Question 1

In the following question, select the odd number arrangement from the alternatives given below.  Three options contain the same set of digits (2, 3, 4) arranged differently, while one option contains a different digit set. Identify the odd one out. …

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Introduction / Context: This odd-one-out problem is based on digit composition. Many number arrangement questions hide a simple rule: several options are permutations of the same digits, while one option includes an extra or different digit. The odd option is the one with a different digit set. Given Data / Assumptions: We compare the digits used in each 3-digit number. Permutations mean the same digits are present but in different order. The odd one out uses at least one different digit. Concept / Approach: List the digits of each option and see whether most options share the same digit set. If four options use digits 2,3,4 and one uses a different set, the different one is the odd choice. Step-by-Step Solution: 234 uses digits {2, 3, 4}. 243 uses digits {2, 4, 3} which is the same set {2, 3, 4}. 432 uses digits {4, 3, 2} which is the same set {2, 3, 4}. 324 uses digits {3, 2, 4} which is the same set {2, 3, 4}. 345 uses digits {3, 4, 5}. This set is different because it includes 5 instead of 2. Verification / Alternative check: A quick verification is to look for digit '5'. Only 345 contains a 5. All other numbers are built only from digits 2, 3, and 4. Therefore 345 cannot be a permutation of the others and is the odd one out. Why Other Options Are Wrong: 234: permutation group member using digits 2,3,4. 243: permutation group member using digits 2,3,4. 432: permutation group member using digits 2,3,4. 324: permutation group member using digits 2,3,4. Common Pitfalls: Students sometimes focus on increasing/decreasing order and miss that the digits themselves are the key. Another mistake is thinking 345 is odd only because it is increasing, but 234 is also increasing. The correct reasoning is about digit set consistency, not ordering alone. Always check whether the same digits repeat across multiple options. Final Answer: 345

Question 2

In the following question, select the odd shape from the alternatives given below.  Three options are 2D plane figures, while one option is a 3D solid shape. Identify the odd one out.  (A) Square  (B) Rectangle  (C) Cylinder  (D) Triangle  (E) Circle

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Introduction / Context: This odd-one-out question is based on geometry classification. Shapes can be broadly grouped as 2D (two-dimensional) plane figures or 3D (three-dimensional) solid figures. The odd shape will be the one that belongs to a different dimensional category than the rest. Given Data / Assumptions: 2D shapes have only length and breadth (area) and lie on a plane. 3D shapes have length, breadth, and height (volume) and occupy space. Square, rectangle, triangle, and circle are standard 2D plane figures. Cylinder is a standard 3D solid figure. Concept / Approach: Identify whether each option is a plane figure or a solid. If four are plane figures and one is a solid, the solid is the odd one out. Step-by-Step Solution: Square: 2D plane figure (has area but no volume). Rectangle: 2D plane figure (has area but no volume). Triangle: 2D plane figure (has area but no volume). Circle: 2D plane figure (has area but no volume). Cylinder: 3D solid (has curved surface and volume; needs height). Verification / Alternative check: A simple check is: can the figure hold volume (like a container)? A cylinder can hold volume and has height. A square, rectangle, triangle, and circle do not have height in their basic form; they are flat. Hence cylinder is the only 3D shape and becomes the odd one out. Why Other Options Are Wrong: Square: 2D, matches the plane-figure group. Rectangle: 2D, matches the plane-figure group. Triangle: 2D, matches the plane-figure group. Circle: 2D, matches the plane-figure group. Common Pitfalls: Some students confuse 'circle' with 'sphere' or 'cylinder' with 'rectangle' because of the net/unfolded view. Always classify by the actual object, not its cross-section or net. Another pitfall is thinking any shape with curved edges is automatically different; but circle is also curved and still 2D. The correct differentiator here is 2D vs 3D. Final Answer: Cylinder

Question 3

In the following question, select the odd letter from the alternatives given below.  Three letters are vowels, while one letter is a consonant. Identify the odd one out.  (A) A  (B) S  (C) U  (D) I  (E) E

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Introduction / Context: This question tests basic English letter classification: vowels vs consonants. Vowels in English are A, E, I, O, U. Any other letter is a consonant. The odd letter is the one that does not belong to the vowel group. Given Data / Assumptions: Vowels are: A, E, I, O, U. Consonants are all remaining letters. We identify which options are vowels and which are not. Concept / Approach: Check each option and classify it as vowel or consonant. If four options are vowels and one is a consonant, that consonant is the odd one out. Step-by-Step Solution: A is a vowel. U is a vowel. I is a vowel. E is a vowel. S is not a vowel; it is a consonant. Verification / Alternative check: Another quick verification is to memorize the vowel set as 'AEIOU'. Compare each letter against this set. A, E, I, and U appear in the vowel set, but S does not. Therefore S is the odd letter. Why Other Options Are Wrong: A: vowel, so not odd. U: vowel, so not odd. I: vowel, so not odd. E: vowel, so not odd. Common Pitfalls: Some students incorrectly include Y as a vowel in every situation, which can cause confusion in other problems. In this question, the classical vowel set is used, so classification is straightforward. Another pitfall is overthinking alphabet position or shape when the simplest and most direct classification (vowel vs consonant) is clearly intended by the options presented. Final Answer: S

Question 4

In the following aptitude question on number classification, four numbers are given (216, 125, 343 and 510). Three of these are perfect cubes, while one number is not a perfect cube. Select the odd number from the given alternatives.

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Introduction / Context: This aptitude question belongs to the odd one out and number classification topic. The options 216, 125, 343 and 510 look similar at first glance, but there is a hidden pattern based on perfect cubes. Your task is to recognise which numbers are exact cubes of integers and then pick the number that does not fit this pattern. Given Data / Assumptions: Given numbers: 216, 125, 343 and 510. We are working with basic number properties, especially powers of integers. Perfect cube means a number of the form n^3 where n is an integer. Exactly one of the four numbers is not a perfect cube. No advanced mathematics is required, only familiarity with small cubes. Concept / Approach: The main concept tested here is recognition of perfect cubes. Many competitive exams expect you to remember cubes of small integers such as 2^3, 3^3, 4^3, 5^3, 6^3, 7^3 and so on. Once you match each option with a known cube, you can easily see which number does not match any integer cube. That non matching number will be the odd one out in the list. Step-by-Step Solution: Step 1: Check 216.Compute 6^3 = 6 * 6 * 6 = 216. So 216 is a perfect cube.Step 2: Check 125.Compute 5^3 = 5 * 5 * 5 = 125. So 125 is also a perfect cube.Step 3: Check 343.Compute 7^3 = 7 * 7 * 7 = 343. So 343 is again a perfect cube.Step 4: Check 510.Try nearby cubes: 7^3 = 343, 8^3 = 512, 9^3 = 729. None of these equal 510, so 510 is not a perfect cube.Step 5: Identify the odd number.Three numbers (216, 125, 343) are exact cubes of integers, but 510 is not, so 510 is the odd one out. Verification / Alternative check: An alternative way to check is to compare 510 with the cube 512. Since 510 is very close to 512 but not equal, and cubes are exact values, 510 cannot be any integer cube. On the other hand, you can directly confirm from memory that 5^3, 6^3 and 7^3 are 125, 216 and 343 respectively, so those three clearly qualify as perfect cubes. This confirms your identification without any doubt. Why Other Options Are Wrong: 216: This is 6^3, so it correctly fits the perfect cube pattern. 125: This is 5^3, and therefore it also follows the same cube rule. 343: This is 7^3, matching the pattern of being a perfect cube. Common Pitfalls: Candidates may not memorise cubes beyond 5^3 and might hesitate with 216 and 343. Some students might also confuse 512 and 510. To avoid errors, it is helpful to know cubes at least up to 10^3, and to remember that cubes are exact. If a number is even slightly off from a known cube, it cannot be a perfect cube. Careful checking of each option prevents careless mistakes in such classification questions. Final Answer: The odd number is 510, because 216, 125 and 343 are perfect cubes of integers, while 510 is not a perfect cube.

