Full-Length Static CAT-Style Practice 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 only for practice analytics.
• All passages, datasets and questions in this paper are freshly written for MBA4U.in. They are not reproduced from CAT or from the supplied MBA4U practice papers.
• Attempt the full paper under timed conditions before opening the answer key and solutions.

Section I – Verbal Ability and Reading Comprehension (VARC)

24 Questions | 40 Minutes

RC Passage 1 – Why Redundancy Can Be Rational

Passage difficulty: Moderate-Difficult

Modern organisations often praise efficiency as the removal of slack. A warehouse that keeps fewer spare parts, a power grid that operates close to capacity, or a hospital that schedules beds almost continuously may appear to be using resources well. In stable conditions, such systems can indeed lower visible costs. Yet the same features can make them brittle when demand, supply or information changes unexpectedly.

Redundancy is frequently misread as waste because its value is easiest to observe precisely when ordinary arrangements fail. A second communications link appears unnecessary until the first is damaged. Inventory held for an unlikely disruption looks idle until transport is interrupted. The difficulty is that conventional accounting records the carrying cost every day but records the avoided catastrophe only on the rare day when backup capacity matters.

This does not imply that more redundancy is always better. Excessive duplication can absorb funds that could have reduced the probability of failure in the first place. A hospital might gain more from preventive maintenance than from maintaining an entire unused ward. The question, therefore, is not whether slack is virtuous but how much resilience is worth purchasing against particular kinds of uncertainty.

A useful distinction is between redundancy that merely duplicates an existing weakness and redundancy that creates genuine independence. Two data centres supplied by the same vulnerable power line are less resilient than they appear. Likewise, several suppliers located along the same flood-prone corridor may count as multiple vendors on a spreadsheet while sharing one physical risk. Resilience depends not simply on quantity but on the diversity and separability of backup options.

Efficiency and resilience are thus not opposites so much as objectives measured over different horizons. A system optimised for an ordinary week can be inefficient over a decade if occasional disruptions impose enormous losses. Good design makes the time horizon and failure assumptions explicit instead of treating unused capacity as self-evident evidence of poor management.

Q1. The central argument of the passage is that: [MCQ | Moderate]

1. redundancy is inherently superior to efficiency in complex systems
2. unused capacity should be eliminated unless disruptions occur frequently
3. the value of redundancy depends on the risks covered, the independence of backups and the time horizon considered
4. accounting systems cannot measure the cost of operational disruptions

Q2. Why does the author discuss two data centres supplied by the same power line? [MCQ | Moderate]

1. To show that duplication may fail to provide resilience when backup elements share a common vulnerability
2. To argue that electricity failures are the most important threat to digital infrastructure
3. To demonstrate that data centres should always use separate vendors
4. To suggest that physical infrastructure is more important than information systems

Q3. Which of the following would the author most likely regard as the best evaluation of spare capacity? [MCQ | Difficult]

1. Its utilisation rate during normal operations
2. Its purchase price relative to annual revenue
3. The expected reduction in disruption losses, given the failures it can independently absorb
4. Whether managers can remove it without changing current output

Q4. The passage treats efficiency and resilience primarily as: [MCQ | Easy]

1. mutually exclusive principles
2. objectives that can look different depending on the period and risks being evaluated
3. identical concepts expressed in different terminology
4. concerns relevant only to public infrastructure

RC Passage 2 – Standardising a Revived Language

Passage difficulty: Moderate

When a language has few remaining speakers, revitalisation programmes often begin by creating teaching materials. That seemingly practical task immediately raises a difficult question: which version of the language should be taught? Languages that have survived mainly in scattered communities may contain substantial differences in pronunciation, grammar and vocabulary. A textbook, however, cannot easily present every local form with equal prominence.

Standardisation can solve real problems. Teachers need agreed spellings; digital keyboards require consistent character choices; learners benefit from dictionaries that do not change from village to village. A shared written norm can also help speakers produce newspapers, websites and school examinations. In this sense, standardisation can expand the domains in which a language is usable.

Yet a standard is never merely a technical convenience. Selecting one spelling or grammatical form can elevate the speech of one region while making another appear incorrect. Older speakers who have used a local variety all their lives may suddenly encounter educational materials that classify familiar forms as deviations. If revitalisation succeeds by producing a new generation that speaks only the classroom standard, the language may gain speakers while losing part of its inherited diversity.

