IBPS SO Prelims 2023 Question Paper with Answers & Explanations

Explanation

The passage states that 188 country representatives adopted an agreement to halt and reverse biodiversity loss by conserving 30% of the world's land and 30% of the world's oceans, known as the 30×30 pledge. This encompasses both curbing and restoring the loss of biological wealth and the conservation of at least 30% of global terrestrial and marine areas.

Explanation

According to the passage, India currently hosts 17% of the global human population as well as 17% of the global area designated under biodiversity hotspots. Together, these two factors place the country at the helm to guide and mentor the world toward becoming biodiversity champions.

Explanation

The passage directly links the pursuit of green growth to India's environmental challenges, stating that the emphasis on green growth serves as welcome news for the nation's biological wealth because the country is facing serious losses of natural assets such as soils, land, water, and biodiversity.

Explanation

According to the text, the National Mission for a Green India focuses on increasing forest cover and protecting existing forested lands across the country as part of India's green growth initiatives.

Explanation

The author explicitly notes that a science-based and inclusive monitoring programme is critical to ensure the success of the conservation efforts and government initiatives like the National Mission for a Green India, MISHTI, and Amrit Dharohar. Monitoring grounded in scientific evidence enables these programmes to accurately respond to the current state of biodiversity and achieve meaningful ecological outcomes.

Explanation

Emphasis denotes special importance, value, or prominence given to something in a particular context. In English vocabulary and the context of the passage, stress is a direct synonym that conveys placing special weight, focus, or priority on an objective.

Explanation

The word protect means to keep safe from harm, injury, damage, or loss, and to preserve or defend. In contrast, ravage means to cause severe and extensive damage to, devastate, or ruin something. Therefore, ravage functions as the direct antonym of protect.

Explanation

All the given statements accurately reflect the facts stated in the passage. The passage mentions that Green Growth is one of the seven priorities or Saptarishis outlined in the Union Budget, the Amrit Dharohar scheme encourages the optimal use of wetlands, mangroves and coastal ecosystems are extraordinarily important for mitigating climate change, and traditional knowledge of local communities should be integrated into implementation plans. Therefore, none of the individual statements are incorrect.

Explanation

The sentence structure requires a past participle following the auxiliary verb was and the adverb strongly. The verb articulated means expressed or conveyed clearly and effectively, making it contextually and grammatically appropriate for communicating the importance of global biodiversity at an international conference.

Explanation

The word integrated means to combine, merge, or incorporate separate elements into a single unified whole. In the context of planning and policies, integrating knowledge involves combining diverse inputs so they function together harmoniously. Amalgamate shares this exact meaning of uniting or merging different components to form a coherent, integrated structure.

Explanation

According to the passage, a vostro account is an account that domestic banks hold for foreign banks in the domestic currency, which domestic banks utilize to provide international banking services to clients having global banking requirements.

Explanation

According to the framework outlined in the passage, the three essential components are invoicing, exchange rate, and settlement. The exchange rate between the currencies of the trading partner countries is explicitly specified to be market-determined rather than fixed by administrative authorities or pegged directly by regulatory acts.

Explanation

According to the passage, the Special Rupee Vostro Account (SRVA) operates as an additional and complementary arrangement alongside the existing financial mechanism that relies on freely convertible currencies.

Explanation

According to the passage, domestic banks utilize vostro accounts to provide international banking services to clients with global needs, enabling them to serve international clients without requiring physical presence abroad. Additionally, it helps domestic banks gain wider access to foreign financial markets, thereby assisting them in expanding their reach globally. Statements indicating that domestic banks provide services to international clients and that the account assists domestic banks in expanding into foreign financial markets are directly supported by the text.

Explanation

The word permitted means officially allowed or authorized by rules and laws. Its direct antonym is prohibited, which means formally forbidden or banned by law, rule, or other authority.

Explanation

In the passage, conduct is used in the context of carrying out or executing business activities. Among the choices, operate means to manage, direct, or perform business operations and functions, serving as the most precise synonym in this banking context.

Explanation

Both statements (a) and (c) are correct. Hence the answer is 'Both (a) and (c)'.

Explanation

In the context of the passage, the word designated refers to a specific account officially allocated or specified for carrying out the transactions. Assigned means allocated, appointed, or specified for a particular function, making it the direct synonym.

Explanation

The word conclude means to bring something to an end, close, or finish. Inaugurate means to begin, initiate, or introduce a new period, system, or practice, making it the direct antonym.

Explanation

The sentence describes handling funds to meet existing trade commitments. In international trade and banking terminology, an order that has been processed, fulfilled, or completed is referred to as an executed order. Grammatically, the adverb already modifies the past participle executed, which functions as an adjective describing export orders.

Explanation

The adjective reluctant means unwilling, hesitant, or disinclined to do something. It grammatically takes the infinitive form to do something, perfectly fitting both sentences to convey that the residents hesitated to get vaccinated and that people are hesitant to put their money into high-risk funds.

Explanation

The adjective "precise" denotes being marked by exactness and accuracy of detail or performance. In the first sentence, it logically describes a measurement technology that yields highly accurate pulse rate readings compared to previous methods. In the second sentence, it pairs naturally with "sharp" to describe clean, exact, and well-controlled cuts made by blades.

Explanation

The verb "alleviate" means to make suffering, deficiency, or a problem less severe or more bearable. In both given sentences, the context demands an action that reduces or mitigates a negative condition, making "alleviate poverty" and "alleviate urban problems" the appropriate and meaningful collocations.

Explanation

The word "retreat" means to withdraw or pull back. In a military context, troops retreat to pull back from dangerous positions upon a sudden enemy attack. In professional contexts, retreating from an assignment or project signifies withdrawing or stepping back from that responsibility.

Explanation

To corroborate means to confirm, substantiate, or support a theory, statement, or claim by providing additional evidence. In the first sentence, scientists confirmed the validity of the galaxy theory using newly discovered evidence. In the second sentence, the advocate provided proof that confirmed the prisoner's innocence, leading to an acquittal.

Explanation

In English grammar, the phrasal verb "look forward to" is always followed by a noun phrase or a gerund (verb + ing) because "to" functions as a preposition rather than an infinitive marker. Therefore, "to receive back" is grammatically incorrect and must be replaced with "to receiving back".

Explanation

Habitual actions, regular routines, and universal truths are expressed using the simple present tense. Since the sentence describes a regular morning routine indicated by "goes for a morning walk", the continuous verb form "is waking up" must be replaced with the simple present form "wakes up".

Explanation

The sentence follows standard subject-verb agreement with the plural subject "cultures" paired with the plural auxiliary verb "have" and the past participle "adopted" to form the present perfect tense. The phrase "manner of conducting weddings" correctly pairs the preposition "of" with the gerund "conducting" followed by its object "weddings". Every segment is grammatically and contextually sound.

Explanation

The subject of the sentence is the singular noun construction, which is modified by the prepositional phrase of green areas. Under standard rules of subject-verb agreement, the finite verb must agree in number with the grammatical subject rather than the intervening plural object of the preposition. Consequently, the singular verb form offers is required in place of the plural verb offer.

Explanation

The sentence follows correct grammatical rules for reported speech, where the past tense reporting verb advised is correctly followed by the past tense copula was in the noun clause. The structure it was time to switch properly uses the to-infinitive form, the preposition to correctly pairs with switch to indicate transition to an alternative, and to generate electricity functions correctly as an infinitive of purpose.

