Question 1

Classification (antonyms): Three pairs are true opposites; one pair is actually a synonym pair. Identify the non-antonym pair among the following.

Accepted Answer

Introduction / Context: Antonym classification questions require you to separate true opposites from words that are similar or only loosely related. In the given set, three pairs express direct oppositions along a single semantic axis, while one pair expresses near synonymy rather than opposition. The task is to find the exception that does not provide an opposite meaning relationship. Given Data / Assumptions: Pairs to examine: Dim : Bright, Wrong : Right, Shallow : Deep, Genuine : Real. We define antonyms as words that stand at opposite ends of the same scale or concept (for example, light vs dark, correct vs incorrect). We define synonyms as words that share similar meanings (for example, authentic and real). Concept / Approach: The approach is to test each pair for a strict binary contrast along one dimension. If both words are commonly used as mutually exclusive alternatives in ordinary usage, the pair is a true antonym pair. If they can substitute for each other in typical contexts without flipping meaning, they are synonyms and therefore the odd pair in an antonym set. Step-by-Step Solution: Dim vs Bright: These are opposites regarding intensity of light or brilliance. When brightness increases, dimness decreases. This is a clear antonym pair.Wrong vs Right: These are canonical opposites in correctness or morality. This is an archetypal antonym pair used in logic and everyday judgment.Shallow vs Deep: These are opposites measuring vertical extent or figurative profundity. Depth and shallowness operate on the same axis, so this is an antonym pair.Genuine vs Real: These are near synonyms meaning authentic, not fake, not counterfeit. They do not form a binary opposition; rather, they reinforce similar meaning. Verification / Alternative check: Attempt substitution in sentences. Replace genuine with real in “This is a genuine diamond.” The sentence “This is a real diamond” preserves the intended meaning, which confirms similarity, not opposition. Why Other Options Are Wrong: Dim : Bright are opposites in luminance.Wrong : Right are opposites in correctness.Shallow : Deep are opposites in depth. Common Pitfalls: A frequent mistake is to assume that two words with overlapping connotations are antonyms. Synonyms like genuine and real cannot be opposites because they do not define a two sided scale. Another pitfall is to judge based on tone rather than meaning. Always check whether replacing one with the other reverses meaning or preserves it. Final Answer: Genuine : Real

Question 2

Classification (antonyms vs related terms): Three pairs show clear opposites; one pair lists related orientation words that are not opposites. Identify the odd pair.

Accepted Answer

Introduction / Context: Verbal classification often mixes true antonyms with words that are merely related. Your goal is to discriminate strict opposites from terms that coexist in similar contexts without forming a binary. This skill ensures precise vocabulary control and semantic reasoning under timed conditions, which is common in competitive exams. Given Data / Assumptions: Pairs: Day : Night, Up : Down, Across : Along, Small : Large. Antonyms are defined as mutually exclusive endpoints on a single semantic dimension (for example, up vs down). Related terms are words that may appear in similar contexts but do not encode direct opposition (for example, across and along describe different directions of movement along a surface or space). Concept / Approach: Test each pair by asking: If one term is true, must the other be false along the same axis? If yes, the pair is likely an antonym pair. If no, the terms may be orthogonal or only contextually connected, and therefore are not opposites. Step-by-Step Solution: Day vs Night: These are temporal opposites within a 24 hour cycle. When it is day, it is not night; this is a canonical binary contrast.Up vs Down: These are spatial opposites along a vertical axis and are mutually exclusive directions.Small vs Large: These are opposites on the size continuum.Across vs Along: Both prepositions relate to orientation and motion relative to a reference surface or boundary. Across indicates traversal from one side to the other, while along indicates movement parallel to a line or edge. They are not opposites. Verification / Alternative check: Substitute the terms in sentences describing movement: “Walk across the road” vs “Walk along the road.” Both can be true in different scenarios without negating one another. Hence the pair does not encode opposition. Why Other Options Are Wrong: Day : Night are strict temporal opposites.Up : Down are strict vertical opposites.Small : Large are strict size opposites. Common Pitfalls: Assuming prepositions in the same domain must be antonyms. Contextual co occurrence does not imply opposition. Focus on whether the dimension is the same and whether the terms negate each other. Final Answer: Across : Along

Question 3

Classification (morphology): Three pairs are formed by adding the suffix “-ship” to a base word; one is not a suffixal formation but an unrelated word. Identify the odd pair.

