Explanation

The sentence requires words that satisfy standard English collocations and idiomatic expressions. The phrase "keep someone busy" (in past tense, "kept the spectators busy") logically describes how the abundance of talent occupied the audience. Additionally, "prove one's mettle" is a fixed idiom meaning to demonstrate one's strength, skill, or resilience in a competitive or challenging situation.

Explanation

The definite article "The" requires the noun form "sale" rather than the verb form "sell" to function as the subject of the clause. In the second clause, the causal conjunction "as" introduces the reason for the proposed ban, requiring a verb that denotes severe harm or injury to wildlife. The singular verb "cripples" grammatically agrees with the singular pronoun "it" and accurately captures the maiming and physical injury inflicted on birds by sharp synthetic kite-flying thread.

Explanation

The verb shared pairs with the preposition with to convey communicating or distributing knowledge and ideas to another person. Additionally, the modal auxiliary can requires the bare infinitive verb form, practice, which appropriately collocates with techniques to denote exercising and applying skills to improve proficiency.

Explanation

In English usage, facts indicate or demonstrate a particular finding, making indicate the appropriate verb for the first blank. In the second blank, the standard idiomatic collocation with care and caution is the verb take, appearing here in the passive voice as taken by the hospital.

Explanation

The sentence describes a historical trend in student demographics. The adverb traditionally fits naturally with the present perfect tense have been to denote a long-standing practice or customary pattern over time, while major is the appropriate adjective modifying contributors to signify that these groups represent a large and significant portion of the international student body.

Explanation

In the idiom to set a benchmark, meaning to establish a standard or point of reference against which others can be evaluated, the noun benchmark must be used. Replacing it with the continuous form or gerund benchmarking is grammatically incorrect.

Explanation

In standard English grammar, the present perfect tense requires the auxiliary verb has or have to be followed by the past participle (V3) of the main verb. Therefore, has taking is grammatically incorrect and should be replaced with has taken.

Explanation

In the given sentence, "flow" functions as a noun, which must be qualified by an adjective instead of an adverb. The adverb "constantly" is grammatically incorrect in this position and should be replaced with the adjective "constant" to correctly form the phrase "a constant flow of".

Explanation

In standard English grammar, the adjective different is followed by the preposition from to indicate distinction between two entities. Therefore, the phrase different than should be replaced by different from.

Explanation

The noun "plans" takes a to-infinitive ("to" + base form of the verb) to express future intent, purpose, or action. Therefore, the phrase must use "to create" rather than "to creating", as the particle "to" functions as an infinitive marker rather than a preposition governing a gerund.

Explanation

The correct idiomatic and technical term to express the measure of deaths in a given population is mortality rate. The word rating refers to an evaluation or classification on a scale, which is contextually improper when referring to a statistical measure of incidence or frequency. Replacing mortality rating with mortality rate corrects the phrase.

Explanation

The given sentence is grammatically correct throughout. The plural subject "The two most important numbers" correctly agrees with the plural main verb "are". Within the relative clause modifying the subject, the plural noun "mandarins" properly takes the plural verb phrase "have to watch", and the indefinite article "an" is used correctly before the vowel-sounding noun "economy".

Explanation

The sentence begins with a participial phrase modifying the subject "instructors". Since the instructors performed the action of observing, the present participle "Witnessing" or the perfect participle "Having witnessed" must be used instead of the past participle "Witnessed".

Explanation

A relative clause introduced by the relative pronoun that requires a finite verb to serve as the predicate. In the given sentence, the present participle causing must be replaced by the simple present plural verb cause to agree with the antecedent jokes and expressions, or the relative pronoun that must be removed to form a proper participial phrase.

Explanation

A modal auxiliary verb such as "won't" (will not) is always followed directly by the base form of the main verb in its bare infinitive form. The participle form "carryng" is grammatically incorrect in this construction and must be replaced by the base verb "carry".

Explanation

In English grammar, the auxiliary verb be in present continuous tense must be followed by the present participle form of the main verb (verb + ing). Therefore, are bring is grammatically incorrect and must be replaced by are bringing or simple present bring to maintain correct subject-verb agreement and tense structure.

Explanation

The passage states that Toyota's 'Right Step' was recognizing that it could not keep selling endlessly to its shrinking home market, so it 'went really aggressive in the western markets' — that is, it looked for newer avenues and markets, matching option (d) exactly. This contrasts with the shortcut taken by other (western) companies of giving loans to non-creditworthy people.

Explanation

According to the first paragraph of the passage, although the Japanese style of management had been widely admired for years, scepticism arose over the last decade because Japan remained in a prolonged recession for more than a decade despite its acclaimed management methods.

Explanation

According to the passage, the shift toward developing nations is driven by developed markets in America and Europe reaching their natural limits to growth and affluence saturation. Developing countries like India possess vast populations that are rapidly transitioning into a consuming middle class, creating immense scope for new consumer demand when provided with purchasing power.

Explanation

According to the passage, the primary cause of the Japanese recession lies in the non-materialistic culture of Japan. The author explains that Japanese consumers do not continually discard and purchase goods endlessly. Once individuals acquire everything they need, the market reaches a saturation point, leading to a shrinking home market and an economic slowdown.

Explanation

The author explains that just as Henry Ford increased his profits by paying his workers higher wages so they could afford his cars, the developed world will likewise transfer purchasing power to developing nations, enabling them to buy goods and fostering mutual economic prosperity worldwide.

Explanation

The passage directly attributes the purchasing of redundant products and the eventual defaults by non-creditworthy borrowers to the aggressive distribution of loans and credit by financial institutions. In contrast, the prospect of poverty becoming almost nonexistent is presented as a future aspiration over the next fifty years, driven by shifting market focus, providing purchasing power, and expanding economic opportunities across developing regions like India, China, Latin America, and Africa.

Explanation

The passage emphasizes that saturated home markets and the ensuing economic downturn force western companies to explore new global destinations for trade. India, with its expanding population transitioning into a consuming middle class, provides an attractive and untapped consumer market for these companies, ultimately driving incoming investments, purchasing power, and long-term economic prosperity.

Explanation

In the passage, the author refers to the dustbinisation of the customer as the marketing and advertising practice of turning consumers into material dustbins by luring them to continuously acquire new goods even when their existing products serve them perfectly well, thereby inducing them to buy items they do not genuinely need.

Explanation

According to the passage, the recession is beneficial for planet Earth because the earth requires sustainable development rather than unchecked consumerism that depletes natural resources and damages the environment. Setting limits to growth curtails environmental degradation caused by excessive consumption and market expansion. Benefiting developing nations through shifted markets relates to human economic prosperity rather than the ecological well-being of the planet itself.

Explanation

The passage uses 'catering' in the sentence: 'Japanese companies grew bigger by catering to the world markets when their home markets shrunk.' Here catering means supplying or serving the needs of the world markets, matching option (c) Supplying.

