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CSAT 2025PYQ

Complete UPSC Civil Services Preliminary Examination General Studies Paper-II / CSAT question paper for 2025.

80Questions
3Subjects
16Topics
QUESTION PAPER

2025 CSAT Questions

All 80 questions from the 2025CSAT paper, classified by subject, topic and subtopic.

Practice 2025 →
Q1
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

Maintaining an ecosystem just to conserve biodiversity will affect its commercial potential as well as the livelihoods dependent on the ecosystem. There is also a conflict between using an ecosystem only for livelihoods, for commercial exploitation, or strictly for conservation. Deforestation caused due to commercial exploitation will lead to indirect harm like floods, siltation problems and microclimatic instability, apart from adversely affecting livelihoods dependent on forests. These conflicts are particularly acute in developing countries where the dependence of people on the ecosystem is significant, and commercial exploitation has the potential to boost national income.

Which one of the following statements best reflects the critical message conveyed by the author of the passage?

AConservation of biodiversity is not an issue to be worried about when some people depend on ecosystems for their livelihoods.
BCommercial exploitation of forests goes against the fundamental rights of the people dependent on forests for food and shelter.
CSustenance of livelihood and degradation of ecosystem while being together exacerbate one another, leading to conflicts and imbalance.
DCommercial exploitation of ecosystems should be completely stopped.
Show answer & explanation
ANSWERC
EXPLANATION

C captures the passage’s central tension between livelihood dependence and ecosystem degradation.

Q2
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

Maintaining an ecosystem just to conserve biodiversity will affect its commercial potential as well as the livelihoods dependent on the ecosystem. There is also a conflict between using an ecosystem only for livelihoods, for commercial exploitation, or strictly for conservation. Deforestation caused due to commercial exploitation will lead to indirect harm like floods, siltation problems and microclimatic instability, apart from adversely affecting livelihoods dependent on forests. These conflicts are particularly acute in developing countries where the dependence of people on the ecosystem is significant, and commercial exploitation has the potential to boost national income.

With reference to the above passage, the following assumptions have been made: I. No country needs to depend on ecosystems to boost national income. II. Resource-rich countries need to share their resources with those of scant resources so as to prevent the degradation of ecosystems. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERD
EXPLANATION

I contradicts the passage’s statement about national income and II is not stated.

Q3
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms' green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.

Which one of the following statements best reflects the central idea of the passage?

AEconomies of scale is essential for transition to green growth.
BModern technological progress is intensely linked to path-dependent innovations.
CCountries with large economies are in a better position to adopt green technologies.
DTiming plays a crucial role in the case of green technology development.
Show answer & explanation
ANSWERD
EXPLANATION

The passage stresses early, gradual movement and the cost of a late transition.

Q4
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

The history of renewable energy suggests there is a steep learning curve, meaning that, as more is produced, costs fall rapidly because of economies of scale and learning by doing. The firms' green innovation is path-dependent: the more a firm does, the more it is likely to do in the future. The strongest evidence for this is the collapse in the price of solar energy, which became about 90% cheaper during the 2010s, repeatedly beating forecasts. Moving early and gradually gives economies more time to adjust, allowing them to reap the benefits of path-dependent green investment without much disruption. A late, more chaotic transition is costlier.

With reference to the above passage, the following assumptions have been made: I. Path-dependent green investments will eventually most likely benefit growth as well as public finances in a country like India. II. If other green technologies follow the same pattern as that of solar energy, there will most likely be an easy green transition. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERC
EXPLANATION

Both assumptions are accepted in the content cross-check as reasonable inferences from the passage.

Q5
Quantitative AptitudeNumber SystemFactors, HCF & LCM

A natural number N is such that it can be expressed as N = p + q + r, where p, q and r are distinct factors of N. How many numbers below 50 have this property?

A6
B7
C8
D9
Show answer & explanation
ANSWERC
EXPLANATION

The qualifying values are 6, 12, 18, 24, 30, 36, 42 and 48.

Q6
Quantitative AptitudeNumber SystemPrime Numbers

Three prime numbers p, q and r, each less than 20, are such that p − q = q − r. How many distinct possible values can we get for (p + q + r)?

A4
B5
C6
DMore than 6
Show answer & explanation
ANSWERA
EXPLANATION

The possible sums are 15, 21, 33 and 39, so there are four distinct values.

Q7
Quantitative AptitudeNumber SystemFractions

How many possible values of (p + q + r) are there satisfying 1/p + 1/q + 1/r = 1, where p, q and r are natural numbers (not necessarily distinct)?

A
BOne
CThree
DMore than three
Show answer & explanation
ANSWERC
EXPLANATION

The unordered solutions are (3,3,3), (2,4,4) and (2,3,6), giving three distinct sums.

Q8
Logical ReasoningNumber SeriesNumber / Alphabet Series

What comes at X and Y respectively in the following sequence? January, January, December, October, X, March, October, Y, September

AJuly, May
BJuly, April
CJune, May
DJune, April
Show answer & explanation
ANSWERB
EXPLANATION

The month numbers follow backward steps 0,1,2,3,4,5,6,7 modulo 12, giving July and April.

Q9
Quantitative AptitudeArithmeticTime, Speed & Distance

Team X scored a total of N runs in 20 overs. Team Y tied the score in 10% less overs. Had team Y’s average run rate (runs per over) been 50% higher, the scores would have been tied in 12 overs. How many runs were scored by team X?

A72
B144
C216
DCannot be determined
Show answer & explanation
ANSWERD
EXPLANATION

The 50% higher-rate condition is automatically satisfied for any N, so N cannot be determined.

Q10
Quantitative AptitudePercentageSuccessive Percentage Change

The price (p) of a commodity is first increased by k%; then decreased by k%; again increased by k%; and again decreased by k%. If the new price is q, then what is the relation between p and q?

