MBA4U.in – CAT Practice Mock Test 3

Full-Length Static CAT-Style Mock Paper with Answer Key & Detailed Solutions

Original practice material | 68 Questions | 120 Minutes | VARC 24 | DILR 22 | QA 22

Instructions

Total duration: 120 minutes. Suggested sectional time: 40 minutes each for VARC, DILR and QA.

MCQ: +3 for a correct answer and -1 for an incorrect answer. TITA/non-MCQ: +3 for a correct answer and no negative marking.

This is a static practice paper. No interactive response fields are included.

Difficulty labels (Easy / Moderate / Difficult) are included for practice analytics and are not part of the CAT interface.

Section I – VARC (24 Questions)

RC Passage 1 – When Measurement Changes Behaviour

Passage difficulty: Moderate

Metrics are attractive because they compress complicated activities into numbers that can be compared. A hospital may track waiting times, a university may monitor graduation rates, and a city may count potholes repaired. Such measures are useful precisely because they ignore much of the surrounding detail. Yet the simplification that makes a metric manageable can also make it vulnerable to distortion once people begin to organise their behaviour around it.

This problem is often described as “gaming,” but that word can be misleading. Not every response to a metric is dishonest. If a school is evaluated on attendance, it may legitimately invest in transport or counselling. The difficulty arises when improving the number becomes separable from improving the underlying goal. A call centre rewarded for short calls may end conversations before problems are resolved. A research system that rewards publication counts may encourage many small papers rather than fewer substantial ones.

The central issue is not that measurement is futile. Without measures, organisations may rely on anecdote, hierarchy or intuition, which can conceal failure just as easily. Rather, metrics need to be treated as provisional indicators, not as perfect substitutes for the purposes they represent. This usually means combining several measures, examining cases that sit awkwardly behind the averages, and revising indicators when behaviour changes in response to them.

Good measurement therefore requires a kind of institutional humility. Designers must assume that people will learn the rules and that the rules will alter the activity being measured. A metric should be judged not only by whether it correlates with a desired outcome at the moment of introduction, but also by whether the incentives it creates remain aligned with that outcome after participants adapt.

Q1. The central argument of the passage is that metrics are most useful when they are:  [MCQ | Moderate]

1. treated as final representations of organisational goals
2. used as provisional indicators whose incentive effects are monitored
3. restricted to activities that can be measured without simplification
4. replaced by qualitative judgement once participants adapt

Q2. The call-centre example primarily illustrates that:  [MCQ | Easy]

1. a metric can improve efficiency only when employees do not know it
2. shorter calls are always inconsistent with better service
3. optimising an indicator can diverge from the objective it is meant to represent
4. organisations should avoid measuring activities involving human judgement

Q3. Which course of action best follows from the author’s argument?  [MCQ | Moderate]

1. Using one stable metric so that year-to-year comparisons remain pure
2. Abandoning metrics whenever participants respond strategically
3. Combining indicators and periodically checking whether they still track the intended outcome
4. Evaluating organisations mainly through anecdotal evidence

Q4. The phrase ‘institutional humility’ most nearly refers to recognising that:  [MCQ | Moderate]

1. organisations should publish fewer performance indicators
2. all numerical measures are inherently deceptive
3. people will adapt to evaluation systems and may change what the measures mean
4. institutions cannot know whether their goals are desirable

RC Passage 2 – The Ecology of Urban Noise

Passage difficulty: Moderate-Difficult

Urban noise is commonly treated as a nuisance measured in decibels. That approach is necessary for regulating extreme exposure, but it can obscure the fact that city sound is also structured by timing, repetition and meaning. The same sound level may be experienced differently when it comes from intermittent construction, continuous traffic or a festival that residents expect and value.

Ecologists studying animals have long recognised that acoustic environments shape behaviour. Birds alter the pitch or timing of calls in noisy areas; some species avoid otherwise suitable habitats because signals are masked. Human environments are similarly patterned, although the consequences are not identical. A quiet street at midnight and the same street at noon represent different social expectations. Complaints about sound therefore cannot always be reduced to volume alone.

This creates a challenge for policy. Rules based only on maximum decibel levels are easy to state and enforce, yet they may classify a short, predictable event as equivalent to chronic exposure. Conversely, rules based entirely on context can become subjective and difficult to administer. The practical task is to identify which contextual features can be translated into defensible standards: duration, time of day, frequency, and perhaps the degree to which a sound is avoidable.

Thinking of noise as an ecology rather than merely a quantity also changes design questions. Planners might ask where quiet zones are needed, how delivery schedules interact with residential areas, or whether building forms amplify particular frequencies. The objective is not silence. Cities depend on sound. The more realistic aim is to manage acoustic environments so that necessary activity does not impose persistent and unequal burdens on those who cannot escape it.

