is the correct answer. Tin size must be a common factor of 144 and 180. 144 = 2⁴ × 3² 180 = 2² × 3² × 5 GCD = 2² × 3² = 4 × 9 = 36. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Number of factors = 9 → hence 9 possible sizes.

#### 1. Question

A container has 144 litres of oil and another has 180 litres of vinegar. They must be packed in tins of equal capacity so that each contains only one type. The tin capacity in litres is an integer. How many different tin sizes are possible?

Answer: c

Exp) Option c is the correct answer.

Tin size must be a common factor of 144 and 180.

144 = 2⁴ × 3² 180 = 2² × 3² × 5

GCD = 2² × 3² = 4 × 9 = 36. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Number of factors = 9 → hence 9 possible sizes.

Answer: c

Exp) Option c is the correct answer.

Tin size must be a common factor of 144 and 180.

144 = 2⁴ × 3² 180 = 2² × 3² × 5

GCD = 2² × 3² = 4 × 9 = 36. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.

Number of factors = 9 → hence 9 possible sizes.

• Question 2 of 5 2. Question Consider the following statements about S=x+y, where x and y are distinct prime numbers each less than 10. The unit digit of S can be 0. The unit digit of S can be 6. The unit digit of S can be 9. Which of the statements given above are correct? a) 1 and 2 only b) 2 and 3 only c) 1 and 3 only d) 1, 2 and 3 Correct Answer: c Solution Primes less than 10: 2,3,5,7. Distinct pairs and sums: 2+3=5 (unit 5), 2+5=7 (unit 7), 2+7=9 (unit 9), 3+5=8, 3+7=10 (unit 0), 5+7=12 (unit 2). Unit digits possible: 0,2,5,7,8,9. So statements 1 (unit 0) and 3 (unit 9) are correct; statement 2 (unit 6) is incorrect. Hence, option c is correct. Incorrect Answer: c Solution Primes less than 10: 2,3,5,7. Distinct pairs and sums: 2+3=5 (unit 5), 2+5=7 (unit 7), 2+7=9 (unit 9), 3+5=8, 3+7=10 (unit 0), 5+7=12 (unit 2). Unit digits possible: 0,2,5,7,8,9. So statements 1 (unit 0) and 3 (unit 9) are correct; statement 2 (unit 6) is incorrect. Hence, option c is correct.

#### 2. Question

Consider the following statements about S=x+y, where x and y are distinct prime numbers each less than 10.

• The unit digit of S can be 0.

• The unit digit of S can be 6.

• The unit digit of S can be 9.

Which of the statements given above are correct?

• a) 1 and 2 only

• b) 2 and 3 only

• c) 1 and 3 only

• d) 1, 2 and 3

Answer: c

Solution

Primes less than 10: 2,3,5,7. Distinct pairs and sums: 2+3=5 (unit 5), 2+5=7 (unit 7), 2+7=9 (unit 9), 3+5=8, 3+7=10 (unit 0), 5+7=12 (unit 2). Unit digits possible: 0,2,5,7,8,9. So statements 1 (unit 0) and 3 (unit 9) are correct; statement 2 (unit 6) is incorrect. Hence, option c is correct.

Answer: c

Solution

• Question 3 of 5 3. Question A and B take part in 100 m race, where A beats B by 10 m. To favour B, A starts 10 m behind the starting line in a second 100 m race, running at their earlier speeds. Which one among the following is true in view of the second race? (a) A and B reach the finishing line simultaneously (b) B beats A by 1 m (c) B beats A by 2 m (d) A beats B by 1 m Correct Answer: Option (d) Explanation: 100 m track (given) ‘A’ beat ‘B’ by 10 m i.e., when B completed 90 m, A completes 100 m. Next round when ‘A’ run 110 m, how much B run? 1st round when A runs 100 m, B covers 90 m 2nd round when A runs 110 m, B covers x m 100 × x = 110 × 90 i.e., x = 99 When A completed 110 m B completes 99 m. A win by 1 m. Hence option (d) is correct answer. Incorrect Answer: Option (d) Explanation: 100 m track (given) ‘A’ beat ‘B’ by 10 m i.e., when B completed 90 m, A completes 100 m. Next round when ‘A’ run 110 m, how much B run? 1st round when A runs 100 m, B covers 90 m 2nd round when A runs 110 m, B covers x m 100 × x = 110 × 90 i.e., x = 99 When A completed 110 m B completes 99 m. A win by 1 m. Hence option (d) is correct answer.