Accepted Answer

Introduction / Context: Morphological classification evaluates whether a derived word genuinely comes from a base via a productive suffix. In English, the suffix “-ship” creates abstract nouns meaning state, condition, rank, or collective relationship (for example, friendship, leadership). In this question, three options involve words that contain the letters “ship” at the end, but only those that are true suffixal derivations from the given base should be considered consistent. The challenge is to detect the pair where the right hand word is not a true “base + ship” formation. Given Data / Assumptions: Pairs: Flag : Flagship, Court : Courtship, War : Worship, Friend : Friendship. “-ship” as a suffix yields nouns like friendship (friend + ship) and courtship (court + ship). “Flagship” is historically a compound noun referring to the ship carrying the commanding officer’s flag; synchronically it behaves as a lexicalized compound, not a standard suffixal abstract noun. Concept / Approach: Check if the right hand term transparently equals left hand base + the suffix “-ship” with an abstract relational sense. Reject cases where the letters “ship” are present but the meaning or formation does not align with suffixal usage (for example, worship does not equal war + ship). Step-by-Step Solution: Friend → Friendship: canonical suffixal derivation (state or relation of being friends).Court → Courtship: canonical suffixal derivation (state or period of wooing).Flag → Flagship: not an abstract “state of being a flag.” Instead, it names the lead ship; semantically and historically this is a compound rather than productive suffixal abstraction, though it still visually ends with “ship.”War → Worship: not war + ship. Worship is from worth + ship historically. Therefore this is not a derivation from war at all. Verification / Alternative check: Paraphrase each right hand term: friendship (state of friends), courtship (period of courting), flagship (the lead vessel), worship (act of reverence). Only worship has no morphological or semantic connection to war. Why Other Options Are Wrong: Friend : Friendship is valid suffixal formation.Court : Courtship is valid suffixal formation.Flag : Flagship, though not purely suffixal in meaning, still relates to the left base flag in a compositional way; it is not an outright mismatch like war → worship. Common Pitfalls: Assuming that any word ending in the letters “ship” must be base + suffix. Always test for semantic transparency and etymology when possible. Visual similarity can be deceptive. Final Answer: War : Worship

Question 4

Classification (whole–part vs co-hyponyms): Three pairs denote a whole–part relationship; one pair denotes two coordinate types rather than part and whole. Identify the odd pair.

Accepted Answer

Introduction / Context: Semantic relation problems frequently contrast whole–part relations with other lexical relations such as co hyponymy (sibling categories under a common supertype). Recognizing these distinctions is essential for accurate classification. In this item, most pairs encode a whole that contains a part, while one pair lists two coordinate items under the same higher category rather than a part and its containing whole. Given Data / Assumptions: Pairs: Tree : Stem, Face : Eye, Chair : Sofa, Plant : Flower. “Whole–part” means the second term is a constituent component of the first (for example, eye is part of a face). “Co hyponyms” are two different kinds of the same broader category (for example, chair and sofa are both types of furniture). Concept / Approach: Test each pair by asking whether the second term can be said to be included as a component within the first. If yes, it is a whole–part pair. If the two terms are merely siblings under a broader type without inclusion, the pair is not whole–part and becomes the exception. Step-by-Step Solution: Tree : Stem → a stem (or trunk) is a principal part of a tree.Face : Eye → an eye is a constituent part of a face.Plant : Flower → a flower is a part or reproductive structure of many plants.Chair : Sofa → neither is a component of the other; both are furniture types. Verification / Alternative check: Attempt the phrase “X has a Y.” “A face has an eye,” “A tree has a stem,” and “A plant has a flower” are natural. “A chair has a sofa” is not natural, confirming that it is not a whole–part relation. Why Other Options Are Wrong: Tree : Stem fits whole–part.Face : Eye fits whole–part.Plant : Flower fits whole–part. Common Pitfalls: Confusing co hyponyms with part–whole pairs due to frequent co occurrence in the same domain. Always test inclusion rather than association. Final Answer: Chair : Sofa

Question 5

Classification (relationship types): Three pairs are antonyms along a single dimension; one pair is a cause–effect or blame assignment relation, not antonymy. Identify the odd pair.