Explanation

In this context, the sentence describes ransomware as being the most widespread, prevalent, or dominant form of cyber threat. The adjective "predominant" means having the greatest power, importance, or prevalence, which accurately fits the grammatical structure and intended meaning of the blank.

Explanation

In the context of ransomware attacks, perpetrators refers to the cybercriminals or attackers who carry out the illegal act and demand ransom payments in exchange for releasing or decrypting withheld data. The sentence requires a plural noun denoting the actors responsible for the cyberattack to agree grammatically with the plural verb demand.

Explanation

In cybersecurity terminology, malicious software or malware is said to infect devices and operating systems by contaminating files, altering programs, and spreading across networks. Grammatically, the modal verb could requires a base form transitive verb that takes all kinds of computer systems as its direct object. The term infect precisely fits both the syntactic requirements and the technical context of the passage.

Explanation

The sentence describes the susceptibility of critical infrastructure such as transportation, power, and banking systems to cyberattacks. The adjective vulnerable means susceptible to physical or emotional attack or harm, and it standardly pairs with the preposition to in the construction vulnerable to assaults.

Explanation

In the given context, countering multi-faceted cyber threats to critical infrastructure, industry, and national security requires an all-encompassing, thorough strategy. The word "comprehensive" means including or dealing with all or nearly all elements and aspects of a subject, making it the grammatically and contextually appropriate descriptor for a complete cybersecurity policy.

Explanation

The auxiliary verb 'have' must be followed by a past participle (V3 form), requiring 'adopted' in the first position. The infinitive particle 'to' must be followed by a base form verb (V1 form), requiring 'catalyze' in the second verb position. Swapping these two words produces the grammatically and contextually correct sentence: "Some women have adopted clean energy-based technologies to catalyze their businesses."

Explanation

Swapping positions A with C places the noun efficacy as the subject and the predicate adjective dependent before the preposition on. Simultaneously swapping positions B with D places the noun organization after the article an, and the noun acumen before of its employees, forming the coherent sentence: The efficacy of an organization is dependent on the acumen of its employees.

Explanation

The adjective present correctly describes the state of the person at the scene of the event, forming the phrase "he was not present at the spot". Concurrently, the past-tense verb occurred appropriately describes the action associated with the noun incident, yielding "where the alleged incident occurred". Interchanging B and D restores the proper syntactic and contextual meaning of the sentence.

Explanation

The infinitive construction requires the base form of the verb following "to", necessitating "remember" in place of "implemented". Correspondingly, the coordinate adjective construction modifying the noun "interventions" requires the past participle "implemented" alongside "well-designed". Exchanging these two words produces the grammatically sound and coherent sentence: "It is important to remember that well-designed and implemented interventions can make a difference."

Explanation

The sentence requires the verb matters to follow the pronoun what, forming the noun clause subject What matters to the common man most. The adjective common correctly modifies man, while the adverb most modifies the verb matters. At the predicate end, the singular noun issue correctly pairs with the compound adjective bread-and-butter to complete the thought. Interchanging A with D and B with C restores the natural collocations common man and bread-and-butter issue.

Explanation

Liberty denotes the state of being free to act, choose, or live without undue restriction or confinement. It correctly conveys having the freedom or autonomy to make personal choices in sentence A, and refers to the fundamental right to personal freedom from restraint in sentence B. In sentence C, the word fails to provide any coherent contextual meaning.

Explanation

Futile is an adjective that means incapable of producing any useful result, ineffective, or pointless. In sentence (B), it functions correctly as a predicate adjective describing the result of persistent hard work. In sentence (C), it is used properly in an adjective clause structure with the preparatory subject it, indicating that asking for permission is pointless.

Explanation

The word impediment functions as a noun meaning a hindrance, obstacle, or obstruction in doing something. In the context of technology adoption, the availability and accessibility of chargers act as an obstacle or barrier for potential consumers, making the usage grammatically and contextually accurate.

Explanation

The verb vandalize means to deliberately destroy, deface, or damage property belonging to someone else or the public. Sentence (C) accurately uses the past participle form vandalized to describe the destructive actions of angry customers causing deliberate physical damage to the retail store before leaving.

Explanation

Disempower means to strip someone of power, legal rights, or authority, or to make them feel less confident and influential.

In sentence B, workers diminishing a supervisor's operational authority appropriately represents disempowerment. In sentence C, depriving citizens of their voting rights directly removes their political power and influence, which is the core meaning of disempowering a population. In sentence A, the word is incorrectly applied to an abstract possibility rather than an individual or a collective group.

Explanation

After the auxiliary verb do or does, the main verb must appear in its base form, so do not takes know rather than knows. When expressing doubt, uncertainty, or an alternative indicated by the phrase or not, the subordinating conjunction whether is grammatically required instead of that. Thus, the phrase correctly uses know whether he will to connect the clause.

Explanation

When transforming direct speech into indirect speech or describing an event that occurred before another event in the past, the past perfect tense is used. Since the reporting verb is in the past tense and the subject actively sold the property, the past perfect active form had auctioned correctly conveys the sequence of events.

Explanation

The phrasal verb look after means to take care of or attend to someone. With the singular third-person subject he, the verb must take the singular form looks after to maintain subject-verb agreement. In the context of the sentence, the adverb still highlights the contrast between the subject being merely a child and his responsibility of taking care of his parents.

Explanation

When two items or methods are compared using the conjunction "than", the comparative degree of the adjective ("better") must be used rather than the superlative degree ("best"). Additionally, the noun "way" is appropriately followed by a to-infinitive ("to get") to express purpose or function rather than a preposition with a bare verb. Therefore, "a better way to get" correctly provides the comparative structure.

Explanation

The subject of the clause is the singular indefinite pronoun "One" in the noun phrase "One of the ways", which requires the singular linking verb "is". The complement following the linking verb is properly formed as a full infinitive ("to drink"), making the original sentence grammatically complete and accurate without any alteration.

Explanation

Numbering the stack from 6 (top) to 1 (bottom): Since at most two boxes are above Q and a Red box is above Q, placing Q (Pink) at position 4 allows S to be at position 5 and the Red box P at position 6.

Position 3 has Red box T (one box between Red box T and S). R is placed at position 2 (two boxes between R and S). U (Blue) is at position 1 (two boxes below T). S at position 5 is Blue (three boxes between U and the other Blue box). R at position 2 is Pink, completing two boxes of each colour.

The final stack from top to bottom is: 6: P (Red) 5: S (Blue) 4: Q (Pink) 3: T (Red) 2: R (Pink) 1: U (Blue)

Box P is at the topmost position.

Explanation

Arranging the boxes from top (position 1) to bottom (position 6) based on the given conditions: Position 1: Box P (Red) Position 2: Box S (Blue) Position 3: Box Q (Pink) Position 4: Box T (Red) Position 5: Box R (Pink) Position 6: Box U (Blue)

Evaluating the given statements: Statement I is true because Box U is at position 6, which is the bottom-most position of the stack, so no box is kept below it. Statement II is true because Box T (position 4) is placed immediately adjacent to Box Q (position 3). Statement III is true because Box R (position 5) is placed below Box S (position 2).

Explanation

Number the positions 1 to 6 from top to bottom:

Since at most two boxes are above Q and a red box as well as S are above Q, Q is at position 3, S is at position 2, and the red box above Q is at position 1. With one box between S and the other red box, position 4 must be red. Box Q is pink at position 3. Two boxes are between S (position 2) and R, which places R at position 5. Box P is above box T, and a blue box is two boxes below T, placing P at position 1, T at position 4 (Red), and the blue box at position 6. This leaves position 6 for box U, meaning box U is blue. Three boxes are between U (position 6) and the second blue box, which means box S (position 2) is blue. The remaining pink box is R at position 5.