Explanation

'Key' appears in the passage as: 'one key question has sprung up' — used adjectivally to mean an important/crucial question, matching option (e) Important.

Explanation

'Aggressive' appears in: 'they went really aggressive in the western markets' describing Toyota's bold, forceful push into new markets (a positive business-expansion sense, not violence). Among the options (Violent, Determined, Demanding, Offensive, Brutish), 'Determined' (b) best captures this forceful-but-positive business connotation.

Explanation

The word prosperous refers to being successful, thriving, and characterized by financial success or material well-being. The term underprivileged refers to people or groups lacking the standard socio-economic opportunities, wealth, and privileges enjoyed by others in a society, making it the exact antonym in a socio-economic context.

Explanation

To consume means to use up, expend, or absorb resources fully. In contrast, to curtail means to reduce, cut back, or restrict the extent or expenditure of something, making it the opposite in meaning.

Explanation

The preposition "from" forms the standard temporal expression "[time period] from now", which is used to project forward into the future starting from the present time. In the context of predicting future demographic trends, "Twenty years from now" appropriately specifies the timeframe occurring two decades after the present moment.

Explanation

The sentence describes the challenge of urbanization by comparing the rate of urban expansion with infrastructure growth using the comparative modifier "much ... than". Since the negative impact arises from city growth outpacing the development of supporting infrastructure, the comparative adjective "faster" correctly completes the phrase "at a much faster rate than infrastructure expansion".

Explanation

In the context of urban planning and public health, sustainability issues must be taken into account or given thoughtful attention before executing development projects. The phrase "need to be" functions as a passive modal construction requiring a past participle verb, and considered accurately conveys the intended meaning of evaluating and integrating these environmental and social concerns into policy decisions.

Explanation

The idiomatic expression at the expense of means doing something that leads to the detriment, sacrifice, or harm of another thing. In the context of the sentence, economic growth should not occur by compromising or damaging public health.

Explanation

The phrase "in abundance" functions as an idiom meaning present in large quantities or plentiful. In the context of the sentence, essential public utilities such as water, electricity, and transportation are fundamental infrastructure requirements that ought to be abundantly available to adequately support an urban population.

Explanation

The relative pronoun that refers to the singular antecedent a detailed report, requiring a singular present-tense verb. Contextually, a research report highlights, stresses, or focuses on a key policy theme. The verb emphasizes fits both grammatically and logically, expressing that the report gives special importance to sustainability in urban service delivery.

Explanation

The sentence identifies the underlying cause behind the rapid rise in private vehicles on city roads. The adjective inadequate means insufficient in quality or quantity, which logically explains why commuters are driven to use private transport when public transit systems fail to meet demand.

Explanation

The idiomatic expression "on the rise" means increasing in amount, number, or frequency. In this context, the passage describes an increasing prevalence of respiratory illnesses and asthma cases among children in urban areas due to pollution.

Explanation

In the context of health and diseases, medical cases are officially recorded, documented, or reported. Following the passive auxiliary "being", a past participle is required, making reported the grammatically and contextually appropriate choice for describing cases of asthma.

Explanation

In formal standard English grammar, when a conditional or alternative interrogative clause serves as the object of a preposition, whether must be used instead of if. Here, the preposition on governs the dependent clause, making whether the grammatically correct choice to complete the sentence.

Explanation

The word is misspelled. The correct spelling is goalkeeper's, which contains the letter a following the letter o to form goal. A goalkeeper is a player in sports like football or hockey whose role is to prevent the ball or puck from entering the goal.

Explanation

The sentence is constructed in the present perfect tense, following the rule subject + has/have + past participle (V3). The base verb form "refrain" is grammatically incorrect following the auxiliary verb "has" and must be replaced with its past participle form, "refrained".

Explanation

The correct idiomatic expression is to save one's own skin, which means to protect oneself from danger, punishment, or blame, especially in an unfair or selfish manner. Replacing skin with skull makes the phrase inappropriate in this context.

Explanation

The possessive determiner "her" must be followed by a noun functioning as the object of the preposition "of". The word "dead" is an adjective, whereas the noun form "death" is required to make the sentence grammatically and contextually correct.

Explanation

The word "laybarinth" is incorrectly spelt. The correct spelling is "labyrinth", which denotes a complicated irregular network of passages or paths in which it is difficult to find one's way.

Explanation

Sentence (B) serves as the opening statement by establishing the core subject, setting, and time—a fierce winter storm hitting New York on Friday. It provides the overarching context before subsequent sentences specify the storm's designated name, the plunge in temperatures, the heavy snowfall, emergency declarations, and flight cancellations.

Explanation

The paragraph begins with B introducing the fierce winter storm and the setting in New York. Sentence A follows by identifying the storm as Hercules and detailing the closure of major roads due to snowdrifts. Sentence E immediately supplements this transport disruption by noting that thousands of flights were also cancelled. Sentence D forms the fourth sentence by detailing the declaration of a state of emergency resulting from the heavy snowfall. Sentence C elaborates on the severe wind chill forecast, and F concludes the paragraph with a general statement on the disastrous impact of storms. The complete logical sequence is B-A-E-D-C-F.

Explanation

The paragraph opens with sentence B introducing the fierce winter storm and dangerous glacial temperatures in New York. Sentence C elaborates on the temperature drop forecast by weather experts. Sentence D follows with the heavy snowfall and declaration of emergency. Sentence A describes road closures due to snowdrifts, and sentence E connects directly to transportation disruptions by adding that thousands of flights were also cancelled. Sentence F provides the concluding observation. Thus, the logical sequence is B-C-D-A-E-F, placing sentence E in the fifth position.

Explanation

The coherent sequence of the sentences begins with an introductory statement about the severe winter storm striking New York, followed by its identification as Winter Storm Hercules, the disruption to road and flight traffic, the declaration of an emergency, and the temperature forecasts. The generalizing remark on the disastrous nature of storms naturally serves as the concluding observation to complete the paragraph.

Explanation

The paragraph opens with sentence B, which introduces the overarching event: a fierce winter storm bringing glacial temperatures to New York. Sentence A immediately follows as the second sentence to name the storm as Hercules and describe its primary impact of blocking major roads with snowdrifts. This sets up the subsequent sentence detailing flight cancellations.

Explanation

Total ratio parts = 5 + 6 + 3 = 14. Value of 1 part = 2800 / 14 = 200.

Original shares: Amit = 5 × 200 = 1000 Sumit = 6 × 200 = 1200 Vinit = 3 × 200 = 600

After adding 200 to each share: Amit = 1000 + 200 = 1200 Sumit = 1200 + 200 = 1400 Vinit = 600 + 200 = 800

New ratio = 1200 : 1400 : 800 = 6 : 7 : 4.