Accepted Answer

Introduction / Context: In verbal classification, antonym sets can be polluted with non antonym relations such as cause–effect, association, or role relations. This item contains three clear antonym pairs and one pair that is not an opposition at all. The task is to distinguish a non opposite relation from three genuine binary contrasts. Given Data / Assumptions: Pairs: Light-Heavy, Short-Long, Man-Woman, Crime-Blame. Antonyms should lie on a single continuum (weight, length, gender categories in common usage). Non antonym relations include causal or normative links (crime entails blame) rather than opposite ends of a scale. Concept / Approach: Ask whether replacing one word with the other in a sentence reverses meaning along the same dimension. If yes, they are antonyms. If the words instead describe different roles or a cause and its social consequence, they are not antonyms. Step-by-Step Solution: Light vs Heavy: Opposites on the mass or weight dimension.Short vs Long: Opposites on the length or duration dimension.Man vs Woman: Opposed gender categories in everyday categorization.Crime vs Blame: This is not an opposite pair. Crime is an unlawful act; blame is social or moral assignment of responsibility. The relation is cause–effect or act–judgment, not a binary scale. Verification / Alternative check: Try to form “X is the opposite of Y.” It works for light–heavy, short–long, man–woman. It does not work for crime–blame. One can say “crime leads to blame,” which signals causation rather than opposition. Why Other Options Are Wrong: Light-Heavy are true opposites.Short-Long are true opposites.Man-Woman are commonly treated as opposite categories in such tests. Common Pitfalls: Confusing frequent association for antonymy. Co occurrence does not imply opposition. Always identify the underlying dimension and ask whether the terms negate each other. Final Answer: Crime-Blame

Question 6

Classification (role–collective/place): Three pairs show a person as a member of a group or housed in a place; one pair shows the person who heads an institution. Identify the odd pair.

Accepted Answer

Introduction / Context: Lexical relation classification often distinguishes membership relations from leadership relations. In this question, three options specify a person as a member of a group or a resident of a place, whereas one option specifies a person who acts as the head of an institution. The latter is not membership but governance, which creates the exception. Given Data / Assumptions: Pairs: Principal : School, Soldier : Barrack, Artist : Troupe, Singer : Chorus. Membership or location relations: artist belongs to a troupe, singer belongs to a chorus, soldier resides in or is stationed at a barrack. Headship relation: a principal is the person in charge of a school, responsible for leadership and administration. Concept / Approach: Identify whether the left term is a member contained in the right term or a leader who oversees the right term. Membership and residence indicate inclusion, while headship indicates control or governance. The mismatch between inclusion and control marks the odd pair. Step-by-Step Solution: Artist : Troupe → member of a group.Singer : Chorus → member of a vocal ensemble.Soldier : Barrack → resident or stationed person in a place.Principal : School → head of an institution, not a member in the same sense. Verification / Alternative check: Rephrase as “X is in Y.” Artist is in a troupe, singer is in a chorus, soldier is in a barrack. “Principal is in a school” may be literally true, but the defining relation is leadership rather than membership. The functional role differs from the other three. Why Other Options Are Wrong: Artist : Troupe fits member–group.Singer : Chorus fits member–group.Soldier : Barrack fits person–place of residence. Common Pitfalls: Focusing on physical co location rather than the type of relation. Leadership versus membership is the key distinction here. Final Answer: Principal : School

Question 7

Classification (derivation vs cause): Three pairs denote a product obtained from a source material; one pair denotes a cause leading to an outcome. Identify the odd pair.