Explanation

Arranging the six boxes from top (position 6) to bottom (position 1) according to the given conditions: Position 6: Box P (Red) Position 5: Box S (Blue) Position 4: Box Q (Pink) Position 3: Box T (Red) Position 2: Box R (Pink) Position 1: Box U (Blue)

Box P is at position 6. There are two pink colour boxes: Q at position 4 and R at position 2. Between box P (6) and box Q (4), there is 1 box (box S). Between box P (6) and box R (2), there are 3 boxes (boxes S, Q, and T). Therefore, the number of boxes between box P and a pink colour box is either one or three.

Explanation

Arranging the 6 boxes from top (6) to bottom (1): Box Q is of pink colour at position 4, satisfying the condition of having at most two boxes above it. Box S is placed at position 5, and the red boxes are at positions 6 and 3, ensuring exactly one box is between S and the red box at position 3.

Box R is placed at position 2, which is two boxes below S. Box T is at position 3 (with box P above it at position 6), so the blue box two boxes below T is at position 1 (box U). With box U at position 1, the second blue box is at position 5 (box S), leaving positions 4 (Q) and 2 (R) for the two pink boxes.

Thus, box R is pink.

Explanation

From the statement All Neons are Crayons, the set of Neons is entirely contained within Crayons. The statement Only a few Crayons are Colours means that some Crayons are Colours and some Crayons are not Colours, but it creates no definite overlap between Neons and Colours, so conclusion I does not follow.

For conclusion II, the restriction on Paint is solely that it cannot overlap with Colours (Colours ∩ Paint = ∅). Crayons can be positioned such that they only intersect Colours while remaining entirely disjoint from Paint (Crayons ∩ Paint = ∅). Since this configuration violates none of the given statements, the condition No Crayons is Paint is a valid possibility.

Explanation

The statement 'Only Shoulder is Legs' converts to 'All Legs are Shoulder' with the exclusive condition that Legs cannot share any relation or overlap with any entity other than Shoulder. Consequently, 'No Legs is Lakme' is definitely true.

The quantifier 'At most' represents a 'Some' relation, meaning some Shoulder are Beauty. Since '100% Beauty are Lakme' indicates that all Beauty are Lakme, the specific portion of Shoulder that is Beauty must also belong to Lakme, confirming that some Shoulder is Lakme.

Explanation

From the statements, Cloud is a subset of May, and May is a subset of Lotion, which means all Cloud is Lotion. Since no Lotion is Motion, the set Lotion is completely disjoint from Motion. Consequently, the entire set of Cloud and the entire set of May are also completely disjoint from Motion. Thus, No Cloud is Motion is a definite true relation, while it is impossible for any part of May to be Motion.

Explanation

The statement "Only a few Brush is Knife" means both "Some Brush is Knife" and "Some Brush is not Knife" are definitely true, making the possibility "All Brush can be Knife" invalid. For the second conclusion, "Some Cup is not Book" only specifies a condition for a subset of Cup, leaving the relationship between Knife and Book completely independent; hence "Some Knife is not Book" cannot be definitively concluded. Consequently, neither conclusion logically follows.

Explanation

There is no definite relation established between ZQ and PL from the given statements, making both individual conclusions uncertain. Since Conclusion I is a particular affirmative proposition and Conclusion II is a universal negative proposition sharing the same elements, they form a mutually contradictory complementary pair where exactly one must hold true. Therefore, either conclusion I or II follows.

Explanation

Assign each letter of REPLICATION its alphabetical position: R(18), E(5), P(16), L(12), I(9), C(3), A(1), T(20), I(9), O(15), N(14).

A pair has the required property if the distance between their positions in the word equals the difference between their alphabetical values:

Pair 1: P (position 3) and R (position 1) have 1 letter between them in the word (E), which matches the 1 letter between them in the alphabet (Q). Pair 2: E (position 2) and N (position 11) have 8 letters between them in the word, matching the 8 letters in the alphabet (F, G, H, I, J, K, L, M). Pair 3: N (position 11) and O (position 10) are adjacent in the word with 0 letters between them, matching their consecutive order in the alphabet.

There are exactly three such pairs.

Explanation

Since M is the only neighbour of Q, Q sits at an extreme end of the row. Placing Q at the right extreme end (position T):

Position of Q = T Position of M = T - 1 Since 3 persons sit between N and M, N is at position T - 5. Since the number of persons between M and N equals that between N and R (3 persons), R sits to the left of N at position T - 9. S sits second to the left of R, placing S at position T - 11. Three persons sit between R and P, placing P at position T - 13. P sits exactly between S and V, which places V at position T - 15. There is 1 person to the right of M (Q), so there must be 2 persons to the left of V. Thus, V is at position 3 from the left end.

Solving T - 15 = 3 gives T = 18. O sits second from the left end at position 2, satisfying all conditions for a total of 18 persons in the row.

Explanation

Placing the persons in a 1-indexed row from left to right facing north: Since M is the only neighbour of Q, Q must be at an extreme end. With Q at position 18 and M at position 17, there is 1 person to the right of M, which means there are 2 persons to the left of V, placing V at position 3.

Three persons sit between N and M, so N is at position 13. Three persons sit between N and R, placing R at position 9. S sits second to the left of R, giving position 7 to S (leaving 5 persons between N and S, satisfying the condition of more than one person). Three persons sit between R and P, placing P at position 5, which lies exactly between S at 7 and V at 3.

Since O sits second from one of the ends and position 17 is occupied by M, O sits at position 2.

The person sitting fifth to the right of O (position 2 + 5 = 7) is S.

Explanation

Arranging the persons based on the given conditions from left to right: Position 1: Left End Position 2: O Position 3: V Position 4: Empty Position 5: P Position 6: Empty Position 7: S Position 8: Empty Position 9: R Positions 10 to 12: Empty Position 13: N Positions 14 to 16: Empty Position 17: M Position 18: Q (Right End)

The total number of persons in the row is 18. The number of persons sitting between M (position 17) and V (position 3) is 17 - 3 - 1 = 13 persons, which is more than ten.

Explanation

Step-by-step arrangement of persons facing north: Since M is the only neighbour of Q, Q is at an extreme end. With the given distances between M, N, R, S, P, and V, Q sits at the extreme right end (position 18) and M at position 17.

Placing the remaining persons based on the given conditions: Position 1: (empty) Position 2: O (second from the left end) Position 3: V (2 persons to the left of V, which is one more than the 1 person to the right of M) Position 4: (empty) Position 5: P (exactly midway between S and V) Position 6: (empty) Position 7: S (second to the left of R) Position 8: (empty) Position 9: R (3 persons between P and R) Positions 10-12: (empty) Position 13: N (3 persons between R and N, and 3 persons between N and M) Positions 14-16: (empty) Position 17: M Position 18: Q

Counting from the right end: Q is 1st, M is 2nd, and N at position 13 is the 6th person from the right end (18 - 13 + 1 = 6).

Explanation

Since M is the only neighbour of Q, Q sits at an extreme end. Setting Q at the right end (position 18) places M at position 17, with 1 person to M's right. The number of persons to the left of V is 2, placing V at position 3.

Three persons sit between M and N, so N is at position 13. Three persons sit between N and R, placing R at position 9. S sits second to the left of R at position 7 (leaving 5 persons between S and N, satisfying the condition of more than one person). Three persons sit between R and P, placing P at position 5, which is exactly between S (position 7) and V (position 3). O sits second from the left end at position 2.

