Question 1

In the following question, select the odd letters from the given alternatives: IKM, OQS, GEC and UWY. In three of these letter groups, the letters are arranged in increasing alphabetical order with a constant step of +2 between consecutive letters, …

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Introduction / Context: This is a letter series odd one out question from the reasoning section. You are given four three-letter groups and must determine which group does not follow the same alphabetical pattern as the others. Three sequences go forward in the alphabet with equal steps, while one sequence goes backward, making it the odd one out. Given Data / Assumptions: Letter groups: IKM, OQS, GEC, UWY. Alphabet positions: A = 1, B = 2, ..., Z = 26. We will compute the position of each letter and examine whether the sequences are ascending or descending. We expect three groups to be ascending with a constant step and one to be descending. Concept / Approach: The approach is to: Convert letters to their numerical positions. Check the difference between consecutive letters. Note whether the letters are increasing or decreasing, and by how much. In three groups, the letters should increase by a fixed step of +2. In the odd group, the letters move in the opposite direction. Step-by-Step Solution: Step 1: For IKM: I = 9, K = 11, M = 13. Differences: K - I = 11 - 9 = 2, M - K = 13 - 11 = 2. This is an increasing sequence with a constant step of +2. Step 2: For OQS: O = 15, Q = 17, S = 19. Differences: Q - O = 17 - 15 = 2, S - Q = 19 - 17 = 2. Again, an increasing sequence with a step of +2. Step 3: For UWY: U = 21, W = 23, Y = 25. Differences: W - U = 23 - 21 = 2, Y - W = 25 - 23 = 2. Once more, an increasing sequence with a step of +2. Step 4: For GEC: G = 7, E = 5, C = 3. Differences: E - G = 5 - 7 = -2, C - E = 3 - 5 = -2. Here, the sequence is decreasing with a step of -2. Step 5: While IKM, OQS and UWY are ascending sequences with equal positive steps, GEC is a descending sequence with equal negative steps, making it different from the others. Verification / Alternative check: An alternative quick check is to recite the alphabet and see whether the letters in each group appear in forward order or reverse order: IKM: I, J, K, L, M – forward. OQS: O, P, Q, R, S – forward. UWY: U, V, W, X, Y – forward. GEC: G, F, E, D, C – backward. Only GEC clearly moves backwards in the alphabet, confirming it as the odd one out. Why Other Options Are Wrong: IKM is not odd because it is an increasing sequence with constant steps of +2. OQS is not odd because it also increases with steps of +2 between letters. UWY is not odd because it similarly follows the +2, +2 forward pattern. GEC alone moves backward in steps of -2, differing from the forward sequences of the others. Common Pitfalls: A common mistake is to focus only on the absolute size of the step and ignore the direction (forward or backward). While the step magnitude is 2 in all groups, the direction is crucial for this question. Another pitfall is misremembering alphabet positions or miscounting, so always check letter order carefully. Final Answer: The letter group that moves in the reverse direction and is therefore the odd one out is GEC.

Question 2

In the following question, select the odd number from the given alternatives: 341, 342, 810 and 405. Three of these numbers are divisible by 9, while one of them is not divisible by 9. Based on this divisibility property, which number is the odd one…

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Introduction / Context: This question is an odd one out problem based on divisibility rules. You are given four numbers and must determine which one does not share the same divisibility property as the others. Specifically, three of the numbers are divisible by 9, while one is not. Such questions are common in aptitude tests and help reinforce knowledge of divisibility rules. Given Data / Assumptions: Numbers: 341, 342, 810, 405. We will apply the divisibility rule for 9. According to this rule, a number is divisible by 9 if the sum of its digits is divisible by 9. Three numbers are expected to satisfy this rule, while one will not. Concept / Approach: The divisibility rule for 9 is: Add the digits of the number. If the total is a multiple of 9 (9, 18, 27, and so on), the number is divisible by 9. Using this, we will find which numbers are divisible by 9 and then identify the one that is not. Step-by-Step Solution: Step 1: Check 342. Sum of digits = 3 + 4 + 2 = 9. Since 9 is a multiple of 9, 342 is divisible by 9. Step 2: Check 810. Sum of digits = 8 + 1 + 0 = 9. Again, 9 is a multiple of 9, so 810 is divisible by 9. Step 3: Check 405. Sum of digits = 4 + 0 + 5 = 9. The sum is 9, so 405 is also divisible by 9. Step 4: Check 341. Sum of digits = 3 + 4 + 1 = 8. The sum 8 is not a multiple of 9, so 341 is not divisible by 9. Step 5: Therefore, 342, 810 and 405 are divisible by 9, but 341 is not. Hence, 341 is the odd one out. Verification / Alternative check: You can verify divisibility by actual division: 342 / 9 = 38, an integer. 810 / 9 = 90, an integer. 405 / 9 = 45, an integer. 341 / 9 is not an integer, as 9 * 37 = 333 and 9 * 38 = 342, so 341 lies between these two multiples. This confirms that only 341 fails the divisibility by 9 test. Why Other Options Are Wrong: 342 is not odd because it passes the divisibility by 9 rule and is exactly divisible by 9. 810 is not odd because it is also exactly divisible by 9. 405 is not odd because it too is divisible by 9. 341 is the only number not divisible by 9, so it stands out from the rest. Common Pitfalls: A common pitfall is to forget or misapply the divisibility rule and instead rely on approximate division or guesswork. Another mistake is to confuse the rule for 3 with the rule for 9. While both involve digit sums, only sums that are multiples of 9 guarantee divisibility by 9. Careful addition and checking of the final sum avoids these errors. Final Answer: The number that is not divisible by 9 and is therefore the odd one out is 341.

Question 3

In the following question, select the odd word/letters/number/number pair from the given alternatives: Dog, Cat, Goat and Lion. Three of these animals are primarily carnivores that feed mainly on meat, while one is a herbivore that feeds mainly on p…

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Introduction / Context: This is an odd one out question based on basic biology and animal classification. You are given four animals: Dog, Cat, Goat and Lion. While all are common animals, they differ in their typical diets. Three of them are primarily carnivorous, feeding largely on meat, while one is herbivorous, feeding mainly on plants. Your task is to identify which animal differs in terms of diet. Given Data / Assumptions: Animals listed: Dog, Cat, Goat, Lion. We consider their natural or typical diet in the wild or in general. Dogs, Cats and Lions are primarily meat eaters (carnivores or omnivores with strong carnivorous tendencies). Goats predominantly eat plants, making them herbivores. Concept / Approach: The main concept is dietary classification: Carnivores: animals that mainly eat meat (for example, lions and wild cats). Herbivores: animals that mainly eat plants (for example, goats, cows and deer). By grouping the animals according to these categories, we can clearly see which animal does not fit with the others. Step-by-Step Solution: Step 1: Consider Dog. Dogs, especially in the wild, have a strong preference for meat and are often classified as carnivores or omnivores with a strong carnivorous tendency. Step 2: Consider Cat. Domestic and wild cats (such as tigers and leopards) are classic carnivores that hunt and eat other animals. Step 3: Consider Lion. Lions are big cats and apex predators that are strictly carnivorous in the wild, relying almost entirely on meat. Step 4: Notice the common pattern: Dog, Cat and Lion all have diets based largely on animal flesh, placing them in or close to the carnivore group. Step 5: Consider Goat. Goats feed mainly on grass, leaves, shrubs and other plant materials, making them herbivorous animals. Step 6: Since Goat does not share the carnivorous nature of the other three animals, Goat is the odd one out. Verification / Alternative check: Another way to confirm is by placing them into diet-based groups: Carnivorous or strongly meat-based diet: Dog, Cat, Lion. Herbivorous diet: Goat. Because only Goat belongs to the herbivore category, it clearly stands apart from the others. Why Other Options Are Wrong: Dog is not odd because it is mainly a meat eater and fits with Cat and Lion. Cat is not odd because it is a carnivore and shares a similar diet pattern with Dog and Lion. Lion is not odd because it is a pure carnivore and strongly matches the dietary profile of the other meat-eating animals. Goat is the only herbivore in the list, making it fundamentally different in terms of diet. Common Pitfalls: Some students may get distracted by other classifications such as wild versus domestic animals. Although Lion is wild and Dog, Cat and Goat can be domesticated, the more consistent and intended classification here is based on diet. Focusing on the most prominent and widely tested characteristic, such as carnivore versus herbivore, leads to the correct answer. Final Answer: The herbivorous animal that differs from the meat-eating others and is therefore the odd one out is Goat.