Accepted Answer

Introduction / Context: In classification items, exam setters often contrast derivational or production relations with causal relations. A production relation indicates that the second item can be obtained from or produced using the first (for example, wine from grapes). A causal relation indicates that the first item is a cause or contributor to the second (for example, disease can lead to death). The task is to separate product from source versus cause leading to effect. Given Data / Assumptions: Pairs: Milk : Butter, Grape : Wine, Water : Oxygen, Death : Disease. Production examples: butter is made from milk through churning and separation; wine is fermented from grapes. Decomposition or extraction example: oxygen may be obtained from water via electrolysis, although oxygen is a component rather than a conventional “product” in daily life. Concept / Approach: Group the pairs by relation type. If the second item is manufactured, processed, or extracted from the first, it belongs to the product from source category. If the second item is an outcome that results from the first as a cause, it is a cause effect relation and thus the exception in a production themed set. Step-by-Step Solution: Milk → Butter: product obtained from milk by processing.Grape → Wine: product obtained from grapes through fermentation.Water → Oxygen: oxygen can be obtained from water by electrolysis or decomposition, so it can be considered extractable from the first term.Death → Disease: disease is a cause that may lead to death; this is not a product from source relation. Verification / Alternative check: Try to rephrase as “Y is obtained from X.” This works naturally for butter from milk and wine from grapes. It can be interpreted for oxygen from water in a scientific context. It does not work for “disease from death” or “death from disease” within a product framework; it is cause effect, not production. Why Other Options Are Wrong: Milk : Butter — clear production relation.Grape : Wine — clear production relation.Water : Oxygen — extraction relation is at least scientifically valid. Common Pitfalls: A common confusion is to reject water : oxygen because oxygen is a component rather than a commercial product. However, in classification tests, extraction is accepted as a kind of “obtained from” relation. The true outlier is the causal pair. Final Answer: Death : Disease

Question 8

Classification (number pairs – powers): Three pairs follow the pattern second number = first number^3; one pair violates this cube relation. Identify the odd pair.

Accepted Answer

Introduction / Context: Numeric classification often uses exponent relations, such as squares and cubes. In this set, the intended relation is second = first^3. Identifying the pair that breaks this rule requires quick recognition of small powers and comfort with mental arithmetic under time pressure. Given Data / Assumptions: Pairs: 2-8, 3-27, 4-32, 5-125. We interpret the dash as an ordered pair (a, b) and test whether b = a^3. Recall cubes: 2^3 = 8, 3^3 = 27, 4^3 = 64, 5^3 = 125. Concept / Approach: Compute cubes of 2, 3, 4, and 5. Compare against the second number of each pair. Any mismatch identifies the odd pair. This is a straightforward recognition task that benefits from memorizing cubes up to at least 10 for speed. Step-by-Step Solution: 2-8 → 2^3 = 8 (fits).3-27 → 3^3 = 27 (fits).4-32 → 4^3 = 64 (does not match 32; 32 equals 2^5).5-125 → 5^3 = 125 (fits). Verification / Alternative check: Note that 32 is a power of 2 (2^5), which can distract solvers who lean on recognition of common powers without checking the base. Confirm by direct multiplication for 4^3: 4*4*4 = 16*4 = 64. Why Other Options Are Wrong: 2-8 follows the cube rule.3-27 follows the cube rule.5-125 follows the cube rule. Common Pitfalls: Confusing powers of 2 with cubes of other integers. Always compute the exact power relation defined by the pattern rather than relying on familiarity with a single number like 32. Final Answer: 4-32

Question 9

Classification (number pairs – square roots): Three pairs show perfect squares where the second equals the square root of the first; one pair is not a perfect square relation. Identify the odd pair.

Accepted Answer

Introduction / Context: Another common numeric classification relies on perfect squares. When a pair is presented as (A, B), many items use the rule B = sqrt(A). Fast recognition of perfect squares saves time and reduces errors in competitive tests. Your task is to detect the pair that fails to meet this square root relation. Given Data / Assumptions: Pairs: 64-8, 36-6, 49-7, 80-9. Known squares: 8^2 = 64, 6^2 = 36, 7^2 = 49. Check whether 9^2 = 81, which would be required for 80-9 to fit the pattern. Concept / Approach: Compute the square of the second number for each pair and compare it to the first. If A equals B^2, the pair fits. Otherwise, it is the exception. Memorizing squares up to 20 accelerates this process. Step-by-Step Solution: 64-8 → 8^2 = 64 (fits).36-6 → 6^2 = 36 (fits).49-7 → 7^2 = 49 (fits).80-9 → 9^2 = 81 (does not equal 80; fails). Verification / Alternative check: Reverse check by taking sqrt(64)=8, sqrt(36)=6, sqrt(49)=7. For 80, the square root is not an integer (approximately 8.944...). Therefore, 80-9 is not a perfect square pair. Why Other Options Are Wrong: 64-8, 36-6, and 49-7 are perfect square relations. Common Pitfalls: Rounding errors or estimating roots without confirming. Always verify by squaring the second number to see if it exactly equals the first. Final Answer: 80-9