If A sits second to the left of Q, A is at position 16. Number of persons to the right of A = 18 - 16 = 2. Number of persons to the left of S = 7 - 1 = 6. Difference = 6 - 2 = 4.

Explanation

In an eight-person square seating arrangement with four at the corners and four at the middle of the sides facing inward:

From Statement I, only partial relative positions for U, T, R, A, and B are given without fixed references to corners or sides, yielding multiple possible arrangements for the seat immediately to the right of U. Thus, Statement I alone is not sufficient.

From Statement II, placing T at a middle seat puts U at the adjacent corner to the right of T (since T is immediately left of U). Two persons between T and A places A at a corner, and since B is opposite A, A must be positioned such that B occupies an empty corner rather than U's seat. This uniquely places T, B, W, A, and U at five positions, but leaves the remaining three side-middle seats completely undetermined, one of which is immediately to the right of U. Thus, Statement II alone is not sufficient.

Combining both statements creates a contradiction, as Statement I requires A and B to sit adjacent to each other, whereas Statement II requires them to sit opposite each other. Hence, the data in both statements together are not sufficient to answer the question.

Explanation

The week starts on Tuesday and ends on Monday: Tuesday (1), Wednesday (2), Thursday (3), Friday (4), Saturday (5), Sunday (6), and Monday (7).

Statement I gives two cases: If A attends on Tuesday (1), X must be on Friday (4), and U is on Wednesday (2) or Sunday (6). If A attends on Friday (4), X must be on Tuesday (1) because X cannot be on Monday (7), which places U on Thursday (3). Statement I alone cannot uniquely determine Thursday.

Statement II gives relative positions (B immediately before R, two persons between U and B, and X before V before M), but no fixed days, so it is not sufficient alone.

Combining Statements I and II: If A is on Tuesday (1) and X is on Friday (4), then whether U is on Wednesday (2) or Sunday (6), placing B and R leaves no valid positions for V and M after X. If A is on Friday (4), then X is on Tuesday (1) and U is on Thursday (3). Since two persons are between U (3) and B, B is on Sunday (6) and R is on Monday (7). The remaining slots for V and M after X place V on Wednesday (2) and M on Saturday (5).

The unique schedule is: Tuesday: X, Wednesday: V, Thursday: U, Friday: A, Saturday: M, Sunday: B, Monday: R. Thus, U attends the class on Thursday.

Explanation

From Statement I alone, only negative constraints are given for H, I, G, and Y, leaving multiple candidates eligible to visit Australia. Thus, Statement I alone is insufficient.

From Statement II alone, with H assigned to India, the remaining countries for Y, N, G, and I are USA, Australia, Japan, and China. Since G cannot visit Australia, any among Y, N, or I could still visit Australia under valid assignments. Thus, Statement II alone is insufficient.

Combining both statements creates a direct contradiction regarding H (Statement I states H does not visit India, whereas Statement II states H visits India), preventing any consistent combined solution. Therefore, the data in both statements together are not sufficient to determine who visits Australia.

Explanation

From Statement I, fixing T at position 1 gives N at position 2 (immediate left of T). Since two persons sit between X and T, X can be at position 4 or 6. Since two persons sit between N and E, E can be at position 5 or 7. Statement I alone is insufficient because Q is not placed.

Statement II alone does not fix the absolute positions of the individuals around the table.

Combining both statements: Because E cannot sit adjacent to X, the configurations with (X = 4, E = 5), (X = 6, E = 5), and (X = 6, E = 7) are eliminated. This uniquely fixes X at position 4 and E at position 7. The vacant positions are 3, 5, 6, and 8. Since W and R sit adjacent to each other, they must occupy positions 5 and 6. Since E at position 7 cannot sit adjacent to C, C cannot be at position 8, so C must be at position 3, leaving position 8 for Q. Since one person sits between W and C, W is at position 5 and R is at position 6. The complete clockwise arrangement is T (1), N (2), C (3), X (4), W (5), R (6), E (7), and Q (8). Opposite to Q (position 8) sits X (position 4). Both statements together are sufficient.

Explanation

From Statement I, since no one sits to the right of I in a row of seven persons facing north, I is at position 7 (extreme right end), F is at position 4, and G is at position 2 or 6. This gives no definitive information about H, making Statement I alone insufficient.

From Statement II, a person sits immediately to the right of I, which yields multiple partial arrangements for D, E, F, and I, but leaves H undetermined, making Statement II alone insufficient.

Combining both statements creates a contradiction because I cannot simultaneously be at the extreme right end and have someone seated to the immediate right. Therefore, the data in both statements together are not sufficient to determine who sits immediate right of H.

Explanation

Taking Point Q as the reference origin (0, 0): Point P is 5m south of Q, giving coordinates (0, -5). Point R is 10m east of P, giving coordinates (10, -5). Point S is 5m south of R, giving coordinates (10, -10). Point U is 10m east of Q, giving coordinates (10, 0).

The distance between U(10, 0) and S(10, -10) along the north-south axis is |0 - (-10)| = 10m. Since the x-coordinates are identical and S lies along the negative y-direction relative to U, Point S is located 10m south of Point U.

Explanation

Taking Point Q as the reference origin (0, 0): Point P is 5m south of Q, giving coordinates (0, -5). Point R is 10m east of P, giving coordinates (10, -5). Point S is 5m south of R, giving coordinates (10, -10).

Relative to Point Q (0, 0), Point S (10, -10) lies along the positive x-axis (East) and negative y-axis (South), placing it in the South-east direction.

Explanation

Tracing the movements step by step and comparing the final position of point P with point V shows that P ends up 5 m to the north of V. Hence the answer is '5m, north'.

Explanation

The total distance between points H and R is obtained by summing the lengths of the connecting segments from H to R: Distance from H to Q = 9m Distance from Q to P = 5m Distance from P to R = 10m Total distance = 9m + 5m + 10m = 24m.

Explanation

Placing the 8 positions in clockwise order (1 to 8) facing the center, right corresponds to the counter-clockwise direction: A is at position 1 (Woman). B sits second to the right of A at position 7 (Man). C sits between A and Q, placing Q at position 3 (opposite B; Man) and C at position 2 (Man). R is at position 5 (Man), with Q sitting second to the right of R. To satisfy the condition that no more than two people of the same gender sit adjacent, positions 4, 6, and 8 must be women. S sits opposite a man (C at position 2), which places S at position 6 (Woman). D's neighbours must be of the same gender, placing D at position 4 (flanked by Q and R, both men) and P at position 8.

With D at position 4 facing the center, the position to the immediate right of D (counter-clockwise) is position 3, where Q is seated.

Explanation

Let the eight positions in counter-clockwise order facing the center be 1 to 8: A is placed at position 1 (Female). B sits second to the right of A at position 3 (Male). Q sits opposite to B at position 7 (Male). C sits between Q and A at position 8 (Male). R sits at position 5 (Male) with one person between B and R, making Q second to the right of R. To prevent three consecutive persons of the same gender, positions 2, 4, and 6 must be Female. S sits opposite a man (C at position 8), so S is at position 4. D is at position 6 so that both of D's neighbors (R and Q) are of the same gender (Male), leaving P at position 2. In this arrangement, S is at position 4, and the person sitting to the immediate left (clockwise) of S is B at position 3.