Explanation

Total sum of the four integers = 4 × 59 = 236. Sum of the remaining two integers = 236 - (83 + 29) = 124. Let the two remaining integers be x and y, where x is the higher integer: x + y = 124 x - y = 28 Adding the two equations yields: 2x = 152 x = 76

Explanation

Net percentage change = x + y + (xy / 100)

Given markup x = +50% and discount y = -30%: Net profit % = 50 - 30 + (50 × (-30) / 100) Net profit % = 20 - 15 = +5%

Since the result is positive, there is a gain of 5%.

Explanation

Let total work = LCM(96, 80, 120) = 480 units.

Hourly work rates: 1 Man + 3 Women + 4 Boys = 480 / 96 = 5 units/hr 2 Men + 8 Boys = 480 / 80 = 6 units/hr, which gives 1 Man + 4 Boys = 3 units/hr 2 Men + 3 Women = 480 / 120 = 4 units/hr

Subtracting (1 Man + 4 Boys) from (1 Man + 3 Women + 4 Boys): 3 Women = 5 - 3 = 2 units/hr

Substituting 3 Women into (2 Men + 3 Women): 2 Men + 2 = 4 units/hr 2 Men = 2 units/hr, which gives 1 Man = 1 unit/hr

Using 1 Man + 4 Boys = 3 units/hr: 4 Boys = 3 - 1 = 2 units/hr, which gives 1 Boy = 0.5 units/hr

Combined efficiency of 5 Men and 12 Boys: 5(1) + 12(0.5) = 5 + 6 = 11 units/hr

Time required to complete the total work: 480 / 11 = 43 7/11 hours

Explanation

Let the amount borrowed at 18% be x. Then the amount borrowed at 15% is 24000 - x.

Total simple interest for 1 year is given by: 0.15 × (24000 - x) + 0.18 × x = 4050 3600 + 0.03x = 4050 0.03x = 450 x = 450 / 0.03 = 15000

Alternatively, using the alligation method: Overall rate of interest = (4050 / 24000) × 100% = 16.875% Ratio of sum at 15% to sum at 18% = (18 - 16.875) : (16.875 - 15) = 1.125 : 1.875 = 3 : 5 Amount borrowed at 18% = (5 / 8) × 24000 = 15000.

Explanation

The pattern governing the series is: Term(n+1) = Term(n) × (7 - n) + n³

Applying this rule to the original series: 3 × 6 + 1³ = 19 19 × 5 + 2³ = 103 103 × 4 + 3³ = 439 439 × 3 + 4³ = 1381 1381 × 2 + 5³ = 2887

Following the identical pattern starting with 5: (a) = 5 × 6 + 1³ = 30 + 1 = 31 (b) = 31 × 5 + 2³ = 155 + 8 = 163

Explanation

The rule governing the original series is: (4 + 9) × 1 = 13 (13 + 7) × 2 = 40 (40 + 5) × 3 = 135 (135 + 3) × 4 = 552 (552 + 1) × 5 = 2765

Applying the identical operation starting with 2: (a) = (2 + 9) × 1 = 11 (b) = (11 + 7) × 2 = 36 (c) = (36 + 5) × 3 = 123

Explanation

The original series follows an alternating pattern of two operations: First operation: × 2 + 2 Second operation: ÷ 2 - 2

Checking the original series: 5 × 2 + 2 = 12 12 ÷ 2 - 2 = 4 4 × 2 + 2 = 10 10 ÷ 2 - 2 = 3 3 × 2 + 2 = 8

Applying the identical rule to the series beginning with 6: (a) = 6 × 2 + 2 = 14 (b) = 14 ÷ 2 - 2 = 5 (c) = 5 × 2 + 2 = 12 (d) = 12 ÷ 2 - 2 = 4 (e) = 4 × 2 + 2 = 10

Explanation

The pattern in the given series is: 3 × 2 + 7 = 13 13 × 2 + 11 = 37 37 × 2 + 13 = 87 87 × 2 + 17 = 191 191 × 2 + 19 = 401

Applying the same rule to the series starting with 1: (a) = 1 × 2 + 7 = 9 (b) = 9 × 2 + 11 = 29 (c) = 29 × 2 + 13 = 71 (d) = 71 × 2 + 17 = 159

Explanation

The pattern in the original series involves successive multiplication where each multiplier increases by 1: 8 × 0.5 = 4 4 × 1.5 = 6 6 × 2.5 = 15 15 × 3.5 = 52.5 52.5 × 4.5 = 236.25

Applying the same rule starting from 12: (a) = 12 × 0.5 = 6 (b) = 6 × 1.5 = 9 (c) = 9 × 2.5 = 22.5

Explanation

Let the speed of train B be v m/s. Then the speed of train A is 1.4v m/s.

Using statement P: Since the trains move in opposite directions, their relative speed is 1.4v + v = 2.4v. Total distance to cross each other = 100 + 180 = 280 m. Time taken = 6 seconds. Relative speed = Distance / Time = 280 / 6 = 140 / 3 m/s. 2.4v = 140 / 3, which gives a unique value for v. Thus, statement P alone is sufficient.

Using statement Q: Difference between speeds = 1.4v − v = 0.4v = 26 kmph. v = 26 / 0.4 = 65 kmph. Thus, statement Q alone is also sufficient.

Since either statement alone is sufficient to find the speed of train B, the correct requirement is "Either P or Q alone is sufficient".

Explanation

From statement I, the total number of students is 60 and the total weight of the class is 60 × 42 = 2520 kg.

From statement III, the total weight of all girls is 1144 kg. Therefore, the total weight of all boys is 2520 - 1144 = 1376 kg.

From statement II, the average weight of boys is 43 kg, which gives the number of boys as 1376 / 43 = 32.

The number of girls is then 60 - 32 = 28, and their average weight is 1144 / 28 = 40.86 kg. Thus, all three statements together are required to answer the question.

Explanation

Let the cost price be C and the original selling price without discount be S.

From statement I: S = 1.2C From statement II: 0.9S - C = 1200 From statement III: C = 15000

Using statements I and II: Substituting C = S / 1.2 into the second equation gives 0.9S - (S / 1.2) = 1200, which simplifies to (2/30)S = 1200, giving S = ₹ 18,000. Using statements I and III: S = 1.2 × 15000 = ₹ 18,000. Using statements II and III: 0.9S - 15000 = 1200, which gives 0.9S = 16200, resulting in S = ₹ 18,000.

Therefore, any combination of two statements is sufficient to find the selling price.

Explanation

Statement I gives the proportion of children who speak only Hindi (20%), which means 80% speak languages other than Hindi. Statement II gives that count as 44 children. Together: 80% of the total = 44, so the total number of children = 44 / 0.80 = 55. Statement III (30 boys) cannot be linked to language ability and is not needed. Hence statements I and II together are sufficient, and III is not required.