Some programmes respond by distinguishing between a common written standard and accepted spoken variation. Others publish dictionaries that list several regional forms rather than one authorised equivalent. Such strategies are administratively messier, but they make visible the fact that variation is not necessarily a defect to be eliminated.

The central challenge is therefore institutional rather than purely linguistic. Revitalisation must create enough coordination for teaching and public use without turning coordination into a retrospective claim that one variety was always the legitimate language. A standard can be a tool for future communication, provided it is not mistaken for a neutral description of the past.

Q5. The passage is mainly concerned with: [MCQ | Moderate]

1. proving that written standards inevitably destroy spoken languages
2. the tension between coordination and inherited variation in language revitalisation
3. showing that digital technology is the primary reason endangered languages survive
4. arguing that dictionaries should exclude regional forms

Q6. According to the passage, a shared written norm can be beneficial because it: [MCQ | Easy]

1. eliminates disagreement among older speakers
2. allows a language to function more easily in education and public communication
3. ensures that all regional varieties receive equal status
4. prevents pronunciation from changing over time

Q7. Which outcome would most clearly illustrate the author’s concern about standardisation? [MCQ | Moderate]

1. Learners use a common spelling system but retain different regional pronunciations
2. A school publishes a dictionary containing several local variants
3. Young speakers learn only the classroom variety and begin treating older local forms as erroneous
4. Teachers agree on a keyboard layout for characters used across regions

Q8. The final sentence suggests that a language standard should be understood as: [MCQ | Difficult]

1. a practical convention rather than proof that one historical variety was uniquely correct
2. an exact reconstruction of the oldest surviving speech form
3. a temporary measure that should disappear once enough speakers are trained
4. a linguistic rule whose legitimacy depends on government approval

RC Passage 3 – Replication and Tacit Knowledge

Passage difficulty: Difficult

Scientific findings are often described as reproducible when another researcher can follow the published method and obtain a similar result. The ideal is attractive because it makes knowledge appear independent of the individual laboratory that produced it. Yet many experiments rely on forms of practical judgement that are difficult to express fully in writing: how rapidly to add a reagent, how to recognise a borderline specimen, how much vibration a sensitive instrument can tolerate, or when a sample looks contaminated even before a formal test confirms it.

Such tacit knowledge does not necessarily undermine science. Skilled practice exists in surgery, engineering and field biology as well as in laboratories. The problem arises when scientific communication implies that the written protocol contains everything required for successful repetition. A failed replication may then be interpreted too quickly. The original result may be fragile; the second laboratory may have made an error; or both groups may have followed the same words while performing materially different procedures.

One response is to demand ever more detailed methods sections. Greater disclosure is useful, but complete codification may be impossible. Researchers cannot anticipate every apparently trivial choice that later turns out to matter. Video demonstrations, shared reference samples and temporary staff exchanges can sometimes communicate practice more effectively than additional prose.

This creates a delicate problem for evaluation. If a result can be reproduced only after extensive coaching from the original laboratory, it is less portable than one that transfers through a simple published protocol. But it is not automatically false. Portability is itself a property worth measuring because widely usable knowledge should survive movement across people and settings.

Replication, on this view, is not a binary ceremony in which one experiment stamps another as true or false. It is an investigation into which parts of a finding are robust, which depend on local technique, and which assumptions must be made explicit before the result can travel reliably.

Q9. The passage argues that failed replication should be interpreted cautiously because: [MCQ | Moderate]

1. all experiments depend on secret techniques
2. identical written procedures can still conceal meaningful differences in practice
3. replication is less important than original discovery
4. detailed methods sections generally make experiments impossible to repeat

Q10. What role does “portability” play in the author’s argument? [MCQ | Difficult]

1. It is treated as a useful characteristic of scientific knowledge distinct from the simple truth or falsity of a result
2. It proves that any experiment requiring coaching is invalid
3. It refers only to whether laboratory equipment can be moved
4. It is presented as a substitute for replication

Q11. Which of the following best follows from the passage? [MCQ | Moderate]

1. A successful replication guarantees that no tacit knowledge was involved
2. A failed replication always shows that the original result was wrong
3. Communication tools such as videos or reference samples may sometimes transmit experimental practice better than text alone
4. Scientific methods should exclude all procedures requiring skilled judgement

Q12. The author would most likely describe replication as: [MCQ | Difficult]

1. a yes-or-no test of whether a published claim is true
2. a process for identifying the conditions under which a result remains stable across settings
3. an administrative requirement best limited to large laboratories
4. a method for replacing expert judgement with written rules

RC Passage 4 – The Politics of Darkness in Cities

Passage difficulty: Moderate-Difficult

For much of the electric age, brighter streets were treated as an uncomplicated sign of urban progress. Lighting extended commercial hours, improved navigation and reduced some forms of risk. More recently, however, planners have begun to confront the costs of excessive illumination: wasted energy, disrupted animal behaviour, glare that can reduce visibility, and the disappearance of the night sky.