Question 5

In the following question on classification of games, four games are listed (Ludo, Chess, Polo and Carrom). Three are indoor board games, while one is an outdoor field sport played on horseback. Select the odd word from the given alternatives.

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Introduction / Context: This verbal reasoning question deals with the classification of games. You are given four game names: Ludo, Chess, Polo and Carrom. In odd man out questions, three items usually share a common feature, while one item belongs to a different category. Here the common feature is whether the game is an indoor board game or an outdoor sport requiring a large field and specialised equipment like horses. Given Data / Assumptions: Ludo: a board game played indoors on a printed board with tokens and dice. Chess: a strategic indoor board game with pieces on a chequered board. Polo: an outdoor team sport played on horseback with mallets and a ball. Carrom: an indoor tabletop board game played by striking discs. Exactly one game is a field based outdoor sport; the others are board or tabletop games usually played indoors. Concept / Approach: The core idea here is to classify games according to where and how they are played. Board and tabletop games are usually played indoors on a small surface and do not require large grounds or animals. Field sports, on the other hand, need open spaces, many players and special gear. By checking each option against these characteristics, you can quickly identify which one does not fit the majority group. Step-by-Step Solution: Step 1: Analyse Ludo.Ludo is a simple indoor board game played on a cross shaped board using dice and coloured pieces. It clearly belongs to the board game category.Step 2: Analyse Chess.Chess is also an indoor board game played on a 8 by 8 chequered board using black and white pieces. It is a classic example of an indoor mind sport.Step 3: Analyse Carrom.Carrom is an indoor tabletop board game. Players flick a striker to move small discs into corner pockets. It is again played on a flat indoor surface.Step 4: Analyse Polo.Polo is a fast outdoor team sport. It is played on horseback on a large grass field with long mallets and a small ball. It is very different from table or board games.Step 5: Identify the odd game.Since Ludo, Chess and Carrom are all indoor board or tabletop games, while Polo is an outdoor equestrian sport, Polo is the odd word in the list. Verification / Alternative check: You can also ask a simple practical question: if there is a power cut or limited space indoors, which of these games cannot reasonably be played in the living room? Ludo, Chess and Carrom can all be played on a table at home. Polo requires horses, a large field and specialised safety arrangements, so it clearly stands apart. This thinking confirms your earlier conclusion about the odd one out. Why Other Options Are Wrong: Ludo: Indoor board game, similar in nature to other tabletop games, so not the odd one. Chess: Another indoor board game, matching Ludo and Carrom. Carrom: Indoor tabletop game, again belonging to the same broad group. Common Pitfalls: Sometimes candidates are tempted to overcomplicate the problem by considering whether each game uses a ball, or whether it is a team game or an individual game. While these differences exist, the intended exam pattern usually focuses on the most obvious classification, which is indoor board game versus outdoor field sport. Focusing on the simplest strong grouping helps avoid confusion and saves time. Final Answer: The odd word is Polo, because Ludo, Chess and Carrom are indoor board or tabletop games, whereas Polo is an outdoor field sport played on horseback.

Question 6

In the following question on alphabet patterns, four three letter groups are given (DGJ, KNQ, RUX and ILN). In three groups, the letters progress with equal jumps in the alphabet, while one group breaks this regular pattern. Select the odd letters f…

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Introduction / Context: This reasoning question focuses on detecting regular patterns in sequences of letters. The groups DGJ, KNQ, RUX and ILN all look similar, but most of them follow a clean progression rule based on fixed jumps in the English alphabet. Your job is to find which group does not follow the same jump pattern and mark it as the odd one out. Given Data / Assumptions: Letter groups: DGJ, KNQ, RUX and ILN. Alphabet positions: A = 1, B = 2, C = 3, ..., Z = 26. Each group contains three letters arranged in a certain pattern. Three groups show equal jumps between consecutive letters, while one group shows a different jump. We consider only alphabetical positions, not pronunciation or meaning. Concept / Approach: The approach is to convert each letter to its numerical alphabet position and examine the differences between consecutive letters inside each group. If in three groups the differences are the same (for example +3, +3) and in one group the pattern changes (for example +3, +2), then the group with the different difference is the odd one. This technique of checking position differences is standard in alphabet series and coding questions. Step-by-Step Solution: Step 1: Analyse DGJ.D = 4, G = 7, J = 10. Differences: 7 - 4 = 3, 10 - 7 = 3. So DGJ follows a +3, +3 pattern.Step 2: Analyse KNQ.K = 11, N = 14, Q = 17. Differences: 14 - 11 = 3, 17 - 14 = 3. KNQ also follows a +3, +3 pattern.Step 3: Analyse RUX.R = 18, U = 21, X = 24. Differences: 21 - 18 = 3, 24 - 21 = 3. RUX again follows a +3, +3 pattern.Step 4: Analyse ILN.I = 9, L = 12, N = 14. Differences: 12 - 9 = 3, 14 - 12 = 2. ILN follows a +3, +2 pattern.Step 5: Identify the odd group.Since DGJ, KNQ and RUX all use +3, +3 jumps, and ILN uses +3, +2 jumps, ILN is the odd letter group. Verification / Alternative check: A quicker check once you know the pattern is to write the letters one below the other and see if they align diagonally with equal spacing: D, G, J; K, N, Q; R, U, X all show a neat step of three letters each time. When you write I, L, N, you notice that L is three steps after I but N is only two steps after L. This visual difference confirms that ILN breaks the otherwise uniform pattern of constant jumps. Why Other Options Are Wrong: DGJ: Follows the rule of equal +3 jumps between letters, so it is not odd. KNQ: Also follows the +3, +3 jump pattern and belongs with DGJ and RUX. RUX: Again uses +3, +3 jumps, so it matches the main pattern of the question. Common Pitfalls: Some candidates may quickly decide based on visual familiarity or because a group contains letters that appear less often in words. However, alphabet series questions almost always rely on consistent positional patterns rather than word frequency or pronunciation. Always convert letters to numbers and systematically check the differences. This habit makes such questions straightforward and reduces guessing. Final Answer: The odd letter group is ILN, because its letters increase by +3 and then +2, while the other three groups all increase by +3 and +3 in the alphabet.