Ap(10^4 − k^2)^2 = q × 10^8
Bp(10^4 − k^2)^2 = q × 10^4
Cp(10^4 − k^2) = q × 10^4
Dp(10^4 − k^2) = q × 10^8
Show answer & explanation
ANSWERA
EXPLANATION

Multiplying the four percentage factors gives q=p(10^4−k²)^2/10^8.

Q11
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

Each State in India faces a distinctive set of challenges regarding the impact of warming, but also offers its own set of opportunities for reducing emissions depending on its natural resources. For example, coastal States need to take action to protect their shores from sea level rise, districts that are drier need to prepare for variable monsoon precipitation. Himalayan regions have their own unique challenges, and selected parts of peninsular India and offshore areas offer great opportunities for harnessing wind power. These various aspects need to be considered for developing clear and sustainable goals for the future.

Which one of the following statements best reflects the most logical, rational and pragmatic message conveyed by the author of the passage?

AThe mitigation and adaptation strategies to address/tackle the climate change is essentially the responsibility of each State.
BIndia is too diverse to implement any effective strategy or programme to address/tackle the climate change.
CIt is basically the responsibility of the Union Government to implement the climate action plans and ensure net zero emissions.
DIndia needs to formulate effective climate change mitigation and adaptation strategies at the State/region level.
Show answer & explanation
ANSWERD
EXPLANATION

The passage emphasizes region-specific risks and opportunities, so strategies need State/region tailoring.

Q12
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

Each State in India faces a distinctive set of challenges regarding the impact of warming, but also offers its own set of opportunities for reducing emissions depending on its natural resources. For example, coastal States need to take action to protect their shores from sea level rise, districts that are drier need to prepare for variable monsoon precipitation. Himalayan regions have their own unique challenges, and selected parts of peninsular India and offshore areas offer great opportunities for harnessing wind power. These various aspects need to be considered for developing clear and sustainable goals for the future.

With reference to the passage, the following assumptions have been made: I. Green energy production can be linked to/integrated with the climate change mitigation and adaptation strategies. II. Effects of climate change are much more severe in coastal and mountainous regions. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERA
EXPLANATION

I is consistent with emissions-reduction opportunities; II is not established by the passage.

Q13
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.

Which one of the following statements best reflects the critical message conveyed by the passage?

AIndia’s political executive should be aware that poverty and social inequality and the consequent sense of insecurity is the main social problem.
BIn India, poverty is the primary reason for social inequality and insecurity.
CPoverty and social inequality are so intricately linked that they pose an unmanageable crisis for India.
DInsecurity, more than poverty, is the main economic issue that Government policies must address.
Show answer & explanation
ANSWERD
EXPLANATION

The passage explicitly emphasizes economic insecurity and policies aimed at mitigating it.

Q14
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

If the social inequality is the most acutely felt social problem in India, insecurity, more than poverty, is the most acutely felt economic problem. Besides those below the official poverty line, even those just over the poverty line are subject to multiple economic insecurities of various kinds (due to wealth and/or health risks, market fluctuations, job-related uncertainties). Many Government policies are actually intended towards mitigating these insecurities.

With reference to the above passage, the following assumptions have been made: I. People above the poverty line also are prone to suffer from anxiety about economic insecurity. II. Eradication of poverty can result in peace and social equality in the country. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERA
EXPLANATION

I is stated in substance; II is not established.

Q15
Quantitative AptitudeGeometry and MensurationGeometric Counting

A solid cube is painted yellow on all its faces. The cube is then cut into 60 smaller but equal pieces by making the minimum number of cuts. Which of the following statements is/are correct? I. The minimum number of cuts is 9. II. The number of smaller pieces which are not painted on any face is 6.

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERC
EXPLANATION

A 3×4×5 subdivision needs 9 cuts and leaves (1×2×3)=6 wholly internal pieces.

Q16
Quantitative AptitudeNumber SystemNumber Properties & Patterns

If 7 * 24 = 25 and 12 * 16 = 20, then what is 16 * 63 equal to?

A70
B66
C65
D64
Show answer & explanation
ANSWERC
EXPLANATION

The operation is the hypotenuse rule, so √(16²+63²)=65.

Q17
Quantitative AptitudePercentagePercentage Applications

The petrol price shot up by 10% as a result of the hike in crude oil prices. The price of petrol before the hike was ₹90 per litre. A person travels 2200 km every month and his car gives a mileage of 16 km per litre. By how many km should he reduce his travel if he wants to maintain his expenditure at the previous level?

A180 km
B200 km
C220 km
D240 km
Show answer & explanation
ANSWERB
EXPLANATION

The price becomes ₹99; maintaining expenditure reduces distance from 2200 to 2000 km, a reduction of 200 km.

Q18
Quantitative AptitudeNumber SystemRemainders

A 4-digit number N is such that when divided by 3, 5, 6, 9 leaves a remainder 1, 3, 4, 7 respectively. What is the smallest value of N?

A1068
B1072
C1078
D1082
Show answer & explanation
ANSWERC
EXPLANATION

1078 satisfies all four remainder conditions.

Q19
Logical ReasoningAlgebraAlgebraic Reasoning

Consider the following statements: I. If A ≤ B > C < D > E > F ≥ G = H; then B is always greater than E. II. If P > Q = R ≥ S = T ≤ U = V > W; then S is always less than V. Which of the statements given above is/are correct?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERD
EXPLANATION

Neither comparison is forced by the stated chains.

Q20
Quantitative AptitudeNumber SystemDigits & Number Formation

What is the unit digit in the multiplication of 1 × 3 × 5 × 7 × 9 × … × 999?

A1
B3
C5
D9
Show answer & explanation
ANSWERC
EXPLANATION

The product contains a factor 5 and all factors are odd, so the unit digit is 5.

Q21
Reading ComprehensionReading ComprehensionInference
PASSAGE

One of the dismal realities of the agricultural sector in independent India has been that it never experienced a high-growth phase, unlike the non-agricultural economy. The highest decadal growth (compound annual growth rate or CAGR) for agriculture has been just 3-5% in the 1980s. Also, after experiencing a spurt in decadal growth during the 1980s, agricultural growth suffered relative stagnation thereafter. This is in sharp contrast to non-agricultural growth, which consistently increased from the 1980s to 2000s.