Question 4

In this odd-man-out reasoning question, select the odd letter-number group from the given alternatives.

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Introduction / Context: This question belongs to the common aptitude topic called odd-man-out or classification. You are given four alphanumeric groups, and exactly one of them follows a different letter-number pattern compared with the others. Such questions test your ability to map letters to their positions in the English alphabet and to notice when a numeric value is deliberately linked to one of those positions. Given Data / Assumptions: Given groups: E5T, O9S, U3A and I7M. We assume standard English alphabet positions: A = 1, B = 2, ..., Z = 26. We look for a consistent pattern that three groups share and one group breaks. Concept / Approach: The most natural approach is to convert each letter to its numeric position in the alphabet and then compare that with the middle digit. For patterns of this kind, the digit may equal the position of the first letter, the last letter, the difference between them, or some other simple function. Once we compute and compare these values, the odd group will be the one that does not follow the shared rule. Step-by-Step Solution: Step 1: Write the alphabet positions of each letter. E = 5, T = 20, O = 15, S = 19, U = 21, A = 1, I = 9 and M = 13. Step 2: Analyse E5T. Here the first letter E has position 5 in the alphabet. The middle symbol is the digit 5, which exactly matches the alphabetical position of the first letter. Step 3: Analyse O9S. O has position 15, S has position 19, while the middle digit is 9. The digit 9 does not equal 15 or 19, nor is it a simple difference such as 19 - 15 = 4. Step 4: Analyse U3A. U has position 21 and A has position 1, while the digit is 3. Again, 3 does not match 21, 1 or an obvious difference such as 21 - 1 = 20. Step 5: Analyse I7M. I has position 9 and M has position 13. The digit 7 does not match 9 or 13, and the difference 13 - 9 = 4 is also different from 7. Step 6: Conclude that in O9S, U3A and I7M the middle digit has no direct equality link with the alphabetical position of the first letter, but in E5T the middle digit is exactly the same as the position of the first letter. Verification / Alternative check: As an additional check, we can attempt other simple rules such as the digit representing the position of the last letter, the average of positions of first and last letters, or their difference. None of these consistently fit three groups while excluding one. The only clean, simple and unique rule is that in E5T the digit equals the alphabetical position of the first letter. Since a good odd-man-out rule must single out exactly one option, this confirms E5T as the correct answer. Why Other Options Are Wrong: O9S is incorrect as the digit 9 does not match the position of O or S, nor does it represent a simple function of those positions that is shared by other groups. U3A is incorrect for the same reason: the digit 3 is unrelated to positions 21 and 1 in a way that matches other groups. I7M is also incorrect because 7 does not stand in a similar relationship to 9 and 13, so it cannot be the unique special group. Common Pitfalls: Many learners try to invent very complicated relationships like sums of positions or multi-step arithmetic. In standard exam reasoning questions, the intended pattern is usually simple and elegant. Another common mistake is to accept a pattern that fits only one or two groups instead of three. The correct approach is to identify a rule that holds for three options, leaving exactly one as the odd-man-out. Final Answer: The odd letter-number group is E5T because only in this group does the middle digit equal the alphabetical position of the first letter, while no such relationship holds for the other three groups.

Question 5

In this aptitude odd-man-out question, select the odd number from the given alternatives.

Accepted Answer

Introduction / Context: This is a basic aptitude odd-man-out question involving simple divisibility rules. You are given four two-digit numbers, and your task is to find the one that does not share a particular common property with the other three. Such questions check your number sense and your familiarity with divisibility by common factors like 3 and 5. Given Data / Assumptions: Numbers given: 45, 56, 55 and 78. We assume standard divisibility rules taught in school mathematics. We are looking for a property that three numbers share and one number does not. Concept / Approach: A natural way to tackle odd-man-out questions with numbers is to test divisibility by small primes such as 2, 3, 5, 7, 11 and so on. We want to find a single property that holds for exactly three of these numbers and fails for one of them. Among common exam patterns, divisibility by 3 or 5 appears frequently, because these rules are easy to verify using the digits of the numbers. Step-by-Step Solution: Step 1: Check divisibility by 5. A number is divisible by 5 if it ends with 0 or 5. Here, 45 and 55 end with 5, so they are divisible by 5. The numbers 56 and 78 do not end with 0 or 5, so they are not divisible by 5. Step 2: Check divisibility by 3. A number is divisible by 3 if the sum of its digits is divisible by 3. For 45, the digit sum is 4 + 5 = 9, which is divisible by 3. For 55, the sum is 5 + 5 = 10, which is not divisible by 3. For 56, the sum is 5 + 6 = 11, which is not divisible by 3. For 78, the sum is 7 + 8 = 15, which is divisible by 3. Step 3: Summarise the results. 45 is divisible by both 3 and 5. 55 is divisible by 5 but not by 3. 78 is divisible by 3 but not by 5. 56 is divisible by neither 3 nor 5. Step 4: Identify the common property. The numbers 45, 55 and 78 are all divisible by either 3 or 5. The number 56 is the only one that is not divisible by 3 and not divisible by 5. Step 5: Conclude that 56 is the odd number because it fails this simple divisibility property that the other three satisfy. Verification / Alternative check: We can double check by considering other possible patterns such as prime factors, parity (odd or even) or relationships with squares. Although 24 and 78 are even and 45 and 55 are odd, this does not create a 3 versus 1 split. Similarly, all four numbers are composite. The only neat and unique pattern here is the one based on divisibility by 3 or 5, which clearly isolates 56. Why Other Options Are Wrong: 45 is not odd-man-out because it is divisible by 3 and 5, so it fits the rule that the number is divisible by at least one of 3 or 5. 55 also fits because it is divisible by 5. 78 fits because it is divisible by 3. Only 56 does not satisfy divisibility by 3 or 5, so the other three are part of the same group and are not the answer. Common Pitfalls: A common mistake is to focus only on whether the numbers are odd or even and quickly choose any even number as the answer. However, in this set, 56 and 78 are both even, so parity alone cannot isolate a single odd-man-out. Another mistake is to look for overly complex patterns when a simple divisibility rule is sufficient. Always test small primes first, because exam questions usually rely on straightforward and elegant properties. Final Answer: The odd number in the list is 56, because it is the only number that is not divisible by 3 or 5, while the other three numbers are divisible by at least one of these two common factors.

Question 6

In this classification question on means of transport, select the odd word from the given alternatives.