Question 7

In the following number classification question, four numbers are given (31, 37, 43 and 49). Three of these are prime numbers, while one is a composite number. Select the odd number from the given alternatives.

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Introduction / Context: This is a basic number theory question from the odd man out and series topic. You are given the numbers 31, 37, 43 and 49. Most of these numbers are prime, meaning they have exactly two distinct positive divisors. One number is composite, meaning it has more than two factors. Your task is to identify the composite number as the odd one out. Given Data / Assumptions: Numbers: 31, 37, 43 and 49. Prime number: has exactly two positive divisors, 1 and itself. Composite number: has more than two positive divisors. Exactly one number in the list is composite. We only use basic divisibility and factor checks. Concept / Approach: The key concept here is the definition of prime and composite numbers. For numbers in the thirties and forties, a quick method is to test divisibility by small primes such as 2, 3, 5 and 7. If a number is not divisible by any of these small primes, and its square root is within that range, the number is prime. If it is divisible by one of these primes, it is composite. By applying this simple test to each option, we can find the number that is not prime. Step-by-Step Solution: Step 1: Check 31.31 is not divisible by 2, 3 or 5. 7^2 is 49, which is greater than 31. So 31 has no divisors other than 1 and 31, therefore it is prime.Step 2: Check 37.37 is not divisible by 2, 3 or 5. 7^2 is 49 which is greater than 37, so there are no smaller prime divisors. Therefore 37 is prime.Step 3: Check 43.43 is not divisible by 2, 3 or 5. Next prime 7 gives 7 * 6 = 42, 7 * 7 = 49, so 7 is not a divisor of 43. Hence 43 is also prime.Step 4: Check 49.49 is equal to 7 * 7. It has divisors 1, 7 and 49, so it is clearly composite.Step 5: Identify the odd number.Three numbers (31, 37 and 43) are prime, while 49 is composite. Therefore, 49 is the odd one out. Verification / Alternative check: A quick alternative check is to remember squares of small primes. You may know that 7^2 = 49, so 49 must be composite. None of the other numbers is a known square or simple product of small primes, and a rapid divisibility test confirms they are prime. This direct recognition of 49 as a square saves time and strongly supports the answer. Why Other Options Are Wrong: 31: It is a prime number and fits the majority pattern with 37 and 43. 37: This is also a prime number and therefore not the odd one. 43: Again a prime number, aligning with 31 and 37. Common Pitfalls: Some learners may rush and assume that all odd numbers are prime, which is incorrect. Composite odd numbers such as 9, 15 or 49 appear frequently in aptitude tests to trap this misconception. Always apply a quick divisibility check, especially by 3, 5 and 7, before deciding whether a number is prime. Familiarity with the squares of small primes also helps you quickly spot composite numbers like 49. Final Answer: The odd number is 49, because 31, 37 and 43 are prime numbers, while 49 is a composite number equal to 7 squared.

Question 8

In the following classification question on professions, four occupations are listed (Teacher, Lawyer, Doctor and Manager). Three are classic professional service roles, while one is a general organisational position rather than a specific professio…

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Introduction / Context: This question is from the verbal classification and odd man out section. You are given four occupational titles: Teacher, Lawyer, Doctor and Manager. Three of these clearly refer to well defined professions with specialised training and recognised professional roles in society. One term, however, is more of a general organisational designation that can exist in many fields. Your task is to pick the one that does not belong to the same category as the others. Given Data / Assumptions: Teacher: a professional who educates students in schools, colleges or other institutions. Lawyer: a legal professional who represents clients and advises on law. Doctor: a medical professional who diagnoses and treats patients. Manager: a job title that describes a person who manages resources or people in many different domains. Three terms refer to classical learned professions, while one is a broader role title. Concept / Approach: The central idea is differentiation between specific professions and general organisational roles. Teacher, Lawyer and Doctor are rooted in distinct disciplines (education, law and medicine). Each requires specialised study and often formal licensing. Manager, in contrast, is a generic position that can occur in any industry such as sales, operations or human resources. Therefore, in classification questions, Manager is typically treated as the odd one out when grouped with clearly defined professions like Teacher, Lawyer and Doctor. Step-by-Step Solution: Step 1: Consider Teacher.A Teacher works in the education sector, usually after obtaining specialised training or degrees in teaching and subject knowledge. It is a well recognised profession.Step 2: Consider Lawyer.A Lawyer is a legal professional who has studied law and is often registered with a bar council. It is a distinct profession.Step 3: Consider Doctor.A Doctor is a medical professional who completes medical education and training to treat patients. This is another classic profession.Step 4: Consider Manager.Manager is a wide role title that can be attached to many fields, such as sales manager or project manager. It describes a position rather than a specialised profession like law or medicine.Step 5: Identify the odd occupation.Teacher, Lawyer and Doctor are specialised professions, while Manager is a generic role, so Manager is the odd one out. Verification / Alternative check: Another way to verify is to ask which of these words can comfortably take the word profession directly, as in teaching profession, legal profession and medical profession. The word Manager is normally used with a qualifier and describes a post within an organisation, not a standalone profession in the same sense. This language based check confirms that Manager behaves differently from the other three terms. Why Other Options Are Wrong: Teacher: A specific professional role in education, not the odd one. Lawyer: A distinct legal professional, aligned with Doctor and Teacher. Doctor: A medical professional, again matching the nature of Lawyer and Teacher. Common Pitfalls: Some learners may think that Manager is also a job and therefore similar to the others. While that is true at a basic level, classification questions focus on more refined groupings. The intended difference here is between specialised professions that define entire fields of study and a broader organisational role that can occur in many industries. Recognising such subtle but common patterns will help you solve many reasoning questions more quickly. Final Answer: The odd word is Manager, because Teacher, Lawyer and Doctor are classic professional roles in specific disciplines, whereas Manager is a generic organisational position that can belong to any field.

Question 9

In the following alphabet reasoning question, four three letter groups are given (DEB, RTP, HIF and NOL). In three of these groups, the first two letters are consecutive in the alphabet, while in one group they are not. Find the odd word or letter g…