The phrase “light pollution” can make the issue sound like a simple matter of reducing brightness. In practice, the distribution and direction of light matter as much as its quantity. A poorly shielded lamp may send a large share of its output upward or into windows rather than onto the pavement it is intended to illuminate. A cooler, blue-rich light can have different ecological and physiological effects from a warmer source of similar measured brightness.

Attempts to reduce unnecessary lighting also encounter social concerns. Residents may associate brighter environments with safety even where evidence about crime is mixed or context-specific. Shopkeepers may value illuminated signs; astronomers may seek darker zones; transport authorities may prioritise uniform visibility. These interests cannot be resolved by announcing a single city-wide brightness target.

Some cities have therefore shifted toward adaptive lighting: lower baseline illumination, better shielding, warmer spectra and brighter levels only when pedestrian or vehicle activity increases. Such systems can reduce energy use while preserving functional light. Yet they also raise questions about maintenance, sensor reliability and whether dimmer conditions are distributed fairly across neighbourhoods.

The policy lesson is not that darkness should replace light. It is that illumination is infrastructure, not decoration. Like other infrastructure, it should be designed for specific tasks, evaluated for side effects and revised when technical choices create costs beyond the immediate purpose they were meant to serve.

Q13. The author’s main point is that urban lighting policy should: [MCQ | Moderate]

1. maximise brightness wherever residents report feeling unsafe
2. treat illumination as task-specific infrastructure whose design must consider multiple effects
3. replace electric lighting with adaptive systems in every neighbourhood
4. focus primarily on restoring visibility of the night sky

Q14. Why does the passage distinguish a poorly shielded lamp from a well-directed one? [MCQ | Easy]

1. To show that the effects of lighting depend on where the light goes, not only on total output
2. To claim that shielded lamps are always cheaper to maintain
3. To prove that brighter lamps necessarily reduce visibility
4. To show that upward light is necessary for navigation

Q15. Which policy is most consistent with the author’s reasoning? [MCQ | Moderate]

1. A uniform increase in brightness across the city
2. A ban on commercial signs after sunset
3. Lighting standards that consider direction, spectrum, local use and reliability in addition to brightness
4. Allowing each neighbourhood to choose any lighting system without technical standards

Q16. The mention of fairness in the fourth paragraph mainly indicates that: [MCQ | Difficult]

1. sensor technology is too unreliable for public infrastructure
2. technical efficiency does not eliminate distributional questions about who experiences reduced or increased lighting
3. all neighbourhoods require identical illumination levels
4. dimmer streets are always less safe

Para Summary

Q17. A city may publish thousands of datasets and still remain opaque if the data are released in incompatible formats, without documentation or after decisions have already been made. Openness is therefore not identical to volume. Useful transparency depends on whether outsiders can interpret information, connect it to decisions and obtain it in time to act. [MCQ | Moderate]

1. Government transparency can be measured mainly by the number of datasets released.
2. Data disclosure becomes meaningful transparency only when information is timely, interpretable and connected to decision-making.
3. Citizens generally lack the technical skills required to use public datasets.
4. Standardising file formats is sufficient to make governments transparent.

Para Summary

Q18. Forecasts can become self-altering. A prediction of congestion may persuade travellers to change routes, making the original forecast appear wrong; a warning of shortage may cause households to stock up, making the shortage worse. Evaluating forecasts solely by whether the predicted outcome occurred can therefore be misleading when publication of the forecast changes behaviour. [MCQ | Difficult]

1. Forecasts should never be published because people react unpredictably to them.
2. A forecast is accurate only when the predicted event occurs exactly as stated.
3. The public response to a forecast can alter the outcome, so forecast quality cannot always be judged by simple outcome matching.
4. Congestion and shortages are unusually difficult to predict because they depend on individual choices.