Explanation

Number the eight positions from 1 to 8 in clockwise order with all individuals facing the center (where moving counter-clockwise is right, and clockwise is left): Let A (woman) be at position 1. B (man) is 2nd to the right of A at position 7. Q (man) sits opposite to B at position 3. C is adjacent to both A and Q, placing C at position 2. R (man) sits with one person between B and R, placing R at position 5. No more than two persons of the same gender sit adjacent, so positions 4, 6, and 8 must be women. S sits opposite to a man, so S is at position 6, opposite C (man). D sits at position 4 where both neighbours (Q and R) are men of the same gender. P occupies the remaining position 8.

With C at position 2 and P at position 8, counting to the right (counter-clockwise) from C gives A at 1st to the right and P at 2nd to the right.

Explanation

Working through the given conditions, the final circular arrangement is D(W), R(M), S(W), B(M), P(W), A(W), C(M), Q(M). Both A and P are women, so the pair satisfying the condition is A and P.

Explanation

Arranging the eight persons sequentially around the circular table gives A (female), P (female), B (male), S (female), R (male), D (female), Q (male), and C (male), ensuring no more than two adjacent persons share the same gender. Among the five given individuals, B, R, Q, and C are all males, while D is a female, making D the one that does not belong to the group.

Explanation

Combining the statements linking elements for conclusion I gives B = C ≥ E < G = H, which simplifies to B ≥ E < H. Due to the opposite inequality symbols (≥ and <) between B and H, no definite relation can be established between H and B, so conclusion I is false.

Combining the statements linking elements for conclusion II gives A > B = C ≥ E < G, which simplifies to A > E < G. Due to the opposite inequality symbols (> and <) between A and G, no definite relation can be established between G and A, so conclusion II is false.

Explanation

Combining the given relations for Conclusion I: 72 > 45 and 45 > 18 yields the direct chain 72 > 45 > 18, which confirms that 72 > 18 is definitely true.

Combining the relations for Conclusion II: 100 ≥ 45 and 45 > 63 (since 18 = 63) yields 100 ≥ 45 > 63, meaning 100 > 63, which contradicts 100 < 63. Thus, only conclusion I is true.

Explanation

From the given statements, combining the relations involving $ and & gives $ > & and & = *, which directly yields $ > *. For the second relation, linking % and # produces the chain % > * = & ≥ ∧ < ! = #. Since opposing inequality symbols (> and <) appear along this path, no definite relation can be determined between % and #.

Explanation

In the fourth statement, Home is coded as iu through comparison with the second statement, and money is coded as al through comparison with the third statement. The remaining words rent and earn correspond to the remaining codes mo and nz. Because neither word appears in any other statement, the exact code for rent cannot be distinguished between mo and nz.

Explanation

Comparing the first statement and the third statement, the common words are Holiday and home, which correspond to the common codes bf and iu.

Comparing the second statement and the fourth statement, the only common word is home, which corresponds to the common code iu.

Since home is coded as iu, Holiday is coded as bf.

Explanation

Comparing the statements to find the unique code for each word:

Home is present in all original statements, and the common code element across them is iu, so home = iu.

Money appears in both Holiday home makes money and Home rent earn money, sharing the common code al, so money = al.

Earn appears in Home rent earn money and Earn money is good, with the shared code nz, so earn = nz.

In the statement Home rent earn money (mo al iu nz), substituting home (iu), money (al), and earn (nz) gives rent = mo.

Holiday appears in both Holiday home is dream and Holiday home makes money with the common code bf, so Holiday = bf.

Combining these gives the code for Holiday home rent as iu bf mo.

Explanation

The given series consists of six three-digit numbers: 259, 674, 359, 427, 783, and 921.

Rearranging the digits within each number in descending order: 259 becomes 952 674 becomes 764 359 becomes 953 427 becomes 742 783 becomes 873 921 becomes 921

Arranging the newly formed numbers in ascending order to find the smallest values: 742 (from 427) is the 1st smallest 764 (from 674) is the 2nd smallest 873 (from 783) is the 3rd smallest 921 (from 921) is the 4th smallest 952 (from 259) is the 5th smallest 953 (from 359) is the 6th smallest

The third smallest number formed is 873, which corresponds to the original number 783.

Explanation

Dividing the given sequence into standard three-digit numbers gives 259, 674, 359, 427, 783, and 921.

Arranging these numbers in ascending order: 259, 359, 427, 674, 783, 921. The second lowest number is 359, whose third digit is 9. The largest number is 921, whose third digit is 1.

Required product = 9 × 1 = 9.

Explanation

Dividing the 18-digit sequence into standard three-digit numbers gives 259, 674, 359, 427, 783, and 921.

A number is divisible by 2 if its units digit is even. After interchanging the first and third digits, the original first digit becomes the new units digit. Therefore, the new number is divisible by 2 if and only if the original first digit is even:

259 begins with 2 (even) → 952 is divisible by 2. 674 begins with 6 (even) → 476 is divisible by 2. 359 begins with 3 (odd) → 953 is not divisible by 2. 427 begins with 4 (even) → 724 is divisible by 2. 783 begins with 7 (odd) → 387 is not divisible by 2. 921 begins with 9 (odd) → 129 is not divisible by 2.

Exactly three numbers satisfy the condition.

Explanation

Arranging the designations in descending order of seniority from 1 to 8: Compliance Officer - A Risk Manager - H Financial Analyst - D Relationship Manager - C Branch Manager - B Loan Officer - G Bank Teller - F Customer Service Representative - E

Since H is senior to B with two designations between them, pos(H) = 2 and pos(B) = 5. With three persons junior to B, there are three persons between H and G, placing G at position 6 (Loan Officer). D is three designations senior to G, placing D at position 3. Two persons are junior to G, meaning three persons are senior to C, placing C at position 4. With zero persons between H and D, A is placed at position 1. F is two designations junior to C at position 7, which is junior to B. The remaining person, E, is at position 8 as the Customer Service Representative.

Explanation

Assigning ranks 1 (Compliance Officer) to 8 (Customer Service Representative) in decreasing order of seniority:

Placing H at 2 and B at 5 gives two designations between them with H senior to B. Since three persons are junior to B (ranks 6, 7, 8), three persons must be between H and G, placing G at rank 6. D is three designations senior to G, which places D at rank 3. Two persons are junior to G, so three persons are senior to C, giving C at rank 4. Because zero persons are between H (2) and D (3), zero persons must be between H (2) and A, placing A at rank 1. With two designations between C (4) and F, F is placed at rank 7, leaving E at rank 8.

The final sequence from rank 1 to 8 is A, H, D, C, B, G, F, E. Between A (rank 1) and B (rank 5), there are exactly three designations: Risk Manager, Financial Analyst, and Relationship Manager.

Explanation

Arranging the eight designations in decreasing order of seniority from 1 (Compliance Officer) to 8 (Customer Service Representative):

H is senior to B with two persons between them, so Rank(B) = Rank(H) + 3. The number of persons between H and G equals the persons junior to B (8 - Rank(B)). With D being three designations senior to G (Rank(D) = Rank(G) - 3), and G not being immediately senior to B, setting H at position 2 and B at position 5 yields G at position 6 and D at position 3.

Since the number of persons between H and D equals that between H and A, A is at position 1. The persons junior to G (2) is one less than persons senior to C, placing C at position 4. With two designations between C and F, and F being junior to B, F is placed at position 7. The remaining person E is placed at position 8.

The complete seniority order from 1 to 8 is A, H, D, C, B, G, F, E.

A is at position 1 (senior-most), B at position 5 is three designations senior to E at position 8, and E is at position 8 (junior-most, so no one is junior to E). Thus, all three statements I, II, and III are true.