Accepted Answer

Introduction / Context: This question is about recognising simple letter patterns in the English alphabet. You are given four groups of three letters: DEB, RTP, HIF and NOL. The pattern is hidden in the relation between the first and second letters of each group. Most groups have the first two letters consecutive in the alphabet, while one group breaks this consecutive pattern. You must identify that group as the odd one out. Given Data / Assumptions: Letter groups: DEB, RTP, HIF and NOL. Alphabet positions: A = 1, B = 2, ..., Z = 26. We focus mainly on the relationship between the first and second letters. In three groups, the first two letters are consecutive alphabetically. Exactly one group does not have consecutive first and second letters. Concept / Approach: The approach is to examine each group and check whether the second letter is exactly one step after the first letter in the alphabet. If so, the pair is consecutive. If the difference is greater than 1, the pair is not consecutive. Once you have checked all four groups, the one where the first two letters do not form a consecutive pair will stand out as the odd group. This type of pattern is very common in coding and series questions involving letters. Step-by-Step Solution: Step 1: Analyse DEB.D = 4 and E = 5. Since 5 - 4 = 1, D and E are consecutive letters. The third letter B is not relevant to this particular pattern.Step 2: Analyse HIF.H = 8 and I = 9. Here 9 - 8 = 1, so H and I are consecutive letters. Third letter F is separate.Step 3: Analyse NOL.N = 14 and O = 15. Again 15 - 14 = 1, so N and O are consecutive letters.Step 4: Analyse RTP.R = 18 and T = 20. Now 20 - 18 = 2, which means R and T are not consecutive; there is one letter S between them.Step 5: Identify the odd group.Three groups (DEB, HIF and NOL) have first two letters consecutive, while RTP does not. Thus RTP is the odd one out. Verification / Alternative check: A quick visual check is to write the alphabet and mark the first two letters of each group. You will see D E, H I and N O appear as neighbours, but R and T appear with S between them. This clearly shows that RTP breaks the consecutive pattern. When you notice such patterns, always compare all options to be sure there is exactly one exception. Why Other Options Are Wrong: DEB: D and E are consecutive letters, so this group follows the main rule. HIF: H and I are consecutive, so this group also fits the pattern. NOL: N and O are consecutive, so this group belongs with DEB and HIF. Common Pitfalls: Sometimes students get distracted by the third letter and try to force a more complicated rule involving all three positions. In many exam questions, however, the key difference rests only in part of the group, such as the first two letters. Therefore, always check simple relationships first, such as adjacency or fixed gaps in the alphabet, before looking for more complex structures. Final Answer: The odd letter group is RTP, because its first two letters are not consecutive in the alphabet, while the first two letters of the other groups are consecutive pairs.

Question 10

In the following number pair reasoning question, four pairs of numbers are given: (6, 612), (5, 521), (4, 46) and (7, 543). In three pairs, the second number is formed by rearranging the digits of the cube of the first number, while one pair breaks …

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Introduction / Context: This question belongs to the number reasoning category with a focus on relationships between numbers in ordered pairs. You are given four pairs: (6, 612), (5, 521), (4, 46) and (7, 543). In such questions, the second number often comes from a transformation of the first number, such as squaring, cubing or rearranging digits. Here, the second number in most pairs is obtained by rearranging the digits of the cube of the first number. One pair fails to follow this cube based digit rearrangement pattern and must be selected as the odd one out. Given Data / Assumptions: Number pairs: (6, 612), (5, 521), (4, 46) and (7, 543). We are looking for a consistent rule linking the first number to the second. The cube of a number is computed as n^3 = n * n * n. In three pairs, the second number is a rearrangement of the digits of n^3. In one pair, this rule does not hold. Concept / Approach: The approach is to compute the cube of each first number and then compare its digits with those of the corresponding second number. If the digits match in some rearranged order, then the pair follows the rule. If the digits differ, then that pair breaks the pattern. Because the numbers involved are small, calculating cubes like 4^3, 5^3, 6^3 and 7^3 is quick, making this an accessible but slightly tricky number puzzle. Step-by-Step Solution: Step 1: Analyse the pair (6, 612).Compute 6^3 = 6 * 6 * 6 = 216. The digits of 216 are 2, 1 and 6, which can be rearranged to form 612. So this pair follows the pattern.Step 2: Analyse the pair (5, 521).Compute 5^3 = 125. The digits 1, 2 and 5 can be rearranged to form 521. So this pair also follows the rule.Step 3: Analyse the pair (4, 46).Compute 4^3 = 64. The digits 6 and 4 can be rearranged to form 46. Thus, this pair again follows the pattern.Step 4: Analyse the pair (7, 543).Compute 7^3 = 343. The digits are 3, 4 and 3, but the second number is 543 which uses digits 5, 4 and 3. The digit 5 does not appear in 343, so this pair does not follow the rule.Step 5: Identify the odd pair.The pair (7, 543) is inconsistent with the cube digit rearrangement pattern, so it is the odd one out. Verification / Alternative check: An alternative verification is to list quickly the cubes involved: 4^3 = 64, 5^3 = 125, 6^3 = 216 and 7^3 = 343. For the first three pairs, you can see that the second number uses exactly the same digits as the cube, just in a different order. For the fourth pair, the cube 343 has no digit 5, yet the second number 543 includes a 5. This contradiction confirms that the fourth pair breaks the pattern and should be selected. Why Other Options Are Wrong: 6 , 612: Follows the pattern because 612 is a rearrangement of 6^3 = 216. 5 , 521: Follows the pattern because 521 is a rearrangement of 5^3 = 125. 4 , 46: Follows the pattern because 46 is a rearrangement of 4^3 = 64. Common Pitfalls: Candidates sometimes search for direct arithmetic operations, such as multiplication or addition, between the two numbers and miss digit based relationships. Another error is miscalculating cubes, especially if you are not comfortable with mental arithmetic. To avoid mistakes, always compute the small cubes carefully and consciously compare digits. Recognising digit rearrangement patterns is an important skill for many reasoning questions. Final Answer: The odd number pair is 7 , 543, because its second number is not formed by rearranging the digits of the cube of the first number, whereas the other three pairs follow this rule.

Question 11

In the following alphabet pattern question, four two letter groups are given (AJ, EN, NW and PW). In three of these groups, the second letter is 9 positions ahead of the first letter in the alphabet, while one group has a different gap. Select the o…

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Introduction / Context: This question checks your ability to recognise fixed gaps between letters in the English alphabet. You are given four letter pairs: AJ, EN, NW and PW. In most of these pairs, the second letter is a fixed number of positions ahead of the first letter. One pair does not follow the same alphabetical gap. Your goal is to find the pair that breaks the pattern and mark it as the odd one out. Given Data / Assumptions: Letter pairs: AJ, EN, NW and PW. Alphabet positions: A = 1, B = 2, ..., Z = 26. We compare the positions of the first and second letters in each pair. Three pairs share the same positive gap, while one pair has a different gap. No other hidden coding rule is assumed. Concept / Approach: The approach is very direct: convert letters to their numerical positions and subtract the first position from the second. If three pairs have a difference of +9 and one pair has a different difference, that pair is the odd one. Fixed gap patterns like +3, +5 or +9 are common in letter series questions, so training yourself to quickly compute these differences can speed up your performance in reasoning sections. Step-by-Step Solution: Step 1: Analyse AJ.A = 1 and J = 10. Difference: 10 - 1 = 9. So AJ has a gap of +9.Step 2: Analyse EN.E = 5 and N = 14. Difference: 14 - 5 = 9. EN also has a gap of +9.Step 3: Analyse NW.N = 14 and W = 23. Difference: 23 - 14 = 9. NW again has a gap of +9.Step 4: Analyse PW.P = 16 and W = 23. Difference: 23 - 16 = 7. The gap here is +7, not +9.Step 5: Identify the odd pair.Since AJ, EN and NW all use a +9 jump, PW with a +7 jump is the odd letter group. Verification / Alternative check: You can also perform a quick mental check by counting forward from each first letter. From A, count nine letters forward (including the next letter), you land at J. From E, nine letters ahead is N. From N, nine letters ahead is W. But from P, nine letters ahead would be Y, not W. This again confirms that PW has a different spacing and therefore does not fit the rule followed by the other three pairs. Why Other Options Are Wrong: AJ: Second letter is 9 positions ahead of the first, fitting the main pattern. EN: Also shows a gap of +9 and is therefore not odd. NW: Has the same +9 gap and belongs with AJ and EN. Common Pitfalls: Some candidates might attempt to see meaning based connections between letters or read them as abbreviations. In examination settings, patterns are usually purely positional. Another common error is miscounting the number of steps between letters, especially under time pressure. Writing down the numerical positions or counting carefully on fingers or a rough diagram helps avoid small arithmetic mistakes. Final Answer: The odd letter group is PW, because its letters differ by 7 positions in the alphabet, whereas the other three pairs all have a fixed gap of 9 positions between the first and second letters.

