IBPS Clerk Prelims 2025 Question Paper with Answers & Explanations

Explanation

Total English books sold by A and B together = 28 + 55 = 83

Number of Hindi books sold by A = 50

Required percentage = (English books sold by A and B together / Hindi books sold by A) × 100

Substituting the values: Required percentage = (83 / 50) × 100 = 83 × 2 = 166%

Explanation

Number of English books sold by A = 28.

Since X sold 25% more English books than A, English books sold by X = 28 × 1.25 = 35.

Number of Hindi books sold by B = 54.

Required difference = 54 - 35 = 19.

Explanation

From the given table, the number of Hindi books sold by B is 54 and the number of Urdu books sold by A is 36.

Required ratio = (Hindi books sold by B) : (Urdu books sold by A) = 54 : 36 = 3 : 2

Explanation

Average number of books sold by B = (Total books of three languages sold by B) ÷ 3

Total books sold by B = 55 (English) + 54 (Hindi) + 32 (Urdu) = 141

Average = 141 ÷ 3 = 47

Explanation

Total books sold by A = 28 + 50 + 36 = 114 Total books sold by B = 55 + 54 + 32 = 141

Difference between total books sold by B and A = 141 - 114 = 27

Explanation

Using standard arithmetic operations, evaluate the given expression step by step:

784 + 1297 - 613

First, perform the addition: 784 + 1297 = 2081

Next, perform the subtraction: 2081 - 613 = 1468

Alternatively, subtracting 613 from 784 first yields 171, and adding 1297 gives 1468.

Explanation

According to the BODMAS rule, operations of equal priority (division and multiplication) are evaluated sequentially from left to right:

Step 1: Evaluate the first division: 225 ÷ 45 = 5 Step 2: Evaluate the second division: 5 ÷ 5 = 1 Step 3: Perform the multiplication: 1 × 75 = 75

Alternatively, converting divisions into reciprocals: ? = 225 × (1 ÷ 45) × (1 ÷ 5) × 75 ? = (225 ÷ 225) × 75 ? = 1 × 75 = 75

Explanation

Express each term on the right-hand side in terms of its prime factors: 343 = 7³ 512 = 2⁹ 64 = 2⁶ 56 = 7 × 2³ 49 = 7²

Substituting these into the expression: RHS = (7³ ÷ 2⁹) × 2⁶ × (7 × 2³) ÷ 7² RHS = (7³ × 7 × 2⁶ × 2³) ÷ (2⁹ × 7²) RHS = (7⁴ × 2⁹) ÷ (7² × 2⁹) RHS = 7⁴⁻² × 2⁹⁻⁹ RHS = 7² × 2⁰ = 7²

Equating 7^? = 7² gives ? = 2.

Explanation

Apply BODMAS to each bracket first: 120 + 36 = 156 and 12 - 6 = 6. Then 156 / 6 = 26, so the question mark stands for 26.

Explanation

Sum the numbers in the brackets: 3080 + 6160 = 9240

Rearranging the equation 9240 ÷ ? = 330 gives: ? = 9240 ÷ 330 = 28

Explanation

Using the BODMAS rule, simplify the division inside the parentheses first:

10800 ÷ 36 = 300

Substitute this back into the given equation: 144 - 300 + ?² = 100

Simplify the constants on the left side: -156 + ?² = 100

Isolate ?² on one side: ?² = 100 + 156 ?² = 256

Taking the square root on both sides: ? = √256 = 16

Explanation

Simplify the root terms: √1225 = 35 (729)¹/³ = 9

By BODMAS rules, the "of" operations are calculated before division: (4/5) of 35 = 28 (1/3) of 9 = 3

Substitute these back into the expression: 28 ÷ 3 = ? + 1/3 28/3 = ? + 1/3

Solving for ?: ? = 28/3 - 1/3 = 27/3 = 9

Explanation

Simplify both sides of the equation step-by-step:

On the left-hand side, (5/8) × 160% simplifies to (5/8) × (160/100) = (5/8) × (8/5) = 1. So, the left-hand side reduces directly to 1 × ? = ?.

On the right-hand side, √225 × 4 = 15 × 4 = 60.

Equating the two sides gives ? = 60.

Explanation

225% of 2400 = (225 ÷ 100) × 2400 = 225 × 24.

Substituting this into the given equation: 24 × ? = 225 × 24

Dividing both sides by 24 yields: ? = 225.