Explanation

Volume of a cylindrical tank is given by V = πr²h = (Base Area) × h.

Using statements I and II: Base Area = X and height h = Y, directly yielding V = XY.

Using statements II and III: Height h = Y. Since diameter d = 2r = h = Y, radius r = Y/2. Thus, V = π(Y/2)²(Y) = πY³/4.

Using statements I and III: Base Area πr² = X gives r = √(X/π), which means diameter d = 2√(X/π). Since height h = d = 2√(X/π), the volume is V = (Base Area) × h = 2X√(X/π).

Any two of the three statements together are sufficient to find the volume.

Explanation

Solving the first quadratic equation by factoring: a² + 5a + 6 = 0 (a + 2)(a + 3) = 0 a = -2, -3

Solving the second quadratic equation by factoring: b² + 3b + 2 = 0 (b + 1)(b + 2) = 0 b = -1, -2

Comparing each value of a with each value of b: For a = -2: a < b when b = -1, and a = b when b = -2. For a = -3: a < b when b = -1, and a < b when b = -2.

Combining all cases yields the relation a ≤ b.

Explanation

Solve equation I: 2a² + 3a + 1 = 0 (2a + 1)(a + 1) = 0 a = -1, -½ (-0.5)

Solve equation II: 12b² + 7b + 1 = 0 (4b + 1)(3b + 1) = 0 b = -⅓ (-0.333), -¼ (-0.25)

Comparing the roots: -1 < -0.333 and -1 < -0.25 -0.5 < -0.333 and -0.5 < -0.25

Every possible value of a is strictly less than every possible value of b, giving a < b.

Explanation

Solving equation I: a² = 4 gives a = 2 or a = -2.

Solving equation II (for variable b): b² = 9 gives b = 3 or b = -3.

Comparing the values: When a = 2 and b = 3, a < b. When a = 2 and b = -3, a > b.

Because the relation changes depending on the signs taken, no consistent relationship between a and b can be established.

Explanation

Solve equation I by factorization: 6a² - 25a + 25 = 0 6a² - 15a - 10a + 25 = 0 3a(2a - 5) - 5(2a - 5) = 0 (3a - 5)(2a - 5) = 0 a = 5/3 ≈ 1.67 or a = 5/2 = 2.5

Solve equation II by factorization: 15b² - 16b + 4 = 0 15b² - 10b - 6b + 4 = 0 5b(3b - 2) - 2(3b - 2) = 0 (5b - 2)(3b - 2) = 0 b = 2/5 = 0.4 or b = 2/3 ≈ 0.67

Comparing the values of a and b: 2.5 > 0.67 and 2.5 > 0.4 1.67 > 0.67 and 1.67 > 0.4

Since every possible value of a is strictly greater than every possible value of b, the relationship is a > b.

Explanation

For equation I: 4a² - 20a + 21 = 0 4a² - 14a - 6a + 21 = 0 2a(2a - 7) - 3(2a - 7) = 0 (2a - 3)(2a - 7) = 0 a = 3/2 = 1.5, 7/2 = 3.5

For equation II: 2b² - 5b + 3 = 0 2b² - 2b - 3b + 3 = 0 2b(b - 1) - 3(b - 1) = 0 (2b - 3)(b - 1) = 0 b = 1, 3/2 = 1.5

Comparing the roots: When a = 1.5 and b = 1, a > b When a = 1.5 and b = 1.5, a = b When a = 3.5 and b = 1, a > b When a = 3.5 and b = 1.5, a > b

Combining these comparisons yields a ≥ b.

Explanation

Average percentage of marks in Subject T = (Sum of percentage marks obtained by all six students) / (Total number of students)

Average percentage = (64 + 56 + 58 + 72 + 77 + 68) / 6 = 395 / 6 = 65.83%

Explanation

Total marks obtained by A in subjects P, Q, and R: Marks in P = 68% of 70 = 47.6 Marks in Q = 84% of 80 = 67.2 Marks in R = 77% of 120 = 92.4 Total for A = 47.6 + 67.2 + 92.4 = 207.2

Total marks obtained by F in subjects S, T, and U: Marks in S = 68% of 125 = 85 Marks in T = 68% of 75 = 51 Marks in U = 71% of 150 = 106.5 Total for F = 85 + 51 + 106.5 = 242.5

Required percentage = (207.2 / 242.5) × 100 = 85.44% ≈ 85%

Explanation

Total maximum marks = 70 + 80 + 120 + 125 + 75 + 150 = 620.

Marks obtained by B in each subject: In P: 49% of 70 = 34.3 In O: 79% of 80 = 63.2 In R: 62% of 120 = 74.4 In S: 85% of 125 = 106.25 In T: 56% of 75 = 42 In U: 76% of 150 = 114

Total marks obtained by B = 34.3 + 63.2 + 74.4 + 106.25 + 42 + 114 = 434.15

Overall percentage = (434.15 / 620) × 100 = 70.024% ≈ 70.02%

Explanation

Total marks obtained by student D across all six subjects are calculated by taking the respective percentage of the maximum marks for each subject:

Subject P: 75% of 70 = 52.5 Subject O: 85% of 80 = 68 Subject R: 82% of 120 = 98.4 Subject S: 68% of 125 = 85 Subject T: 72% of 75 = 54 Subject U: 78% of 150 = 117

Total marks = 52.5 + 68 + 98.4 + 85 + 54 + 117 = 474.9.

Explanation

Sum of percentage of marks obtained by the six students in subject Q = 84 + 79 + 81 + 85 + 66 + 70 = 465%

Average percentage = 465% / 6 = 77.5%

Average marks obtained out of 80 = 77.5% × 80 = (77.5 / 100) × 80 = 62

Explanation

Area of a circle is given by A = πr².

Area of the larger circle = π × 5² = 25π cm² Area of the smaller circle = π × 3² = 9π cm² Area of the annular zone = 25π - 9π = 16π cm²

Ratio of the annular zone area to the larger circle area: Ratio = (16π) / (25π) = 16:25

Explanation

The base of a right circular cone is a circle with perimeter 2πr = 8 cm, giving r = 4/π cm. Given height h = 21 cm, the volume is: V = (1/3)πr²h = (1/3) × π × (4/π)² × 21 = 7 × (16/π) = 112/π cm³.

Explanation

Age of retired teacher = Age of new teacher + (Total number of teachers × Decrease in average age)

Substituting the given values: Age of retired teacher = 25 + (10 × 3) = 25 + 30 = 55 years.