Question 12

In the following number classification question, four numbers are given (170, 290, 360 and 530). Three of these are 10 times a prime number, while one is not of that form. Select the odd number from the given alternatives.

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Introduction / Context: This question comes from the number reasoning and classification section. The numbers 170, 290, 360 and 530 all end with a zero, suggesting that each might be 10 times some smaller integer. In three of these cases, the smaller integer is a prime number, while in one case it is composite. You need to recognise this structure and select the number that does not fit the pattern as the odd one out. Given Data / Assumptions: Numbers: 170, 290, 360 and 530. Each number can be written as 10 multiplied by another integer. A prime number has exactly two positive divisors. Three numbers are of the form 10 * prime, while one is 10 * composite. No more complicated operations are required. Concept / Approach: Because all four numbers end in zero, we can factor out 10 from each option and inspect the remaining factor. If the remaining factor is a prime number, then the original number can be described as 10 times a prime. The one number whose remaining factor is not prime will be the odd one out. This simple factorisation approach is an efficient way to tackle such questions in competitive exams. Step-by-Step Solution: Step 1: Factor 170.170 = 10 * 17. The factor 17 is a prime number.Step 2: Factor 290.290 = 10 * 29. The factor 29 is a prime number.Step 3: Factor 530.530 = 10 * 53. The factor 53 is a prime number.Step 4: Factor 360.360 = 10 * 36. The factor 36 is not prime; it can be written as 6 * 6 or 4 * 9, so it is composite.Step 5: Identify the odd number.Since 170, 290 and 530 are 10 times prime numbers, and 360 is 10 times a composite number, 360 is the odd one out. Verification / Alternative check: An alternative check is to perform prime testing directly on the factors. For 17, 29 and 53, none of these factors are divisible by 2, 3 or 5, and their square roots are less than 8, so they can be safely identified as primes. For 36, it is obvious that 36 = 6 * 6, making it composite. This practical test reconfirms that only 360 has a composite factor after removing the common factor 10. Why Other Options Are Wrong: 170: Equal to 10 * 17, where 17 is prime, so it fits the main pattern. 290: Equal to 10 * 29, where 29 is prime, so it is not the odd one. 530: Equal to 10 * 53, with 53 prime, again matching the pattern. Common Pitfalls: Some students might look for patterns in the sum of digits or differences between the numbers instead of checking factors. While such patterns sometimes exist, the cleanest and most reliable pattern here is the prime factor structure. Always try simple factorisation or divisibility rules first when dealing with numbers ending in zero or five, as it often reveals the intended logic quickly. Final Answer: The odd number is 360, because 170, 290 and 530 are 10 times prime numbers, whereas 360 is 10 times the composite number 36.

Question 13

In the following word relationship question, four word pairs are given (Calendar : Dates, Dairy : Milk, Notebook : Notes and Accounts : Entries). In three pairs, the first item is something that stores or records the second item, while one pair show…

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Introduction / Context: This verbal reasoning question explores relationships between word pairs. The pairs are Calendar : Dates, Dairy : Milk, Notebook : Notes and Accounts : Entries. In three of these pairs, the first item serves as a medium or place where the second item is recorded or stored. In one pair, the relation is different: the first produces the second. Your task is to identify this different relationship and mark that pair as the odd one out. Given Data / Assumptions: Calendar : Dates – a calendar is used to display or record dates. Dairy : Milk – a dairy is a place or industry that produces or processes milk. Notebook : Notes – a notebook is used to write and store notes. Accounts : Entries – accounts consist of recorded entries of transactions. We classify pairs as storage or record relationships versus producer product relationships. Concept / Approach: The main idea is to examine what role the first word plays with respect to the second. For Calendar, Notebook and Accounts, the second item is content that appears inside or is maintained within the first item. They have a container content or record relationship. Dairy, on the other hand, is not a container for milk in the same sense; it is an organisation or establishment that produces, processes or distributes milk. This makes Dairy : Milk fundamentally different, and thus the odd one out. Step-by-Step Solution: Step 1: Analyse Calendar : Dates.A calendar is specifically designed to show days, months and dates. Dates are recorded or displayed in a calendar, so the relationship is that the calendar stores or organises dates.Step 2: Analyse Notebook : Notes.A notebook is a place where notes are written and stored. Here again, the notebook acts as a container for the notes.Step 3: Analyse Accounts : Entries.Accounts are financial records consisting of many entries. The entries are the individual records that form the accounts. So accounts store entries.Step 4: Analyse Dairy : Milk.A dairy is an enterprise that produces or processes milk. Milk is not something stored as content in a book like the other examples; instead, it is the product of the dairy. This relationship is producer product, not container content.Step 5: Identify the odd pair.Since Calendar, Notebook and Accounts all hold or store their associated items, and Dairy produces milk, Dairy : Milk is the odd pair. Verification / Alternative check: You can also think in terms of what questions you can sensibly ask. You can ask “What does a calendar contain?” and answer “Dates.” You can ask “What does a notebook contain?” and answer “Notes.” For accounts, you ask “What do accounts contain?” and answer “Entries.” However, if you ask “What does a dairy contain?” the natural answer would be cows, employees or equipment, not milk as a stored record. Milk is something produced and sent out. This language based reasoning confirms that Dairy : Milk is distinct. Why Other Options Are Wrong: Calendar : Dates: The second item is content displayed or recorded in the first, so it follows the main pattern. Notebook : Notes: The notebook holds notes, again matching the container content relationship. Accounts : Entries: Accounts are made up of entries, so this pair also fits the storage or record idea. Common Pitfalls: Some learners might think of a dairy as a building that contains milk products and therefore confuse it with a storage relationship. In logical classification questions, however, the more important relation is that a dairy is a production or processing unit, not a recording medium. Keeping this distinction clear will help you answer similar analogy and relationship questions more accurately. Final Answer: The odd word pair is Dairy : Milk, because Dairy produces or processes milk, whereas Calendar, Notebook and Accounts are places where dates, notes and entries are recorded or stored.