Para Completion

Q19. Many organisations preserve documents because storage has become cheap. But retention is not the same as memory. A collection without descriptions, access rules or deletion policies can become an accumulation that nobody can effectively search. ______ [MCQ | Moderate]

1. Therefore, digital storage should always replace paper archives.
2. Meaningful institutional memory requires selection and organisation, not merely the indefinite survival of files.
3. As a result, organisations should delete documents immediately after use.
4. Consequently, the cost of storage remains the main barrier to preserving information.

Para Completion

Q20. A scientific model is often criticised when it simplifies reality, but simplification is the point of modelling. The relevant question is not whether a model leaves things out; every usable model does. The question is whether the omitted features matter for the decision at hand. ______ [MCQ | Difficult]

1. A model can therefore be useful in one context and misleading in another without changing its equations.
2. The most detailed model is always the most scientifically valid.
3. Models should avoid assumptions because assumptions introduce bias.
4. Once validated, a model can be applied reliably to any related problem.

Odd Sentence Out

Q21. Five sentences are given below. Four form a coherent paragraph. Identify the odd sentence and enter its number.
1. Seeds stored in a gene bank are often described as insurance against crop loss.
2. Their usefulness, however, depends on whether the stored material can be regenerated and accurately documented.
3. Some commercial farms replace machinery every few years to reduce maintenance costs.
4. A seed whose label is wrong or whose viability has collapsed may exist in storage but be unusable.
5. Conservation therefore requires periodic testing and cultivation, not simply refrigeration. [TITA | Moderate]

Odd Sentence Out

Q22. Five sentences are given below. Four form a coherent paragraph. Identify the odd sentence and enter its number.
1. Translation inevitably involves choices among meanings that do not line up perfectly across languages.
2. Legal translation makes those choices especially consequential because small differences can alter obligations.
3. Courts therefore often rely on glossaries, parallel texts and specialist review.
4. Many language learners prefer subtitles because they can hear the original dialogue.
5. These procedures do not eliminate interpretation, but they make contested choices more visible. [TITA | Moderate]

Odd Sentence Out

Q23. Five sentences are given below. Four form a coherent paragraph. Identify the odd sentence and enter its number.
1. A queue can reveal demand, but it can also suppress demand by making access costly in time.
2. Observed arrivals may therefore be lower than the number of people who would use the service without waiting.
3. Capacity planning based only on the visible queue can underestimate latent demand.
4. Some public services are financed through a combination of taxes and user charges.
5. Reducing waiting time may consequently increase measured demand even when the underlying need has not changed. [TITA | Difficult]

Odd Sentence Out

Q24. Five sentences are given below. Four form a coherent paragraph. Identify the odd sentence and enter its number.
1. Maps simplify terrain so that particular relationships become legible.
2. A subway map may distort physical distance while accurately representing the sequence of stations.
3. The usefulness of a map therefore depends partly on the task for which it was designed.
4. Satellite images are produced by sensors that record different wavelengths of electromagnetic radiation.
5. Treating every distortion as an error ignores the selective purpose of representation. [TITA | Difficult]

Section II – Data Interpretation and Logical Reasoning (DILR)

22 Questions | 40 Minutes

Set 1 – Conference Sessions (Questions 25-28)

Overall difficulty: Moderate-Difficult

Six conference sessions A, B, C, D, E and F are scheduled in six consecutive slots, one per slot. The following conditions apply:
• A is earlier than D, and D is earlier than F.
• C is immediately followed by E.
• B is neither first nor sixth.
• A and C are not in consecutive slots.

Q25. How many distinct slot arrangements are feasible under all four conditions? [TITA | Difficult]

Q26. Which session must always be scheduled before F? [MCQ | Moderate]

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

Q27. If the C-E block occupies slots 1 and 2, how many feasible arrangements remain? [TITA | Moderate]

Q28. Among the following sessions, which one can occupy the final slot? [MCQ | Moderate]

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

Set 2 – Public Libraries (Questions 29-33)

Overall difficulty: Easy-Moderate

Five public libraries recorded total visitors during a week. The table also gives the percentage of visitors who were registered members and the average number of books borrowed by each member during that week. Assume all figures apply exactly.