Explanation

Using BODMAS rules, simplify the expression within the brackets first: (40)² × 8 = 1600 × 8 = 12800

Now perform the division operations: [(40)² × 8] ÷ 50 ÷ 16 = 12800 ÷ (50 × 16) = 12800 ÷ 800 = 16

Explanation

Simplify the given expression step by step:

First, evaluate 65% of (1700 ÷ 13): 65% × (1700 ÷ 13) = (65 ÷ 100) × (1700 ÷ 13) = (65 ÷ 13) × (1700 ÷ 100) = 5 × 17 = 85

Next, evaluate the square term: 17² = 289

Adding the two values gives: 85 + 289 = 374

Explanation

To find the value of (35% of 40 × 10) + 29, simplify the expression step by step using standard order of operations:

First, evaluate the term inside the bracket: 40 × 10 = 400

Next, calculate 35% of 400: (35 / 100) × 400 = 35 × 4 = 140

Finally, add 29 to the result: 140 + 29 = 169

Explanation

Initial quantity of milk = 56 × (4 / 7) = 32 liters. Initial quantity of water = 56 × (3 / 7) = 24 liters.

Since only water is added, the quantity of milk remains unchanged at 32 liters.

In the new mixture, the ratio of milk to water is 8 : 7. 8 parts = 32 liters, which gives 1 part = 4 liters. New quantity of water = 7 parts = 7 × 4 = 28 liters.

The quantity of water added, Y = 28 − 24 = 4 liters.

Explanation

Profit ratio in a partnership is determined by the product of investment amount and the time period for which the money is invested:

(Investment_A × Time_A) / (Investment_B × Time_B) = Profit_A / Profit_B

A invested ₹2400 for the full year (12 months), while B joined 3 months later, investing ₹X for 9 months (12 - 3 months).

Substituting the values into the formula:

(2400 × 12) / (X × 9) = 2 / 1

28800 / 9X = 2

3200 / X = 2

X = 1600

Thus, the investment of B, X, is ₹1600.

Explanation

Let the initial values of A and B be 3x and 2x, respectively, based on their given ratio of 3:2.

According to the given condition, subtracting 16 from A and adding 16 to B changes the ratio to 19:26:

(3x - 16) / (2x + 16) = 19 / 26

Cross-multiplying to solve for x: 26(3x - 16) = 19(2x + 16) 78x - 416 = 38x + 304 40x = 720 x = 18

Substituting x back to find the initial value of A: A = 3x = 3 × 18 = 54

Explanation

Using the Simple Interest formula, SI = (P × R × T) / 100.

From the first case: 840 = (1600 × X × 5) / 100 840 = 80X X = 10.5%

For the second case: New rate = 10.5 + 5 = 15.5% p.a. Interest received = (1600 × 15.5 × 3) / 100 = 16 × 46.5 = Rs 744.

Explanation

Area of a right-angled triangle = ½ × base × height

Substituting the given values: 180 = ½ × base × 24 180 = 12 × base base = 15 cm

The side of the square is 3 cm less than the base of the triangle: Side of square = 15 - 3 = 12 cm

Area of the square = side² = 12² = 144 cm²

Explanation

Let the present ages of A and B be 9x and 5x years, respectively.

According to the question: (9x + 5) / (5x - 5) = 16 / 5

Cross-multiplying: 5(9x + 5) = 16(5x - 5) 45x + 25 = 80x - 80 35x = 105 x = 3

Present age of A = 9 × 3 = 27 years Present age of B = 5 × 3 = 15 years

Sum of their present ages = 27 + 15 = 42 years

After 10 years, both A and B will grow older by 10 years each: Sum of ages after 10 years = 42 + 10 + 10 = 62 years.

Explanation

Downstream speed = 192 ÷ 4 = 48 km/h Upstream speed = 210 ÷ 5 = 42 km/h

Speed of the boat in still water = ½ × (Downstream speed + Upstream speed) = ½ × (48 + 42) = 45 km/h

When the speed of the boat in still water is decreased by 20%: New speed = 45 × (1 - 0.20) = 45 × 0.8 = 36 km/h

Distance covered in 3 hours at the reduced speed = Speed × Time = 36 × 3 = 108 km.

Explanation

Let X be the total number of chocolates.

If distributed among 30 friends, each receives X/30 chocolates. When 3 friends do not arrive, 27 friends receive X/27 chocolates each.

Given that each remaining friend receives 1 extra chocolate: X/27 - X/30 = 1

Taking the common denominator: X × (30 - 27) / (27 × 30) = 1 3X / 810 = 1 X = 270

Explanation

With a + c = 50 and 30a + 20c = 1350: 10a + 1000 = 1350, so a = 35 adults.

Explanation

Net profit percentage on article A = 25 - 10 - (25 × 10)/100 = 12.5%.