Question 14

In the following question on letter classification, four single letters are given (M, E, S and W). Three of these letters are commonly used to represent cardinal directions on a map, while one letter is not used as a direction symbol. Select the odd…

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Introduction / Context: This question tests your basic general knowledge and pattern recognition involving common abbreviations. The letters given are M, E, S and W. On a compass or a map, the main cardinal directions are represented by single letters: N for North, E for East, S for South and W for West. Three of the given letters match these direction abbreviations, while one does not. Your task is to identify the letter that is not used as a compass direction symbol. Given Data / Assumptions: Options: M, E, S and W. Standard cardinal directions: North, East, South and West. These directions are abbreviated as N, E, S and W on maps and compasses. We work with these common conventions, not any specialised codes. Exactly one letter in the list does not correspond to a cardinal direction abbreviation. Concept / Approach: The approach is to recall the abbreviations for the four main directions. East is written as E, South as S and West as W. The remaining direction North is written as N, not as M. Therefore, E, S and W clearly match the usual direction letters, while M does not. So M must be the odd letter. This type of classification question checks everyday awareness and the ability to connect letters with standard real world meanings. Step-by-Step Solution: Step 1: List the cardinal directions.The main directions are North, East, South and West.Step 2: Recall their standard abbreviations.North is N, East is E, South is S and West is W.Step 3: Compare each option.E matches East, S matches South and W matches West.Step 4: Check the remaining letter M.M does not correspond to any of the four main cardinal directions. It is not used as a standard direction symbol.Step 5: Identify the odd letter.Therefore, M is the odd letter among the options. Verification / Alternative check: You can double check by imagining a compass diagram with four arrows. Each arrow is labelled with N, E, S or W. Now compare these labels with the given letters. You immediately find three matches (E, S and W). The letter M does not appear anywhere on this basic compass representation, which confirms it as the outlier. Why Other Options Are Wrong: E: Represents East on maps and compasses, so it fits the direction abbreviation pattern. S: Represents South, another of the four cardinal directions. W: Represents West, again a standard compass direction. Common Pitfalls: This is a simple question, but some candidates may overthink and search for more complex letter patterns. In many reasoning tests, however, examiners deliberately include straightforward questions to reward clear recall of basic facts. When you see common letters like E, S and W together, it is useful to immediately think of compass directions and map symbols, which leads directly to the correct classification. Final Answer: The odd letter is M, because E, S and W are standard abbreviations for East, South and West, whereas M is not used as a cardinal direction symbol.

Question 15

In the following number classification question, four numbers are given (26, 50, 82 and 120). In three of them, the number can be written as n^2 + 1 for an odd integer n, while one number follows a different rule. Select the odd number from the give…

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Introduction / Context: This question is from the odd one out and number pattern topic. The numbers 26, 50, 82 and 120 appear unrelated, but they are actually close to perfect squares. By examining how each number relates to the square of a nearby odd integer, you can find that three follow the pattern n^2 + 1, while one does not. That non matching number is the required odd one out. Given Data / Assumptions: Numbers: 26, 50, 82 and 120. We consider nearby perfect squares of odd integers. Perfect squares of odd numbers: 5^2 = 25, 7^2 = 49, 9^2 = 81, 11^2 = 121 and so on. Three numbers equal square of an odd number plus 1. One number equals square of an odd number minus 1. Concept / Approach: The strategy is to compare each given number with nearby perfect squares and see whether it is one more or one less than a square. In many reasoning questions, a series is built from expressions like n^2 + 1 or n^2 - 1 with n increasing in steps. Here, 26, 50 and 82 fit n^2 + 1 for n = 5, 7 and 9 respectively, whereas 120 fits 11^2 - 1. Recognising this contrast leads directly to the correct answer. Step-by-Step Solution: Step 1: Compare 26 with nearby squares.5^2 = 25, so 25 + 1 = 26. Thus 26 = 5^2 + 1.Step 2: Compare 50 with nearby squares.7^2 = 49, so 49 + 1 = 50. Thus 50 = 7^2 + 1.Step 3: Compare 82 with nearby squares.9^2 = 81, so 81 + 1 = 82. Thus 82 = 9^2 + 1.Step 4: Compare 120 with nearby squares.11^2 = 121. Now 121 - 1 = 120, so 120 = 11^2 - 1, not 11^2 + 1.Step 5: Identify the odd number.Three numbers fit the rule n^2 + 1 for odd n, but 120 fits n^2 - 1. Therefore, 120 is the odd one out. Verification / Alternative check: To verify, you can list the sequence of n^2 + 1 for n = 5, 7, 9 and 11. You get 26, 50, 82 and 122. Among the given options, 26, 50 and 82 appear in this list, but 120 does not. Instead, 120 appears in the sequence n^2 - 1 for n = 11, which gives 121 - 1 = 120. This confirms that 120 belongs to a different pattern than the other three numbers. Why Other Options Are Wrong: 26: Equal to 5^2 + 1, matches the main pattern. 50: Equal to 7^2 + 1, again following the same rule. 82: Equal to 9^2 + 1, also consistent with the n^2 + 1 structure. Common Pitfalls: Many students first attempt to look at differences between numbers or factors, which can make the pattern hard to see. When numbers are close to well known squares like 25, 49, 81 or 121, a better first step is to check whether they are one more or one less than these squares. Remembering squares of odd integers up to at least 15^2 gives you a strong advantage in detecting such patterns quickly. Final Answer: The odd number is 120, because 26, 50 and 82 are of the form n^2 + 1 for odd n, whereas 120 is of the form n^2 - 1 for n = 11.

Question 16

In the following number series question, you are given the sequence 7, 26, ?, 124, 215, 342. The pattern is based on adding successively larger differences. Select the missing number from the given alternatives.