Question 10

Classification (number pairs – squares): Three pairs follow the pattern second number = first number^2; one pair violates the square relation. Identify the odd pair.

Accepted Answer

Introduction / Context: Square relations are among the most frequent patterns in number classification tasks. Rapid recognition of n^2 values helps identify mistakes or deliberate distractors. In this problem, three pairs are correct square mappings while one is incorrect. Your job is to spot the incorrect mapping quickly and reliably. Given Data / Assumptions: Pairs: 11-121, 12-144, 13-169, 14-186. Squares to recall: 11^2 = 121, 12^2 = 144, 13^2 = 169, 14^2 = 196. Check consistency of each pair against the rule b = a^2. Concept / Approach: Compute squares for 11 through 14 and directly compare with the second number in each pair. Any mismatch signals the exception. Keeping a mental table of squares 1 through 25 makes these problems trivial. Step-by-Step Solution: 11-121 → 11^2 = 121 (fits).12-144 → 12^2 = 144 (fits).13-169 → 13^2 = 169 (fits).14-186 → 14^2 = 196 (does not match 186; fails). Verification / Alternative check: Perform multiplication to confirm: 14*14 = 196. Since the pair lists 186, it is incorrect. There is no square integer that equals 186, confirming it as the outlier. Why Other Options Are Wrong: 11-121, 12-144, and 13-169 all adhere to the square rule and therefore are not exceptions. Common Pitfalls: Mistyping or misreading nine and six in 196 as 186 is a common transcription trap. Verifying by explicit multiplication avoids such slips. Final Answer: 14-186

Question 11

Identify the odd pair: In each pair A–B, the second number should be the cube of the first number (i.e., B = A^3). Choose the pair that does not follow this rule.

Accepted Answer

Introduction / Context: Classification questions test your ability to detect the rule that connects items and then spot the item that breaks that rule. Here, each option is a pair A–B. The intended rule is B = A^3 (the cube of A). Given Data / Assumptions: We have four pairs: 1–1, 2–8, 3–27, 4–32. Target rule: B must equal A^3. All calculations use exact integer cubes. Concept / Approach: The cube operation is defined as A^3 = A * A * A. Verify each pair by computing A^3 and comparing to B. Step-by-Step Solution: Check 1–1: 1^3 = 1, so B = 1 matches.Check 2–8: 2^3 = 8, so B = 8 matches.Check 3–27: 3^3 = 27, so B = 27 matches.Check 4–32: 4^3 = 64, but B = 32, which does not match. Verification / Alternative check: You can reverse-check by taking the cube root of B. cube_root(32) is not 4 (4^3 = 64). Hence this pair violates the rule. Why Other Options Are Wrong: 1–1 follows B = A^3 exactly.2–8 follows B = A^3 exactly.3–27 follows B = A^3 exactly. Common Pitfalls: Mixing up squares and cubes is common. Another slip is computing 4^3 as 32 (it is 64). Always compute A * A * A carefully to avoid mental-math errors. Final Answer: 4 - 32 is the odd pair because 32 ≠ 4^3 (which is 64).

Question 12

Find the correctly matched pair: In each pair A–B, the second number should be the square root of the first number (i.e., B = sqrt(A)). Select the pair that satisfies this relation.