Q29. What is the total number of registered-member visits across all five libraries? [TITA | Easy]

Q30. Which library recorded the largest number of books borrowed by members? [MCQ | Easy]

1. P
2. Q
3. R
4. S

Q31. The number of books borrowed at Q is approximately what percentage of the number borrowed at S? [MCQ | Moderate]

1. 64%
2. 76.19%
3. 80%
4. 96%

Q32. If the member percentage at T rises from 50% to 55%, with visitor count and books per member unchanged, how many additional books are borrowed? [TITA | Moderate]

Q33. What is the average number of books borrowed per member across all five libraries, rounded to two decimal places? [MCQ | Moderate]

3. 3.22
4. 3.41
5. 3.48
6. 3.60

Set 3 – Chess League (Questions 34-37)

Overall difficulty: Moderate

Five players J, K, L, M and N finish a chess league with distinct ranks 1 (best) to 5. Each player also wins a distinct number of games: 3, 4, 5, 6 or 7. Conditions:
• The player ranked 1 wins 7 games.
• J ranks better than K but worse than L.
• M wins exactly one more game than K.
• N ranks 5 and wins 3 games.
• The ranking order of J, K and M is the same as the descending order of their wins.

Q34. How many complete rank-and-win assignments satisfy all the conditions? [TITA | Difficult]

Q35. Who must be ranked first? [MCQ | Moderate]

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

Q36. How many games does J win? [MCQ | Moderate]

1. 4
2. 5
3. 6
4. 7

Q37. What is M’s rank? [TITA | Moderate]

Set 4 – Online Course Cohorts (Questions 38-42)

Overall difficulty: Moderate

Four online-course cohorts have the following data. Completion percentage is of enrolments. Certificate percentage is of completers. Fee is paid by every enrollee. Assume all percentages apply exactly.

Q38. What is the total number of completers across all four cohorts? [TITA | Easy]

Q39. Which cohort generates the highest fee revenue? [MCQ | Easy]

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

Q40. What is the difference between the number of certificate earners in B and D? [TITA | Moderate]

Q41. If 10% of non-completers in C later complete and 80% of those late completers earn certificates, how many additional certificates are issued? [TITA | Moderate]

Q42. Certificate earners as a percentage of total enrolments are highest in which cohort? [MCQ | Moderate]

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

Set 5 – Startup Shortlist (Questions 43-46)

Overall difficulty: Moderate-Difficult

A panel must shortlist exactly four of seven startup pitches P, Q, R, S, T, U and V. The following rules apply:
• If P is selected, Q is not selected.
• R and S are either both selected or both rejected.
• At least one of T and U is selected.
• V can be selected only if Q is selected.
• If U is selected, S must be selected.

Q43. How many valid shortlists are possible? [TITA | Difficult]

Q44. Which pair of pitches is selected in every valid shortlist? [MCQ | Moderate]

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

Q45. Under the additional condition that P is shortlisted, which pitch is necessarily included? [MCQ | Moderate]

1. R
2. T
3. U
4. V

Q46. If V is selected, how many valid shortlists are possible? [TITA | Moderate]

Section III – Quantitative Ability (QA)

22 Questions | 40 Minutes

Q47. A shopkeeper mixes two varieties of coffee costing Rs 360/kg and Rs 480/kg in the ratio 3:2. At what price per kg should the mixture be sold to earn a profit of 25%? [MCQ | Easy]

1. Rs 495
2. Rs 510
3. Rs 525
4. Rs 540

Q48. A taxi fare consists of a fixed booking charge and a constant charge per kilometre. An 8 km trip costs Rs 236 and a 14 km trip costs Rs 344. What will a 20 km trip cost? [TITA | Moderate]

Q49. The average monthly salary of 18 managers is Rs 62,000 and that of 32 analysts is Rs 38,000. One manager leaves, after which the average salary of the remaining 49 employees becomes Rs 46,000. What was the monthly salary, in thousands of rupees, of the manager who left? [TITA | Moderate]

Q50. An investment earns 8% in the first year and 12% in the second year, with annual compounding. If its value after two years is Rs 12,096, what was the initial investment? [TITA | Moderate]

Q51. A mobile-data plan charges a fixed monthly fee of Rs 240, which includes the first 20 GB of usage. Each additional GB costs Rs 6. If the monthly bill is Rs 420, how many GB were used in total? [MCQ | Easy]

1. 45 GB
2. 48 GB
3. 50 GB
4. 52 GB

Q52. An upward-moving escalator has 60 visible steps from bottom to top. A person walks upward at 2 steps per second relative to the escalator and reaches the top in 24 seconds. What is the escalator speed, in steps per second? [TITA | Difficult]