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Introduction / Context: This is a simple verbal classification or odd-man-out question based on common means of transport. You are given four vehicle-related words, and you need to identify which one represents a qualitatively different category. Such questions check everyday general knowledge and your ability to group items by basic shared properties like medium of travel, design and usage. Given Data / Assumptions: Options: Truck, Car, Motorcycle and Airplane. All four are vehicles used to transport people or goods. We assume standard meanings of these common English words. Concept / Approach: To solve a verbal odd-man-out question, we try to group the options by obvious categories. The most natural classification here is by the medium in which the vehicle operates: on land, on water or in air. Another secondary classification could be based on having wheels, running on roads or being a typical road transport vehicle. The key is to find a single property that three options share and one clearly does not share. Step-by-Step Solution: Step 1: Consider the vehicle Truck. A truck is a heavy motor vehicle that moves on roads using wheels and is used for transporting goods on land. Step 2: Consider the vehicle Car. A car is a smaller motor vehicle, also road based, with wheels, and is used for carrying passengers on land. Step 3: Consider the vehicle Motorcycle. A motorcycle is a two-wheeler with an engine that also runs on roads and is mainly used for carrying one or two people on land. Step 4: Consider the vehicle Airplane. An airplane is an aircraft designed for flying through the air at high altitude, using wings and engines. It travels in the air and not on roads. Step 5: Compare the groups. Truck, Car and Motorcycle are all road vehicles that move on land on wheels. Airplane is an aircraft that moves in the air and does not primarily use roads. Step 6: Conclude that Airplane is the odd word because its mode of travel is air, whereas the other three are land vehicles. Verification / Alternative check: We can also check other features like typical usage, number of wheels and size. Although a car and a motorcycle differ greatly in size and wheel count, both are clearly road vehicles, as is a truck. All three are part of the broader category of motor road transport. Airplane stands apart in every such comparison, because it requires runways and airspace and is governed by aviation rules, not road traffic rules. This confirms our choice. Why Other Options Are Wrong: Truck is not odd because it belongs with Car and Motorcycle as a wheeled road vehicle that operates on land. Car is also in the same category of road transport, so it cannot be the odd choice. Motorcycle, despite being a two-wheeler, is still a land vehicle and fits with the other two. Only Airplane belongs to air transport and is therefore the odd one out. Common Pitfalls: Some learners get distracted by differences in size or load capacity and may incorrectly mark Truck as odd because it is much larger and used mainly for goods. However, the odd-man-out concept is about shared fundamental category, not minor differences. The best habit is to first check the broadest property, such as medium of travel, before considering any less important details. Final Answer: The odd word is Airplane, because it is an air transport vehicle, whereas Truck, Car and Motorcycle are all land vehicles that operate on roads.

Question 7

In this letter-classification odd-man-out question, select the odd group of letters from the given alternatives.

Accepted Answer

Introduction / Context: This question is a classic letter-series odd-man-out item from reasoning and aptitude tests. Each option is a group of three letters. Typically, such letter groups follow a fixed pattern based on positions of letters in the English alphabet. Three options follow a similar positional pattern, and one breaks that pattern. Your task is to detect the pattern and identify the group that does not fit. Given Data / Assumptions: Options: FLR, KQW, PIB and CIO. We assume the standard English alphabet with positions A = 1 to Z = 26. We look for numerical relationships among the positions of the three letters in each group. Concept / Approach: In letter classification questions, a common pattern is a fixed difference between consecutive letters in each group. For example, letters may be spaced by plus 2, plus 3 or plus 6 positions. To apply this approach, we convert each letter into its alphabet position and then study the jumps from first to second and from second to third letters. The group that does not follow the shared difference rule will be the odd-man-out. Step-by-Step Solution: Step 1: Write the alphabet positions. F = 6, L = 12, R = 18, K = 11, Q = 17, W = 23, P = 16, I = 9, B = 2, C = 3, I = 9 and O = 15. Step 2: Analyse FLR. The differences are L - F = 12 - 6 = 6 and R - L = 18 - 12 = 6. So in FLR, consecutive letters increase by 6 positions each time. Step 3: Analyse KQW. The differences are Q - K = 17 - 11 = 6 and W - Q = 23 - 17 = 6. Again we have increases of 6 and 6, matching the same pattern. Step 4: Analyse CIO. The differences are I - C = 9 - 3 = 6 and O - I = 15 - 9 = 6. Once more, both jumps are plus 6, so CIO also follows the same rule. Step 5: Analyse PIB. The positions are P = 16, I = 9 and B = 2. Now the differences are I - P = 9 - 16 = -7 and B - I = 2 - 9 = -7. In PIB, both jumps are minus 7, that is, letters move backward in the alphabet instead of forward by 6. Step 6: Compare the patterns. FLR, KQW and CIO have a consistent pattern of +6 and +6, while PIB has a pattern of -7 and -7. PIB clearly does not follow the same forward spacing rule and is therefore the odd group. Verification / Alternative check: We can verify our conclusion by checking if any other simple rule could make PIB similar to the others, such as equal absolute difference ignoring direction. However, the others all move forward, not backward, and their absolute difference is 6, not 7. No alternative symmetric rule unites PIB with the other three without breaking their clean +6 structure. Thus, identifying PIB as the odd one out is consistent and logically sound. Why Other Options Are Wrong: FLR is not odd because its letters progress forward by 6 positions each time and match the pattern. KQW also follows +6 and +6, so it is part of the majority group. CIO satisfies the same rule and is therefore similar. PIB alone uses backward jumps of -7, which makes it different from all the others, so the other three cannot be the answer. Common Pitfalls: Students sometimes only look at the first and third letter and try to guess a pattern based on the overall span, ignoring the second letter. Others may assume that any group with reversed direction is acceptable, without checking for consistency across options. In classification questions, it is important to confirm that a single rule applies to three options and fails for exactly one option. Always compute the numerical differences rather than relying purely on visual guesswork. Final Answer: The odd group of letters is PIB, because in this group the letters move backward by 7 positions, whereas in all the other groups the letters move forward by 6 positions each time.

Question 8

In this number-classification question, select the odd four-digit number from the given alternatives.

Accepted Answer

Introduction / Context: This is a straightforward numerical odd-man-out question. You are given four four-digit numbers, and exactly one of them is structurally different from the rest. Questions like this often use a simple visible property such as divisibility by 10, pattern of digits or multiples of a certain base. Your goal is to quickly test these obvious properties and find the one number that does not fit. Given Data / Assumptions: Numbers given: 6210, 7020, 1431 and 1280. We use standard base 10 representation. We are looking for a common structural property that three numbers share and one does not share. Concept / Approach: One of the easiest structural properties to check with four-digit numbers is whether they end in zero. Numbers that end in zero are multiples of 10. Often, exam setters give three multiples of 10 and one number that is not a multiple of 10 to create a quick odd-man-out question. Therefore we start by checking the unit digit of each number, which requires minimal computation and gives an immediate pattern if it exists. Step-by-Step Solution: Step 1: Observe the unit digits. For 6210, the last digit is 0. For 7020, the last digit is again 0. For 1431, the last digit is 1. For 1280, the last digit is 0. Step 2: Identify which numbers are multiples of 10. A number is a multiple of 10 if it ends in 0. Therefore, 6210, 7020 and 1280 are all multiples of 10. The number 1431 ends in 1, so it is not a multiple of 10. Step 3: Check whether any other simple pattern could change our conclusion. For instance, 6210, 7020 and 1280 are even numbers and also divisible by 10. The number 1431 is odd and not divisible by 10. Thus 1431 clearly behaves differently. Step 4: Since three numbers are divisible by 10 and one is not, the one that is not divisible by 10 must be the odd-man-out under a clean and simple rule. Step 5: Conclude that 1431 is the odd number. Verification / Alternative check: To confirm, we can also examine other properties, such as the sum of digits. However, such checks are not necessary when we already have a strong and simple pattern that matches three numbers exactly. None of the alternative observations like being even or odd, or specific prime factorisations, provide as tidy a 3 versus 1 split as the divisibility by 10 property does. This strengthens our confidence that the intended classification is based on the last digit of the numbers, making 1431 the correct choice. Why Other Options Are Wrong: 6210 is not odd because it ends with 0 and is a multiple of 10, just like 7020 and 1280. 7020 also ends with 0 and fits into the same group. 1280 ends with 0 and is a multiple of 10 as well. Therefore, these three numbers form a similar class. Only 1431 breaks this pattern because it ends with 1 and is not a multiple of 10, so the other three options are not valid odd-men-out choices. Common Pitfalls: Learners sometimes overcomplicate such questions by searching for hidden factor patterns or digit sum relationships. While such patterns can appear in some questions, in many classification items the examiner expects you to notice very simple features like ending digits, parity or basic divisibility. Ignoring these obvious checks and jumping straight into heavy calculations can waste time and still miss the correct pattern. The safe strategy is to first check simple visible properties such as last digit, number of digits and divisibility by 10 or 5. Final Answer: The odd number is 1431, because it is the only number that is not a multiple of 10, whereas 6210, 7020 and 1280 all end in zero and are divisible by 10.