Accepted Answer

Introduction / Context: This classification item asks you to recognize the correct functional mapping between two numbers in a pair. The mapping is B = sqrt(A). Exactly one option follows this rule; the rest are distractors. Given Data / Assumptions: Pairs to test: 42–4, 36–6, 32–2, 15–5. All square roots considered are principal (non-negative) roots. Concept / Approach: If B = sqrt(A), then A must be a perfect square of B. Equivalently, A = B^2. We can check faster by squaring B and comparing to A. Step-by-Step Solution: Check 42–4: 4^2 = 16 ≠ 42 → not correct.Check 36–6: 6^2 = 36 = A → correct.Check 32–2: 2^2 = 4 ≠ 32 → not correct.Check 15–5: 5^2 = 25 ≠ 15 → not correct. Verification / Alternative check: Take sqrt(A) directly. sqrt(36) = 6 (integer). For 42, 32, and 15, the square roots are not integers matching the listed B values. Hence only 36–6 works. Why Other Options Are Wrong: 42–4 fails because 42 is not 4^2.32–2 fails because 32 is not 2^2.15–5 fails because 15 is not 5^2. Common Pitfalls: Confusing square roots with other operations (like halving) or assuming near-perfect squares qualify. Only exact perfect squares satisfy the relation. Final Answer: 36 - 6 is the only correctly matched pair.

Question 13

Identify the odd pair: In each pair X–Y, the intended pattern is Y = X + 3. Choose the pair that does not follow this +3 rule.

Accepted Answer

Introduction / Context: Many classification questions rely on detecting a simple arithmetic relation. Here, each option is a pair X–Y, and the rule to test is Y = X + 3. We must find the pair that breaks this rule. Given Data / Assumptions: Options: 8–11, 1–4, 7–10, 3–5. Rule under test: Add 3 to the first term to get the second. Concept / Approach: Compute X + 3 for each X and compare to its Y. The odd pair will be the one where Y ≠ X + 3. Step-by-Step Solution: For 8–11: 8 + 3 = 11 → correct.For 1–4: 1 + 3 = 4 → correct.For 7–10: 7 + 3 = 10 → correct.For 3–5: 3 + 3 = 6, but Y = 5 → violation. Verification / Alternative check: Compute the difference Y − X for each pair: 3, 3, 3, and 2 respectively. Only 3–5 has a difference of 2, confirming it as the odd pair. Why Other Options Are Wrong: 8–11 fits the +3 rule.1–4 fits the +3 rule.7–10 fits the +3 rule. Common Pitfalls: Rushing differences and miscomputing 3 + 3 as 5. To avoid this, always verify by subtraction as well (Y − X should equal 3). Final Answer: 3 - 5 is the odd pair.

Question 14

Find the odd pair: Three options are consecutive perfect-square pairs (n^2, (n+1)^2). Identify the pair that is NOT of this form.

Accepted Answer

Introduction / Context: Squares feature heavily in number-classification problems. Here, most options form pairs of consecutive perfect squares, i.e., (n^2, (n+1)^2). The task is to detect the one pair that does not follow this structure. Given Data / Assumptions: Pairs: 8–15, 25–36, 49–64, 81–100. Perfect squares to recall: 5^2 = 25, 6^2 = 36; 7^2 = 49, 8^2 = 64; 9^2 = 81, 10^2 = 100. Concept / Approach: Check whether each pair corresponds to (n^2, (n+1)^2) for some integer n. Non-squares or mismatched pairs will betray the odd one out. Step-by-Step Solution: 25–36: 25 = 5^2 and 36 = 6^2 → consecutive squares.49–64: 49 = 7^2 and 64 = 8^2 → consecutive squares.81–100: 81 = 9^2 and 100 = 10^2 → consecutive squares.8–15: 8 is not a perfect square and 15 is not a perfect square → not of the form (n^2, (n+1)^2). Verification / Alternative check: Observe that legitimate pairs differ by (n+1)^2 − n^2 = 2n + 1 (an odd number). The listed square pairs differ by 11, 15, and 19 respectively. The pair 8–15 differs by 7 and neither term is a perfect square, confirming it as the odd one out. Why Other Options Are Wrong: They are correct examples of consecutive square pairs, so they are not the odd item. Common Pitfalls: Confusing “consecutive integers” with “consecutive squares,” or checking only the difference without confirming each term is a perfect square. Final Answer: 8 - 15 is the odd pair.

Question 15

Spot the distinct pair: Choose the pair in which both numbers are prime, while in the other pairs at least one number is composite.