Since 12.5% of the cost price of article A corresponds to Rs 75, the cost price of article A = 75 / 0.125 = Rs 600.

sensitivity/proportion calculation: Cost price of article B = 140% of cost price of article A = 1.4 × 600 = Rs 840.

With a 20% loss on article B, its selling price = 80% of cost price of article B = 0.8 × 840 = Rs 672.

Explanation

When a body travels equal distances at two different speeds v₁ and v₂, the average speed for the entire journey is given by the harmonic mean formula:

Average Speed = 2v₁v₂ / (v₁ + v₂)

Substituting v₁ = 60 km/h and v₂ = 90 km/h:

Average Speed = (2 × 60 × 90) / (60 + 90) = 10800 / 150 = 72 km/h

Explanation

A+B+C do 1/10 per day and B+C do 1/25 per day, so A alone does 1/10 - 1/25 = 3/50 per day and takes 50/3 = 16.67 days.

Explanation

Percentage of students in cultural events = 100% - (40% + 25%) = 35%.

Since 35% of the total students equals 315, 1% of the total students is 315 ÷ 35 = 9 students.

The percentage difference between students participating in the science fair and sports is 40% - 25% = 15%.

Required difference = 15 × 9 = 135.

Explanation

In the context of the passage, "trained" refers to the process of developing specific behaviors, skills, and discipline in an animal through systematic instruction and practice. The word "conditioned" means accustomed or taught to react in a specific way under given circumstances through practice and habituation. The passage itself reinforces this relationship by describing how Snowy was trained at the academy and conditioned to remain calm under pressure, making "conditioned" the exact synonym for "trained."

Explanation

In the context of the sentence "They are not just supporting figures; they are front-line defenders," the word "just" functions as an adverb meaning "merely" or "simply." Replacing it with "only" retains the exact intended meaning that military dogs perform a crucial role far beyond merely acting as supporting figures. Therefore, "only" is the correct synonym in this specific context.

Explanation

The passage emphasizes that military dogs are front-line defenders equipped with specialized training from military academies to handle critical field operations. They are trained to detect hidden explosives, track infiltrators, respond to silent signals, and remain calm in high-pressure environments. As demonstrated in Snowy's real-time interception of border infiltrators, their quick instincts and operational discipline enable them to detect and neutralize immediate security threats effectively.

Explanation

The phrase perked up means to suddenly become alert, active, or attentive. In the given context, Snowy senses an unexpected movement near the perimeter during a quiet night. When dogs detect subtle sounds or threats, their ears perk up as a natural reflex to focus their hearing and stay vigilant. This sudden alertness directly leads to his sharp bark and timely action in warning the guards, making perked up the most appropriate fit for the sentence.

Explanation

The passage describes Snowy's formal military training as focusing strictly on operational skills, such as mastering commands, detecting explosives, adapting to difficult terrains, responding to silent signals, and building discipline. His emotional connection with the soldiers and his ability to sense their anxiety developed naturally as a bond beyond his operational duties, rather than being part of his structured academy training.

Explanation

According to the passage, Snowy was trained to adapt to challenging terrains and harsh environments at a specialized military academy. His ability to act proactively during critical moments is demonstrated when, on a freezing night at a remote border post, he sensed movement near the perimeter and acted without hesitation by barking sharply and running toward the fence to alert the guards, thereby averting a potential security threat.

Explanation

In the given context, sentinel refers to a guard or watchperson whose primary role is to remain vigilant, stand watch, and protect a group or territory from potential threats. The word guardian directly mirrors this meaning, as it denotes someone who watches over, guards, and protects others from harm. The passage specifically highlights sentinels as watchful, fearless figures who stand watch when danger lurks, which perfectly aligns with the function and definition of a guardian.

Explanation

Snowy's reaction on the freezing night is a pivotal event in the passage because his heightened senses and quick instincts enabled him to detect border infiltrators before any of the human guards noticed them. While the soldiers were resting after a long day, Snowy immediately sensed movement near the perimeter and alerted the camp, allowing the guards to spot and intercept the threat in time. This event demonstrates the indispensable value of a trained military dog, illustrating how its acute senses and swift response allow it to react faster than human guards to safeguard lives and secure the border.

Explanation

The passage explicitly states that Snowy received his name due to his gleaming white coat, not because it influenced his placement at the remote border post. Snowy was assigned to the border unit following his rigorous preparation at a specialized military academy, where he learned explosive detection and tactical commands. The claim that his coat color was the primary reason for his border deployment is a misinterpretation of the text.

Explanation

The sentence needs the collocation 'has recently taken a remarkable step'. 'Taken' is the only option that fits.