Explanation

Ordering the designations from senior-most (1) to junior-most (8): 1 - Compliance Officer: A 2 - Risk Manager: H 3 - Financial Analyst: D 4 - Relationship Manager: C 5 - Branch Manager: B 6 - Loan Officer: G 7 - Bank Teller: F 8 - Customer Service Representative: E

H is senior to B with two designations between them, fixing H at 2 and B at 5. Since 3 persons are junior to B, there must be 3 persons between H and G, placing G at 6. D is three designations senior to G, so D is at 3. Number of persons junior to G (2) is one less than persons senior to C (3), placing C at 4. With 0 persons between H and D, A is at 1. F is two designations away from C and junior to B, placing F at 7. Thus, G is the Loan Officer.

Explanation

From the given conditions, the designations from senior-most to junior-most (ranks 1 to 8) are determined as: Compliance Officer: A Risk Manager: H Financial Analyst: D Relationship Manager: C Branch Manager: B Loan Officer: G Bank Teller: F Customer Service Representative: E

When all persons are arranged in alphabetical order from junior-most (rank 8) to senior-most (rank 1): Rank 8 (CSR) = A Rank 7 (BT) = B Rank 6 (LO) = C Rank 5 (BM) = D Rank 4 (RelM) = E Rank 3 (FA) = F Rank 2 (RM) = G Rank 1 (CO) = H

Comparing the original arrangement with the new arrangement at each rank shows that no person remains at the same designation.

Explanation

The underlying pattern assigns each letter its positional value in the English alphabet (A = 1, B = 2, ..., Z = 26), where the position of the third letter equals the sum of the positions of the first two letters. In LMZ, L has a positional value of 12 and M has a positional value of 13. Their sum is 12 + 13 = 25, which corresponds to the letter Y rather than Z (26).

Explanation

The 2nd, 5th, 6th, and 7th letters from the left end of the word HOPEFUL are O, F, U, and L respectively.

Arranging these four letters to form a meaningful English word yields FOUL.

Reading from the right end of FOUL, the 1st letter is L and the 2nd letter is U.

Explanation

The coding logic for each word consists of three elements: Number: Count of consonants in the word multiplied by 2. Letter: Second letter of the word shifted +3 places in alphabetical order. Symbol: '@' if the word ends with a consonant, and '' if the word ends with a vowel.

For the missing word "related": Number of consonants (r, l, t, d) = 4, so the number is 4 × 2 = 8. Second letter is 'e' (5th letter); shifting +3 gives the 8th letter, 'H'. Last letter is 'd' (a consonant), so the symbol is '@'.

Combining these gives the code 8H@.

Explanation

The coding logic for each word follows three rules: Number: Number of consonants in the word × 2. Letter: Alphabetical position of the second letter of the word + 3. Symbol: '' if the word ends in a vowel, and '@' if it ends in a consonant.

In the second sentence, the existing words decode as: Mostly (5 consonants, second letter O, ends in consonant) = 10R@ new (2 consonants, second letter E, ends in consonant) = 4H@ activated (5 consonants, second letter C, ends in consonant) = 10F@

The remaining code for blank (II) is 8U. For the code 8U: Consonants required = 8 / 2 = 4 consonants. Second letter = U (21) - 3 = 18 = R.

Profile has 4 consonants (P, r, f, l), second letter 'r', and ends in a vowel 'e', perfectly matching 8U.

Explanation

Applying the given coding pattern to the term, the source code works out to 6R$, which matches option (c).

Explanation

Applying the given operations to the sequence '@ 9 # 2 5 % 7 * 6 8':

Subtract 2 from each digit: 9 becomes 7 2 becomes 0 5 becomes 3 7 becomes 5 6 becomes 4 8 becomes 6

Replace each symbol with the specified number: @ becomes 3 becomes 2 becomes 6 % becomes 5 becomes 7 becomes 4

The resulting sequence is: 3, 7, 2, 0, 6, 3, 5, 5, 7, 4, 4, 6

From the left end: The 2nd element is 7. The 7th element is 5.

Sum = 7 + 5 = 12

Explanation

Find the differences between consecutive terms: 77 − 68 = 9 88 − 77 = 11 (difference increases by 2) 102 − 88 = 14 (difference increases by 3)

The second-order differences form the sequence +2, +3, +4, +5. The next difference is 14 + 4 = 18. The missing term is 102 + 18 = 120.

Verification for the final term: 120 + (18 + 5) = 120 + 23 = 143.

Explanation

Calculate the differences between consecutive terms in the series: 319 - 234 = 85 234 - 164 = 70 164 - 109 = 55 109 - 69 = 40

The differences form an arithmetic sequence with a common difference of 15 (85, 70, 55, 40).

The preceding difference must be 40 - 15 = 25.

Therefore, the missing first term is 69 - 25 = 44.

Explanation

Calculate the differences between consecutive terms from the end of the series: 315 - 225 = 90 225 - 163 = 62 163 - 122 = 41

The second differences are: 90 - 62 = 28 62 - 41 = 21

The second differences follow the pattern of multiples of 7: 7, 14, 21, 28. Working backwards: The previous difference is 41 - 14 = 27. The initial difference is 27 - 7 = 20.

Applying this to the first term gives 75 + 20 = 95 (and verifying: 95 + 27 = 122).

Explanation

Calculate the differences between the given consecutive terms: 4219.2 − 3258.2 = 961 = 31² 3258.2 − 2358.2 = 900 = 30² 2358.2 − 1517.2 = 841 = 29²

Following this pattern of decreasing integer squares, the preceding difference must be 28² = 784: Missing term = 1517.2 − 784 = 733.2

Verifying with the first term: 733.2 − 4.2 = 729 = 27²

Explanation

The series follows an alternating pattern of division and multiplication by decreasing natural numbers: 45 ÷ 5 = 9 9 × 4 = 36 36 ÷ 3 = 12 12 × 2 = 24 24 ÷ 1 = 24

Explanation

Setting up the equation 11P = 13200 and solving gives P = 1200. Hence the answer is 1200.

Explanation

Let the initial volume of the mixture be V ml.

When 180 ml is removed and X ml of milk along with 2X ml of water is added, the new total volume is: V - 180 + (X + 2X) = V - 180 + 3X

Given that the resultant volume is 144 ml less than the original volume: V - 180 + 3X = V - 144

Simplifying the equation: 3X = 180 - 144 3X = 36 X = 12

Explanation

Let the length of the platform be P meters. Then, train length T = P + 120 meters, and bridge length B = P - 40 meters.

Since the speed of the train remains constant: Speed = (Distance crossed) / Time (T + P) / 11 = (T + B) / 10 (2P + 120) / 11 = (2P + 80) / 10

Cross-multiplying: 10 × (2P + 120) = 11 × (2P + 80) 20P + 1200 = 22P + 880 2P = 320 P = 160 meters

Train length T = P + 120 = 160 + 120 = 280 meters.

Explanation

Let the present ages of P and Q be P and Q years respectively.

Given: (P + 3) / (Q - 5) = 5 / 2 2P + 6 = 5Q - 25 2P - 5Q = -31

Also, P + Q = 44 Multiplying by 5 gives: 5P + 5Q = 220

Adding both equations: 7P = 189 P = 27

Substituting P = 27 into P + Q = 44 gives: Q = 44 - 27 = 17

Age of P ten years hence = 27 + 10 = 37 years Age of Q three years ago = 17 - 3 = 14 years

Required difference = 37 - 14 = 23 years

Explanation

Let the smallest odd number be x. The three consecutive odd numbers are x, x + 2, and x + 4. Their sum is 3x + 6.