Accepted Answer

Introduction / Context: Prime detection is a common theme in classification. Here you must identify the pair in which both numbers are prime. The distractors include at least one composite number per pair, making them unlike the target pair. Given Data / Assumptions: Pairs: 547–563, 71–55, 517–523, 248–231. We treat 1 as neither prime nor composite (not present here). Primality checks rely on standard divisibility reasoning. Concept / Approach: Test each number for primality. A composite detection in any pair disqualifies it. The surviving pair must have two primes. Step-by-Step Solution: 547: not divisible by small primes up to sqrt(547). It is prime. 563: similarly passes small-prime tests and is known prime. → Pair qualifies.71 is prime; 55 = 5 * 11 is composite → pair disqualified.517 = 11 * 47 is composite; 523 is prime → pair disqualified.248 = 8 * 31 is composite; 231 = 3 * 7 * 11 is composite → pair disqualified. Verification / Alternative check: Quick filters: even numbers > 2 are composite; numbers ending with 5 and greater than 5 are composite; sums of digits divisible by 3 indicate divisibility by 3. These filters immediately flag 55, 231, and 248 as composite. 517’s factor 11 emerges from divisibility by 11 test patterns. Why Other Options Are Wrong: Each contains at least one composite number, hence not both-prime pairs. Common Pitfalls: Assuming that closeness (like 517–523) implies similar primality; or overlooking basic composite cues (even endings, multiple-of-5 endings, digit-sum rules). Always test both numbers. Final Answer: 547 - 563 is the only pair where both numbers are prime.

Question 16

Find the odd pair: In each pair N–M, the second number should be exactly double the first (M = 2 * N). Identify the pair that breaks this doubling rule.

Accepted Answer

Introduction / Context: Arithmetic-mapping classification tasks often use linear relations. Here, the intended mapping is M = 2 * N (the second number is double the first). The odd pair violates this relation. Given Data / Assumptions: Pairs: 12–24, 14–28, 23–46, 36–70. Check exact doubling, not approximate. Concept / Approach: Compute 2 * N for each pair and compare with M. Any mismatch identifies the odd pair. Step-by-Step Solution: 12–24: 2 * 12 = 24 → correct.14–28: 2 * 14 = 28 → correct.23–46: 2 * 23 = 46 → correct.36–70: 2 * 36 = 72, but M = 70 → violation. Verification / Alternative check: Compute M − 2N for each pair: 0, 0, 0, and −2 respectively. Non-zero difference confirms the mismatch in 36–70. Why Other Options Are Wrong: They accurately represent doubling and so are not the odd item. Common Pitfalls: Rounding or mental slips (e.g., mistaking 2 * 36 as 70). Always multiply exactly. Final Answer: 36 - 70 is the odd pair.

Question 17

Choose the odd pair: In these pairs A–B, most have a constant difference of −3 (B = A − 3). Identify the pair that does not follow this pattern.

Accepted Answer

Introduction / Context: Constant-difference relations are common in classification items. Here, the expected relation is B = A − 3, i.e., the second number is 3 less than the first. Find the pair that breaks this consistency. Given Data / Assumptions: Pairs: 5–2, 19–16, 27–23, 31–28. We measure B − A to confirm the difference. Concept / Approach: Compute A − B (or B − A) and check whether the difference equals 3 consistently. The odd pair will have a different gap. Step-by-Step Solution: 5–2: 5 − 2 = 3 → matches.19–16: 19 − 16 = 3 → matches.27–23: 27 − 23 = 4 → violates.31–28: 31 − 28 = 3 → matches. Verification / Alternative check: Using B − A gives −3, −3, −4, −3 respectively. The lone −4 confirms 27–23 as the violator. Why Other Options Are Wrong: They fit the −3 pattern exactly and therefore are not the odd item. Common Pitfalls: Miscalculating simple differences, especially when scanning quickly. A one-off mistake can hide the true odd pair. Final Answer: 27 - 23 is the odd pair.

Question 18

Find the odd set: In each triple (a, b, c), the largest number should equal the sum of the other two (largest = sum of smaller two). Identify the set that does NOT follow this rule.