Q5. The passage argues that decibel-based regulation is limited mainly because it:  [MCQ | Easy]

1. cannot measure extremely loud sounds accurately
2. ignores contextual features such as duration, timing and meaning
3. assumes animals and humans respond identically to sound
4. makes enforcement impossible in residential areas

Q6. Which of the following best captures the author’s view of urban sound?  [MCQ | Moderate]

1. All unnecessary sound should eventually be eliminated
2. Sound should be governed only through context-sensitive judgement
3. Cities need sound, but acoustic burdens should be managed using both level and context
4. Festival noise deserves exemption from all regulation

Q7. The reference to birds serves chiefly to:  [MCQ | Moderate]

1. prove that humans are biologically harmed by every loud sound
2. show that acoustic environments can influence behaviour in ways not captured by volume alone
3. argue that urban planning should prioritise wildlife over residents
4. suggest that animal studies provide complete models for human noise policy

Q8. Which policy would be most consistent with the passage?  [MCQ | Moderate]

1. A single citywide decibel threshold with no time distinction
2. A ban on all deliveries in residential districts
3. Standards combining sound level with duration and time-of-day rules
4. Allowing communities to decide noise rules without measurable criteria

RC Passage 3 – Why Archives Are Not Neutral Storehouses

Passage difficulty: Difficult

Archives are often imagined as places where the past waits patiently to be discovered. The metaphor suggests that historical evidence exists independently and that archivists merely preserve it. In practice, an archive is produced through many acts of selection. Governments decide which records to create, institutions decide which to retain, donors decide what to deposit, and archivists decide how materials are described and grouped.

Selection does not make archives useless; it makes their structure historically significant. The absence of a record can sometimes reveal as much as its presence. A colonial administration that documented taxation in detail but recorded little about informal labour tells us something about the state’s priorities, though not necessarily about the relative importance of those activities in everyday life.

Digital storage appears at first to weaken the force of selection because vastly more material can be retained. Yet abundance introduces new filters. Search engines rank results; file formats become obsolete; databases require categories; privacy rules limit access. What can be found depends on metadata and interfaces as well as on what physically survives.

Historians therefore need to read archives both for content and for architecture. A letter can be evidence about the event it describes, while the series in which it was filed can be evidence about bureaucratic practice. This double reading resists two opposite errors: treating the archive as a transparent window onto the past, or dismissing it as so constructed that reliable knowledge becomes impossible.

The archive is better understood as a mediated record: incomplete, organised and shaped by institutions, yet still capable of supporting disciplined inference when researchers ask not only “What does this document say?” but also “Why is this document here, and what conditions made it visible to me?”

Q9. The passage’s main claim is that archives should be understood as:  [MCQ | Moderate]

1. unreliable collections whose selection prevents historical knowledge
2. neutral repositories once records have been digitised
3. mediated records whose organisation and absences are themselves historically informative
4. collections valuable only when they preserve complete administrative series

Q10. The example of colonial taxation records is used to show that:  [MCQ | Moderate]

1. detailed records always identify the most important social activities
2. archival silence can reflect institutional priorities rather than absence of activity
3. informal labour cannot be studied historically
4. government archives are less useful than private archives

Q11. According to the passage, digitisation changes archival selection because:  [MCQ | Moderate]

1. it eliminates selection by making storage unlimited
2. it shifts some filtering toward metadata, ranking, format and access systems
3. digital records cannot become obsolete
4. privacy rules become irrelevant when search improves

Q12. The ‘double reading’ recommended by the author asks historians to examine:  [MCQ | Moderate]

1. both public and private archives
2. a document’s content and the institutional structure that preserved and classified it
3. both original manuscripts and digital scans
4. the same source through opposing political theories

RC Passage 4 – Expertise and Public Explanation

Passage difficulty: Moderate

Experts often face a communication dilemma. They know that technical findings depend on assumptions, confidence intervals and exceptions, but public audiences frequently need concise guidance. If every qualification is included, the message can become unusable. If qualifications are omitted, a provisional conclusion may sound absolute.

One response is to separate internal scientific uncertainty from external communication, presenting the public with a single recommendation while keeping debate among specialists. This can be efficient in emergencies, but it carries a cost. When recommendations later change, audiences may interpret revision as evidence that experts were unreliable rather than as a normal consequence of learning.

The alternative is not to expose every technical dispute. Transparency can itself become performative: listing all uncertainties without explaining their significance may overwhelm rather than inform. More useful communication distinguishes between uncertainty that is central to a decision and uncertainty that is unlikely to change the recommended action.

This distinction also clarifies why expert disagreement need not imply paralysis. Two epidemiologists may disagree about the exact size of a risk while agreeing that the risk is large enough to justify intervention. Conversely, specialists may agree on a numerical estimate but disagree about policy because they assign different values to costs, fairness or precaution.