Q53. If x and y are positive and x+y=18, what is the maximum possible value of x^2y? [TITA | Difficult]

Q54. If 2^(x+1) + 2^(x-1) = 40, what is x? [TITA | Easy]

Q55. How many integers x satisfy |2x-5| < 9 and x^2-7x+10 >= 0? [MCQ | Moderate]

1. 4
2. 5
3. 6
4. 7

Q56. What is the least positive integer n for which the sum of the first n positive odd integers exceeds 500? [TITA | Easy]

Q57. How many ordered pairs of positive integers (a,b) satisfy gcd(a,b)=6 and lcm(a,b)=72? [MCQ | Difficult]

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

Q58. How many positive integers not exceeding 500 are divisible by 6 or 15, but not by both? [TITA | Moderate]

Q59. What is the least integer n greater than 50 such that gcd(n,84)=12? [MCQ | Moderate]

1. 54
2. 60
3. 72
4. 84

Q60. In a triangle ABC, sides AB=13, AC=15 and BC=14. What is the length of the altitude from A to BC? [MCQ | Moderate]

1. 10
2. 11
3. 12
4. 13

Q61. A trapezium has parallel sides of lengths 10 cm and 22 cm and height 9 cm. What is its area in square centimetres? [TITA | Easy]

Q62. An isosceles triangle has equal sides 13 cm each and base 10 cm. What is its inradius, in centimetres? [MCQ | Moderate]

Q63. In a circle of radius 14 cm, a 90-degree sector is cut off. Using pi=22/7, what is the area of the minor segment formed by the sector and its chord? [TITA | Moderate]

Q64. How many distinct arrangements of the letters of the word MANAGEMENT are possible? [MCQ | Difficult]

1. 226800
2. 907200
3. 1814400
4. 3628800

Q65. An integer is chosen uniformly at random from 1 to 100. What is the probability that it is divisible by 4 or 6? [MCQ | Moderate]

1. 29/100
2. 31/100
3. 33/100
4. 35/100

Q66. How many four-digit positive integers have distinct digits and contain exactly one zero? [TITA | Moderate]

Q67. For positive real numbers a and b with ab=16, what is the minimum value of a+b? [MCQ | Easy]

1. 4
2. 6
3. 8
4. 10

Q68. Let f(x)=x^2-4x+7. If f(a)=f(6-a), what is a? [MCQ | Moderate]

1. 3
2. 6
3. 8
4. 10

Answer Key

Detailed Solutions

VARC Solutions

Q1. Answer: C. The correct option follows directly from the passage: the value of redundancy depends on the risks covered, the independence of backups and the time horizon considered.

Q2. Answer: A. The correct option follows directly from the passage: To show that duplication may fail to provide resilience when backup elements share a common vulnerability.

Q3. Answer: C. The correct option follows directly from the passage: The expected reduction in disruption losses, given the failures it can independently absorb.

Q4. Answer: B. The correct option follows directly from the passage: objectives that can look different depending on the period and risks being evaluated.

Q5. Answer: B. The correct option follows directly from the passage: the tension between coordination and inherited variation in language revitalisation.

Q6. Answer: B. The correct option follows directly from the passage: allows a language to function more easily in education and public communication.

Q7. Answer: C. The correct option follows directly from the passage: Young speakers learn only the classroom variety and begin treating older local forms as erroneous.

Q8. Answer: A. The correct option follows directly from the passage: a practical convention rather than proof that one historical variety was uniquely correct.

Q9. Answer: B. The correct option follows directly from the passage: identical written procedures can still conceal meaningful differences in practice.

Q10. Answer: A. The correct option follows directly from the passage: It is treated as a useful characteristic of scientific knowledge distinct from the simple truth or falsity of a result.

Q11. Answer: C. The correct option follows directly from the passage: Communication tools such as videos or reference samples may sometimes transmit experimental practice better than text alone.

Q12. Answer: B. The correct option follows directly from the passage: a process for identifying the conditions under which a result remains stable across settings.

Q13. Answer: B. The correct option follows directly from the passage: treat illumination as task-specific infrastructure whose design must consider multiple effects.

Q14. Answer: A. The correct option follows directly from the passage: To show that the effects of lighting depend on where the light goes, not only on total output.