Explanation

Given the relation: x / (x² - 2x + 1) = 1/3

Taking the reciprocal on both sides: (x² - 2x + 1) / x = 3 x - 2 + 1/x = 3 x + 1/x = 5

Using the standard algebraic identity: x³ + 1/x³ = (x + 1/x)³ - 3(x + 1/x)

Substitute x + 1/x = 5: x³ + 1/x³ = 5³ - 3(5) = 125 - 15 = 110

Explanation

The compound interest formula for semi-annual compounding is: A = P × (1 + R/200)⁽2t)

Substitute P = 80,000, A = 92,610, and R = 10%: 92,610 = 80,000 × (1 + 10/200)⁽2t) 92,610 / 80,000 = (21/20)⁽2t) 9,261 / 8,000 = (21/20)⁽2t) (21/20)³ = (21/20)⁽2t)

Equating exponents: 2t = 3 t = 3/2 = 1½ years

Explanation

Total capacity = LCM(12, 15) = 60 units. Rate of P = 60 / 12 = 5 units/min. Rate of Q = 60 / 15 = 4 units/min. Combined rate of P and Q = 5 + 4 = 9 units/min.

Work completed together in 3 minutes = 9 × 3 = 27 units. Remaining work = 60 - 27 = 33 units.

Additional time required by pipe Q alone = Remaining work / Rate of Q = 33 / 4 = 8¼ minutes.

Explanation

Let the speed of the swimmer in still water be u and the speed of the current be v.

Distance upstream in 5 minutes = 5(u - v) Distance downstream in 5 minutes = 5(u + v)

The net separation AB between the starting point and the ending point is: AB = 5(u + v) - 5(u - v) = 10v

Given AB = 100 metres: 10v = 100 v = 10 metres/minute

Converting to kilometres per hour: v = (10 × 60) / 1000 = 0.6 km/h

Explanation

Speeds of A, B, and C are 1/5 km/min, 1/8 km/min, and 1/10 km/min respectively.

When A starts walking (2 minutes after C and 1 minute after B): Lead of B over A = 1 × (1/8) = 1/8 km. Relative speed of A with respect to B = 1/5 - 1/8 = 3/40 km/min. Time for A to catch B = (1/8) / (3/40) = 5/3 min.

Lead of C over A = 2 × (1/10) = 1/5 km. Relative speed of A with respect to C = 1/5 - 1/10 = 1/10 km/min. Time for A to catch C = (1/5) / (1/10) = 2 min.

Explanation

Let the cost price of the first bicycle be x and that of the second bicycle be y.

The total profit in the first scenario is 0.10x + 0.20y, and the total profit in the second scenario is 0.20x + 0.10y.

The difference in total profit is: (0.20x + 0.10y) - (0.10x + 0.20y) = 5 0.10x - 0.10y = 5 0.10(x - y) = 5 x - y = 5 / 0.10 = 50

Thus, the difference between the cost prices of the two bicycles is ¥ 50.

Explanation

Total number of ways to draw 2 cards from 52 cards is ⁵²C₂ = (52 × 51) / 2 = 1326.

Number of ways to draw 2 black cards from 26 black cards is ²⁶C₂ = (26 × 25) / 2 = 325. Number of ways to draw 2 queens from 4 queens is ⁴C₂ = (4 × 3) / 2 = 6. Number of ways to draw 2 black queens from 2 black queens is ²C₂ = 1.

Using the addition theorem of probability: Favourable outcomes = ²⁶C₂ + ⁴C₂ - ²C₂ = 325 + 6 - 1 = 330.

Required probability = 330 / 1326 = 55 / 221.

Explanation

The word DIRECTOR has 8 letters consisting of 3 vowels (I, E, O) and 5 consonants (D, R, C, T, R), where the letter R appears twice.

Treat the 3 vowels as a single block (IEO). The entities to arrange are the 5 consonants plus the 1 vowel block, making 6 items in total where R is repeated 2 times.

Number of ways to arrange these 6 items = 6! / 2! = 720 / 2 = 360.

The 3 distinct vowels within the block can be arranged among themselves in 3! = 6 ways.

Total number of words = (6! / 2!) × 3! = 360 × 6 = 2160.

Explanation

To find the minimum whole number of pens, convert the fractional ratio into the smallest integer ratio by multiplying each term by the least common multiple (LCM) of the denominators 3, 4, 5, and 6.

LCM(3, 4, 5, 6) = 60

Multiplying each fraction by 60 gives the integer parts: A receives 60 × (1/3) = 20 B receives 60 × (1/4) = 15 C receives 60 × (1/5) = 12 D receives 60 × (1/6) = 10

Minimum total number of pens = 20 + 15 + 12 + 10 = 57.

Explanation

Use the work equivalence formula: (M₁ × D₁) / W₁ = (M₂ × D₂) / W₂

Given: Initial workforce M₁ = 120 men Time elapsed D₁ = 64 days Work completed W₁ = 2/3

Remaining work W₂ = 1 - 2/3 = 1/3 Remaining time D₂ = 124 - 64 = 60 days

Substitute the values into the formula: (120 × 64) / (2/3) = (M₂ × 60) / (1/3) (120 × 64) / 2 = 60 × M₂ 3840 = 60 × M₂ M₂ = 64 men

Number of men that can be discharged = 120 - 64 = 56.

Explanation

Let the amount received by each son be x. Each daughter receives 2x, and the wife receives x - 300.

The total amount divided among 4 sons, 3 daughters, and the wife is: 4(x) + 3(2x) + (x - 300) = 9600 4x + 6x + x - 300 = 9600 11x = 9900 x = 900

The total amount received by all three daughters is: 3 × 2x = 6x = 6 × 900 = ₹ 5,400

Explanation

A probation period is established precisely because an appointee's actual job performance cannot be fully verified prior to hiring, which makes the first assumption implicit. Additionally, stipulating a review at the end of this period as a prerequisite for permanent confirmation assumes that the individual will strive to demonstrate their competence and worth throughout the probation period, making the second assumption implicit as well.

Explanation

Recommending an ideal age of five for entering school assumes that children attain the necessary developmental and cognitive maturity to begin structured learning at that stage. The statement establishes an optimal entry point for formal education and does not imply any upper age limit or admission restriction imposed by schools.

Explanation

The sharp increase in international crude oil prices is an outcome driven by global market forces such as geopolitical tensions, OPEC supply decisions, or changes in worldwide demand. In contrast, domestic fuel prices remaining constant despite rising global crude costs represents a separate outcome resulting from domestic policy interventions, such as government price controls, reduction in excise duties, or state-funded fuel subsidies. Because both statements describe observable results produced by entirely distinct, unrelated factors, both are effects of independent causes.

Explanation

The severe agitation by parents protesting against the exorbitant fees charged by unaided professional institutions compelled the government to step in and regulate the fee structure. The protest serves as the direct cause, and the government's subsequent policy intervention fixing lower fees is its effect.

Explanation

A nation requires foreign exchange reserves to import essential commodities, advanced technology, crude oil, and capital equipment that are not readily available domestically. Encouraging exports is indispensable to generate these foreign currency earnings and sustain international trade. Furthermore, selective encouragement allows a country to export surplus or high-value commodities without aggravating domestic shortages of essential goods.