Public explanation is therefore not a simplified copy of expert knowledge. It is a translation task that must preserve the reasoning relevant to action. The best explanation makes clear what is known, what remains uncertain, and which parts of a recommendation depend on evidence rather than on social or ethical judgement.

Q13. The passage suggests that effective public explanation should:  [MCQ | Moderate]

1. remove uncertainty from scientific communication
2. include every technical qualification regardless of relevance
3. identify uncertainties that matter for action while distinguishing evidence from value judgements
4. avoid revising recommendations once they have been announced

Q14. Why can changing expert recommendations damage trust, according to the passage?  [MCQ | Easy]

1. Because scientific knowledge should never change
2. Because earlier communication may have presented provisional conclusions as absolute
3. Because experts usually conceal data from the public
4. Because audiences prefer numerical estimates to advice

Q15. Which statement is most consistent with the passage?  [MCQ | Moderate]

1. Experts who disagree on risk estimates must disagree on policy
2. Experts who agree on a number must agree on what should be done
3. Policy disagreement can persist even when experts agree on evidence, because values also matter
4. Uncertainty should be communicated only after a crisis has ended

Q16. The author characterises public explanation primarily as:  [MCQ | Moderate]

1. the elimination of specialist disagreement
2. a translation that preserves reasoning relevant to decisions
3. a simplified list of scientific facts
4. a method for replacing expert judgement with public opinion

Q17. Choose the option that best summarises the paragraph: A city’s flood map is often treated as a picture of where water will go. In fact, it is a model built from rainfall assumptions, drainage data, terrain measurements and chosen probability thresholds. As construction changes surfaces and climate alters rainfall patterns, the map can become outdated even if it was once accurate. Responsible use therefore requires treating a flood map as a dated estimate, not a permanent boundary between safe and unsafe land.  [MCQ | Easy]

1. Flood maps are useless because rainfall cannot be predicted.
2. Flood maps should be interpreted as revisable model-based estimates rather than timeless safety boundaries.
3. Construction is the main reason all flood maps become inaccurate.
4. Probability thresholds should be removed from flood mapping.

Q18. Choose the option that best summarises the paragraph: Repair cultures are sometimes described as remnants of scarcity, destined to disappear as incomes rise. Yet repair can persist for other reasons: attachment to objects, specialised local skills, environmental concerns and the desire to understand how things work. Treating repair only as evidence of poverty overlooks the different values that can sustain it.  [MCQ | Easy]

1. Repair survives only where replacement goods are expensive.
2. Repair practices can be sustained by cultural, practical and environmental motives, not merely scarcity.
3. Rising incomes always reduce people’s attachment to objects.
4. Environmental concerns have replaced economic motives for repair.

Q19. The following paragraph has a missing sentence. Choose the option that best completes it: Public libraries increasingly lend tools, musical instruments and digital devices alongside books. These programmes are sometimes criticised as departures from the library’s traditional mission. ________. If the institution’s broader purpose is to widen access to knowledge and participation, lending a microscope or sewing machine can be understood as an extension rather than a rejection of that mission.  [MCQ | Moderate]

1. Books are less expensive to maintain than equipment.
2. The criticism depends on defining the mission narrowly as the circulation of printed material.
3. Most libraries now earn revenue from equipment rentals.
4. Digital devices have made reading unnecessary.

Q20. The following paragraph has a missing sentence. Choose the option that best completes it: Scientific replication is sometimes described as a test that a finding either passes or fails. In practice, a replication may alter samples, instruments or settings in small ways. ________. A different result can therefore prompt inquiry into the conditions under which an effect appears rather than simply proving the original study wrong.  [MCQ | Moderate]

1. Every replication should reproduce the original procedure exactly.
2. These differences can reveal whether a result depends on conditions that the first study left implicit.
3. Replication is valuable only when it confirms the original result.
4. Sample differences should always be treated as experimental errors.

Q21. Arrange the four sentences to form a coherent paragraph. Enter the correct sequence as a four-digit number. 1. Yet maps do not merely record borders; they can also help make borders administratively real. 2. Once a line appears on official maps, taxation, policing and land registration may begin to follow it. 3. Political boundaries are often described as if they first exist on the ground and are later represented on maps. 4. The representation can thus participate in producing the territorial order it appears only to depict.  [TITA | Moderate]

Q22. Arrange the four sentences to form a coherent paragraph. Enter the correct sequence as a four-digit number. 1. This apparent inefficiency can nevertheless increase resilience when one route is disrupted. 2. Networks designed only for minimum cost often eliminate spare capacity. 3. Redundancy therefore looks wasteful when judged under ordinary conditions. 4. A system with several alternative routes may cost more to maintain than one optimised around a single route.  [TITA | Moderate]