Which one of the following statements best reflects the corollary to the above passage?

AThe benefit of economic reforms percolates down more slowly to the agriculture sector than in other sectors of the economy.
BFor India, the green revolution was not as useful as it was expected to be.
CIndia lagged behind other countries in adapting mechanized and modern farming.
DRural-to-urban migration resulted in the stagnant agriculture sector.
Show answer & explanation
ANSWERA
EXPLANATION

The passage supports the relative stagnation/divergence of agriculture but does not identify the other specific causes.

Q22
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

One of the dismal realities of the agricultural sector in independent India has been that it never experienced a high-growth phase, unlike the non-agricultural economy. The highest decadal growth (compound annual growth rate or CAGR) for agriculture has been just 3-5% in the 1980s. Also, after experiencing a spurt in decadal growth during the 1980s, agricultural growth suffered relative stagnation thereafter. This is in sharp contrast to non-agricultural growth, which consistently increased from the 1980s to 2000s.

With reference to the passage, the following assumptions have been made: The growing divergence between the fortunes of the agricultural and non-agricultural economy in India could have been reduced/contained by: I. adapting large-scale cultivation of commercial crops and viable corporate farming. II. providing free insurance for all crops and heavily subsidizing seeds, fertilizers, electricity and farm machinery at par with developed countries. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERD
EXPLANATION

The passage does not establish either specific intervention as the cause or solution.

Q23
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

In our country, handlooms are equated with a culture that ensures a continuity of tradition. This idea has become part of the public policy-framing and provides a legitimate basis for the State to support the sector. But the notion of tradition as a single, linear entity is being strongly contested today. The narratives dominant in defining culture/tradition in a particular way are seen to have emerged as the identities and histories of large sections. The discounted and, at times, forcibly stifled identities are fighting for their rightful place in history. Against this backdrop, when we promote handloom as a traditional industry, it is not surprising that large sections of our population choose to ignore it.

Which one of the following statements best reflects the most logical and rational message conveyed by the author of the passage?

AWe need to free the handloom industry from the limited narrative linked to preserving cultural heritage.
BContinued State support to the handloom industry ensures the preservation of some of our glorious art forms and old traditions.
CHousehold units of the handloom sector should be modernized and made an economically viable organized industry.
DHandloom products need to be converted to machine-made designer products so as to make them more popular.
Show answer & explanation
ANSWERA
EXPLANATION

The passage critiques the narrow traditional-industry narrative and its alienating effects.

Q24
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

In our country, handlooms are equated with a culture that ensures a continuity of tradition. This idea has become part of the public policy-framing and provides a legitimate basis for the State to support the sector. But the notion of tradition as a single, linear entity is being strongly contested today. The narratives dominant in defining culture/tradition in a particular way are seen to have emerged as the identities and histories of large sections. The discounted and, at times, forcibly stifled identities are fighting for their rightful place in history. Against this backdrop, when we promote handloom as a traditional industry, it is not surprising that large sections of our population choose to ignore it.

With reference to the above passage, the following assumptions have been made: I. There is no need for the State to be involved in any manner in the handloom sector. II. Handloom products are no longer appealing and attractive in the rapidly changing modern world. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERD
EXPLANATION

The passage says State support has a legitimate basis and does not claim handloom products are inherently unattractive.

Q25
Quantitative AptitudeNumber SystemDivisibility

Consider the first 100 natural numbers. How many of them are not divisible by any one of 2, 3, 5, 7 and 9?

A20
B21
C22
D23
Show answer & explanation
ANSWERC
EXPLANATION

9 is redundant because it is divisible by 3; inclusion-exclusion gives 22.

Q26
Quantitative AptitudeAlgebraAlgebraic Reasoning

If 4 ≤ x ≤ 8 and 2 ≤ y ≤ 7, then what is the ratio of maximum value of (x + y) to minimum value of (x − y)?

A6
B15/2
C−15/2
DNone of the above
Show answer & explanation
ANSWERD
EXPLANATION

Maximum x+y=15 and minimum x−y=−3, so the ratio is −5, not listed.

Q27
Quantitative AptitudeNumber SystemPrime Numbers

Let both p and k be prime numbers such that (p² + k) is also a prime number less than 30. What is the number of possible values of k?

A4
B5
C6
D7
Show answer & explanation
ANSWERB
EXPLANATION

The possible k values are 2,3,7,13,19, giving five.

Q28
Quantitative AptitudeNumber SystemFactors, HCF & LCM

There are n sets of numbers each having only three positive integers with LCM equal to 1001 and HCF equal to 1. What is the value of n?

A6
B7
C8
DMore than 8
Show answer & explanation
ANSWERD
EXPLANATION

Enumerating 3-element divisor sets gives 32, so n is more than 8.

Q29
Quantitative AptitudeNumber SystemDigits & Number Formation

Let PQR be a 3-digit number, PPT be a 3-digit number and PS be a 2-digit number, where P, Q, R, S, T are distinct non-zero digits. Further, PQR − PS = PPT. If Q = 3 and T < 6, then what is the number of possible values of (R, S)?

A2
B3
C4
DMore than 4
Show answer & explanation
ANSWERB
EXPLANATION

There are three valid (R,S) pairs under the digit constraints.

Q30
Logical ReasoningNumber SeriesNumber / Alphabet Series

Consider the sequence AB_CC_A_BCCC_BBC_C that follows a certain pattern. Which one of the following completes the sequence?

AB, C, B, C, A
BA, C, B, C, A
CB, C, B, A, C
DC, B, B, A, C
Show answer & explanation
ANSWERC
EXPLANATION

Option C yields ABBCCC repeated three times.