Explanation

Variations in genetics, diet, body mass, and metabolic rates across different ethnic populations significantly impact drug pharmacokinetics and pharmacodynamics. Consequently, drugs formulated for Western populations may require calibrated dosages or alternate regimens to ensure efficacy and safety in Indian patients. Clinical trial testing on representative local samples is a standard, essential regulatory step to safeguard public health before granting commercial drug licenses.

Explanation

The passage states that individual and organisational goals are mutually interdependent, linked through employee motivation — members satisfy their personal goals by contributing to organisational objectives. This supports the general statement that motivation is crucial for the survival of both the individual and the organisation (option b). Option (a) misstates the passage (it describes motivation as a means, not as prioritising personal goals over organisational ones), (d) contradicts the internally-driven, personal-goal framing described, and (c) and (e) introduce ideas not supported by the passage (physical energy, society).

Explanation

The passage contrasts past consumer behavior, where low-fat ice cream was rarely ordered, with current market dynamics where increased health awareness and better product selection have turned it into a highly profitable offering. Because consumer demand has risen significantly and generates substantial profit, store owners recognize that low-fat ice cream has moved beyond being an unpopular product.

Explanation

Comparing the first and second statements: '3a, 2b, 7c' = 'Truth is Eternal' '7c, 9a, 8b, 3a' = 'Enmity is not Eternal' The common words are 'is' and 'Eternal', which correspond to the common codes '3a' and '7c'.

Comparing the second and third statements: '7c, 9a, 8b, 3a' = 'Enmity is not Eternal' '9a, 4d, 2b, 6b' = 'Truth does not perish' The common word is 'not', which corresponds to the common code '9a'.

Eliminating '3a', '7c', and '9a' from the second statement leaves the word 'Enmity' paired uniquely with the code '8b'.

Explanation

The code is determined by adding the alphabetical position values of each letter (where A = 1, B = 2, ..., Z = 26).

For KEEP: K (11) + E (5) + E (5) + P (16) = 37

For DRAFT: D (4) + R (18) + A (1) + F (6) + T (20) = 4 + 18 + 1 + 6 + 20 = 49

Explanation

College B contains only two students: W studying Electrical and T studying Mechanical. Since P and Z cannot study in college B or C, they study Electronics in college A along with S, who studies Mechanical. College C contains R (Mechanical), V (Electrical), and Q (Electrical). Thus, the combination of college B, student W, and specialization Electrical is correct.

Explanation

College B has only two students, W (Electrical) and T (Mechanical), meaning College A and College C each have three students. Since P, Z, and S do not study in College C or B, all three study in College A. With S studying Mechanical and a maximum limit of three students per discipline, P and Z must study Electronics. This leaves Q in College C alongside R (Mechanical) and V (Electrical). Since Mechanical already has three students (T, R, and S) and Q cannot study Electronics, Q must study Electrical. Therefore, College C is the only college where two students (V and Q) study in the Electrical discipline.

Explanation

College B contains only two students, W (Electrical) and T (Mechanical), which leaves College A and College C with three students each.

Since P and Z do not study in College C and College B is full, they must be in College A. S also belongs to College A because S does not study in College C. Thus, College A has P, Z, and S, which places Q in College C alongside R and V.

Three students already study Mechanical: T, R, and S. Because no discipline can have more than three students, Mechanical is full. Since Q does not study Electronics and cannot study Mechanical, Q must study Electrical.

Explanation

College B has exactly two students, W (Electrical) and T (Mechanical), leaving three students each for colleges A and C. Since P and Z do not study in college C, they study in college A along with S, who studies Mechanical because S cannot be in college C (where R is) or college B. In college C, R studies Mechanical alongside V (Electrical) and Q (Electrical). Thus, the three students pursuing Mechanical are S in college A, T in college B, and R in college C, meaning every college has at least one Mechanical student.

Explanation

College B has exactly two students, W and T, which means the remaining six students are equally distributed between colleges A and C with three students each. Since S does not study in college C where R studies, and college B has no additional capacity, S must study in college A.

Explanation

For the word BDATFE, the individual letter codes are B = 6, D = $, A = 8, T = 1, F = 4, and E = @. Since the first letter is a consonant (B) and the last letter is a vowel (E), condition (ii) applies, requiring the codes of the first and last letters to be interchanged. Thus, the first position takes the code of E (@), the last position takes the code of B (6), and the intermediate letters remain unchanged, giving the final sequence @$8146.

Explanation

The given word AWBRND begins with the vowel A and ends with the consonant D. Therefore, neither condition (i) nor condition (ii) applies, and each letter is substituted directly with its corresponding code:

A = 8 W = 5 B = 6 R = 3 N = © D = Combining these yields 8563©.

Explanation

The given word is EMNTKU. The first letter E and the last letter U are both vowels, so neither condition applies. By directly substituting each letter with its corresponding code: E = @ M = # N = © T = 1 K = % U = *

Combining these in sequence gives the coded representation @#©1%*.

Explanation

The individual codes assigned to each letter are M = #, D = $, E = @, A = 8, J = 2, and I = 9.

According to condition (ii), since the first letter M is a consonant and the last letter I is a vowel, their respective codes are interchanged. Therefore, the code for M becomes 9 and the code for I becomes #, while the intermediate letters retain their original codes: D = $, E = @, A = 8, and J = 2.

Combining these gives the coded sequence 9$@82#.

Explanation

The given word RKUMFP starts with consonant R and ends with consonant P. According to condition (i), both the first and last letters take the code of the last letter P, which is 7. Coding the intermediate letters using the standard table gives K = %, U = , M = #, and F = 4. Combining these gives the correct coded sequence 7%#47.

Explanation

Statement I provides information only about the membership of Dine club, which gives no data regarding Gymkhana club. Statement II mentions only the number of newly added members (120) to Gymkhana club without stating the existing or previous membership count. Even when combining both statements, the total number of members in Gymkhana club cannot be determined.

Explanation

Let the incomes in 1999, 2000, and 2001 be x, y, and z respectively. From statement I: x + y + z = 10000. From statement II: y = 1.25x. Substituting statement II into statement I yields 2.25x + z = 10000. Since this is a single linear equation with two independent unknowns (x and z), the exact value of z (income in 2001) cannot be uniquely determined. Thus, both statements together are not sufficient.

Explanation

According to the divisibility rule for 8, a number is divisible by 8 if the number formed by its last three digits is divisible by 8. Any number whose last three digits are zeros is a multiple of 1000. Since 1000 = 8 × 125, every multiple of 1000 is strictly divisible by 8. Thus, Statement II alone uniquely confirms divisibility by 8. In contrast, being divisible by 4 only ensures divisibility by 2², which is insufficient to determine divisibility by 2³ = 8.