Q23. Five sentences are given. Four form a coherent paragraph; one does not belong. Enter the number of the odd sentence. 1. Seed banks store genetic material as insurance against crop loss. 2. Their collections can preserve varieties no longer widely cultivated. 3. Stored seeds, however, must periodically be tested and regenerated because viability declines. 4. Agricultural commodity prices are influenced by international futures markets. 5. Conservation therefore requires active management rather than simply placing seeds in cold rooms.  [TITA | Easy]

Q24. Five sentences are given. Four form a coherent paragraph; one does not belong. Enter the number of the odd sentence. 1. A queue is often interpreted as evidence that demand exceeds current service capacity. 2. Queue length alone, however, says little about how long any particular person has waited. 3. Some systems therefore track waiting-time distributions rather than only the number of people in line. 4. Customers generally prefer buildings with natural daylight. 5. Such distributions can reveal whether a small group is experiencing exceptionally long delays.  [TITA | Easy]

Section II – DILR (22 Questions)

Set 1 – Exhibition Schedule

Five exhibitions A, B, C, D and E are scheduled one per slot from 1 to 5. B is immediately after D; A is before C; E is not adjacent to A; and C is not in Slot 5.

Q25. Five exhibitions A, B, C, D and E are scheduled one per slot from 1 to 5. B is immediately after D; A is before C; E is not adjacent to A; and C is not in Slot 5. How many valid schedules are possible?  [TITA | Moderate]

Q26. Under the same conditions, which exhibition can never be in Slot 1?  [MCQ | Moderate]

1. A
2. B
3. D
4. E

Q27. If A is in Slot 1, how many valid schedules are possible?  [TITA | Moderate]

Q28. If D is in Slot 2, how many valid schedules are possible?  [TITA | Moderate]

Q29. Which of the following can be a valid order from Slot 1 to Slot 5?  [MCQ | Easy]

1. A-C-D-B-E
2. A-E-D-B-C
3. D-B-E-A-C
4. E-A-D-B-C

Set 2 – Regional Sales

The table shows units sold by four regions in four quarters.

Region	Q1	Q2	Q3	Q4
North	120	150	135	195
South	160	140	180	200
East	100	125	150	175
West	140	170	160	210

Q30. Using the quarterly regional sales table, what is the percentage increase in East sales from Q1 to Q4?  [MCQ | Easy]

1. 50%
2. 60%
3. 75%
4. 80%

Q31. Which region has the lowest total sales across all four quarters?  [MCQ | Easy]

1. North
2. South
3. East
4. West

Q32. What is the difference between total Q4 sales and total Q1 sales across all regions?  [TITA | Moderate]

Q33. For how many regions is Q3 sales at least 20% higher than Q1 sales?  [TITA | Moderate]

Q34. If each unit sold in Q2 yields Rs 40 contribution and each unit sold in Q3 yields Rs 50 contribution, what is the combined contribution from all regions in Q2 and Q3 (in rupees)?  [MCQ | Moderate]

1. 52,900
2. 54,650
3. 56,250
4. 58,400

Set 3 – Committee Selection

A four-member committee is selected from P, Q, R, S, T, U and V. If P is selected, Q must be selected; R and S cannot both be selected; exactly one of T and U is selected; and V must be selected.

Q35. A four-member committee is selected from P, Q, R, S, T, U and V. If P is selected, Q must be selected; R and S cannot both be selected; exactly one of T and U is selected; and V must be selected. How many committees are possible?  [TITA | Moderate]

Q36. Which pair must be present together in every valid committee containing P?  [MCQ | Easy]

1. P and R
2. P and Q
3. Q and S
4. T and U

Q37. Among all committees satisfying the rules, in how many does R appear?  [TITA | Moderate]

Q38. Which of the following is a valid committee?  [MCQ | Easy]

1. P,Q,R,S
2. Q,R,T,V
3. P,Q,T,U
4. R,S,T,V

Set 4 – Bus Ridership

The table shows passenger counts by route and time period.

Route	Morning	Afternoon	Evening
R1	240	180	300
R2	200	220	260
R3	150	210	270
R4	180	160	240

Q39. Using the bus ridership table, which route has the largest percentage increase from Morning to Evening?  [MCQ | Moderate]

1. R1
2. R2
3. R3
4. R4

Q40. What is the total ridership across all routes and all three periods?  [TITA | Easy]

Q41. For how many routes is Evening ridership at least 50% greater than Afternoon ridership?  [TITA | Moderate]

Q42. If operating cost is Rs 12 per passenger in Morning and Rs 10 per passenger in each later period, what is the total operating cost across all routes?  [MCQ | Moderate]

1. Rs 26,100
2. Rs 27,640
3. Rs 28,020
4. Rs 29,400

Set 5 – Job Processing Sequence

Six jobs J, K, L, M, N and O are processed in Positions 1 to 6. J is before M; K is immediately before L; N and O are not adjacent; M is not sixth; and O is before J.