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Introduction / Context: This question tests your skill in recognising patterns in number sequences. The given series is 7, 26, ?, 124, 215, 342. One term in the middle is missing, and you must determine it using the pattern followed by the rest of the sequence. Such series often use differences that themselves follow a smaller sequence or rule, so analysing the gaps between terms is the key to solving the problem. Given Data / Assumptions: Known terms: 7, 26, ?, 124, 215, 342. The missing term is between 26 and 124. Options for the missing term: 63, 65, 66 and 67. We assume a consistent rule for the differences between consecutive terms. Differences may themselves form a simple increasing pattern. Concept / Approach: The standard approach for such series is to compute the differences between consecutive known terms. If those differences appear irregular, we check whether the differences of the differences form a pattern. Here, when we insert a candidate for the missing term and compute all the differences, we find that the differences follow a second level increasing pattern based on adding 18, 24, 30 and 36. This reveals a systematic design behind the series rather than random jumps. Step-by-Step Solution: Step 1: Let the missing term be X.The sequence becomes 7, 26, X, 124, 215, 342.Step 2: Compute the known differences around X in a general way.From 7 to 26, the difference is 26 - 7 = 19.From 26 to X, the difference is X - 26.From X to 124, the difference is 124 - X.From 124 to 215, the difference is 91.From 215 to 342, the difference is 127.Step 3: Look for a pattern in differences.Suppose the differences are 19, 37, 61, 91 and 127. This suggests X - 26 = 37 and 124 - X = 61.Step 4: Solve for X.From X - 26 = 37, we get X = 26 + 37 = 63. Check 124 - 63 = 61, which is consistent.Step 5: Verify the second level pattern in differences.Differences: 19, 37, 61, 91, 127. Now the increments between these are 37 - 19 = 18, 61 - 37 = 24, 91 - 61 = 30, 127 - 91 = 36. These increments themselves increase by 6 each time, showing a clear pattern. Verification / Alternative check: After inserting 63 into the series, write it completely as 7, 26, 63, 124, 215, 342. Check each difference: 26 - 7 = 19, 63 - 26 = 37, 124 - 63 = 61, 215 - 124 = 91 and 342 - 215 = 127. The pattern in these differences is that each new difference is larger than the previous one by 18, 24, 30 and 36 respectively. Since this structure is smooth and consistent, 63 is the only option that fits such a neat design, confirming it as the correct missing term. Why Other Options Are Wrong: 65, 66 and 67: If you substitute any of these instead of 63, the resulting differences do not form a consistent second level pattern with fixed increments between successive differences. This breaks the elegant structure observed with 63 and indicates that these choices are incorrect. Common Pitfalls: Students sometimes give up after checking only the first level differences, especially when the numbers look irregular. Another frequent mistake is trying only one candidate from the options without ensuring that a clean pattern holds for the entire sequence. For exam success, it is important to verify that your chosen term makes the sequence follow a simple and meaningful rule throughout, rather than working by guesswork. Final Answer: The missing number in the series is 63, so the complete sequence is 7, 26, 63, 124, 215, 342.

Question 17

In the following reasoning question, four groups of three numbers are given: (8, 23, 15), (17, 52, 33), (12, 35, 23) and (15, 44, 29). In three groups, the difference between the second and third number equals the first number, while one group does …

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Introduction / Context: This is a number relationship and classification question. You are given four ordered triples: (8, 23, 15), (17, 52, 33), (12, 35, 23) and (15, 44, 29). In such problems, the second and third numbers are usually related to the first by some arithmetic rule. Here, in most groups, the difference between the second and third number equals the first number, while one group breaks this pattern. You must identify that exceptional group as the odd one out. Given Data / Assumptions: Number triples: (8, 23, 15), (17, 52, 33), (12, 35, 23) and (15, 44, 29). We are looking for a simple arithmetic relation between the three numbers in each group. Difference between second and third numbers is a likely candidate for the pattern. In three groups, second number minus third number equals the first number. Exactly one group does not satisfy this rule. Concept / Approach: The easiest way to detect the pattern is to compute, for each group, the value of (second number minus third number) and compare it with the first number. If they match, the group follows the rule. If not, that group is the odd one out. This type of relationship is common in reasoning questions because it is simple but not always immediately obvious unless you systematically test it. Step-by-Step Solution: Step 1: Analyse (8, 23, 15).Compute 23 - 15 = 8, which exactly equals the first number. So this group follows the rule.Step 2: Analyse (12, 35, 23).Compute 35 - 23 = 12, again matching the first number. This group also follows the rule.Step 3: Analyse (15, 44, 29).Compute 44 - 29 = 15, which is equal to the first number. So this group fits the pattern.Step 4: Analyse (17, 52, 33).Compute 52 - 33 = 19, which does not equal the first number 17. So this group does not follow the same rule.Step 5: Identify the odd triple.Since three groups satisfy the condition second minus third equals first, and (17, 52, 33) does not, (17, 52, 33) is the odd one out. Verification / Alternative check: As an additional check, you can express the rule algebraically for the valid triples: if the group is (a, b, c), then b - c = a. Substitute values from each group to verify. For (8, 23, 15), 23 - 15 = 8. For (12, 35, 23), 35 - 23 = 12. For (15, 44, 29), 44 - 29 = 15. Only for (17, 52, 33) do we get 52 - 33 = 19 which is not equal to 17. This confirms that the second group is inconsistent with the general pattern. Why Other Options Are Wrong: (8, 23, 15): Follows b - c = a, so it is not the odd group. (12, 35, 23): Also obeys b - c = a and belongs with the main pattern. (15, 44, 29): Again satisfies the same relation and thus is not the exception. Common Pitfalls: Sometimes candidates try more complicated formulas like b = 3a - 1 or c = 2a - 1 and get lost in unnecessary algebra. In many triple based reasoning questions, simple operations such as addition, subtraction or doubling are sufficient. It is a good habit to check simple expressions like b + c, b - c or a + c before moving on to more complex possibilities, as that often reveals the intended pattern quickly. Final Answer: The odd number group is (17, 52, 33), because only in this group does the difference between the second and third numbers not equal the first number.

Question 18

In the following question on game classification, four games are listed (Baseball, Football, Hockey and Snooker). Three are outdoor field games played on a ground, while one is an indoor cue sport played on a table. Select the odd word from the give…

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Introduction / Context: This classification question focuses on differentiating between outdoor field sports and an indoor cue sport. The games listed are Baseball, Football, Hockey and Snooker. In three of these, teams play on a large outdoor ground or field, often involving running and tackling. One game is played indoors on a table using a cue and balls. Identifying this difference in playing environment and equipment will lead you to the odd one out. Given Data / Assumptions: Baseball: outdoor team game played on a diamond shaped field with bat and ball. Football: outdoor team sport played on a rectangular ground with a ball. Hockey: typically an outdoor field sport (in field hockey) played with sticks and a ball on a turf or grass ground. Snooker: indoor cue sport played on a baize covered table using a cue and coloured balls. We classify games as outdoor field sports versus indoor tabletop or cue sports. Concept / Approach: The concept is to group games based on the type of playing area and style. Baseball, Football and Hockey are all field based sports that require large outdoor grounds, many players and vigorous physical movement. Snooker, in contrast, is played indoors on a special table and focuses more on precision and cue control than running or physical contact. This clear difference in environment and gameplay makes Snooker the odd one out among the four options. Step-by-Step Solution: Step 1: Consider Baseball.Baseball is played outdoors on a field. It involves running between bases and fielding across a large area.Step 2: Consider Football.Football is also played outdoors on a large rectangular ground, with two teams trying to score goals.Step 3: Consider Hockey.In its common field form, Hockey is played outdoors on grass or artificial turf with sticks and a ball. It is again a field sport.Step 4: Consider Snooker.Snooker is played indoors on a special table. Players stand around the table and strike balls with a cue stick; there is no large field or outdoor setting.Step 5: Identify the odd game.Because Baseball, Football and Hockey are outdoor field games, and Snooker is an indoor cue sport, Snooker is the odd one out. Verification / Alternative check: To verify, imagine where each game is played in a typical sports complex. Baseball, Football and Hockey occupy big outdoor grounds or stadiums, while Snooker is found in indoor halls or clubs on tables. They also differ in the number of players: the field games require large teams, whereas snooker is often played one versus one or in small groups. These practical differences in setting and structure confirm that Snooker is categorically different from the other three. Why Other Options Are Wrong: Baseball: Outdoor field sport, belongs to the main category. Football: Another outdoor field sport, consistent with Baseball and Hockey. Hockey: Field game played outdoors, so it is not the odd one. Common Pitfalls: Some may think of ice hockey as an indoor game, but the more typical exam reference is field hockey, which is outdoor. Even if one considers ice hockey, it is still played in a large arena, not on a small table. The intended distinction is clearly between large field or arena sports and the confined, table based cue sport of Snooker. Keeping this broader context in mind avoids misclassification. Final Answer: The odd word is Snooker, because Baseball, Football and Hockey are outdoor field games, whereas Snooker is an indoor cue sport played on a table.