Explanation

From Statement I, the inequality is (E + D) < B < (A + C). This allows multiple possibilities where either A, B, or C can have the maximum salary; for example, if B = 10, A = 6, C = 5, then B is highest, but if A = 12, B = 10, C = 2, then A is highest. Hence, Statement I alone is not sufficient.

From Statement II, C holds the second rank in the descending order of salaries. The only position strictly higher than the second rank is the first rank. Since A's salary is strictly greater than C's salary, A must occupy the first rank, uniquely identifying A as the highest salary earner. Hence, Statement II alone is sufficient.

Explanation

Let the length and breadth of the rectangle be l and b respectively.

From Statement I: l² + b² = 7² = 49 A single equation in two variables has infinitely many solutions and is insufficient alone.

From Statement II: 2(l + b) = 22, which simplifies to l + b = 11 This also provides only one equation in two variables and is insufficient alone.

Combining both statements: Using the algebraic identity (l + b)² = l² + b² + 2lb: 11² = 49 + 2lb 121 = 49 + 2lb 2lb = 72, which gives lb = 36

With the sum of the dimensions (l + b = 11) and their product (lb = 36), the dimensions are given by the roots of the quadratic equation t² − 11t + 36 = 0. Therefore, both statements together are necessary to determine the dimensions of the rectangle.

Explanation

Condition (i) requires the candidate to hold a degree in commerce or science with a minimum of 60% marks at graduation level and to be a post-graduate with second division. While Nirmal fulfills the requirements for age, CAT score, work experience, salary, nationality, and minimum graduation percentage, the given profile lacks details regarding her graduation discipline and post-graduation status. Therefore, the data provided is inadequate to decide the course of action.

Explanation

Rahul meets condition (i) with a science degree at 70% and a second-division post-graduation, condition (iii) with 71% in CAT, condition (iv) with 3 years as a management trainee, condition (v) with a monthly salary of ₹8000, and condition (vi) being an Indian national.

Born on 1 December 1978, his age on 1 January 2002 was 23 years and 1 month, failing the minimum age criterion of 25 years specified in condition (ii). As per the relaxation rule, a candidate meeting all requirements except condition (ii) is to be referred to the Assistant Manager.

Explanation

Criterion (iii) strictly requires a candidate to secure at least 70% marks in the written examination through the CAT paper, with no exemption or alternative provided for this condition. Gaurav secured only 65% in the CAT written test, failing this mandatory requirement. Therefore, the candidate cannot be admitted for the interview.

Explanation

Chandni holds a B.Com degree with 72% marks and an M.Sc with second division, satisfying condition (i). She is 26 years old (running her 27th year), satisfying the age requirement of at least 25 years under condition (ii). She scored 73% in CAT, satisfying condition (iii). She draws ₹7500 per month and is an Indian citizen, fulfilling conditions (v) and (vi). Although she lacks 3 years of work experience as a management trainee as required by condition (iv), she has 1½ years of experience as a manager in an MNC, which fulfills exception criterion (viii). Therefore, her case must be referred to the director.

Explanation

The recruitment criteria for the MBA interview list are: (i) a commerce/science degree with 60%+ marks and a postgraduate degree in second division; (ii) age 25 years or above as on 01.01.02; (iii) 70%+ marks in the written entrance exam; (iv) 3+ years' experience as a management trainee; (v) salary of Rs 7,000 per month or more; (vi) Indian nationality. As an exception, if a candidate meets all criteria except (ii), she should be referred to the Assistant Manager. Meena has a first division B.Com and a second division M.Sc. (satisfies i), a good percentage in the written exam (satisfies iii), 3 years' work experience (satisfies iv), a salary above Rs 10,000 (satisfies v), and is Indian (satisfies vi), but she is only 23 years old, failing criterion (ii). Since she meets every criterion except age, she falls under the stated exception and should be referred to the Assistant Manager.

Explanation

The given attributes partition the volumes as follows: Red covers: N, O, R New volumes: M, P, N English films: M, O, N

Taking the intersection of these three sets: {N, O, R} ∩ {M, P, N} ∩ {M, O, N} = {N}

Only volume N satisfies all three conditions simultaneously, meaning no pair of two volumes meets the criteria.

Explanation

Evaluating the attributes of each cassette volume based on the given information:

Cover color: M, P, and Q are white; N, O, and R are red. Age: M, P, and N are new; O, Q, and R are old. Language: M, O, and N are English films; P, Q, and R are Hindi films.

Taking the intersection of the sets of old volumes {O, Q, R}, white-covered volumes {M, P, Q}, and Hindi films {P, Q, R} yields volume Q.

Explanation

Categorising the six volumes by age and language: New volumes: M, P, N Old volumes: O, Q, R English films: M, O, N Hindi films: P, Q, R

The volumes that are both old and Hindi films are Q and R. Volume R satisfies both required conditions.

Explanation

Set of white-covered cassettes = {M, P, Q} Set of new cassettes = {M, P, N} Set of English films = {M, O, N}

Taking the intersection of all three sets: {M, P, Q} ∩ {M, P, N} ∩ {M, O, N} = {M}

Explanation

Categorising the cassettes based on the given criteria: Red covered volumes = {N, O, R} Old volumes = {O, Q, R} English films = {M, O, N}

Taking the intersection of these three sets to find the volume satisfying all conditions: {N, O, R} ∩ {O, Q, R} ∩ {M, O, N} = {O}

Volume O is the only cassette that is a red-covered, old English film.

Explanation

Combining the universal statements All locks are keys and All keys are bats directly gives All locks are bats. By the standard conversion rule of universal affirmative propositions (All A are B implies Some B are A), All locks are bats yields Some bats are locks. Watches only intersect with bats, meaning no necessary overlap with keys is established, and universal statements cannot be symmetrically converted to universal statements. Therefore, only the first conclusion is valid.

Explanation

By the rule of immediate conversion of particular affirmative (I-type) propositions, Some answers are writers directly converts to Some writers are answers.

Combining the particular affirmative premise Some answers are writers (I) with the universal affirmative premise All writers are poets (A) via the standard syllogistic rule I + A = I yields the intermediate conclusion Some answers are poets, which converts by simple conversion to Some poets are answers.

Explanation

From the statement that all books are papers and some papers are journals, the subset of papers that are journals does not necessarily overlap with books, so neither some journals are books nor some books are journals follows. Similarly, since some papers are journals and some journals are calendars, the middle term journals is not distributed in either premise, yielding no valid connection between calendars and papers or calendars and books. Therefore, none of the four conclusions follow.

Explanation

All given premises are affirmative statements: Some cars are jeeps (I-type), All boxes are jeeps (A-type), and All pens are cars (A-type).

From purely affirmative premises, no definite negative conclusion can be drawn, which immediately invalidates the second conclusion.