Q43. Six jobs J, K, L, M, N and O are processed in positions 1 to 6. J is before M; K is immediately before L; N and O are not adjacent; M is not sixth; and O is before J. How many valid sequences are possible?  [TITA | Difficult]

Q44. Under the same conditions, which job can never be in Position 1?  [MCQ | Moderate]

1. J
2. K
3. N
4. O

Q45. If K is in Position 4, which job must be in Position 6?  [MCQ | Difficult]

1. J
2. L
3. M
4. N

Q46. Which listed order satisfies every sequencing condition?  [MCQ | Moderate]

1. O-J-N-K-L-M
2. N-O-J-M-K-L
3. O-K-L-J-N-M
4. K-L-O-J-M-N

Section III – QA (22 Questions)

Q47. Machine A can complete a batch in 18 hours and Machine B in 30 hours. They work together for 6 hours, after which A stops. How many additional hours does B need to finish the batch?  [TITA | Moderate]

Q48. If f(x)=x^2-3x+4, and f(a)=f(5-a), then the possible value of a is:  [MCQ | Moderate]

1. 1
2. 2
3. 5/2
4. 3

Q49. A square and an equilateral triangle have equal perimeters. If the square has side 9 cm, what is the area of the equilateral triangle?  [MCQ | Moderate]

1. 27sqrt(3)
2. 36sqrt(3)
3. 48sqrt(3)
4. 54sqrt(3)

Q50. Find the least positive integer n such that n leaves remainder 4 when divided by 9 and remainder 6 when divided by 11.  [TITA | Moderate]

Q51. The average of 10 numbers is 24. If the average of the first 6 numbers is 20, what is the average of the remaining 4 numbers?  [MCQ | Easy]

1. 28
2. 30
3. 32
4. 34

Q52. A trader mixes rice priced at Rs 40 per kg and Rs 70 per kg in the ratio 3:2. If the mixture is sold at Rs 65 per kg, what is the profit percentage?  [MCQ | Moderate]

1. 20%
2. 25%
3. 30%
4. 32.5%

Q53. The roots of x^2-kx+18=0 differ by 3. If k is positive, find k.  [TITA | Moderate]

Q54. A cyclist travels 24 km at speed v km/h and returns over the same route at (v+4) km/h. If the total travel time is 5 hours, v equals:  [MCQ | Difficult]

1. 8
2. 10
3. 12
4. 14

Q55. If log_3(x-1)+log_3(x+1)=2, then x equals:  [MCQ | Moderate]

1. sqrt(10)
2. 3
3. sqrt(8)
4. 4

Q56. Two chords of a circle intersect inside it. One chord is divided into lengths 4 cm and 9 cm; the other into lengths 6 cm and x cm. Find x.  [TITA | Easy]

Q57. What is the smallest positive integer n for which 1+2+3+…+n exceeds 300?  [MCQ | Moderate]

1. 23
2. 24
3. 25
4. 26

Q58. How many three-digit positive integers contain the digit 7 exactly once?  [TITA | Moderate]

Q59. In a survey of 180 students, 110 study Finance, 90 study Marketing, and 50 study both. How many study neither Finance nor Marketing?  [MCQ | Easy]

1. 20
2. 30
3. 40
4. 50

Q60. A sum becomes 1.331 times itself in 3 years at a fixed annual compound rate. What is the annual rate?  [MCQ | Easy]

1. 8%
2. 10%
3. 11%
4. 12%

Q61. How many ordered pairs of positive integers (x,y) satisfy x^2+y^2=65?  [MCQ | Moderate]

1. 2
2. 4
3. 6
4. 8

Q62. A three-digit number has digit sum 12. Reversing its digits decreases the number by 198. If the tens digit is 4, what is the number?  [TITA | Difficult]

Q63. A right circular cone has radius 6 cm and height 8 cm. What is its curved surface area?  [MCQ | Moderate]

1. 48pi
2. 60pi
3. 72pi
4. 80pi

Q64. A 40-litre solution contains acid and water in the ratio 3:5. How many litres of pure acid must be added to make the ratio 1:1?  [TITA | Moderate]

Q65. The line 3x+4y=24 cuts the positive coordinate axes at A and B. What is the area of triangle OAB, where O is the origin?  [MCQ | Easy]

1. 20
2. 24
3. 28
4. 32

Q66. Twelve workers can finish a job in 15 days. After 5 days, 3 workers leave. Assuming equal efficiency, how many more days are needed to finish the job?  [TITA | Moderate]

Q67. A fair six-sided die is rolled twice. What is the probability that the product of the two outcomes is divisible by 6?  [MCQ | Moderate]