Accepted Answer

Introduction / Context: This classification problem uses an additive relation inside triples. The rule: in each triple, the largest member must equal the sum of the other two. One triple fails to meet this requirement; that is the odd set you must identify. Given Data / Assumptions: Triples: (2, 15, 13), (7, 12, 4), (4, 15, 11), (6, 18, 12). Assume standard integer arithmetic. Concept / Approach: For each triple, sort or mentally identify the largest value, then verify largest = sum of the other two. If equality fails, that triple is the odd one out. Step-by-Step Solution: (2, 15, 13): largest 15; 2 + 13 = 15 → fits.(7, 12, 4): largest 12; 7 + 4 = 11 ≠ 12 → fails.(4, 15, 11): largest 15; 4 + 11 = 15 → fits.(6, 18, 12): largest 18; 6 + 12 = 18 → fits. Verification / Alternative check: Re-express as largest − (sum of others) should equal 0. Only the second triple yields 12 − (7 + 4) = 1 ≠ 0, confirming the violation. Why Other Options Are Wrong: They satisfied the additive identity exactly and thus are not the odd item. Common Pitfalls: Picking the wrong largest element or mis-adding small numbers under time pressure. Always identify the maximum first, then add carefully. Final Answer: 7, 12, 4 is the odd set.

Question 19

Identify the odd triple: Three options form an arithmetic progression with common difference 2 (even-step AP or near-AP). Choose the triple that does NOT form an exact AP.

Accepted Answer

Introduction / Context: Arithmetic progressions (AP) are sequences where consecutive terms differ by a constant. Here, the intended AP has common difference 2 after arranging terms in ascending order. One triple fails to be an exact AP. Given Data / Assumptions: Triples: (20, 16, 18), (14, 11, 13), (18, 14, 16), (16, 12, 14). We may reorder triples to test for AP. Concept / Approach: Sort each triple and check whether middle − smallest = largest − middle (both should equal 2). Any deviation marks the odd triple. Step-by-Step Solution: (20, 16, 18) → sorted: 16, 18, 20 → differences 2 and 2 → AP.(14, 11, 13) → sorted: 11, 13, 14 → differences 2 and 1 → not an AP.(18, 14, 16) → sorted: 14, 16, 18 → differences 2 and 2 → AP.(16, 12, 14) → sorted: 12, 14, 16 → differences 2 and 2 → AP. Verification / Alternative check: An AP with common difference 2 must satisfy smallest + largest = 2 * middle. For 11, 13, 14: 11 + 14 = 25 ≠ 26, confirming the mismatch. Why Other Options Are Wrong: They all form neat APs with common difference 2 upon sorting. Common Pitfalls: Forgetting to sort before checking differences, or miscomputing one of the differences and rejecting a valid AP. Final Answer: 14, 11, 13 is the odd triple.

Question 20

Find the set that is like the given set (13 : 20 : 27). The three numbers must form an arithmetic progression with a common difference of 7.

Accepted Answer

Introduction / Context: Similarity questions often rely on reproducing the same structural relation in a new set. The reference set (13 : 20 : 27) is an arithmetic progression with common difference 7. We must choose the option that also forms an AP with d = 7. Given Data / Assumptions: Reference: 13, 20, 27 → differences: +7 and +7. Options: (3, 11, 18), (18, 25, 32), (18, 27, 72), (7, 14, 28). Concept / Approach: For each option, compute consecutive differences. A matching set must have both gaps equal to 7. Step-by-Step Solution: (3, 11, 18): differences +8 and +7 → not consistent (d ≠ 7 for first gap).(18, 25, 32): differences +7 and +7 → perfect match.(18, 27, 72): differences +9 and +45 → not an AP with d = 7.(7, 14, 28): differences +7 and +14 → not equal gaps. Verification / Alternative check: AP condition: middle − first = last − middle. Only (18, 25, 32) satisfies 25 − 18 = 32 − 25 = 7. Why Other Options Are Wrong: They either do not have equal gaps or have gaps different from 7. Common Pitfalls: Assuming that one difference being 7 is enough. For an AP, both differences must be equal (here, both must be 7). Final Answer: (18 : 25 : 32) is like the given set.

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