Explanation

An excavation refers to the act or process of digging up the ground to uncover hidden archaeological remains, fossils, or ancient structures. In the passage, the context explicitly mentions an archaeological department unearthing ancient ruins, artifacts, and a human skeleton in a remote desert region, making excavation the precise term to describe this activity.

Explanation

The sentence describes a formal partnership between two distinct fields of study, archaeologists and medical scientists, working together on a joint project. The noun collaboration specifically means the act of working jointly with someone or across disciplines to produce something or achieve a common goal. It fits both grammatically after the article and adjective phrase "a unique" and semantically to convey an interdisciplinary research partnership.

Explanation

In the context of using advanced imaging and 3D modeling techniques on ancient skeletal remains, the term "recreate" accurately expresses the process of reproducing, forming, or building again the physical structure of the individual. Using digital technology to form a complete representation of the original skeletal structure allows researchers to analyze ancient health conditions and physical characteristics effectively.

Explanation

The word "insights" is a plural noun that correctly fits after the adjective "valuable" and standardly pairs with the preposition "into". The idiomatic phrase "insights into" means gaining a deep, clear understanding of a complex subject. In the context of the sentence, the interdisciplinary research provided valuable, deep understanding into historical practices, genetic traits, and disease patterns, making it both contextually and grammatically appropriate for the blank.

Explanation

In this context, the noun "remains" refers to the surviving physical parts or traces of an ancient human body, such as the skeleton mentioned in the text, or archaeological remnants. The phrase "ancient remains" fits both grammatically and semantically as the plural noun subject of the clause, accurately reflecting how studying historical human remnants can provide valuable insights to guide modern medical research.

Explanation

The word discord means disagreement, strife, or lack of harmony between people or groups. In statement (I), it correctly refers to friction and disagreement among team members following a missed deadline. In statement (III), it is accurately used to describe political disagreement and friction between two nations causing long-term tension. Statement (II) misuses the word because discord implies harsh disharmony, making it contextually contradictory when paired with sweet and peace. Thus, the word is used in a contextually and grammatically correct manner in both statements (I) and (III).

Explanation

The verb "restrain" means to hold back, suppress, or keep under control. The phrase "restrain her excitement" is grammatically sound, idiomatic, and contextually appropriate in English, conveying that she was unable to hold back her joy upon receiving the news. Since the original sentence is completely correct as written, no replacement is necessary.

Explanation

The original sentence is both grammatically sound and contextually appropriate. The verb "curb" means to restrain, limit, or keep in check, which perfectly fits the context of a leader attempting to manage rising dissatisfaction among workers. The phrase "growing unrest" correctly describes increasing agitation or turmoil. Because the original sentence expresses the intended meaning clearly and accurately without any grammatical error, no replacement is required.

Explanation

The original sentence is both grammatically correct and contextually precise. The verb mask means to conceal, disguise, or cover up an emotion or condition. In this context, mask her embarrassment appropriately conveys the idea of hiding feelings of awkwardness after making an error. Since the original phrasing is natural, accurate, and completely sound in meaning and structure, no replacement is required.

Explanation

The verb "temper" means to soften, moderate, or bring strong emotions into balance. In the given sentence, "temper her frustration" accurately describes managing and controlling one's anger or irritation in response to a delay. Since the original sentence is grammatically sound, contextually accurate, and conveys the intended meaning clearly, it requires no substitution.

Explanation

Subject-verb agreement requires a singular subject to take a singular verb. Here, the subject "The judge" is singular, so it must be accompanied by the singular auxiliary verb "has" instead of the plural verb "have". The correct phrasing is "The judge has ordered...".

Explanation

The sentence is grammatically sound and contains no errors. It correctly uses the correlative conjunction structure "so... that" to express a cause-and-effect relationship, where the severity of the attack resulted in the service disruptions. The simple past tense verbs "was" and "disrupted" are consistent with the past time adverbial "yesterday," and the subject-verb agreement is properly maintained throughout the sentence.

Explanation

The structure "the number of" is always followed by a plural countable noun. In part (C), "station" is in the singular form and must be corrected to the plural form "stations" (i.e., "the number of EV charging stations").

Explanation

The error lies in the incorrect form of the auxiliary verb. The sentence uses the present perfect continuous tense to describe an action that started in the past and continues into the present. This tense requires the auxiliary verb structure 'has been' followed by the present participle 'reporting'. Using 'being' instead of 'been' after 'has' is grammatically incorrect, as the present perfect tense requires the past participle form 'been'. Therefore, 'has being' must be corrected to 'has been'.

Explanation

Modal auxiliary verbs like "will", "can", "shall", "may", "must", and "should" are always followed by the base form (bare infinitive) of the verb. They do not take an 's' or 'es' ending regardless of whether the subject is singular or plural. Therefore, "will affects" is grammatically incorrect and should be replaced with "will affect".