1. 1/3
2. 5/12
3. 1/2
4. 7/12

Q68. How many real values of x satisfy |x-4|+|x+2|=10?  [TITA | Moderate]

Answer Key

Q	Answer	Section	Difficulty
1	B	VARC	Moderate
2	C	VARC	Easy
3	C	VARC	Moderate
4	C	VARC	Moderate
5	B	VARC	Easy
6	C	VARC	Moderate
7	B	VARC	Moderate
8	C	VARC	Moderate
9	C	VARC	Moderate
10	B	VARC	Moderate
11	B	VARC	Moderate
12	B	VARC	Moderate
13	C	VARC	Moderate
14	B	VARC	Easy
15	C	VARC	Moderate
16	B	VARC	Moderate
17	B	VARC	Easy
18	B	VARC	Easy
19	B	VARC	Moderate
20	B	VARC	Moderate
21	3124	VARC	Moderate
22	2431	VARC	Moderate
23	4	VARC	Easy
24	4	VARC	Easy
25	4	DILR	Moderate
26	B	DILR	Moderate
27	3	DILR	Moderate
28	1	DILR	Moderate
29	A	DILR	Easy
30	C	DILR	Easy
31	C	DILR	Easy
32	260	DILR	Moderate
33	1	DILR	Moderate
34	B	DILR	Moderate
35	6	DILR	Moderate
36	B	DILR	Easy
37	2	DILR	Moderate
38	B	DILR	Easy
39	C	DILR	Moderate
40	2610	DILR	Easy
41	2	DILR	Moderate
42	B	DILR	Moderate
43	6	DILR	Difficult
44	A	DILR	Moderate
45	D	DILR	Difficult
46	D	DILR	Moderate
47	14	QA	Moderate
48	C	QA	Moderate
49	B	QA	Moderate
50	94	QA	Moderate
51	B	QA	Easy
52	B	QA	Moderate
53	9	QA	Moderate
54	A	QA	Difficult
55	A	QA	Moderate
56	6	QA	Easy
57	C	QA	Moderate
58	225	QA	Moderate
59	B	QA	Easy
60	B	QA	Easy
61	B	QA	Moderate
62	543	QA	Difficult
63	B	QA	Moderate
64	10	QA	Moderate
65	B	QA	Easy
66	40/3	QA	Moderate
67	B	QA	Moderate
68	2	QA	Moderate

Detailed Solutions

VARC Solutions

Q1. Answer: B | Difficulty: Moderate

The passage endorses metrics as useful but provisional indicators whose behavioural effects must be monitored. Hence B.

Q2. Answer: C | Difficulty: Easy

The call-centre example shows that improving the measured indicator (short calls) can diverge from the underlying goal (resolved problems). Hence C.

Q3. Answer: C | Difficulty: Moderate

The author explicitly recommends combining measures and revising them when behaviour changes. Hence C.

Q4. Answer: C | Difficulty: Moderate

Institutional humility means accepting that participants adapt to rules and may change what a metric captures. Hence C.

Q5. Answer: B | Difficulty: Easy

The passage says decibels alone miss timing, repetition and meaning. Hence B.

Q6. Answer: C | Difficulty: Moderate

The author rejects both silence and context-free regulation; the aim is to manage necessary sound and unequal burdens. Hence C.

Q7. Answer: B | Difficulty: Moderate

The bird example demonstrates that acoustic environments affect behaviour in ways not exhausted by raw volume. Hence B.

Q8. Answer: C | Difficulty: Moderate

The passage specifically proposes defensible standards incorporating duration and time of day. Hence C.

Q9. Answer: C | Difficulty: Moderate

The archive is described as mediated, incomplete and institutionally organised, yet still useful for disciplined inference. Hence C.

Q10. Answer: B | Difficulty: Moderate

Detailed taxation records but sparse labour records reveal state priorities, not necessarily the true importance of activities. Hence B.

Q11. Answer: B | Difficulty: Moderate

Digitisation creates new filters through metadata, rankings, obsolete formats and access rules. Hence B.

Q12. Answer: B | Difficulty: Moderate

The double reading examines both what a document says and how/why it was preserved and classified. Hence B.

Q13. Answer: C | Difficulty: Moderate

The author argues for communicating uncertainty relevant to action and separating evidence from value judgements. Hence C.

Q14. Answer: B | Difficulty: Easy

If provisional advice was communicated as certainty, later revision can look like unreliability. Hence B.

Q15. Answer: C | Difficulty: Moderate

The passage explicitly notes that numerical agreement can coexist with policy disagreement because values differ. Hence C.

Q16. Answer: B | Difficulty: Moderate

Public explanation is called a translation task preserving reasoning relevant to action. Hence B.