Q31
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

In our country, regrettably, teaching and learning for the examination have been our forte but the new demands of society and the future of work require critical and independent thinking, learning through doing, asking questions from multiple disciplinary perspectives on the same issue, using evidence for building arguments, and reflecting and articulation. Higher education should not either be a mere servant of the government policy or a passive respondent to public mood. Higher learning is all about how to think rather than what to think. Teaching has to be re-invented.

Which one of the following statements best reflects the central idea conveyed by the passage?

AIndia does not have enough resources for promoting quality education in its universities.
BThe institutions of higher learning in the country should not be under the control of the Government.
CClassroom approach to higher education should be done away with.
DClassroom needs to be reimagined and teaching needs to be re-invented.
Show answer & explanation
ANSWERD
EXPLANATION

The passage calls for re-invented teaching and learning focused on how to think.

Q32
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

In our country, regrettably, teaching and learning for the examination have been our forte but the new demands of society and the future of work require critical and independent thinking, learning through doing, asking questions from multiple disciplinary perspectives on the same issue, using evidence for building arguments, and reflecting and articulation. Higher education should not either be a mere servant of the government policy or a passive respondent to public mood. Higher learning is all about how to think rather than what to think. Teaching has to be re-invented.

With reference to the above passage, the following assumptions have been made: I. Higher education is a constantly evolving subject that needs to align towards new developments in all spheres of society. II. In our country, sufficient funds are not allocated for promoting higher education. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERA
EXPLANATION

I follows from the changing demands; II is not mentioned.

Q33
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

If there is inequality in the pattern of population growth, there is greater inequality in food production and utilization. As societies become wealthier, their consumption of animal products increases. This means that a greater proportion of such basic foodstuff as grains and legumes that could feed humans directly is instead being converted into feed for poultry and large farm animals. Yet this conversion of plant-based food into animal food for humans is far from efficient. Only 16% of the calories fed to chickens are recovered by us when we eat them. This conversion rate goes down to five to seven per cent in large animals that are fed grain to add fat and some protein before slaughter.

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

AThere is an urgent need for a public policy to promote the consumption of cereal-based foods in wealthier societies.
BAnimal-based food is far less efficient than grain/plant-based food in terms of production and utilization.
CPlant-based protein should replace the animal-based protein in our daily diets.
DInequality in food production and consumption is inevitable in any fast changing society.
Show answer & explanation
ANSWERB
EXPLANATION

The passage emphasizes the inefficiency of converting plant calories into animal food.

Q34
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

If there is inequality in the pattern of population growth, there is greater inequality in food production and utilization. As societies become wealthier, their consumption of animal products increases. This means that a greater proportion of such basic foodstuff as grains and legumes that could feed humans directly is instead being converted into feed for poultry and large farm animals. Yet this conversion of plant-based food into animal food for humans is far from efficient. Only 16% of the calories fed to chickens are recovered by us when we eat them. This conversion rate goes down to five to seven per cent in large animals that are fed grain to add fat and some protein before slaughter.

With reference to the above passage, the following assumptions have been made: I. The food manufacturing and processing industries in every country should align their objectives and processes in accordance with the changing needs of the societies. II. Wealthier societies tend to incur great loss of calories of food materials due to indirect utilization of their agricultural produce. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERB
EXPLANATION

Both are consistent with the passage’s description of changing consumption and calorie losses through animal feed.

Q35
Quantitative AptitudeNumber SystemPrime Numbers

What is the maximum value of n such that 7 × 343 × 385 × 1000 × 2401 × 77777 is divisible by 35^n?

A3
B4
C5
D7
Show answer & explanation
ANSWERB
EXPLANATION

There are four factors of 5 and ten factors of 7; 5 is limiting, so n=4.

Q36
Logical ReasoningNumber SeriesNumber / Alphabet Series

What is X in the sequence 24, X, 12, 18, 36, 90?

A18
B12
C9
D6
Show answer & explanation
ANSWERB
EXPLANATION

The multipliers 1.5,2,2.5 extend backward to 1 and 0.5, giving X=12.

Q37
Quantitative AptitudeTime and WorkWork & Time

P and Q walk along a circular track. They start at 5:00 a.m. from the same point in opposite directions. P walks at an average speed of 5 rounds per hour and Q walks at an average speed of 3 rounds per hour. How many times will they cross each other between 5:20 a.m. and 7:00 a.m.?

A12
B13
C14
D15
Show answer & explanation
ANSWERB
EXPLANATION

Relative speed is 8 rounds/hour; counting crossings strictly between 5:20 and 7:00 gives 13.

Q38
Logical ReasoningMathematical OperationsOperator / Symbol Problems

If P = +, Q = −, R = ×, S = ÷, then insert the proper notations between the successive numbers in the equation 60_15_3_20_4 = 20:

ASPRQ
BQRPS
CQRSP
DSPQR
Show answer & explanation
ANSWERB
EXPLANATION

QRPS gives 60−15×3+20÷4=20.

Q39
Quantitative AptitudeTime, Speed and DistanceRelative Speed / Meeting

A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram?

A15 m
B18 m
C20 m
D24 m
Show answer & explanation
ANSWERC
EXPLANATION

Equating relative-speed expressions gives tram speed 12 km/h and length 20 m.

Q40
Quantitative AptitudeNumber SystemNumber Properties & Patterns

If N² = 12345678987654321, then how many digits does the number N have?

A8
B9
C10
D11
Show answer & explanation
ANSWERB
EXPLANATION

A 17-digit square has a 9-digit square root here.

Q41
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

Over the next 30 years, many countries are promising to move to net-zero carbon, implying that household emissions will have to be cut to close to nothing. A leading climate scientist reckons that, at best, half the reduction might be achieved through demand-side measures, such as behavioural changes by individuals and households. And even that would require companies and governments to provide more incentives to change through supply-side investments to make low-carbon options cheaper and more widely available.

Which one of the following statements best reflects the central idea conveyed by the passage?