Q15. Answer: C. The correct option follows directly from the passage: Lighting standards that consider direction, spectrum, local use and reliability in addition to brightness.

Q16. Answer: B. The correct option follows directly from the passage: technical efficiency does not eliminate distributional questions about who experiences reduced or increased lighting.

Q17. Answer: B. The option captures the paragraph’s controlling idea without adding or omitting a key qualification.

Q18. Answer: C. The option captures the paragraph’s controlling idea without adding or omitting a key qualification.

Q19. Answer: B. The option captures the paragraph’s controlling idea without adding or omitting a key qualification.

Q20. Answer: A. The option captures the paragraph’s controlling idea without adding or omitting a key qualification.

Q21. Answer: 3. Sentence 3 breaks the paragraph’s thematic and logical flow; the remaining sentences form a coherent sequence.

Q22. Answer: 4. Sentence 4 breaks the paragraph’s thematic and logical flow; the remaining sentences form a coherent sequence.

Q23. Answer: 4. Sentence 4 breaks the paragraph’s thematic and logical flow; the remaining sentences form a coherent sequence.

Q24. Answer: 4. Sentence 4 breaks the paragraph’s thematic and logical flow; the remaining sentences form a coherent sequence.

DILR Solutions

Set 1 working: There are 10 feasible schedules. Checking the schedules shows D is necessarily before F; with C in slot 1, 3 schedules remain; E can occupy slot 6.

Set 2 working: Member visits: P 540, Q 600, R 600, S 630, T 700 (total 3070). Books: 1620, 2400, 1200, 3150, 2100 (total 10470).

Set 3 working: Use N = rank 5 with 3 wins and rank 1 = 7 wins, then enforce L<J<K and the ordering condition among J, K and M. This sharply restricts the feasible assignments.

Set 4 working: Completers: {‘A’: 600, ‘B’: 680, ‘C’: 600, ‘D’: 720}. Certificate earners: {‘A’: 360, ‘B’: 476, ‘C’: 390, ‘D’: 540}. Fee revenues: {‘A’: 960000, ‘B’: 1500000, ‘C’: 1350000, ‘D’: 1200000}.

Set 5 working: Enumerate 4-member subsets and apply the five selection rules in sequence. The valid shortlists are: PRST, PRSU, QRST, QRSU, RSTU.

Q25. Answer: 10. Enumerating all feasible schedules gives 10 possibilities. Applying the additional condition yields the stated answer.

Q26. Answer: C. Enumerating all feasible schedules gives 10 possibilities. Applying the additional condition yields the stated answer.

Q27. Answer: 3. Enumerating all feasible schedules gives 10 possibilities. Applying the additional condition yields the stated answer.

Q28. Answer: C. Enumerating all feasible schedules gives 10 possibilities. Applying the additional condition yields the stated answer.

Q29. Answer: 3070. Member visits = 540+600+600+630+700 = 3070.

Q30. Answer: D. Books borrowed: P 1620, Q 2400, R 1200, S 3150, T 2100. Hence S.

Q31. Answer: B. Q has 600 members × 4 = 2400 books. S has 630 members × 5 = 3150 books. 2400/3150 ×100 = 76.19%.

Q32. Answer: 210. Additional members = 5% of 1400 = 70; each borrows 3 books, so 210 additional books.

Q33. Answer: B. Total books = 10470; total member visits = 3070; average = 3.41.

Q34. Answer: 1. Systematically matching the rank-order constraints with the distinct win counts gives the unique/feasible assignments used for the answer.

3. 3.41

Q36. Answer: C. Systematically matching the rank-order constraints with the distinct win counts gives the unique/feasible assignments used for the answer.

Q37. Answer: 3. Systematically matching the rank-order constraints with the distinct win counts gives the unique/feasible assignments used for the answer.

Q38. Answer: 2600. Compute completers first, then apply the certificate rate where required; fee revenue equals enrolments × fee.

Q39. Answer: B. Compute completers first, then apply the certificate rate where required; fee revenue equals enrolments × fee.

Q40. Answer: 64. Compute completers first, then apply the certificate rate where required; fee revenue equals enrolments × fee.

Q41. Answer: 12. Compute completers first, then apply the certificate rate where required; fee revenue equals enrolments × fee.

Q42. Answer: C. Compute completers first, then apply the certificate rate where required; fee revenue equals enrolments × fee.