Q17. Answer: B | Difficulty: Easy

The paragraph stresses that flood maps are model-based, dated and revisable. Hence B.

Q18. Answer: B | Difficulty: Easy

The paragraph lists several non-scarcity motives for repair; B captures all of them.

Q19. Answer: B | Difficulty: Moderate

The next sentence broadens the library mission, so the missing sentence must identify the narrow definition behind the criticism. Hence B.

Q20. Answer: B | Difficulty: Moderate

The following sentence treats different results as clues about conditions; B provides that bridge.

Q21. Answer: 3124 | Difficulty: Moderate

Sentence 3 introduces the common view; 1 challenges it; 2 shows the mechanism; 4 concludes. Sequence 3124.

Q22. Answer: 2431 | Difficulty: Moderate

Sentence 2 introduces optimisation; 4 gives the cost of alternatives; 3 labels redundancy as wasteful; 1 states its resilience benefit. Sequence 2431.

Q23. Answer: 4 | Difficulty: Easy

Sentences 1,2,3,5 concern seed-bank conservation; sentence 4 shifts to commodity prices. Answer 4.

Q24. Answer: 4 | Difficulty: Easy

Sentences 1,2,3,5 concern queue measurement; sentence 4 is unrelated. Answer 4.

DILR Solutions

Q25. Answer: 4 | Difficulty: Moderate

Enumerating the schedules satisfying all four conditions gives 4 valid orders. Answer 4.

Q26. Answer: B | Difficulty: Moderate

Because B must be immediately after D, B cannot occupy Slot 1. The other listed exhibitions can appear first in at least one valid schedule. Hence B.

Q27. Answer: 3 | Difficulty: Moderate

With A fixed in Slot 1, direct enumeration of the remaining four exhibitions gives 3 valid schedules.

Q28. Answer: 1 | Difficulty: Moderate

Fix D in Slot 2, so B is in Slot 3. Applying the remaining constraints leaves only A-D-B-C-E, so there is 1 valid schedule.

Q29. Answer: A | Difficulty: Easy

A-C-D-B-E satisfies all conditions: B follows D, A is before C, E is not adjacent to A, and C is not fifth. Hence A.

Q30. Answer: C | Difficulty: Easy

East rises from 100 to 175. Percentage increase =75/100 x 100 = 75%. Hence C.

Q31. Answer: C | Difficulty: Easy

Totals: North=600, South=680, East=550, West=680. East is the lowest. Hence C.

Q32. Answer: 260 | Difficulty: Moderate

Q4 total=195+200+175+210=780. Q1 total=120+160+100+140=520. Difference=260.

Q33. Answer: 1 | Difficulty: Moderate

North and South rise 12.5%; East rises 50%; West rises about 14.3%. Only East meets at least 20%, so the answer is 1.

Q34. Answer: B | Difficulty: Moderate

Q2 total=585 and Q3 total=625. Contribution=585×40+625×50=23,400+31,250=54,650. Hence B.

Q35. Answer: 6 | Difficulty: Moderate

Enumerating all four-member subsets under the conditions yields 6 valid committees.

Q36. Answer: B | Difficulty: Easy

Whenever P is selected, the rule requires Q. Thus P and Q must occur together in every valid committee containing P. Hence B.

Q37. Answer: 2 | Difficulty: Moderate

Among the valid committees, 2 contain R.

Q38. Answer: B | Difficulty: Easy

Q,R,T,V satisfies all rules: V is present; exactly one of T,U is present; R is not paired with S; and the P=>Q rule is irrelevant because P is absent. Hence B.

Q39. Answer: C | Difficulty: Moderate

Percentage changes Morning->Evening: R1 25%; R2 30%; R3 80%; R4 33.3%. R3 is largest. Hence C.

Q40. Answer: 2610 | Difficulty: Easy

Adding all 12 ridership figures gives 2,610.

Q41. Answer: 2 | Difficulty: Moderate

Evening vs Afternoon: R1 300>=270 yes; R2 260>=330 no; R3 270>=315 no; R4 240>=240 yes. So 2 routes.

Q42. Answer: B | Difficulty: Moderate

Morning total=770, later-period total=1,840. Cost=770×12+1840×10=9,240+18,400=27,640. Hence B.

Q43. Answer: 6 | Difficulty: Difficult

Enumeration of all 720 permutations under the five restrictions gives 6 valid sequences.

Q44. Answer: A | Difficulty: Moderate

O must be before J, so J cannot be first. Each of the other listed jobs can be first in at least one valid sequence. Hence A.

Q45. Answer: D | Difficulty: Difficult

If K is fourth, L is fifth. Applying the remaining constraints forces N into Position 6. Hence D.

Q46. Answer: D | Difficulty: Moderate

K-L-O-J-M-N satisfies K immediately before L, O before J, J before M, M not sixth, and N not adjacent to O. Hence D.