AMoving to net-zero carbon is possible only by the reduction in household emissions.
BLow-carbon behaviour in people can be brought about by incentivising them.
CCheaper goods and services can be made available to people by using low-carbon technologies.
DManufacturing industries that use low-carbon technologies should be provided with subsidies.
Show answer & explanation
ANSWERB
EXPLANATION

The passage links behavioural change to incentives and supply-side investment that makes low-carbon options cheaper.

Q42
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

Over the next 30 years, many countries are promising to move to net-zero carbon, implying that household emissions will have to be cut to close to nothing. A leading climate scientist reckons that, at best, half the reduction might be achieved through demand-side measures, such as behavioural changes by individuals and households. And even that would require companies and governments to provide more incentives to change through supply-side investments to make low-carbon options cheaper and more widely available.

With reference to the above passage, the following assumptions have been made: I. Supply-side investments in companies can result in low-carbon behaviour in people. II. People are not capable of adapting low-carbon behaviour without the involvement of Government and Companies. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERA
EXPLANATION

The passage supports I directly; II is treated as too absolute in the content check, so A.

Q43
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

In only 50 years, the world's consumption of raw materials has nearly quadrupled, to more than 100 billion tons. Less than 9% of this is reused. Batteries of old vehicles contain materials such as lithium, cobalt, manganese and nickel that are pricey and can be hard to obtain. Supply chains are long and complicated. Buyers' risks are being aggravated by their suppliers' poor environmental and labour standards. Reusing materials makes sense. Once batteries reach the ends of their lives, they should go back to a factory where their ingredients can be recovered and put into new batteries.

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

AGreen economy is not possible without reusing critical minerals.
BEvery sector of economy should adapt the reuse of material resources immediately.
CCircular economy can be beneficial for sustainable growth.
DCircular use of material resources is the only option for some industries for their survival.
Show answer & explanation
ANSWERC
EXPLANATION

The passage supports circular use as beneficial for sustainable growth without claiming exclusivity.

Q44
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

In only 50 years, the world's consumption of raw materials has nearly quadrupled, to more than 100 billion tons. Less than 9% of this is reused. Batteries of old vehicles contain materials such as lithium, cobalt, manganese and nickel that are pricey and can be hard to obtain. Supply chains are long and complicated. Buyers' risks are being aggravated by their suppliers' poor environmental and labour standards. Reusing materials makes sense. Once batteries reach the ends of their lives, they should go back to a factory where their ingredients can be recovered and put into new batteries.

With reference to the above passage, the following assumptions have been made: I. Automobile factories are examples of the circular economy. II. Economic growth is compatible with circular use of mineral resources. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERB
EXPLANATION

Only II is supported by the passage’s discussion of reuse and resource recovery.

Q45
Quantitative AptitudeTime and WorkPipes & Cisterns

A set (X) of 20 pipes can fill 70% of a tank in 14 minutes. Another set (Y) of 10 pipes fills 3/8th of the tank in 6 minutes. A third set (Z) of 16 pipes can empty half of this tank in 20 minutes. If half of the pipes of set X are closed and only half of the pipes of set Y are open, and all pipes of the set Z are open, then how long will it take to fill 50% of the tank?

A8 minutes
B10 minutes
C12 minutes
D16 minutes
Show answer & explanation
ANSWERD
EXPLANATION

Net rate is 0.03125 tank/min, so 50% takes 16 minutes.

Q46
Quantitative AptitudeNumber SystemRemainders

If n is a natural number, then what is the number of distinct remainders of (1^n + 2^n) when divided by 4?

A0
B1
C2
D3
Show answer & explanation
ANSWERC
EXPLANATION

Odd n gives remainder 3 and even n gives remainder 1: two distinct remainders.

Q47
Quantitative AptitudeNumber SystemFactors, HCF & LCM

Let P = QQQ be a 3-digit number. What is the HCF of P and 481?

A1
B13
C37
D481
Show answer & explanation
ANSWERC
EXPLANATION

P=111Q and 481=13×37; 111 contains 37, giving HCF 37 for Q=1–9.

Q48
Quantitative AptitudeNumber SystemDigits & Number Formation

What is the 489th digit in the number 123456789101112... ?

A0
B3
C6
D9
Show answer & explanation
ANSWERD
EXPLANATION

After 9+180=189 digits, the next 300 digits are 100–199, ending at 199; the 489th digit is 9.

Q49
Logical ReasoningStatement & ConclusionStatement, Assumption & Conclusion

A mobile phone has been stolen. There are 3 suspects P, Q and R. They were questioned knowing that only one of them is guilty. Their responses are as follows: P: I did not steal. Q stole it. Q: R did not steal. I did not steal. R: I did not steal. I do not know who did it. Who stole the mobile phone?

AP
BQ
CR
DCannot be concluded
Show answer & explanation
ANSWERA
EXPLANATION

Under the intended truth/lie convention, P is the guilty person. The booklet does not explicitly state that convention, so this item is interpretive.

Q50
Logical ReasoningPuzzlesLogic Puzzles & Scheduling

Three teams P, Q, R participated in a tournament in which the teams play with one another exactly once. A win fetches a team 2 points and a draw 1 point. A team gets no point for a loss. Each team scored exactly one goal in the tournament. The team P got 3 points, Q got 2 points and R got 1 point. Which of the following statements is/are correct? I. The result of the match between P and Q is a draw with the score 0–0. II. The number of goals scored by R against Q is 1.

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERC
EXPLANATION

The unique score pattern is P–Q 0–0, P–R 1–0, Q–R 1–1; both statements follow.

Q51
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

It is hard to predict how changes in the climate and the atmosphere's chemistry will affect the prevalence and virulence of agricultural diseases. But there is a risk that such changes will make some plant infections more common in all climatic zones, perhaps catastrophically so. Part of the problem is that centuries of selective breeding have refined the genomes of most high-value crops. They are spectacular at growing in today's conditions but genetic variations that are not immediately useful to them have been bred out. This is good for yields but bad for coping with changes. A minor disease or even an unknown one could suddenly rampage through a genetically honed crop.