Question 9

In this number-classification odd-man-out question, select the number that does not follow the same divisibility pattern as the others.

Accepted Answer

Introduction / Context: This is a numerical odd-man-out question where all the options are two or three digit integers. The task is to detect a property common to three of them and absent in one. Many such questions use divisibility by a fixed prime as the hidden theme. Here, checking divisibility by 17 reveals a neat and unique pattern that allows us to identify the odd number quickly. Given Data / Assumptions: Numbers given: 86, 68, 136 and 102. We use standard integer arithmetic and divisibility. We aim to find one number that does not share a key divisor with the other three. Concept / Approach: A good way to approach such questions is to check for common divisors. Because the numbers are not extremely large, we can try divisibility by primes like 2, 3, 5, 7, 11, 13 and 17. Once we see that several numbers share a specific prime factor, we can verify whether one number is missing that factor. If so, that number is the odd-man-out. In this problem, all four numbers are even, so divisibility by 2 does not help, but checking divisibility by 17 is productive. Step-by-Step Solution: Step 1: Factor 68. Divide 68 by 17. We get 68 / 17 = 4, so 68 is a multiple of 17. Step 2: Factor 136. Divide 136 by 17. We get 136 / 17 = 8, so 136 is also a multiple of 17. Step 3: Factor 102. Divide 102 by 17. We get 102 / 17 = 6, so 102 is again a multiple of 17. Step 4: Check 86 for divisibility by 17. Divide 86 by 17. We get 86 / 17 = 5.0588..., which is not an integer. Therefore, 86 is not divisible by 17. Step 5: Summarise. We have discovered that 68, 136 and 102 are all divisible by 17, while 86 is not. Step 6: Conclude that since three numbers share the prime factor 17 and one does not, the number that is not divisible by 17 is the odd-man-out. Verification / Alternative check: We can look briefly at other properties such as multiples of 4, 8 or 3. For example, 68, 136 and 102 are all even, and so is 86, so parity does not help. Some of them are divisible by 4, but not all of them, and that does not create a clean 3 versus 1 split. The only elegant classification that clearly groups three numbers together is based on the factor 17. Therefore, any alternative scheme is either more contrived or fails to satisfy the odd-man-out condition cleanly. Why Other Options Are Wrong: 68 is not the odd number because it is divisible by 17 and stands in the same class as 136 and 102. 136 is often noticed as a larger number, but size alone is not the basis of classification here; it is divisible by 17 just like the others. 102 also shares the factor 17. These three numbers therefore belong to one category. Only 86 fails the divisibility by 17 test and is consequently different from the rest. Common Pitfalls: A frequent error is to choose a number simply because it looks different, for example by being the smallest or largest, without checking arithmetic properties. Another mistake is to stop after checking divisibility by 2 or 3 and assuming there is no pattern. In exam situations, once you see that all numbers are even, it is a good idea to test slightly larger primes such as 7, 11, 13 or 17. This often reveals the intended classification, as it does very cleanly in this question. Final Answer: The odd number is 86, because 68, 136 and 102 are all divisible by 17, whereas 86 is not a multiple of 17.

Question 10

In this vocabulary-based odd-man-out question, select the odd word from the given alternatives.

Accepted Answer

Introduction / Context: This is a verbal reasoning question that tests basic vocabulary and classification skills. The idea is to spot which word does not belong to the same general category as the others. Three options represent occupations, while one option represents an abstract concept rather than a profession. Identifying this difference correctly is the key to solving the problem. Given Data / Assumptions: Options provided: Teacher, Justice, Lawyer and Chef. We assume standard dictionary meanings of these English words. We look for a broad category that includes three words but excludes one. Concept / Approach: In vocabulary classification questions, a very common approach is to check whether the words are occupations, objects, places, feelings or abstract concepts. If three words name people who perform jobs and one word names a quality or idea, then the abstract term will be the odd-man-out. Therefore, we begin by asking: is this word the name of a person doing a job, or is it a concept or value? Step-by-Step Solution: Step 1: Consider the word Teacher. A teacher is a person whose occupation is to educate students, usually in a school, college or training environment. It clearly denotes a profession. Step 2: Consider the word Lawyer. A lawyer is a person whose occupation is to practice law, represent clients in legal matters and advise them about legal rights and duties. This is again a professional role. Step 3: Consider the word Chef. A chef is a professional cook, especially one who is in charge of a kitchen in a restaurant or hotel. This too names a person and an occupation. Step 4: Consider the word Justice. Justice is an abstract noun that refers to fairness, the quality of being just or the legal ideal in which people receive what they deserve. It does not refer to a person who performs a job, but to a principle or value. Step 5: Summarise. Teacher, Lawyer and Chef are clearly roles or professions carried out by individual people. Justice is an intangible concept, not a profession. Step 6: Conclude that Justice is the odd word because it is not the name of a profession, while the other three words are. Verification / Alternative check: We can attempt to classify the words in any other way, for example by relatability to education, law or food. Teacher is associated with education, Lawyer with law and Chef with food preparation. Justice, however, does not fit any of these occupational groupings as a person or job title. While there is a title called Justice in some legal systems for a judge, the common classroom sense in reasoning questions treats Justice as an abstract noun referring to fairness. Under that standard interpretation, the odd-man-out remains clear. Why Other Options Are Wrong: Teacher is not odd because it is a profession and groups naturally with Lawyer and Chef. Lawyer is also the name of a professional person, so it belongs to the same category. Chef similarly denotes a person with a specific job role in cooking. These three are all occupations and therefore similar. Justice alone refers to a moral or legal ideal and not to a job, which is why it cannot be grouped with the other three. Common Pitfalls: One possible confusion is to think that Lawyer and Justice are closely related to law and therefore choose another word like Chef as odd. However, the classification question is not about which field the words belong to but about their grammatical and conceptual category. When you focus on whether each word is a person or a concept, the distinction becomes clear. To avoid such mistakes, always ask what kind of thing each word represents, not just what subject it is associated with. Final Answer: The odd word is Justice, because it is an abstract concept, while Teacher, Lawyer and Chef are all names of professions or job roles.

Question 11

In this number-pair odd-man-out question, select the pair that does not follow the square relationship between the numbers.