Question 19

In the following alphabet pattern question, four three letter groups are given (BOH, ERK, HUO and KXQ). In three of these groups, the first to second letter moves forward by 13 positions and the second to third letter moves backward by 7 positions i…

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Introduction / Context: This is an alphabet coding and pattern recognition question. You are given four letter groups: BOH, ERK, HUO and KXQ. In three of these groups, there is a consistent rule governing the jumps from the first letter to the second and from the second to the third. One group does not follow this rule. Your job is to identify which group breaks the pattern and therefore is the odd one out. Given Data / Assumptions: Letter groups: BOH, ERK, HUO and KXQ. Alphabet positions: A = 1, B = 2, ..., Z = 26. We examine differences between consecutive letters in each group. In three groups, first to second letter increases by 13 positions and second to third decreases by 7 positions. Exactly one group fails to satisfy the second part of this pattern. Concept / Approach: The approach is to convert each letter into its numerical position and calculate the difference between letters. The pattern here is that in three groups, second position minus first position equals +13, and third position minus second position equals -7. One group instead has a decrease of only 6 in the second jump. Identifying this group requires careful arithmetic but becomes straightforward once you write down the positions. Step-by-Step Solution: Step 1: Analyse BOH.B = 2, O = 15, H = 8. First jump: 15 - 2 = 13. Second jump: 8 - 15 = -7. So BOH follows the +13, -7 pattern.Step 2: Analyse ERK.E = 5, R = 18, K = 11. First jump: 18 - 5 = 13. Second jump: 11 - 18 = -7. ERK also follows the pattern.Step 3: Analyse KXQ.K = 11, X = 24, Q = 17. First jump: 24 - 11 = 13. Second jump: 17 - 24 = -7. So KXQ fits the same rule.Step 4: Analyse HUO.H = 8, U = 21, O = 15. First jump: 21 - 8 = 13, which is correct for the first part. Second jump: 15 - 21 = -6, not -7. So HUO breaks the second part of the rule.Step 5: Identify the odd group.BOH, ERK and KXQ all apply the +13, -7 pattern. Only HUO uses +13, -6, so HUO is the odd one out. Verification / Alternative check: To verify, you can sketch the alphabet with numbers and trace the moves. For example, starting at B (2), move 13 steps forward to reach O (15), then move 7 steps backward to reach H (8). Repeat this idea for E to R to K and K to X to Q. All three follow the same structure. When you attempt the same for H to U to O, you see that U back to O is only 6 steps, not 7. This visual check reinforces the conclusion that HUO is inconsistent with the established pattern. Why Other Options Are Wrong: BOH: Correctly follows the +13, -7 pattern and is therefore not odd. ERK: Also fits the same positional moves between letters. KXQ: Again satisfies the +13, -7 jumps and belongs to the main pattern. Common Pitfalls: The most common mistake is miscalculating alphabet positions or differences, especially when dealing with double digit positions like 18, 21 or 24. Another error is stopping after noticing that the first jump is +13 in all four groups and assuming that all groups are similar. The key to solving such questions is to check both the first and the second jumps for consistency across all options. Final Answer: The odd letter group is HUO, because its second jump between letters is -6, while in the other three groups the second jump is -7 after a first jump of +13.

Question 20

In the following number classification question, four numbers are given (145, 463, 581 and 651). Three of these are composite numbers, while one is a prime number. Select the odd number from the given alternatives.

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Introduction / Context: This question comes from the number theory and odd one out section. The numbers 145, 463, 581 and 651 must be checked for primality and factor structure. Three of them turn out to be composite numbers with non trivial factors, while one is a prime number with no divisors other than 1 and itself. Your task is to identify the prime number as the odd one out. Given Data / Assumptions: Numbers to analyse: 145, 463, 581 and 651. Prime number: has exactly two positive divisors, 1 and itself. Composite number: has more than two positive divisors. We apply divisibility tests using small primes such as 2, 3, 5, 7, 11, 13, 17 and 19. Exactly one number in the list is prime. Concept / Approach: The concept is simple prime testing for three digit numbers. For each number, we try dividing by small primes up to roughly the square root of the number. If no divisor works, the number is prime. If we find a non trivial factor, the number is composite. By applying this method to all four options, we can see which one is prime and therefore the odd one out in a set dominated by composite numbers. Step-by-Step Solution: Step 1: Test 145.145 ends in 5, so it is divisible by 5. In fact, 145 = 5 * 29. Therefore, 145 is composite.Step 2: Test 581.Check divisibility by 7: 7 * 80 = 560, 7 * 83 = 581. Therefore, 581 = 7 * 83 and is composite.Step 3: Test 651.Check divisibility by 3: sum of digits is 6 + 5 + 1 = 12, which is divisible by 3. Hence 651 is divisible by 3. Indeed, 651 = 3 * 217, so it is composite.Step 4: Test 463.463 is not even, so not divisible by 2. Sum of digits is 4 + 6 + 3 = 13, not divisible by 3, so not divisible by 3. It does not end in 0 or 5, so not divisible by 5.Step 5: Continue testing 463 with primes up to its square root.Square root of 463 is a little more than 21. Try 7: 7 * 66 = 462, so 7 is not a divisor. Try 11: 11 * 42 = 462. Try 13: 13 * 35 = 455. Try 17: 17 * 27 = 459. Try 19: 19 * 24 = 456. None divide 463 exactly, so 463 has no small prime divisors and is prime. Verification / Alternative check: Once you have factored 145, 581 and 651, it is clear they are composite. At that point, 463 is the only candidate left to be prime. A quick double check confirms there is no easy factor: its last digit is 3, ruling out divisibility by 2 and 5, and the digit sum is 13, ruling out divisibility by 3. Testing common primes up to 21 secures that 463 has no divisors, completing the verification that it is prime. Why Other Options Are Wrong: 145: Composite because 145 = 5 * 29. 581: Composite because 581 = 7 * 83. 651: Composite because 651 is divisible by 3 and can be factored further. Common Pitfalls: Students sometimes assume that any number ending in 1, 3, 7 or 9 is prime, which is not true. Many composite numbers, including 21 or 51, also end in these digits. In multiple choice tests, it is safer to run through quick divisibility tests and basic factorisation rather than relying on appearance. This habit ensures more reliable identification of primes and composites. Final Answer: The odd number is 463, because it is a prime number, whereas 145, 581 and 651 are composite numbers with non trivial factors.

Odd Man Out and Series Questions