#### 3. Question

A and B take part in 100 m race, where A beats B by 10 m. To favour B, A starts 10 m behind the starting line in a second 100 m race, running at their earlier speeds. Which one among the following is true in view of the second race?

• (a) A and B reach the finishing line simultaneously

• (b) B beats A by 1 m

• (c) B beats A by 2 m

• (d) A beats B by 1 m

Answer: Option (d)

Explanation:

100 m track (given)

‘A’ beat ‘B’ by 10 m

i.e., when B completed 90 m, A completes 100 m.

Next round when ‘A’ run 110 m, how much B run?

1st round when A runs 100 m, B covers 90 m

2nd round when A runs 110 m, B covers x m

100 × x = 110 × 90

i.e., x = 99

When A completed 110 m B completes 99 m.

A win by 1 m. Hence option (d) is correct answer.

Answer: Option (d)

Explanation:

100 m track (given)

‘A’ beat ‘B’ by 10 m

i.e., when B completed 90 m, A completes 100 m.

Next round when ‘A’ run 110 m, how much B run?

1st round when A runs 100 m, B covers 90 m

2nd round when A runs 110 m, B covers x m

100 × x = 110 × 90

i.e., x = 99

When A completed 110 m B completes 99 m.

A win by 1 m. Hence option (d) is correct answer.

• Question 4 of 5 4. Question Debates on justice often pivot between distributive fairness and recognition of difference. While egalitarian theories focus on redistributing resources to correct structural imbalances, critics argue that such approaches risk erasing cultural identities by imposing uniform standards. Conversely, recognition-based models seek to affirm distinct group identities but may tolerate persistent material inequalities if symbolic respect is achieved. Some theorists propose hybrid models, yet tensions remain: can justice be both materially equal and culturally plural without one undermining the other? This ongoing discourse exposes deep philosophical divides over the very nature and aims of justice in diverse societies. Which one of the following statements best reflects the crux of the above passage? (a) Resolves the tension between distributive and recognition-based models of justice through a unified framework. (b) Argues that cultural recognition is sufficient for justice, even without material equality. (c) Problematizes the reconciliation of material equality and cultural pluralism in theories of justice. (d) Demonstrates that distributive justice is inherently incompatible with recognition-based justice. Correct Solution: (c) Explanation: • The passage presents distributive and recognition-based justice as distinct approaches, noting that attempts to merge them face unresolved tensions. • Option (c) captures the key dilemma—whether justice can be both materially equal and culturally plural without conflict. Other options are incorrect: • (a) Incorrect — the passage does not resolve the tension, it leaves it open. • (b) Incorrect — this is only one side of the debate, not the author’s conclusion. • (d) Incorrect — incompatibility is not asserted as absolute; it’s posed as a question. Incorrect Solution: (c) Explanation: • The passage presents distributive and recognition-based justice as distinct approaches, noting that attempts to merge them face unresolved tensions. • Option (c) captures the key dilemma—whether justice can be both materially equal and culturally plural without conflict. Other options are incorrect: • (a) Incorrect — the passage does not resolve the tension, it leaves it open. • (b) Incorrect — this is only one side of the debate, not the author’s conclusion. • (d) Incorrect — incompatibility is not asserted as absolute; it’s posed as a question.