Accepted Answer

Introduction / Context: This is a number-pair classification question that focuses on the relationship between two numbers in each pair. In many reasoning tests, such pairs are used to represent operations like squaring, cubing or multiplying by a constant. Three of the pairs here show a perfect square relationship, while one pair does not. The task is to identify which pair breaks that pattern and is therefore the odd-man-out. Given Data / Assumptions: Number pairs: 11 – 121, 12 – 144, 15 – 225 and 13 – 171. The first number in each pair is on the left, and the second number is on the right. We are looking for a consistent mathematical operation linking the two numbers. Concept / Approach: When the right-hand number is noticeably larger than the left-hand number, a natural pattern to test is whether the second number equals the square of the first. Squaring is a very common pattern in such questions because it creates nicely recognisable results. We therefore compute the square of each left-hand number and compare it with the right-hand number to see which pairs follow this relationship exactly. Step-by-Step Solution: Step 1: Analyse 11 – 121. Compute 11^2. We have 11^2 = 11 * 11 = 121. This matches the right-hand number exactly, so this pair follows the relation second number = square of first number. Step 2: Analyse 12 – 144. Compute 12^2. We have 12^2 = 12 * 12 = 144. Again, the right-hand number equals the square of the left-hand number. Step 3: Analyse 15 – 225. Compute 15^2. We have 15^2 = 15 * 15 = 225. This continues the same pattern. Step 4: Analyse 13 – 171. Compute 13^2. We have 13^2 = 13 * 13 = 169. However, the right-hand number given in the pair is 171, which is not equal to 169. Step 5: Summarise the pattern. Three pairs satisfy the rule second number = first number squared. One pair does not. Step 6: Conclude that 13 – 171 is the odd pair because its second number is not the correct square of the first number. Verification / Alternative check: We can check whether 171 has any other simple relation with 13, such as 13 * 13 + 2 or 13 * 13 + some constant. However, the other pairs match exact squares without any additional constant. Introducing an extra offset only for one pair would break the clean symmetry. Therefore, the only consistent and elegant rule is that the second number should be the exact square of the first. Under that rule, 13 – 171 fails and must be the odd-man-out. Why Other Options Are Wrong: The pair 11 – 121 is not odd because 121 is exactly 11^2, so it follows the main pattern. The pair 12 – 144 fits since 144 = 12^2. The pair 15 – 225 also fits because 225 = 15^2. These three pairs are therefore similar and should not be chosen as the answer. Only 13 – 171 breaks the square relationship by giving 171 instead of 169, so the others are all correct examples of the rule rather than exceptions to it. Common Pitfalls: One common error is simple calculation mistakes when squaring numbers, especially 13. If a learner misremembers 13^2 as 171 instead of 169, they might falsely think all four pairs follow the same rule and get confused. To avoid such mistakes, always compute squares carefully, or memorise common squares such as 11^2 = 121, 12^2 = 144, 13^2 = 169 and 15^2 = 225. Another pitfall is looking for unnecessary complex patterns when a straightforward square relationship explains most of the data. Final Answer: The odd number pair is 13 – 171, because in this pair the second number is not the exact square of the first number, whereas in all the other pairs the second number equals the square of the first.

Question 12

In this letter-classification odd-man-out question, select the odd group of letters from the given alternatives.

Accepted Answer

Introduction / Context: This question is based on alphabet positions and letter patterns. Each option is a group of three letters. In three of the groups, the letters follow a consistent numerical spacing pattern in the alphabet. In one group, this pattern breaks. Identifying this difference requires converting each letter to its alphabet position and analysing the jumps between consecutive letters. Given Data / Assumptions: Options: MSY, KQW, RXC and DJP. We use standard alphabet positions: A = 1, B = 2, ..., Z = 26. We look for equal differences between consecutive letters within each group. Concept / Approach: A common pattern in letter-group questions is that the second letter is a fixed number of positions ahead of the first, and the third letter is the same number of positions ahead of the second. Often the difference is 2, 3, 4 or 6. To find the odd group, we compute the differences between letters in each option and see which group does not share the same constant step value as the others. We also may need to consider circular movement from Z back to A for some groups. Step-by-Step Solution: Step 1: Convert letters in MSY to positions. M = 13, S = 19 and Y = 25. The differences are 19 - 13 = 6 and 25 - 19 = 6. So MSY follows a +6, +6 pattern. Step 2: Convert letters in KQW to positions. K = 11, Q = 17 and W = 23. The differences are 17 - 11 = 6 and 23 - 17 = 6. KQW also follows a +6, +6 pattern. Step 3: Convert letters in DJP to positions. D = 4, J = 10 and P = 16. The differences are 10 - 4 = 6 and 16 - 10 = 6. DJP again follows a +6, +6 pattern. Step 4: Convert letters in RXC to positions. R = 18, X = 24 and C = 3. The difference from R to X is 24 - 18 = 6, which fits +6. To go from X to C, we can think in two ways. Directly, 3 - 24 = -21. If we use circular counting from Z = 26 back to A = 1, moving forward from X (24) by 6 positions gives 30, which corresponds to 30 - 26 = 4, that is D, not C. So the second jump is not +6; it is effectively -21 or +? depending on direction, but it is not +6. Step 5: Summarise. MSY, KQW and DJP all have consistent forward jumps of +6 between each pair of letters. RXC has the first jump as +6 but the second jump is not +6 in any straightforward forward counting. Step 6: Conclude that RXC is the odd group because it breaks the repeated +6 stepping pattern that the other three groups follow. Verification / Alternative check: We can try to see whether RXC might follow some different but common pattern, such as alternating directions or equal backward steps. R to X is forward, while X to C is a big backward jump, so it does not mirror the harmonious forward stepping seen in other options. No alternate simple pattern unites RXC with the remaining three groups. The cleanest and most symmetric rule is that each group should feature two equal positive steps of 6, which RXC does not satisfy. Why Other Options Are Wrong: MSY is not odd because it fits the pattern of +6 and +6 jumps. KQW also has differences of +6 and +6 between consecutive letters. DJP similarly follows the same +6 spacing, so all three belong to one consistent category. Since they all satisfy the same simple rule, none of them can be considered the odd-man-out. Only RXC breaks the pattern and therefore must be the answer. Common Pitfalls: One frequent mistake is to look only at the first two letters and ignore the relationship between the second and third letters. This can cause a student to overlook the fact that RXC breaks the pattern on the second jump. Another common issue is to forget about circular wrapping from Z to A or to misapply it. When checking possible forward movement from X by 6 steps, careful counting shows it would land on D, not C. Being precise with alphabet positions and differences avoids these errors. Final Answer: The odd group of letters is RXC, because only this group does not show two equal forward jumps of 6 positions between its consecutive letters, unlike MSY, KQW and DJP.

Question 13

In this three-number group odd-man-out question, select the group whose numbers do not follow the same linear relationship.