Explanation

Replacing demand at position A with development forms the compound noun phrase urban development projects, which correctly describes large-scale civic initiatives. Retaining historical at position B accurately modifies sites. Replacing development at position C with demand creates the grammatically correct infinitive verb phrase to demand stricter cultural preservation laws following the object phrase prompting activists. This yields the coherent sequence CBA.

Explanation

The plural verb "aim" requires a plural subject, making "regulations" (B) the correct word for the first position. Conversely, the singular verb "remains" (C) requires a singular subject, making "enforcement" (A) the correct fit for the second position. Arranging the words in the sequence BAC yields a grammatically and contextually sound sentence: "New regulations aim to protect user data online, yet enforcement across international platforms remains inconsistent."

Explanation

Trade tensions typically occur between major economies (nations), which disrupts global supply chains and forces individual businesses to alter and diversify their sourcing strategies. Swapping "businesses" and "economies" restores the correct contextual meaning, resulting in the proper word order: tensions (A), economies (C), and businesses (B).

Explanation

The phrase "leading" requires the preposition "to" to form the complete phrasal verb "leading to," whereas "altering" directly takes "marine ecosystems" as its direct object. Placing "altering" in the first position creates the grammatically sound clause "altering marine ecosystems," while placing "leading" in the second position correctly pairs it with "to" to form "leading to shifts in species distribution." The word "distribution" is already correctly placed. Therefore, exchanging the positions of the first two words yields the correct sequence BAC.

Explanation

In the sentence, the highlighted words are grammatically and contextually placed out of order. "Increased" fits after the noun "turnout" to indicate that voter participation went up ("turnout increased"). "Influenced" acts as the transitive verb governed by the subject "misinformation campaigns" to express impact ("misinformation campaigns still influenced"). Finally, "behavior" forms a meaningful noun phrase with "voter" ("voter behavior"). Replacing position A with C (increased), position B with A (influenced), and position C with B (behavior) restores proper grammatical structure, yielding the sequence CAB.

Explanation

Determining the order of boxes from top (8) to bottom (1):

Since T is two boxes above R, and P is just below T, the relative sequence from top to bottom is T, P, R.

Three boxes are placed between R and W with P above W, which places W four positions below R.

Two boxes are placed between P and V, and S is placed three boxes below V. Fitting this in an 8-box stack gives: T at position 8 P at position 7 R at position 6 V at position 4 S at position 1

Since Q is adjacent to W at position 2 and position 1 is occupied by S, Q must be at position 3.

The remaining position 5 is occupied by U.

The complete arrangement from top to bottom is T, P, R, U, V, Q, W, S.

The boxes placed above box U are T, P, and R, making a total of three boxes.

Explanation

Arranging the stack from top to bottom (positions 1 to 8):

Box T is placed two boxes above box R, and box P is placed just below box T, giving the initial sequence T (1), P (2), R (3). Since box P is above box W and three boxes lie between R and W, box W is placed at position 7. Two boxes between P (2) and V places V at position 5. Box S is three boxes below V, placing S at position 8. Box Q is adjacent to W (7), and since position 8 is occupied by S, Q takes position 6. Box U occupies the remaining position 4.

The complete arrangement from top to bottom is T (1), P (2), R (3), U (4), V (5), Q (6), W (7), S (8), placing box V directly above box Q.

Explanation

Arranging the eight boxes from top (position 8) to bottom (position 1) according to the conditions:

Box T is placed 2 boxes above R with P directly below T, positioning T, P, and R at positions 8, 7, and 6 respectively. Three boxes are between R (6) and W, placing W at position 2. Two boxes lie between P (7) and V, putting V at position 4. Box S is 3 boxes below V (4), giving S position 1. Box Q is adjacent to W (2) at position 3, leaving box U for position 5.

The complete stack from top to bottom is T, P, R, U, V, Q, W, S.

Box T occupies position 8, which is the topmost position. Box R at position 6 is immediately adjacent to box U at position 5.

Explanation

Based on the given clues, the stack from top to bottom (positions 1 to 8) is arranged as T, P, R, U, V, Q, W, and S.

Arranging all eight boxes alphabetically from top to bottom gives the order P, Q, R, S, T, U, V, and W for positions 1 through 8 respectively.

Comparing the original arrangement (T, P, R, U, V, Q, W, S) with the alphabetical arrangement (P, Q, R, S, T, U, V, W), only box R stays at position 3 in both stacks. Thus, exactly one box remains in the same position.