The smallest even number is x - 9. The three consecutive even numbers are x - 9, x - 7, and x - 5. Their sum is 3x - 21.

According to the given condition: (3x + 6) + (3x - 21) = 231 6x - 15 = 231 6x = 246 x = 41

The largest odd number is x + 4 = 41 + 4 = 45.

Explanation

Simple Interest formula is SI = (P × R × T) / 100.

Given X : Y = 1 : 2, let X = P and Y = 2P.

Interest from scheme A: SI_A = (P × R × T) / 100

Interest from scheme B: SI_B = (2P × (R + 4) × T) / 100

Given SI_B = 3 × SI_A: (2P × (R + 4) × T) / 100 = 3 × (P × R × T) / 100

Dividing both sides by (P × T) / 100: 2(R + 4) = 3R 2R + 8 = 3R R = 8

Explanation

Let the cost price and selling price of article A be CP(A) = 5x and SP(A) = 8x respectively.

Cost price of article B = SP(A) × 1.25 = 8x × 1.25 = 10x. Selling price of article B with a 30% loss = CP(B) × (1 - 0.30) = 10x × 0.70 = 7x.

Average selling price of A and B = (SP(A) + SP(B)) / 2 = (8x + 7x) / 2 = 7.5x.

Given: 7.5x = 112.5 x = 15

Cost price of article B = 10x = 10 × 15 = 150.

Explanation

Total distance = (Distance covered by X) + (Distance covered by Y) Distance = Speed × Time

Time traveled by X from 3 AM to 10 AM = 7 hours Distance covered by X = 7 km/hr × 7 hr = 49 km

Time traveled by Y from 5 AM to 10 AM = 5 hours Distance covered by Y = 4 km/hr × 5 hr = 20 km

Total distance between P and Q = 49 km + 20 km = 69 km

Explanation

Given a + b = 21 and a × b = 108 with a > b: The quadratic equation with roots a and b is x² - 21x + 108 = 0. Factoring gives (x - 12)(x - 9) = 0. Since a > b, a = 12 and b = 9.

The difference between a and b is: a - b = 12 - 9 = 3

Since c is four more than the difference between a and b: c = (a - b) + 4 = 3 + 4 = 7

The product of b and c is: b × c = 9 × 7 = 63

Explanation

Rate of pipe P = 1/10 of the tank per hour. Rate of pipe Q = 1/20 of the tank per hour.

Combined rate of P and Q = 1/10 + 1/20 = 3/20 of the tank per hour. Part of the tank filled by P and Q together in 5 hours = 5 × (3/20) = 3/4.

Time taken by pipe R to empty the full tank = 2 × 20 = 40 hours. Emptying rate of pipe R = 1/40 of the tank per hour.

Time taken by R to empty 3/4 of the tank = (3/4) / (1/40) = (3/4) × 40 = 30 hours.

Explanation

Total duet songs by B and E: Duet songs by B = 500 × (1 - 3/5) = 500 × (2/5) = 200 Duet songs by E = 360 × (1 - 5/12) = 360 × (7/12) = 210 Total duet songs (B + E) = 200 + 210 = 410

Total solo songs by A and C: Solo songs by A = 300 × (2/5) = 120 Solo songs by C = 420 × (5/7) = 300 Total solo songs (A + C) = 120 + 300 = 420

Required ratio = 410 : 420 = 41 : 42

Explanation

Duet songs downloaded by A = 300 × (1 − 2/5) = 300 × 3/5 = 180. Duet songs downloaded by D = 180 × (1 − 4/9) = 180 × 5/9 = 100.

Total duet songs downloaded by D and A together = 180 + 100 = 280. Total songs downloaded by B = 500.

Required percentage = [(500 − 280) / 500] × 100 = (220 / 500) × 100 = 44%.

Explanation

Total songs downloaded by F = 360 × (1 + 0.25) = 450.

Duet songs downloaded by B = 500 × (1 - 3/5) = 200.

Duet songs downloaded by F = 200 × (13/25) = 104.

Solo songs downloaded by F = 450 - 104 = 346.

Solo songs downloaded by C = 420 × (5/7) = 300.

Difference between solo songs downloaded by C and F = 346 - 300 = 46.

Explanation

Solo songs downloaded by E = 360 × (5/12) = 150 Classic songs downloaded by A = (1/3) × 150 = 50

Fraction of duet songs downloaded by D = 1 - 4/9 = 5/9 Duet songs downloaded by D = 180 × (5/9) = 100

Average = (50 + 100) / 2 = 150 / 2 = 75

Explanation

Solo songs downloaded by C = 420 × (5/7) = 300

Fraction of duet songs downloaded by E = 1 - 5/12 = 7/12 Duet songs downloaded by E = 360 × (7/12) = 210

Difference = 300 - 210 = 90

Required percentage = (90 / 300) × 100 = 30%

Explanation

For equation I: 2x² - 17x + 26 = 0 Splitting the middle term using factors of 52 (4 and 13): 2x² - 4x - 13x + 26 = 0 (2x - 13)(x - 2) = 0 x = 2, 6.5

For equation II: 2y² - 6y + 4 = 0 Dividing by 2 gives y² - 3y + 2 = 0: (y - 1)(y - 2) = 0 y = 1, 2

Comparing the values: 6.5 > 2 and 6.5 > 1 2 = 2 and 2 > 1

Combining these comparisons gives x ≥ y.

Explanation

To find the roots of equation I: 12x² - 7x + 1 = 0 12x² - 4x - 3x + 1 = 0 4x(3x - 1) - 1(3x - 1) = 0 (4x - 1)(3x - 1) = 0 x = 1/4 = 0.25, or x = 1/3 ≈ 0.333

To find the roots of equation II: 6y² - 5y + 1 = 0 6y² - 3y - 2y + 1 = 0 3y(2y - 1) - 1(2y - 1) = 0 (3y - 1)(2y - 1) = 0 y = 1/3 ≈ 0.333, or y = 1/2 = 0.50

Comparing the values of x and y: For x = 0.25: x < 0.333 and x < 0.50 For x = 0.333: x = 0.333 and x < 0.50

Combining these comparisons gives x ≤ y.

Explanation

Factorizing the first equation: x² + 11x + 24 = 0 (x + 8)(x + 3) = 0 x = -8, -3

Factorizing the second equation: 4y² + 13y + 10 = 0 4y² + 8y + 5y + 10 = 0 4y(y + 2) + 5(y + 2) = 0 (4y + 5)(y + 2) = 0 y = -1.25, -2

Comparing the values: For x = -8: -8 < -2 and -8 < -1.25. For x = -3: -3 < -2 and -3 < -1.25.

Since every value of x is strictly less than every value of y, the relation is x < y.

Explanation

For equation I: 2x² - 19x + 17 = 0 2x² - 2x - 17x + 17 = 0 2x(x - 1) - 17(x - 1) = 0 (2x - 17)(x - 1) = 0 x = 1, 8.5

For equation II: 3y² - y - 14 = 0 3y² + 6y - 7y - 14 = 0 3y(y + 2) - 7(y + 2) = 0 (3y - 7)(y + 2) = 0 y = -2, 7/3 ≈ 2.33

Comparing the roots: For x = 1: 1 > -2, but 1 < 2.33. Since x is greater than one value of y and less than another, no definite relationship can be established between x and y.