#### 4. Question

Debates on justice often pivot between distributive fairness and recognition of difference. While egalitarian theories focus on redistributing resources to correct structural imbalances, critics argue that such approaches risk erasing cultural identities by imposing uniform standards. Conversely, recognition-based models seek to affirm distinct group identities but may tolerate persistent material inequalities if symbolic respect is achieved. Some theorists propose hybrid models, yet tensions remain: can justice be both materially equal and culturally plural without one undermining the other? This ongoing discourse exposes deep philosophical divides over the very nature and aims of justice in diverse societies.

Which one of the following statements best reflects the crux of the above passage?

• (a) Resolves the tension between distributive and recognition-based models of justice through a unified framework.

• (b) Argues that cultural recognition is sufficient for justice, even without material equality.

• (c) Problematizes the reconciliation of material equality and cultural pluralism in theories of justice.

• (d) Demonstrates that distributive justice is inherently incompatible with recognition-based justice.

Solution: (c)

Explanation: • The passage presents distributive and recognition-based justice as distinct approaches, noting that attempts to merge them face unresolved tensions. • Option (c) captures the key dilemma—whether justice can be both materially equal and culturally plural without conflict. Other options are incorrect: • (a) Incorrect — the passage does not resolve the tension, it leaves it open. • (b) Incorrect — this is only one side of the debate, not the author’s conclusion. • (d) Incorrect — incompatibility is not asserted as absolute; it’s posed as a question.

Solution: (c)

• Question 5 of 5 5. Question Carbon taxes aim to internalize environmental costs by making emitters pay for their greenhouse gas output. Economists praise them as efficient market-based tools, yet their regressive nature means lower-income households often bear proportionally higher costs. Policymakers face the dilemma of whether to prioritize environmental goals over short-term affordability, or to design compensatory measures such as rebates and targeted subsidies. The challenge extends to balancing domestic competitiveness with climate commitments, especially when trading partners adopt weaker policies. Ultimately, carbon taxes embody a trade-off between economic equity, political feasibility, and environmental necessity. Which one of the following statements best reflects the most logical, rational, and practical message implied by the passage? (a) Carbon taxes should be avoided as they harm economic competitiveness. (b) Carbon taxes are effective but require equity measures to protect vulnerable groups. (c) Carbon taxes are regressive and therefore cannot be politically justified. (d) Carbon taxes work best when international coordination is absent. Correct Solution: (b) Explanation: The passage supports carbon taxes as efficient but acknowledges equity and competitiveness challenges. It suggests balancing environmental effectiveness with fairness through measures like rebates. Option (b) captures this dual focus; others are either extreme or contradict the nuanced argument. Incorrect Solution: (b) Explanation: The passage supports carbon taxes as efficient but acknowledges equity and competitiveness challenges. It suggests balancing environmental effectiveness with fairness through measures like rebates. Option (b) captures this dual focus; others are either extreme or contradict the nuanced argument.

#### 5. Question

Carbon taxes aim to internalize environmental costs by making emitters pay for their greenhouse gas output. Economists praise them as efficient market-based tools, yet their regressive nature means lower-income households often bear proportionally higher costs. Policymakers face the dilemma of whether to prioritize environmental goals over short-term affordability, or to design compensatory measures such as rebates and targeted subsidies. The challenge extends to balancing domestic competitiveness with climate commitments, especially when trading partners adopt weaker policies. Ultimately, carbon taxes embody a trade-off between economic equity, political feasibility, and environmental necessity.

Which one of the following statements best reflects the most logical, rational, and practical message implied by the passage?

• (a) Carbon taxes should be avoided as they harm economic competitiveness.

• (b) Carbon taxes are effective but require equity measures to protect vulnerable groups.

• (c) Carbon taxes are regressive and therefore cannot be politically justified.

• (d) Carbon taxes work best when international coordination is absent.

Solution: (b)

Explanation: The passage supports carbon taxes as efficient but acknowledges equity and competitiveness challenges. It suggests balancing environmental effectiveness with fairness through measures like rebates. Option (b) captures this dual focus; others are either extreme or contradict the nuanced argument.

Solution: (b)

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