Explanation

According to the given clues, box T is placed two boxes above box R, and box P is placed just below box T, giving the top-to-bottom sequence T, P, R at positions 1, 2, and 3 respectively. Since three boxes are placed between box R and box W, box W is at position 7, which keeps box P above box W. Two boxes placed between box P (position 2) and box V puts box V at position 5. Box S being three boxes below box V places box S at position 8. Box Q is adjacent to box W (position 7), so box Q is at position 6. Box U occupies position 4. The complete stack from top to bottom (1 to 8) is T, P, R, U, V, Q, W, S. Counting five boxes below box T at position 1 gives position 6, which is occupied by box Q.

Explanation

To evaluate Conclusion I (M > F), trace the path from M to F: M = J > T ≤ F. The relationship contains conflicting inequality signs (> and ≤), which means no definite relation can be established between M and F. Thus, Conclusion I is false.

To evaluate Conclusion II (R > T), trace the path from R to T: R > M = J > T. Combining these inequalities gives R > T directly, so Conclusion II is true.

Explanation

From the given statement L ≤ T < W < Z = D ≤ P < G:

For Conclusion I (P > T): Tracing the chain from T to P gives T < W < Z = D ≤ P. Because of the strict inequality symbol (<) between T and W, it directly follows that T < P, which is equivalent to P > T. Thus, Conclusion I is true.

For Conclusion II (L < Z): Tracing the chain from L to Z gives L ≤ T < W < Z. The presence of the strict inequality symbol (<) between T and W ensures that L < Z. Thus, Conclusion II is true.

Therefore, both conclusions I and II are true.

Explanation

For Conclusion I, combining the path from Y to C gives Y > B ≥ X > C. Since all inequality symbols point in the same direction, Y > C is definitely true.

For Conclusion II, combining the path from M to F gives M > Y > B ≥ X > C ≤ F. The presence of conflicting inequality symbols (> and ≤) breaks the relation chain, so no definite relation can be established between M and F.

Explanation

A pair of digits satisfies the given condition if the absolute difference between the two digits equals the absolute difference between their position indices in the number, represented as |a - b| = |i - j|.

In the number 37481265, assigning position indices 1 through 8 from left to right:

Forward direction: Digits 1 and 2 appear at position indices 5 and 6. Here, |2 - 1| = 1 and the position difference |6 - 5| = 1. Thus, (1, 2) forms a valid pair.

Backward direction: Digits 5 and 6 appear at position indices 8 and 7. Here, |6 - 5| = 1 and the position difference |8 - 7| = 1. Thus, (5, 6) forms a valid pair.

No other pair of digits in the number satisfies |a - b| = |i - j|. Therefore, exactly two such pairs exist.

Explanation

Taking point C as the origin (0, 0): Point B is 9m north of C, so B = (0, 9). Point D is 12m east of C, so D = (12, 0). Point E is 15m north of D, so E = (12, 15). Point F is 12m west of E, so F = (12 - 12, 15) = (0, 15). Point G is 4m north of F, so G = (0, 15 + 4) = (0, 19).

Since both point C at (0, 0) and point G at (0, 19) lie on the same vertical axis, the shortest distance between C and G is the difference in their vertical coordinates: 19 - 0 = 19m.

Explanation

Taking point C as the origin (0, 0):

C = (0, 0) B = (0, 9) A = (-5, 9) D = (12, 0)

To find the direction of point D with respect to point A, calculate the displacement vector AD = D - A = (12 - (-5), 0 - 9) = (17, -9).

Since the x-displacement (+17) is towards the East and the y-displacement (-9) is towards the South, point D is in the South-East direction relative to point A.

Explanation

By plotting the points on a coordinate plane with point C at (0, 0), the positions are B(0, 9), A(-5, 9), D(12, 0), E(12, 15), F(0, 15), and G(0, 19). Point E is located to the North-East of point B because both its x-coordinate and y-coordinate are strictly greater (+12, +6). In every other pair, the second point lies to the South-East relative to the first point, as the x-coordinate increases while the y-coordinate decreases.

Explanation

Position the eight persons at eight equidistant spots around a circular table numbered 1 to 8 in clockwise order, facing the center (where moving clockwise represents left and counter-clockwise represents right).

Assign H to position 1. Since K sits to the immediate left of H, K is at position 2. H sits second to the left of Y, which places Y at position 7. Three persons sit between M and H, so M is directly opposite H at position 5.

The remaining vacant spots are 3, 4, 6, and 8. P sits second to the right of T, which places T at position 8 and P at position 6. Two persons sit between P and O, putting O at position 3. The remaining spot, position 4, is occupied by X.