For the relation between cars and boxes, the common term is jeeps. In the premise All boxes are jeeps, jeeps is the predicate of a universal affirmative proposition and is undistributed. In Some cars are jeeps, jeeps is the predicate of a particular affirmative proposition and is also undistributed. Because the middle term jeeps is not distributed in either premise, no valid relationship can be established between cars and boxes. Consequently, neither the first conclusion nor the third conclusion follows. Thus, none of the three conclusions follow.

Explanation

By the rule of immediate conversion of a particular affirmative (I-type) proposition, a statement of the form "Some A are B" logically converts to "Some B are A". Applying this conversion directly to the premise "Some seals are adhesives" yields "Some adhesives are seals". Because two particular premises (I + I) yield no valid mediated conclusion, no relational deduction can be established between non-adjacent categories.

Explanation

Decoding the given inequality symbols: $ represents ≥ © represents <

represents >

% represents ≤ @ represents =

Combining the decoded statements: R > J ≥ D = K ≤ T

Evaluating the conclusions: From D = K ≤ T, it follows that D ≤ T, or T ≥ D. Therefore, either T > D (conclusion I) or T = D (conclusion II) must be true. From R > J ≥ D = K, it follows directly that R > K (conclusion III), which is definitely true. From J ≥ D = K ≤ T, the presence of opposing inequality signs means a definite relation between J and T cannot be determined (conclusion IV is not definitely true).

Thus, conclusion III is true along with either conclusion I or II.

Explanation

Decoding the symbols gives: means ≥ © means < means > % means ≤ @ means =

Converting the given statements: T ≤ R, R ≥ M, M = D, D < H Combining these relations gives T ≤ R ≥ M = D < H.

Testing the conclusions: For conclusion I (D ≤ R): Since R ≥ M and M = D, it directly follows that R ≥ D, or D ≤ R. Hence, conclusion I is definitively true. For conclusion II (H > R): R ≥ D and H > D, so the relationship between H and R cannot be determined. For conclusion III (T < M): T ≤ R and R ≥ M, so the relationship between T and M cannot be determined due to opposite inequality signs. For conclusion IV (T ≤ D): T ≤ R and R ≥ D, so the relationship between T and D cannot be determined.

Only conclusion I is true.

Explanation

Decoding the symbols based on the given definitions: means ≥ © means < means > % means ≤ @ means =

Converting the given statements into standard mathematical relations: M = B, B > N, N ≥ R, R < K

Combining these gives the continuous inequality chain: M = B > N ≥ R < K

Evaluating each conclusion: I. K # B means K > B. Since the inequality signs between B and K are in opposite directions (B > N ≥ R < K), no definite relation can be determined. II. R © B means R < B. From B > N ≥ R, it strictly follows that B > R, which means R < B. III. M R means M ≥ R. From M = B > N ≥ R, the definite relation is M > R, not M ≥ R. IV. N © M means N < M. From M = B > N, it follows directly that M > N, which means N < M.

Therefore, only conclusions II and IV are true.

Explanation

Decoding the given symbols into mathematical relations: means ≥ © means < means > % means ≤ @ means =

Converting the given statements: F > H, H = M, M < E, and E ≥ J. Combining these into a single chain gives F > H = M < E ≥ J.

Evaluating each conclusion: I. J < M is undetermined because M < E and E ≥ J have opposite/diverging comparison signs. II. E > H is true because H = M < E directly yields E > H. III. M < F is true because F > H = M directly yields M < F. IV. F > E is undetermined because F > M and E > M have opposite comparison signs.

Only conclusions II and III are true.

Explanation

Decoding the symbols based on the given definitions: means ≥ © means < means > % means ≤ @ means =

Converting the given statements: D % A gives D ≤ A A @ B gives A = B B © K gives B < K K % M gives K ≤ M

Combining them into a single chain of inequalities gives D ≤ A = B < K ≤ M.

Testing the conclusions against the chain: I. B D means B ≥ D, which holds true since D ≤ A = B. II. K # A means K > A, which holds true since A = B < K. III. M # B means M > B, which holds true since B < K ≤ M. IV. A © M means A < M, which holds true since A = B < K ≤ M.

Therefore, all conclusions I, II, III, and IV are true.

Explanation

The rearrangement alternates between numbers in ascending order at odd positions (31, 45, 49, 86) and words in reverse alphabetical order at even positions (shut, open, door, always).

Input: 86 open shut door 31 49 always 45 Step I: 31 86 open shut door 49 always 45 Step II: 31 shut 86 open door 49 always 45 Step III: 31 shut 45 86 open door 49 always Step IV: 31 shut 45 open 86 door 49 always Step V: 31 shut 45 open 49 86 door always Step VI: 31 shut 45 open 49 door 86 always

After Step VI, the remaining elements 86 and always automatically occupy their correct positions, completing the arrangement in 6 steps.

Explanation

In machine rearrangement algorithms where elements are shifted to specific positions from left to right, the exact original positions of the rearranged elements (25, yes, 37) prior to Step III cannot be identified with certainty. Therefore, moving backwards from any given intermediate step to determine the original input is not possible.

Explanation

The machine arranges numbers in ascending order (18, 34, 61, 71) and words in descending alphabetical order (win, victory, now, if) alternately from left to right.

Given Step II: 18 win 71 34 now if victory 61

Step III moves the next smallest number (34): 18 win 34 71 now if victory 61

Step IV moves the next word in descending order (victory): 18 win 34 victory 71 now if 61

Step V moves the next smallest number (61): 18 win 34 victory 61 71 now if

Step VI moves the next word in descending order (now): 18 win 34 victory 61 now 71 if

At Step VI, the remaining elements 71 and if are automatically in their correct final positions. Therefore, 4 more steps are required to complete the rearrangement.

Explanation

The rearrangement rule alternates between placing the smallest remaining number and the word highest in reverse alphabetical order at each step from left to right.

Input: where 47 59 12 are they going 39 Step I: 12 where 47 59 are they going 39 Step II: 12 they where 47 59 are going 39 Step III: 12 they 39 where 47 59 are going Step IV: 12 they 39 where 47 going 59 are

In Step III, the elements where and 47 are already in their correct fourth and fifth positions. Moving going to the sixth position in Step IV simultaneously places 59 and are in their correct final positions. Thus, Step IV is the last step, and the last but one step is Step III.

Explanation

The rearrangement alternates between numbers in ascending order (33, 52, 75, 81) and words in descending alphabetical order (store, of, goods, full), placing one element from left to right in each step.

Given Step II: 33 store 81 75 full of goods 52

Step III: 33 store 52 81 75 full of goods (moves the next smallest number, 52, to position 3)

Step IV: 33 store 52 of 81 75 full goods (moves the next word alphabetically, of, to position 4)

Step V: 33 store 52 of 75 81 full goods (moves the next smallest number, 75, to position 5)

Step VI: 33 store 52 of 75 goods 81 full (moves the next word alphabetically, goods, to position 6)