Explanation

For equation I: 6x² + 17x + 5 = 0 Factorizing using product 30 and sum 17: 6x² + 15x + 2x + 5 = 0 3x(2x + 5) + 1(2x + 5) = 0 (3x + 1)(2x + 5) = 0 x = -1/3 ≈ -0.33, -5/2 = -2.5

For equation II: 2y² + 21y + 49 = 0 Factorizing using product 98 and sum 21: 2y² + 14y + 7y + 49 = 0 2y(y + 7) + 7(y + 7) = 0 (2y + 7)(y + 7) = 0 y = -7/2 = -3.5, -7

Comparing each value of x with each value of y: -0.33 > -3.5 and -0.33 > -7 -2.5 > -3.5 and -2.5 > -7

Since every root of x is strictly greater than every root of y, x > y.

Explanation

The required ratio works out to 15/20, which simplifies to 3:4.

Explanation

Total employees in Company A is determined from the salary distribution: Employees with salary > X = 20 Employees with salary = X = 25 − 20 = 5 Employees with salary ≤ X = 20, which gives employees with salary < X = 20 − 5 = 15 Total employees in Company A = 20 + 5 + 15 = 40

Total females in Company A = (3/5) × 40 = 24 Females with salary > X = 20 / 2 = 10 Females with salary = X = 12.5% of 24 = (1/8) × 24 = 3

Females with salary < X = Total females − (Females > X + Females = X) = 24 − (10 + 3) = 11

Explanation

Number of employees having salary more than Rs. X in Company A = 20. Number of employees having salary more than Rs. X in Company B = 30.

Average number of employees having salary more than Rs. X in both companies = (20 + 30) / 2 = 50 / 2 = 25.

Explanation

In Company A: Employees with salary > X = 20 Employees with salary ≥ X = 25, so salary = X is 25 − 20 = 5 Employees with salary ≤ X = 20, so salary < X is 20 − 5 = 15 Total employees in Company A = 20 + 5 + 15 = 40

In Company B: Total employees in Company B = 40 × (3/2) = 60 Employees with salary = X is 2 × 5 = 10 Employees with salary > X = 30 Employees with salary < X = 60 − (30 + 10) = 20

Combined values: Total employees with salary > X in both companies = 20 + 30 = 50 Total employees with salary < X in both companies = 15 + 20 = 35

Percentage more = [(50 − 35) / 35] × 100 = (15 / 35) × 100 = 300 / 7 ≈ 42.86% ≈ 43%

Explanation

For Company A: Employees with salary equal to X = (salary ≥ X) - (salary > X) = 25 - 20 = 5. Total employees in Company A = (salary ≤ X) + (salary > X) = 20 + 20 = 40.

For Company B: Employees with salary equal to X = 2 × 5 = 10. Total employees in Company B = 40 × (3 / 2) = 60.

Total employees with salary equal to X in both companies = 5 + 10 = 15. Required percentage = (15 / 60) × 100 = 25%.

Explanation

Setting up the equation 8D = 5600 and solving gives D = 700. Hence the answer is 700.

Explanation

Combined one-day work of P and R: 1/P + 1/R = 1/10 − 1/30 = 1/15

Let R take r days alone; then P takes (r − 16) days. 1/(r − 16) + 1/r = 1/15 (2r − 16) / (r² − 16r) = 1/15 r² − 46r + 240 = 0 (r − 40)(r − 6) = 0

Since r > 16, r = 40 days.

Time taken by R to complete 50% of the work: 40 × 50% = 20 days

Explanation

Sum of all four numbers: P + Q + R + S = 4 × 20 = 80 Sum of three numbers: P + R + S = 3 × 20 = 60

Subtracting the two equations gives: Q = 80 - 60 = 20

Using the ratio Q : R = 5 : 4: R = 20 × (4 / 5) = 16

Since P is 25% less than R: P = 16 × (1 - 0.25) = 12

Finding S from P + R + S = 60: S = 60 - (12 + 16) = 32

Difference between P and S: |S - P| = 32 - 12 = 20

Explanation

Total profit = Rs. 1450 and profit of B exceeds profit of A by Rs. 250. Profit of B = (1450 + 250) / 2 = Rs. 850 Profit of A = 1450 - 850 = Rs. 600

Profit ratio of A to B = (Investment of A × Time of A) / (Investment of B × Time of B) 600 / 850 = (x × 12) / [(x + 900) × 8] 12 / 17 = 3x / [2(x + 900)] 4 / 17 = x / [2(x + 900)] 8(x + 900) = 17x 8x + 7200 = 17x 9x = 7200 x = 800

Explanation

Total distance between X and Y = 510 km. Time taken to meet = 5 hours 40 minutes = 5 + 40/60 = 17/3 hours.

Relative speed of trains moving towards each other: Relative speed = Distance / Time = 510 / (17/3) = (510 × 3) / 17 = 90 km/hr.

Let the speed of train P be Sp and speed of train Q be Sq. Sp + Sq = 90 km/hr Sq - Sp = 22 km/hr

Adding the two equations: 2 × Sq = 112 Sq = 56 km/hr

Substituting Sq: Sp = 90 - 56 = 34 km/hr

Thus, the speeds of trains P and Q are 34 km/hr and 56 km/hr respectively.

Explanation

Let the monthly income of X be I. Combined expenditure on education and household = 10% + 20% = 30%. Remaining income after these expenses = I × (1 - 30/100) = (7/10) × I. After spending 25% on shopping, the remaining fraction is (1 - 1/4) = 3/4. Amount left = (7/10) × I × (3/4) = (21/40) × I. After spending (100/7)% = 1/7 on entertainment, the remaining fraction is (1 - 1/7) = 6/7. Final savings = (21/40) × I × (6/7) = (9/20) × I. Equating to the given savings: (9/20) × I = 3600 I = (3600 × 20) / 9 = 8000.

Explanation

Cost price of the mixture (CP) = (1 × 80 + 3 × 120) / (1 + 3) = (80 + 360) / 4 = Rs. 110 per kg.

Selling price (SP) = Rs. 143 per kg.

Profit percentage = [(SP - CP) / CP] × 100 = [(143 - 110) / 110] × 100 = (33 / 110) × 100 = 30%.

Explanation

Total number of shirts = 6 + 5 = 11.

Total ways to select 2 shirts out of 11: Total outcomes = ¹¹C₂ = (11 × 10) / 2 = 55

Number of ways to select 2 shirts of the same color: Both red = ⁶C₂ = (6 × 5) / 2 = 15 Both black = ⁵C₂ = (5 × 4) / 2 = 10 Total favorable outcomes = 15 + 10 = 25

Probability = 25 / 55 = 5/11

Explanation

Radius of the circle r = 42 / 2 = 21 cm. Area of the circle = πr² = (22/7) × 21 × 21 = 1386 cm². Area of the rectangle = 2136 - 1386 = 750 cm². Length of the rectangle = Area / Breadth = 750 / 30 = 25 cm. Perimeter of the rectangle = 2(Length + Breadth) = 2 × (25 + 30) = 110 cm. Circumference of the circle = 2πr = 2 × (22/7) × 21 = 132 cm. Difference = 132 - 110 = 22 cm.

Explanation

Total work for the first piece of work is equal for both groups: 21 × M × 15 = 35 × W × 11 315M = 385W 9M = 11W, so M/W = 11/9

For the second piece of work, equating the total work done by 18 men and 20 women: 18 × M × (Y - 4) = 20 × W × Y

Substituting M = 11 and W = 9: 18 × 11 × (Y - 4) = 20 × 9 × Y 198(Y - 4) = 180Y 11(Y - 4) = 10Y 11Y - 44 = 10Y Y = 44