Which one of the following statements best reflects the central idea conveyed by the passage?

AGlobal climate change adversely affects the productivity of crops.
BOur total dependence on genetically honed crops entails possible food insecurity.
COur food security should not depend on agricultural productivity alone.
DGenetically honed crops should be replaced with their wild varieties in our present cultivation practices.
Show answer & explanation
ANSWERB
EXPLANATION

The passage emphasizes vulnerability of genetically honed crops and consequent food insecurity risk.

Q52
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

It is hard to predict how changes in the climate and the atmosphere's chemistry will affect the prevalence and virulence of agricultural diseases. But there is a risk that such changes will make some plant infections more common in all climatic zones, perhaps catastrophically so. Part of the problem is that centuries of selective breeding have refined the genomes of most high-value crops. They are spectacular at growing in today's conditions but genetic variations that are not immediately useful to them have been bred out. This is good for yields but bad for coping with changes. A minor disease or even an unknown one could suddenly rampage through a genetically honed crop.

With reference to the above passage, the following assumptions have been made: I. Global climate change can result in the migration of several plant diseases to new areas. II. Scientific understanding of the wild relatives of our present crops would enable us to strengthen food security. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERC
EXPLANATION

Both are accepted as reasonable inferences from spread across climatic zones and the need to recover genetic diversity.

Q53
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

A good statesman, like any other sensible human being, learns more from his opponents than from his fervent supporters. For his supporters will push him to disaster unless his opponents show him where the dangers are. So if he is wise he will often pray to be delivered from his friends, because they will ruin him. But, though it hurts, he ought also to pray never to be left without opponents; for they keep him on the path of reason and good sense. The national unity of free people depends upon a sufficiently even balance of political power to make it impracticable for the administration to be arbitrary and for opposition to be revolutionary and irreconcilable.

Which one of the following statements best reflects the critical message conveyed by the author of the passage?

AWithout opposition parties, the administration in a democracy tends to become more responsible.
BDemocracy needs to have revolutionaries in opposition to keep the government alert.
CRulers in a democracy need the support of opposition for their political survival.
DIn a democracy, the opposition is indispensable for the balance of political power and good governance.
Show answer & explanation
ANSWERD
EXPLANATION

The author emphasizes an even balance of political power and the corrective role of opposition.

Q54
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

A good statesman, like any other sensible human being, learns more from his opponents than from his fervent supporters. For his supporters will push him to disaster unless his opponents show him where the dangers are. So if he is wise he will often pray to be delivered from his friends, because they will ruin him. But, though it hurts, he ought also to pray never to be left without opponents; for they keep him on the path of reason and good sense. The national unity of free people depends upon a sufficiently even balance of political power to make it impracticable for the administration to be arbitrary and for opposition to be revolutionary and irreconcilable.

With reference to the above passage, the following assumptions have been made: I. In a democracy, a strong opposition is required only if the Head of Government is indifferent. II. The more aggressive the opposition, the better is the governance in a democracy. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERD
EXPLANATION

Neither is supported; the passage calls for balance, not indifference-dependent or aggressive opposition.

Q55
Logical ReasoningBlood RelationsFamily Relations

P is the brother of Q and R. S is R’s mother. T is P’s father. How many of the following statements are definitely true? I. S and T are a couple. II. Q is T’s son. III. T is Q’s father. IV. S is P’s mother. V. R is T’s daughter. VI. P is S’s son. Select the correct answer using the code given below:

AOnly two
BOnly three
COnly four
DOnly five
Show answer & explanation
ANSWERC
EXPLANATION

II, III, IV and VI are definite; I assumes couple status and V assumes R is female.

Q56
Logical ReasoningCoding-DecodingLetter / Number Coding

If NO is coded as 210, NOT is coded as 4200 and NOTE is coded as 21000, then how is NOTES coded?

A399000
B420000
C440000
D630000
Show answer & explanation
ANSWERB
EXPLANATION

Multiply alphabet positions: 14×15×20×5×19=399000.

Q57
Logical ReasoningCoding-DecodingLetter / Number Coding

If FRANCE is coded as 654321 and GERMANY is coded as 9158437, then how is YEMEN coded?

A54321
B81913
C71913
D71813
Show answer & explanation
ANSWERD
EXPLANATION

The fixed mapping gives Y=7,E=1,M=8,E=1,N=3, hence 71813.

Q58
Quantitative AptitudeNumber SystemDigits & Number Formation

The 5-digit number PQRST (all distinct digits) is such that T ≠ 0. P is thrice T. S is greater than Q by 4, while Q is greater than R by 3. How many such 5-digit numbers are possible?

A3
B4
C5
D6
Show answer & explanation
ANSWERB
EXPLANATION

Testing the digit constraints yields four valid numbers.

Q59
Quantitative AptitudeTime and WorkWork & Efficiency

X can complete one-third of a certain work in 6 days, Y can complete one-third of the same work in 8 days and Z can complete three-fourth of the same work in 12 days. All of them work together for n days and then X and Z quit and Y alone finishes the remaining work in 8 2/3 days. What is n equal to?

A3
B4
C5
D6
Show answer & explanation
ANSWERB
EXPLANATION

Rates are 1/18,1/24,1/16; solving the remaining work after Y’s 26/3 days gives n=4.

Q60
Logical ReasoningNumber SeriesNumber / Alphabet Series

What is X in the sequence 1, 3, 6, 11, 18, X, 42?

A26
B27
C29
D30
Show answer & explanation
ANSWERC
EXPLANATION

Differences are 2,3,5,7,11,13, so X=29.

Q61
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

There has been no democracy that has grown economically without corporate capitalism. It helps in modernizing the economy and enabling the transition from rural to urban, and agriculture to industry and services, which are inevitable with growth. It generates jobs — and there is no other way to fix a country's unemployment challenge without a further impetus to private business. Big companies can operate on a large scale and become competitive both domestically and externally. A vibrant corporate capitalist base also leads to additional revenues for the State — which in turn, can be used for greater welfare for the marginalized and creating a more level playing field in terms of opportunities.