The final clockwise seating arrangement is H (1), K (2), O (3), X (4), M (5), P (6), Y (7), and T (8). Moving counter-clockwise (to the right) from Y at position 7, the first spot is P, the second is M, and the third is X. Thus, X sits third to the right of Y.

Explanation

Number eight positions from 1 to 8 in a clockwise direction around the circular table. Facing inside, moving clockwise represents the left direction and anti-clockwise represents the right direction.

Placing T at position 1, P sits second to the right of T at position 7. Since two persons sit between P and O, O is placed at position 4. Three persons between M and H means they sit directly opposite each other, which leaves positions 2 and 6 as the only available opposite pair. Given that K sits immediate left of H and H sits second to the left of Y, H must be at position 2, placing K at position 3, Y at position 8, M at position 6, and X at position 5.

Counting from the left of T (moving clockwise from position 1 to position 4), the persons sitting between T and O are H at position 2 and K at position 3. Therefore, exactly two persons sit between O and T when counted from the left of T.

Explanation

Numbering the eight positions clockwise from 1 to 8 with all persons facing inside:

Since three persons sit between M and H, they are seated diametrically opposite each other. Placing H at position 1 puts M at position 5.

K sits to the immediate left of H (clockwise), placing K at position 2. Since H sits second to the left of Y, Y is at position 7.

Placing T at position 8 puts P second to the right of T (counter-clockwise) at position 6. Two persons sit between P and O, placing O at position 3.

The remaining vacant spot for X is position 4.

The complete arrangement clockwise from position 1 to 8 is H, K, O, X, M, P, Y, and T.

Facing inside from position 4 (X), moving counter-clockwise (to the right), the first person is O at position 3 and the second person to the right of X is K at position 2.

Explanation

Solving the eight-person circular arrangement (all facing inside) gives the clockwise order T, Y, P, M, X, O, K, H, under which the pair K-O satisfies the asked relationship.

Explanation

In an eight-person circular seating arrangement facing inside, moving clockwise corresponds to moving left, and moving counter-clockwise corresponds to moving right. Sitting fourth to the left of any person means sitting directly opposite to them.

Assigning positions clockwise from 1 to 8: If Y is placed at position 1, H (sitting second to the left of Y) is at position 3. K sits at the immediate left of H at position 4. Since three persons sit between M and H, M sits at position 7.

To satisfy the remaining conditions—P sitting second to the right of T, and two persons sitting between P and O—T is placed at position 2, P at position 8, X at position 6, and O at position 5.

Thus, position 5 is occupied by O, who sits fourth to the left of Y.

Explanation

Since no one sits to the left of D, D occupies position 1 at the extreme left end. Three persons sit between D and C, which places C at position 5. C sits to the immediate right of E, putting E at position 4. Two persons sit between B and E. Placing B to the left of E would put B at position 1, which is already occupied by D, so B must be placed to the right of E at position 7. Comparing the positions, D is at position 1 and B is at position 7, which means B is located sixth to the right of D.

Explanation

In the row, D=1 (no one to his left), C=5, E=4, B=7 and A=10; the remaining condition fixes the total at 16 persons.

Explanation

With D at position 1 and A at position 10 in the same row, the persons sitting between them are positions 2-9, i.e. Eight.

Explanation

In the given series, 2 # 4 5 § * 8 3 9 2 7 1 & 1 6 % 4 9 3 @ 2 5, we locate each symbol and check if the character immediately following it is an even digit (0, 2, 4, 6, 8):

is followed by 4 (even digit) § is followed by * (symbol)

• is followed by 8 (even digit) is followed by 9 (odd digit) & is followed by 1 (odd digit) % is followed by 4 (even digit) @ is followed by 2 (even digit)

The four symbols immediately followed by an even digit are #, *, %, and @.

Explanation

Counting 11 positions from the rightmost end of the series (2 # 4 5 § * 8 3 9 2 7 1 & 1 6 % 4 9 3 @ 2 5): 5 (1st), 2 (2nd), @ (3rd), 3 (4th), 9 (5th), 4 (6th), % (7th), 6 (8th), 1 (9th), & (10th), and 1 (11th). The 11th element from the right end is 1.

Explanation

Between the symbols # and %, the sequence of characters is: 4, 5, §, *, 8, 3, ^, 9, 2, 7, 1, &, 1, 6.

Extracting all the digits from this sequence gives: 4, 5, 8, 3, 9, 2, 7, 1, 1, 6.

Among these, the odd digits are 5, 3, 9, 7, 1, and 1. Counting them yields a total of 6 odd digits.

Explanation

Scanning the given series from the left end, the even digits encountered in order are 2 (first even digit), 4 (second even digit), and 8 (third even digit). Starting from 8 and moving towards the right, the symbols that appear in order are (first symbol) and & (second symbol). Consequently, the second symbol to the right of the third even digit from the left end is &.