Accepted Answer

Introduction / Context: This is a number-group classification question in which each option is an ordered triple of numbers. In such reasoning questions, the second and third numbers are usually related to the first by a simple arithmetic rule. Three groups follow the same pair of rules, and one group breaks that pattern. Our task is to identify the group that does not respect the same linear relationships. Given Data / Assumptions: Groups given: (8, 17, 33), (11, 23, 45), (13, 27, 51) and (17, 35, 69). Each triple is written as (first, second, third). We are looking for a consistent arithmetic relation that three triples share but one does not. Concept / Approach: The pattern here involves expressing the second and third numbers in terms of the first. A very natural attempt is to check whether the second number is approximately double the first and the third number approximately double the second. Specifically, we test simple linear forms such as second = 2 * first + constant and third = 2 * second - constant. When this form uses the same constants for three groups but fails for one group, that group is the odd-man-out. Step-by-Step Solution: Step 1: Analyse (8, 17, 33). Compare the second and first numbers. We have 2 * 8 + 1 = 17. So second = 2 * first + 1. Compare the third and second numbers. We have 2 * 17 - 1 = 33. So third = 2 * second - 1. Step 2: Analyse (11, 23, 45). Compute 2 * 11 + 1 = 23, so second = 2 * first + 1 again. Now compute 2 * 23 - 1 = 45, so third = 2 * second - 1. This triple follows the same pair of formulas. Step 3: Analyse (17, 35, 69). Compute 2 * 17 + 1 = 35, so the second number again obeys second = 2 * first + 1. Next compute 2 * 35 - 1 = 69, which matches the third number. Thus, this triple also follows the same rules. Step 4: Analyse (13, 27, 51). Compute 2 * 13 + 1 = 27, so the second number fits second = 2 * first + 1. Now compute 2 * 27 - 1 = 53, but the third number given is 51. Therefore, third ≠ 2 * second - 1 in this triple. Step 5: Summarise. Three triples satisfy two common linear relations: second = 2 * first + 1 and third = 2 * second - 1. The triple (13, 27, 51) satisfies only the first relation but fails the second. Step 6: Conclude that (13, 27, 51) is the odd group because its third term does not follow the same linear rule that applies to the other groups. Verification / Alternative check: We may also express the third term directly in terms of the first term to see the pattern more clearly. For (8, 17, 33), using third = 4 * first + 1 gives 4 * 8 + 1 = 33. For (11, 23, 45), 4 * 11 + 1 = 45. For (17, 35, 69), 4 * 17 + 1 = 69. So for three groups, third = 4 * first + 1. For the triple (13, 27, 51), we get 4 * 13 + 1 = 53, while the third term is 51. This again shows that the third term does not match the same formula, independently confirming our earlier conclusion. Why Other Options Are Wrong: (8, 17, 33) is not odd because it perfectly fits both relations: second = 2 * first + 1 and third = 2 * second - 1. (11, 23, 45) also follows both rules. (17, 35, 69) continues the pattern exactly. Since all three triples are structurally identical under the same set of formulas, they cannot be the odd-man-out. Only (13, 27, 51) breaks the relationship for the third term. Common Pitfalls: Some learners only check the relation between the first and second numbers and stop as soon as they see that all groups satisfy second = 2 * first + 1. If they do not verify the relation between the second and third numbers, they might think there is no odd-man-out at all. A second pitfall is trying to guess patterns based solely on differences rather than testing simple linear formulas systematically. The best practice is to test all parts of the triple so that you do not miss an inconsistency like the one in this question. Final Answer: The odd group is (13, 27, 51), because in this group the third number does not satisfy the rule third = 2 * second - 1, while all the other groups do follow this linear pattern exactly.

Question 14

In this word-classification odd-man-out question, select the odd word from the given alternatives.

Accepted Answer

Introduction / Context: This is a basic general knowledge and vocabulary classification question. The options given are common food items. Three of them are fruits, while one is a nut or seed. Odd-man-out questions of this type test your everyday knowledge of categories like fruits, vegetables, dry fruits and nuts. Given Data / Assumptions: Options: Apple, Mango, Orange and Almond. We use everyday culinary classifications rather than strict botanical definitions. We are looking for one item that does not belong to the group of fresh fruits. Concept / Approach: In reasoning exams, fruits are usually understood as fresh edible parts of plants that are typically juicy and eaten as a sweet or tangy food. Nuts such as almonds are considered separate because they are hard, dry seeds with a tough shell and are often categorised as dry fruits. To solve this question, we identify which of the options is not normally referred to as a fruit in daily language and cooking. Step-by-Step Solution: Step 1: Consider Apple. Apple is a common fresh fruit, juicy, sweet or slightly tangy, eaten raw or used in desserts and juices. It clearly belongs to the fruit category. Step 2: Consider Mango. Mango is a well-known tropical fruit, sweet and juicy when ripe, widely eaten as a fruit or used in shakes and desserts. It is also a fruit. Step 3: Consider Orange. Orange is a citrus fruit, juicy and rich in vitamin C, commonly consumed as a fruit or juice. It fits fully in the fruit category. Step 4: Consider Almond. Almond is a type of nut or edible seed. It is hard, dry, has a shell and is typically classified as a dry fruit or nut rather than a fresh fruit. Step 5: Summarise. Apple, Mango and Orange are all fresh fruits, whereas Almond is a nut or dry fruit. Step 6: Conclude that Almond is the odd word among the given options. Verification / Alternative check: Even if we consider botanical definitions, Almond remains different. Apple, Mango and Orange are all fleshy fruits with edible pulp, while Almond is essentially a seed inside a hard shell. In everyday usage, it is grouped with nuts such as cashew and walnut, not with apples and oranges. Therefore, whether we apply a culinary perspective or a basic biological view, Almond stands apart from the other three items. Why Other Options Are Wrong: Apple is not odd because it is clearly a fruit just like Mango and Orange. Mango is also a fruit, so it shares the main category with Apple and Orange. Orange is a typical fruit as well. Since these three all belong to the same group of fresh fruits, none of them can be the odd-man-out. Only Almond is different in type and therefore must be the answer. Common Pitfalls: Sometimes students overthink simple questions, looking for obscure properties like colour or shape. For example, they might notice that Almond is brown, whereas the others are often green or orange from outside, and misinterpret the pattern. The correct approach in reasoning questions is to focus on primary category differences like fruit versus nut or plant versus animal. Paying attention to obvious and common groupings usually leads to the right answer quickly. Final Answer: The odd word is Almond, because Apple, Mango and Orange are all fruits, while Almond is a nut or dry fruit.

Question 15

In this alphabet-series odd-man-out question, select the odd group of letters from the given alternatives.

Accepted Answer

Introduction / Context: This question deals with simple alphabet sequences. Each option is a group of three letters, and three options follow one descending pattern while one option follows a slightly different pattern. You must detect the underlying rule for how letters change from first to second and from second to third, and then identify which group does not fit that rule. Given Data / Assumptions: Options: UTS, PNM, KIH and FDC. We use standard alphabet positions A = 1, B = 2, ..., Z = 26. We will analyse the step difference between consecutive letters in each group. Concept / Approach: All groups appear to show letters in decreasing order from left to right. However, the size of the step from one letter to the next may differ. A careful analysis of the numerical differences helps us find the single group that behaves differently. The main pattern that emerges is that in three of the groups the first and second letters differ by 2 positions, while in one group they differ by only 1 position. Step-by-Step Solution: Step 1: Convert UTS to numeric positions. U = 21, T = 20 and S = 19. The differences are T - U = 20 - 21 = -1 and S - T = 19 - 20 = -1. So in UTS, the letters decrease by 1 and then by 1 again. Step 2: Convert PNM to positions. P = 16, N = 14 and M = 13. The differences are N - P = 14 - 16 = -2 and M - N = 13 - 14 = -1. The first step is -2, the second step is -1. Step 3: Convert KIH to positions. K = 11, I = 9 and H = 8. The differences are I - K = 9 - 11 = -2 and H - I = 8 - 9 = -1. Again we see a -2 step followed by a -1 step. Step 4: Convert FDC to positions. F = 6, D = 4 and C = 3. The differences are D - F = 4 - 6 = -2 and C - D = 3 - 4 = -1. So this group also shows -2 then -1. Step 5: Compare the patterns. PNM, KIH and FDC all follow the pattern of a drop of 2 positions from the first letter to the second, followed by a drop of 1 position from the second to the third. UTS is the only group where both drops are -1. Step 6: Conclude that UTS is the odd group because its step pattern is (-1, -1) instead of (-2, -1). Verification / Alternative check: If we try to classify based purely on whether letters are descending, then all four groups would appear similar, which does not help. The examiner clearly intends a more specific rule about how many positions each letter moves. The fact that three groups share (-2, -1) exactly and one group does not gives a very strong basis for classification. No other simple pattern cleanly isolates just one group, so our conclusion is reliable. Why Other Options Are Wrong: PNM is not odd because it follows the (-2, -1) pattern in its letter steps. KIH also follows (-2, -1) and aligns with PNM and FDC. FDC follows the same pattern as well. Since these three groups share identical step sizes, they form the main category and cannot be considered the odd-man-out. Only UTS shows a different pattern of (-1, -1) and therefore stands out. Common Pitfalls: Some learners focus only on whether the letters are consecutive or not and might mistakenly think that PNM, KIH and FDC are irregular because they skip one letter between the first and second positions. However, the aim in an odd-man-out question is not to find groups that look strange individually, but to find a single group that does not share a common rule. If you compute and compare the exact step sizes, the pattern becomes clear and UTS emerges as the only exception. Final Answer: The odd group of letters is UTS, because its letters decrease by 1 step twice, whereas in the other groups the letters first decrease by 2 steps and then by 1 step.