Which one of the following statements best reflects the critical message conveyed by the author of the passage?

ACorporate capitalism is important for economic growth of a State and also for democracy.
BCorporate capitalism is imperative for a modern State to achieve its political objectives.
CNo State can ensure its economic survival for long without the role of corporate capitalism.
DCorporate capitalism and democracy have mutual dependence for their continued existence.
Show answer & explanation
ANSWERA
EXPLANATION

The passage directly links corporate capitalism with economic growth and democracy.

Q62
Reading ComprehensionReading ComprehensionAssumption
PASSAGE

There has been no democracy that has grown economically without corporate capitalism. It helps in modernizing the economy and enabling the transition from rural to urban, and agriculture to industry and services, which are inevitable with growth. It generates jobs — and there is no other way to fix a country's unemployment challenge without a further impetus to private business. Big companies can operate on a large scale and become competitive both domestically and externally. A vibrant corporate capitalist base also leads to additional revenues for the State — which in turn, can be used for greater welfare for the marginalized and creating a more level playing field in terms of opportunities.

With reference to the above passage, the following assumptions have been made: I. Corporate capitalism promotes the growth of labour force and provides more employment opportunities. II. Poor and marginalized sections of population are benefited by corporate capitalism due to trickle-down effect. Which of the above assumptions is/are valid?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERC
EXPLANATION

The intended reading accepts both employment generation and welfare benefits mediated through State revenues.

Q63
Reading ComprehensionReading ComprehensionArgument / Reasoning
PASSAGE

A network of voluntary associations stands as a ‘buffer’ between the relatively powerless individual and the potentially powerful State.

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

AIt emphasizes the inability of the State to enforce its will in practice against the opposition of certain groups within it.
BIt is a cooperative organization for the promotion of the well-being and development of the personality of its members.
CIt takes individuals out of a state of isolation and gives them a chance to participate in the common endeavour.
DIt permits citizens to have a variety of loyalties and allegiance.
Show answer & explanation
ANSWERC
EXPLANATION

C gives the direct mechanism by which associations buffer individuals from State power.

Q64
Quantitative AptitudeNumber SystemFactors, HCF & LCM

Consider the following statements: I. There exists a natural number which when increased by 50% can have its number of factors unchanged. II. There exists a natural number which when increased by 150% can have its number of factors unchanged. Which of the statements given above is/are correct?

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERC
EXPLANATION

n=2 witnesses both statements because d(2)=d(3)=d(5)=2.

Q65
Quantitative AptitudeAnalytical & Critical ReasoningAnalytical / Critical Reasoning

There are 7 places A, B, C, D, E, F and G in a city connected by various roads AB, AC, CD, DE, BF, EG and FG. A is 6 km south of B. A is 10 km west of C. D is 5 km east of E. C is 6 km north of D. F is 9 km west of B. F is 12 km north of G. A person travels from D to F through these roads. What is the distance covered by the person?

A20 km
B25 km
C31 km
D37 km
Show answer & explanation
ANSWERC
EXPLANATION

The route D-C-A-B-F is 6+10+6+9=31 km.

Q66
Logical ReasoningCoding-DecodingLetter / Number Coding

In a certain code if 64 is written as 343 and 216 is written as 729, then how is 512 written in that code?

A1000
B1331
C1728
D2197
Show answer & explanation
ANSWERB
EXPLANATION

Cube roots 4 and 6 map to 7 and 9, so 8 maps to 11 and 11³=1331.

Q67
Quantitative AptitudeNumber SystemRemainders

What is the remainder when 9^5 + 9^6 + 9^7 + … + 9^100 is divided by 6?

A0
B1
C2
D3
Show answer & explanation
ANSWERA
EXPLANATION

Every positive power of 9 is congruent to 3 modulo 6. There are 96 terms, so the sum is 96×3, divisible by 6; remainder 0.

Q68
Logical ReasoningData SufficiencyTwo-Statement / Data Sufficiency

A question is given followed by two Statements I and II. Question: What is the smallest 1-digit number having exactly 4 distinct factors? Statement I: 2 is one of the factors. Statement II: 3 is one of the factors. Which one of the following is correct in respect of the above Question and the Statements?

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
BThe Question can be answered by using either Statement alone.
CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
DThe Question can be answered even without using any of the Statements.
Show answer & explanation
ANSWERD
EXPLANATION

The base question itself gives 6 as the smallest one-digit number with four factors, so D.

Q69
Logical ReasoningData SufficiencyTwo-Statement / Data Sufficiency

A question is given followed by two Statements I and II. Question: Let P, Q, R, S be distinct non-zero digits. If PP × PQ = RRSS, where P ≤ 3 and Q ≤ 4, then what is Q equal to? Statement I: R = 1. Statement II: S = 2. Which one of the following is correct in respect of the above Question and the Statements?

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
BThe Question can be answered by using either Statement alone.
CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
DThe Question can be answered even without using any of the Statements.
Show answer & explanation
ANSWERB
EXPLANATION

The unique digit solution is P=3,Q=4,R=1,S=2; either statement alone is sufficient.

Q70
Logical ReasoningData SufficiencyTwo-Statement / Data Sufficiency

A question is given followed by two Statements I and II. Question: How is Q related to P? Statement I: P has two sisters, R and S. Statement II: R’s father is the brother of Q. Which one of the following is correct in respect of the above Question and the Statements?

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
BThe Question can be answered by using either Statement alone.
CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
DThe Question cannot be answered even using any of the Statements.
Show answer & explanation
ANSWERC
EXPLANATION

Together the statements establish Q as P’s paternal uncle; neither alone is sufficient.