Explanation

Checking every digit in the printed series, none is both immediately preceded and immediately followed by a symbol, so the answer is None.

Explanation

In the given letter groups, the pattern between the first and second letter follows a backward shift of 3 positions in the alphabetical series:

R - 3 = O J - 3 = G L - 3 = I V - 3 = S

In DFA, the relation between the first two letters is D + 2 = F, which breaks this pattern. Therefore, DFA is the odd one out.

Explanation

In the word CATEGORIZE, counting the positions from the left end yields: 1st letter: C 2nd letter: A 4th letter: E 8th letter: I

The four letters extracted are C, A, E, and I. No valid four-letter meaningful English word can be formed using these four letters. According to the instructions provided in the question, if no meaningful word can be formed, the answer is marked as X.

Explanation

G is the mother-in-law of M, which means M is married to G's daughter, K. Since H is the son of G's spouse and C is a male member in this generation, C is the husband of G. Since G is the mother-in-law of M, her husband C is the father-in-law of M. The eight members are C, G, their children H and K, K's husband M, M and K's children V and B, and B's wife D. Thus, C is the father-in-law of M.

Explanation

G is the mother-in-law of M, meaning M is married to G's daughter, K. G's spouse is C (male member), making H their son and K their daughter. M and K have two children, V and B. Since D is the sister-in-law of unmarried V, D is married to V's sibling, B, making B male. Given that K has only one daughter between her two children (V and B), and B is male, V is K's daughter.

Explanation

Since G is the mother-in-law of M, M is married to G's daughter. H is the son of G's spouse, which makes H the son of G and the brother of M's wife. M is the father of V and B. Since V is unmarried and D is V's sister-in-law, D must be married to B, making B a male. As B is the son of M's wife, H is B's maternal uncle. Therefore, B is the nephew of H.

Explanation

Arranging the months in chronological order yields February, March, April, May, June, July, October, and November. Since S was born after June, placing S in July (6th position) leaves three persons between S and T, placing T in March (2nd position). Q was born just before T, which puts Q in February (1st position). As zero persons were born before Q, zero persons were born after P, placing P in November (8th position). R was born three positions before P, placing R in June (5th position). V was born just before U, which uniquely fits the adjacent vacant slots of April (3rd position) for V and May (4th position) for U. W occupies the remaining slot in October (7th position). Consequently, the month-wise schedule is Q in February, T in March, V in April, U in May, R in June, S in July, W in October, and P in November.

Explanation

Arranging the eight months chronologically gives: 1. February, 2. March, 3. April, 4. May, 5. June, 6. July, 7. October, and 8. November.

Since S was born after June, three persons were born between S and T, and Q was born just before T (and not in March), S is in July (6), T is in March (2), and Q is in February (1).

With zero persons born before Q, zero persons were born after P, placing P in November (8). R was born three persons before P, putting R in June (5). V was born just before U, so V and U occupy April (3) and May (4) respectively. The remaining person W is placed in October (7).

The final order from February to November is: Q, T, V, U, R, S, W, P.

Between T (March) and W (October), there are four persons: V, U, R, and S.

Explanation

Arranging the eight months in chronological order gives February, March, April, May, June, July, October, and November. Since S was born after June and three persons were born between S and T, placing S in July puts T in March, which allows Q to be in February (just before T and not in March). Zero persons were born before Q, so zero persons were born after P, placing P in November. R was born three persons before P, placing R in June. Since V was born just before U, they occupy consecutive positions April and May respectively. This leaves the month of October for W.

Explanation

By placing the persons according to the given conditions, the birth months from February to November are Q in February, T in March, V in April, U in May, R in June, S in July, W in October, and P in November. T, U, S, and W were all born in months containing 31 days (March, May, July, and October), whereas R was born in June, which has 30 days. This makes R the odd one out as it does not belong to the 31-day group.

Explanation

Arranging the eight months chronologically gives February, March, April, May, June, July, October, and November. Since S was born after June and three persons were born between S and T, T was born in March and S in July (if T were in April, Q would be in March, which is forbidden). Q was born just before T, placing Q in February. Since zero persons were born before Q, zero persons were born after P, placing P in November. R was born three persons before P, putting R in June. V was born just before U, so they occupy April and May respectively, leaving W in October. The complete birth order from February to November is Q, T, V, U, R, S, W, P.

Statement I is false because two persons (S and W) were born between R and P. Statement II is true because exactly two persons (Q and T) were born before V. Statement III is false because U was born in May while S was born in July, meaning U is older than S. Thus, only Statement II is true.