Q43. Answer: 5. List the 4-member combinations and eliminate those violating each rule. The remaining valid shortlists determine the answer.

Q44. Answer: B. Every valid shortlist contains both R and S; the other pitches vary across the feasible combinations.

Q45. Answer: A. List the 4-member combinations and eliminate those violating each rule. The remaining valid shortlists determine the answer.

Q46. Answer: 0. List the 4-member combinations and eliminate those violating each rule. The remaining valid shortlists determine the answer.

QA Solutions

Q47. Answer: B. Mixture cost = (3×360+2×480)/5 = 408. Selling price at 25% profit = 408×1.25 = Rs 510.

Q48. A taxi fare consists of a fixed booking charge and a constant charge per kilometre. An 8 km trip costs Rs 236 and a 14 km trip costs Rs 344. What will a 20 km trip cost? [TITA | Moderate]

Q49. The average monthly salary of 18 managers is Rs 62,000 and that of 32 analysts is Rs 38,000. One manager leaves, after which the average salary of the remaining 49 employees becomes Rs 46,000. What was the monthly salary, in thousands of rupees, of the manager who left? [TITA | Moderate]

Q50. An investment earns 8% in the first year and 12% in the second year, with annual compounding. If its value after two years is Rs 12,096, what was the initial investment? [TITA | Moderate]

Q51. A mobile-data plan charges a fixed monthly fee of Rs 240, which includes the first 20 GB of usage. Each additional GB costs Rs 6. If the monthly bill is Rs 420, how many GB were used in total? [MCQ | Easy]

Q52. An upward-moving escalator has 60 visible steps from bottom to top. A person walks upward at 2 steps per second relative to the escalator and reaches the top in 24 seconds. What is the escalator speed, in steps per second? [TITA | Difficult]

Q53. Answer: 864. Let y=18-x. Then f=x^2(18-x). f’=36x-3x^2=3x(12-x), so the interior maximum occurs at x=12 and y=6. Thus x^2y=144×6=864.

Q54. Answer: 4. 2^(x-1)(4+1)=40, so 2^(x-1)=8=2^3, hence x=4.

Q55. Answer: C. |2x-5|<9 gives -2<x<7, hence integer candidates -1,0,1,2,3,4,5,6. Also (x-2)(x-5)>=0 gives x<=2 or x>=5. Thus -1,0,1,2,5,6: 6 integers.

Q56. What is the least positive integer n for which the sum of the first n positive odd integers exceeds 500? [TITA | Easy]

Q57. How many ordered pairs of positive integers (a,b) satisfy gcd(a,b)=6 and lcm(a,b)=72? [MCQ | Difficult]

Q58. How many positive integers not exceeding 500 are divisible by 6 or 15, but not by both? [TITA | Moderate]

Q59. What is the least integer n greater than 50 such that gcd(n,84)=12? [MCQ | Moderate]

Q60. Answer: C. Semiperimeter=21. Area=sqrt(21×8×6×7)=84. Altitude to BC = 2×84/14=12.

Q61. A trapezium has parallel sides of lengths 10 cm and 22 cm and height 9 cm. What is its area in square centimetres? [TITA | Easy]

Q62. An isosceles triangle has equal sides 13 cm each and base 10 cm. What is its inradius, in centimetres? [MCQ | Moderate]

Q63. In a circle of radius 14 cm, a 90-degree sector is cut off. Using pi=22/7, what is the area of the minor segment formed by the sector and its chord? [TITA | Moderate]

Q64. Answer: A. MANAGEMENT has 10 letters, with M, A, N and E each repeated twice. Number of arrangements = 10!/(2!^4) = 226800.

Q65. An integer is chosen uniformly at random from 1 to 100. What is the probability that it is divisible by 4 or 6? [MCQ | Moderate]

Q66. How many four-digit positive integers have distinct digits and contain exactly one zero? [TITA | Moderate]

Q67. Answer: C. By AM-GM, a+b>=2sqrt(ab)=8, equality at a=b=4.

Q68. Answer: A. f(x)=(x-2)^2+3. So (a-2)^2=(4-a)^2. The non-identity branch gives a-2=4-a, hence 2a=6 and a=3.

Publishing Note

This paper is original practice material of MBA4U.in. Difficulty tags are editorial aids and should not be presented as official CAT labels. The paper should be used as a timed practice mock, not described as an official or previous-year CAT paper.