Q71
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

A single number for inflation is an aggregate across different commodities and services — the price rise differs for different items of consumption. So, the single number is arrived at by assigning weights to different commodities and services. For WPI, the weights in production are used; for CPI, the consumption basket is used. But people are not homogeneous. The consumption basket is vastly different for the poor, the middle classes, and the rich. Hence, the CPI is different for each of these classes and a composite index requires averaging the baskets.

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

AWe must use WPI exclusively in measuring price rise and CPI should be done away with.
BThe present calculation of inflation rate does not correctly measure price rise of individual item/commodity.
CInflation data under-presents services in the consumption basket.
DKnowledge of inflation rate is not really of any use to anybody in the country.
Show answer & explanation
ANSWERB
EXPLANATION

A single aggregate inflation number cannot represent the price rise of every individual item or group equally.

Q72
Reading ComprehensionReading ComprehensionMain Idea / Central Theme
PASSAGE

Trust stands commonly defined as being vulnerable to others. Entrepreneurship implies trust in others and willingness to expose oneself to betrayal. Trust in expert systems is the essence of globalizing behaviour; trust itself emerges as a super-commodity in the social market and defines the characteristics of goods and services in a global market. Trusting conduct also means holding others in good esteem, and an optimism that they are, or will be, competent in certain respects.

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

ATrustworthiness cannot be expected in entrepreneurship.
BTrustworthy people are the most vulnerable people.
CNo economic activity is possible without being exposed to betrayal.
DTrust is important though it entails risk.
Show answer & explanation
ANSWERD
EXPLANATION

The passage repeatedly links trust with entrepreneurship, globalization and vulnerability.

Q73
Logical ReasoningData SufficiencyTwo-Statement / Data Sufficiency

A question is given followed by two Statements I and II. Question: In a football match, team P playing against Q was behind by 3 goals with 10 minutes remaining. Does team P win the match? Statement I: Team P scored 4 goals in the last 10 minutes. Statement II: Team Q scored a total of 4 goals in the match. Which one of the following is correct in respect of the above Question and the Statements?

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
BThe Question can be answered by using either Statement alone.
CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
DThe Question cannot be answered even using any of the Statements.
Show answer & explanation
ANSWERD
EXPLANATION

Statement I alone does not control Q’s scoring; statement II does not yield a valid determination of the outcome.

Q74
Logical ReasoningData SufficiencyTwo-Statement / Data Sufficiency

A question is given followed by two Statements I and II. Question: Is (p + q)^2 − 4pq, where p, q are natural numbers, positive? Statement I: p < q. Statement II: p > q. Which one of the following is correct in respect of the above Question and the Statements?

AThe Question can be answered by using one of the Statements alone, but cannot be answered using the other statement alone.
BThe Question can be answered by using either Statement alone.
CThe Question can be answered by using both the Statements together, but cannot be answered using either Statement alone.
DThe Question can be answered even without using any of the Statements.
Show answer & explanation
ANSWERB
EXPLANATION

The expression is (p−q)^2; either p<q or p>q guarantees positivity.

Q75
Quantitative AptitudeArithmeticBasic Arithmetic

In a T20 cricket match, three players X, Y and Z scored a total of 37 runs. The ratio of the number of runs scored by X to the number of runs scored by Y is equal to the ratio of number of runs scored by Y to the number of runs scored by Z. Value-I = Runs scored by X. Value-II = Runs scored by Y. Value-III = Runs scored by Z. Which one of the following is correct?

AValue-I < Value-II < Value-III
BValue-III < Value-II < Value-I
CValue-I < Value-III < Value-II
DCannot be determined due to insufficient data
Show answer & explanation
ANSWERD
EXPLANATION

Positive integer triples include both 9,12,16 and 16,12,9, so the ordering is not unique.

Q76
Quantitative AptitudeAlgebraAlgebraic Reasoning

Let p + q = 10, where p, q are integers. Value-I = Maximum value of p × q when p, q are positive integers. Value-II = Maximum value of p × q when p ≥ −6, q ≥ −4. Which one of the following is correct?

AValue-I < Value-II
BValue-II < Value-I
CValue-I = Value-II
DCannot be determined due to insufficient data
Show answer & explanation
ANSWERC
EXPLANATION

Both maxima occur at p=q=5, giving 25.

Q77
Quantitative AptitudeNumber SystemIntegers

Consider a set of 11 numbers: Value-I = Minimum value of the average of the numbers of the set when they are consecutive integers ≥ −5. Value-II = Minimum value of the product of the numbers of the set when they are consecutive non-negative integers. Which one of the following is correct?

AValue-I < Value-II
BValue-II < Value-I
CValue-I = Value-II
DCannot be determined due to insufficient data
Show answer & explanation
ANSWERC
EXPLANATION

The minimum average is 0 for −5,…,5 and the minimum product is 0 because the non-negative set can include 0.

Q78
Quantitative AptitudeAlgebraAlgebraic Reasoning

The average of three numbers p, q and r is k. p is as much more than the average as q is less than the average. What is the value of r?

Ak
Bk−1
Ck+1
Dk/2
Show answer & explanation
ANSWERA
EXPLANATION

Let p=k+d and q=k−d; then r=k.

Q79
Quantitative AptitudeAlgebraPowers & Functions

Let x be a real number between 0 and 1. Which of the following statements is/are correct? I. x² > x³. II. x > √x. Select the correct answer using the code given below:

AI only
BII only
CBoth I and II
DNeither I nor II
Show answer & explanation
ANSWERA
EXPLANATION

For 0<x<1, x²>x³ but x<√x, so I only.

Q80
Quantitative AptitudeNumber SystemFactors, HCF & LCM

The difference between any two natural numbers is 10. What can be said about the natural numbers which are divisible by 5 and lie between these two numbers?

AThere is only one such number.
BThere are only two such numbers.
CThere can be more than one such number.
DNo such number exists.
Show answer & explanation
ANSWERC
EXPLANATION

Between 1 and 11, for example, both 5 and 10 lie strictly between and are divisible by 5.