Question 16

In this animal-classification odd-man-out question, select the odd word from the given alternatives.

Accepted Answer

Introduction / Context: This is a simple general knowledge odd-man-out question about animals. Three of the given options are land mammals, while one is an aquatic animal that belongs to a different biological category. These questions check your ability to classify living beings based on basic traits such as habitat and class (mammal, bird, fish, etc.). Given Data / Assumptions: Options: Rat, Cat, Fish and Cow. We use common school-level biological categories. We are looking for one animal that does not share the group's main classification. Concept / Approach: Rat, Cat and Cow are all mammals. Mammals are warm-blooded animals that generally give birth to live young and feed them with milk. They mostly live on land and breathe air with lungs. Fish, on the other hand, are aquatic animals that live in water, breathe through gills and belong to a different vertebrate class. Identifying this class difference helps us find the odd-man-out quickly. Step-by-Step Solution: Step 1: Consider Rat. A rat is a small rodent and a mammal. It lives mainly on land, breathes air and gives birth to live young. Step 2: Consider Cat. A cat is also a mammal, kept as a pet in many homes. It lives on land, feeds its kittens with milk and shares the typical features of mammals. Step 3: Consider Cow. A cow is a large domestic mammal, used primarily for milk and farming. It lives on land and is also clearly a mammal. Step 4: Consider Fish. Fish is a general term for aquatic animals that live in water, breathe through gills and lay eggs. They are not mammals and belong to a different vertebrate class. Step 5: Summarise. Rat, Cat and Cow are all land mammals, while Fish represents aquatic animals that are not mammals. Step 6: Conclude that Fish is the odd word. Verification / Alternative check: We can also classify by habitat. Rat, Cat and Cow primarily live on land, whereas Fish primarily lives in water. Even under this simpler viewpoint, Fish stands apart from the other three options. Under both the biological classification and habitat comparison, there is a clean 3 versus 1 split, confirming that Fish is the correct answer. Why Other Options Are Wrong: Rat is not odd because it is a land mammal just like Cat and Cow. Cat is a typical mammal as well, so it fits the main group. Cow is also a mammal and shares all the major features of mammals. These three options therefore form a natural group and cannot be treated as the odd-man-out. Only Fish differs as a non-mammal aquatic organism. Common Pitfalls: Sometimes learners overthink and focus on size, domestic status or diet when answering such questions. For example, one might think Cow is odd because it is larger and used for farming. However, category-based classification is about the basic type of animal, not secondary features. Always consider broad biological categories first, such as mammal versus fish, to avoid such errors. Final Answer: The odd word is Fish, because Rat, Cat and Cow are all land mammals, whereas Fish is an aquatic animal and not a mammal.

Question 17

In this number-pair odd-man-out question, select the pair of numbers that does not follow the same difference pattern.

Accepted Answer

Introduction / Context: This question involves simple number pairs where the second number is related to the first by addition. In three of the pairs, the second number is obtained by adding the same constant to the first, while in one pair, a different increment is used. The objective is to identify the pair that does not fit the common difference pattern and mark it as the odd-man-out. Given Data / Assumptions: Number pairs: 31 – 33, 33 – 35, 37 – 39 and 35 – 39. The first number is on the left of the dash, and the second on the right. We check how much is added to the first number to obtain the second number in each pair. Concept / Approach: The obvious thing to check here is the difference between numbers in each pair. For three of the options, the jump is constant at +2. If one pair shows a different jump, that pair must be the odd one out. Questions based on constant differences are intended to be solved quickly using mental arithmetic. Step-by-Step Solution: Step 1: For the pair 31 – 33, compute the difference: 33 - 31 = 2. So the rule is second = first + 2. Step 2: For the pair 33 – 35, compute the difference: 35 - 33 = 2. This pair again follows second = first + 2. Step 3: For the pair 37 – 39, compute the difference: 39 - 37 = 2. This also fits the same pattern second = first + 2. Step 4: For the pair 35 – 39, compute the difference: 39 - 35 = 4. This time the difference is +4, not +2. Step 5: Summarise. Three pairs show a constant difference of +2 between the first and second numbers. One pair shows a larger difference of +4. Step 6: Conclude that 35 – 39 is the odd pair because its difference is different from the others. Verification / Alternative check: We can also think of these pairs as representing consecutive odd numbers. 31 and 33 are consecutive odd numbers, as are 33 and 35, and 37 and 39. The pair 35 and 39, however, skips 37 and thus does not consist of consecutive odd numbers. So we have two equivalent ways of expressing the same idea: a difference of 2 or consecutive odd numbers. Both views select the same pair, 35 – 39, as the odd-man-out. Why Other Options Are Wrong: 31 – 33 is not odd because it uses a difference of 2 and represents consecutive odd numbers. 33 – 35 also has a difference of 2. 37 – 39 fits the same pattern. These three pairs all show the same simple relationship and thus belong to one group. Only 35 – 39 has a difference of 4 and skips an odd number, so the other pairs cannot be considered the odd ones. Common Pitfalls: Some learners may confuse themselves by focusing on individual properties of the numbers, such as whether they are prime or composite. For example, 31 and 37 are prime, while 33, 35 and 39 are composite, but this does not help classify the pairs consistently. The simpler and intended pattern is the constant difference between the numbers. Always check for basic arithmetic relationships first in such questions, as they are usually enough to solve the problem quickly. Final Answer: The odd number pair is 35 – 39, because the difference between the two numbers is 4, whereas in all the other pairs the difference is only 2.

Question 18

In this three-number group odd-man-out question, choose the group whose numbers do not follow the same decreasing pattern.