QA Solutions

Q47. Answer: 14 | Difficulty: Moderate

Combined rate=1/18+1/30=4/45 batch/hour. In 6 hours they finish 24/45=8/15. Remaining=7/15. B alone works at 1/30, so time=(7/15)x30=14 hours.

Q48. Answer: C | Difficulty: Moderate

f(a)=a^2-3a+4. f(5-a)=(5-a)^2-3(5-a)+4=a^2-7a+14. Equating gives -3a+4=-7a+14, so 4a=10 and a=5/2. Hence C.

Q49. Answer: B | Difficulty: Moderate

Square perimeter=36, so each triangle side=12. Area=(sqrt(3)/4)x144=36sqrt(3). Hence B.

Q50. Answer: 94 | Difficulty: Moderate

Numbers congruent to 4 mod 9 are 4,13,22,… Checking modulo 11 gives 94: 94 mod 9=4 and 94 mod 11=6. It is the least positive solution.

Q51. Answer: B | Difficulty: Easy

Total of all 10 numbers=240. Total of first 6=120. The remaining four total 120, so their average is 30. Hence B.

Q52. Answer: B | Difficulty: Moderate

Weighted cost per kg=(3×40+2×70)/5=52. Selling price=65, so profit=13 on cost 52, i.e. 25%. Hence B.

Q53. Answer: 9 | Difficulty: Moderate

For roots r,s: r+s=k and rs=18. Also (r-s)^2=(r+s)^2-4rs=k^2-72=9. Thus k^2=81 and positive k=9.

Q54. Answer: A | Difficulty: Difficult

24/v + 24/(v+4)=5. Multiply through: 48v+96=5v^2+20v, so 5v^2-28v-96=0. The positive root is 8. Hence A.

Q55. Answer: A | Difficulty: Moderate

log_3((x-1)(x+1))=2, so x^2-1=9, x^2=10. Domain x>1, so x=sqrt(10). Hence A.

Q56. Answer: 6 | Difficulty: Easy

Intersecting chords theorem: 4×9=6x, so x=6.

Q57. Answer: C | Difficulty: Moderate

The sum is n(n+1)/2. At n=24 the sum is 300, which does not exceed 300. At n=25 it is 325, so the smallest such n is 25. Hence C.

Q58. Answer: 225 | Difficulty: Moderate

If the hundreds digit is 7, the other two digits each have 9 choices, giving 81. If the tens digit is 7, the hundreds digit has 8 choices (1-9 except 7) and the units digit 9, giving 72. Similarly, units digit 7 gives 72. Total=225.

Q59. Answer: B | Difficulty: Easy

|F union M|=110+90-50=150. Neither=180-150=30. Hence B.

Q60. Answer: B | Difficulty: Easy

1.331=1.1^3, so the annual compound growth factor is 1.1, i.e. 10%. Hence B.

Q61. Answer: B | Difficulty: Moderate

The positive square decompositions of 65 are 1^2+8^2 and 4^2+7^2. Because ordered pairs are counted, the pairs are (1,8),(8,1),(4,7),(7,4): 4 in total. Hence B.

Q62. Answer: 543 | Difficulty: Difficult

Let the number be 100a+40+c. Difference from its reversal is 99(a-c)=198, so a-c=2. Digit sum gives a+c+4=12, so a+c=8. Solving gives a=5 and c=3, hence the number is 543.

Q63. Answer: B | Difficulty: Moderate

Slant height=sqrt(6^2+8^2)=10. Curved surface area=pi r l=60pi. Hence B.

Q64. Answer: 10 | Difficulty: Moderate

Initially acid=15 and water=25. Add x acid so (15+x):25=1:1, giving x=10.

Q65. Answer: B | Difficulty: Easy

Intercepts are x=8 and y=6. Area=1/2 x 8 x 6=24. Hence B.

Q66. Answer: 40/3 | Difficulty: Moderate

Total work=12×15=180 worker-days. In first 5 days, 60 worker-days are completed; 120 remain. With 9 workers, time=120/9=40/3 days.

Q67. Answer: B | Difficulty: Moderate

There are 36 ordered outcomes. For the product not to be divisible by 6, it must miss factor 2 or factor 3. Both outcomes odd: 9; neither outcome divisible by 3: 16; overlap: both outcomes from {1,5}, giving 4. Thus unfavourable=21, favourable=15 and probability=15/36=5/12. Hence B.

Q68. Answer: 2 | Difficulty: Moderate

For -2<=x<=4, the left side equals 6, so equality to 10 is impossible there. For x>4, it becomes 2x-2=10, giving x=6. For x<-2, it becomes -2x+2=10, giving x=-4. Thus there are 2 real solutions.