Accepted Answer

Introduction / Context: This is a classification question involving groups of three numbers that decrease according to certain steps. In three of the groups, the numbers decrease by the same pair of fixed differences. One group uses a different set of differences, which makes it the odd-man-out. Detecting this requires us to find the difference between consecutive terms in each group and compare the patterns. Given Data / Assumptions: Groups: (104, 101, 96), (109, 106, 101), (97, 94, 89) and (121, 118, 111). Each triple is ordered as (first, second, third). We analyse the sequence of differences first to second and second to third in each group. Concept / Approach: All sequences here are decreasing. The key observation is whether the differences are the same across groups. In three groups, the numbers decrease first by 3 and then by 5. In one group, the second decrease is bigger, breaking the pattern. Identifying this difference pattern reveals the odd group. Step-by-Step Solution: Step 1: Analyse (104, 101, 96). The first difference is 101 - 104 = -3. The second difference is 96 - 101 = -5. So this group uses steps of -3 and then -5. Step 2: Analyse (109, 106, 101). The first difference is 106 - 109 = -3. The second difference is 101 - 106 = -5. This group also decreases by -3 and then -5. Step 3: Analyse (97, 94, 89). The first difference is 94 - 97 = -3. The second difference is 89 - 94 = -5. So it again follows -3, then -5. Step 4: Analyse (121, 118, 111). The first difference is 118 - 121 = -3. The second difference is 111 - 118 = -7. Here, the decreases are -3 and then -7, not -3 and -5. Step 5: Summarise. Three groups share the same pattern of subtracting 3 and then subtracting 5, while one group subtracts 3 and then subtracts 7. Step 6: Conclude that (121, 118, 111) is the odd group because it does not follow the common -3, -5 decreasing pattern. Verification / Alternative check: We can also express the third term in terms of the first term. In the first three groups, the third term equals first - 8, because -3 and then -5 gives a net -8. For example, 104 - 8 = 96, 109 - 8 = 101 and 97 - 8 = 89. In the last group, however, 121 - 8 = 113, not 111. Instead, 111 = 121 - 10, which confirms the second step there is larger. Thus, under both the difference pattern and net change perspective, (121, 118, 111) fails to match the others. Why Other Options Are Wrong: (104, 101, 96) is not the odd group because it follows the standard -3, -5 pattern. (109, 106, 101) also decreases by the same amounts and fits in with the others. (97, 94, 89) is again perfectly consistent with -3, then -5. Since these three share identical difference patterns, they cannot be considered the odd-man-out. Only (121, 118, 111) uses -3 and then -7, which makes it different. Common Pitfalls: Students sometimes focus only on whether the numbers are prime or composite, or they may check only the first difference and ignore the second one. If you look only at the first step, all groups have -3 and appear similar. You must always check the second step as well to see the full pattern. Another issue is trying to invent complex formulas when a simple difference analysis is enough. Always compute both differences for each group to avoid missing such subtle mismatches. Final Answer: The odd group of numbers is (121, 118, 111), because in this group the numbers decrease by 3 and then 7, whereas in all the other groups they decrease by 3 and then 5.

Question 19

In this number-classification odd-man-out question, select the number that does not follow the same divisibility pattern as the others.

Accepted Answer

Introduction / Context: This is a straightforward numerical odd-man-out question. Four two-digit numbers are given, and three of them share the property of being divisible by 3, while one does not. Recognising this divisibility pattern allows us to identify the odd number quickly, using the familiar rule for divisibility by 3. Given Data / Assumptions: Numbers given: 24, 39, 65 and 51. We use basic divisibility rules taught in school mathematics. We seek a single property common to three numbers but absent in one. Concept / Approach: The key idea is the rule for divisibility by 3: a number is divisible by 3 if the sum of its digits is divisible by 3. We can apply this rule to each of the given numbers. If three numbers satisfy this rule and one does not, then the number that fails the test is the odd-man-out. This test is quick and avoids the need for full long division. Step-by-Step Solution: Step 1: Check 24. The digit sum is 2 + 4 = 6. Since 6 is divisible by 3, 24 is divisible by 3. Step 2: Check 39. The digit sum is 3 + 9 = 12. Since 12 is divisible by 3, 39 is divisible by 3. Step 3: Check 51. The digit sum is 5 + 1 = 6. Since 6 is divisible by 3, 51 is divisible by 3. Step 4: Check 65. The digit sum is 6 + 5 = 11. Since 11 is not divisible by 3, 65 is not divisible by 3. Step 5: Summarise results. 24, 39 and 51 are all multiples of 3, while 65 is not a multiple of 3. Step 6: Conclude that 65 is the odd number. Verification / Alternative check: We can further verify by performing division or factoring. 24 = 3 * 8, 39 = 3 * 13 and 51 = 3 * 17, clearly showing they are multiples of 3. Meanwhile, attempting 65 / 3 gives a non-integer value, confirming 65 is not divisible by 3. This supports our conclusion from the digit sum method. No other equally simple pattern gives a clean 3 versus 1 split among these numbers. Why Other Options Are Wrong: 24 is not odd because it is divisible by 3 and belongs with 39 and 51. 39 is also a multiple of 3 and fits the same group. 51 is again divisible by 3, so it behaves just like the other two. Since these three share a clear divisibility property, they cannot be treated as odd. Only 65 fails to be divisible by 3, which makes it the odd-man-out. Common Pitfalls: Some students may focus on divisibility by 5 because 65 ends in 5, but that property does not distinguish 65 cleanly from the others. The number 24 is not divisible by 5, but neither are 39 and 51, so that does not create a 3 versus 1 grouping. The correct distinguishing feature is divisibility by 3. Therefore, always consider which divisibility rule gives a consistent pattern across most numbers before making a choice. Final Answer: The odd number is 65, because 24, 39 and 51 are all divisible by 3, while 65 is not a multiple of 3.

Question 20

In this geography-based odd-man-out question, select the odd word from the given alternatives.

Accepted Answer

Introduction / Context: This question tests basic geography and classification knowledge. The given words name large natural features of the Earth. Three of them are forms of water bodies, while one is a dry landform with very little water. The objective is to recognise which term does not belong to the water-related category and mark it as the odd-man-out. Given Data / Assumptions: Options: Ocean, Sea, Desert and River. We use standard geographic meanings. We aim to classify them by whether they are water bodies or not. Concept / Approach: Ocean, Sea and River are all different kinds of water bodies: oceans are the largest saltwater bodies, seas are smaller saltwater bodies partly enclosed by land and rivers are flowing freshwater bodies. A desert, on the other hand, is a dry region with very low rainfall and very little surface water. This fundamental difference in the presence of water is the key idea for classification. Step-by-Step Solution: Step 1: Consider Ocean. An ocean is a huge, continuous body of saltwater that covers most of the Earth's surface. It is clearly a water body. Step 2: Consider Sea. A sea is a large body of saltwater, typically connected to an ocean and partly enclosed by land. It is also a water body. Step 3: Consider River. A river is a natural freshwater stream that flows across land, eventually joining a sea, lake or ocean. It is again a water body. Step 4: Consider Desert. A desert is a large region of very low rainfall, often sandy or rocky, where vegetation and surface water are scarce. It is a type of dry landform, not a water body. Step 5: Summarise. Ocean, Sea and River all represent water bodies, while Desert represents a dry land area. Step 6: Conclude that Desert is the odd word among the four. Verification / Alternative check: Even if we categorise features by climate or moisture level, the result is the same. Oceans, seas and rivers are associated with abundant water, humidity, and often support a wide range of aquatic life. Deserts are associated with aridity, scarce water, and specialised flora and fauna adapted to dryness. From both the perspective of physical geography and climate, Desert stands apart from the other three terms, confirming our choice. Why Other Options Are Wrong: Ocean is not odd because it clearly belongs to the group of water bodies along with Sea and River. Sea also fits this category as a saltwater body. River is a flowing water body and is grouped naturally with the others. Since these three options are all examples of water bodies, they cannot be considered the odd-man-out. Only Desert does not contain surface water as a defining feature and therefore is the correct answer. Common Pitfalls: Some learners may overcomplicate the question by thinking about whether the feature is salty or fresh, or whether it is still or flowing. However, those secondary distinctions split the water bodies among themselves and do not single out a unique odd option. The main and simplest category distinction is water body versus dry landform. Keeping your focus on the broadest category prevents such confusion in reasoning questions. Final Answer: The odd word is Desert, because Ocean, Sea and River are all water bodies, whereas Desert is a dry landform with very little water.

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