Question 1

In this number-pair odd-man-out question, select the pair that does not follow the same constant-difference rule.

Accepted Answer

Introduction / Context: This odd-man-out question involves simple number pairs. In three of the pairs, the second number is obtained by adding the same constant to the first number. In one pair, the difference is smaller, which makes that pair the odd one out. The problem is designed to check your ability to detect constant differences quickly. Given Data / Assumptions: Number pairs: 101 – 105, 103 – 107, 102 – 106 and 104 – 106. We look at the increase from the first number to the second number in each pair. We assume no hidden operations beyond simple addition. Concept / Approach: An efficient way to approach such problems is to compute the difference second - first for each pair. If three of these differences are equal and one is not, the pair with the different difference is the odd-man-out. Here, we will see that three pairs have a difference of +4 and one pair has a difference of only +2. Step-by-Step Solution: Step 1: For 101 – 105, compute the difference: 105 - 101 = 4. So this pair follows second = first + 4. Step 2: For 103 – 107, compute the difference: 107 - 103 = 4. This pair also follows second = first + 4. Step 3: For 102 – 106, compute the difference: 106 - 102 = 4. This again matches the same rule. Step 4: For 104 – 106, compute the difference: 106 - 104 = 2. This pair follows second = first + 2, not +4. Step 5: Summarise. Three pairs show an increment of 4, while one pair shows an increment of only 2. Step 6: Conclude that 104 – 106 is the odd pair because its difference is different from the others. Verification / Alternative check: We can also observe that in the first three pairs both numbers are odd or both are even, and the gap of 4 preserves that parity. For example, 101 and 105 are odd, 103 and 107 are odd and 102 and 106 are even. In the last pair, 104 and 106 are both even, but that alone does not isolate this pair. The key distinguishing factor remains the smaller difference of 2 compared to 4 for the others. Thus, our conclusion is fully supported by the difference pattern. Why Other Options Are Wrong: 101 – 105 is not odd because it follows the rule second = first + 4. 103 – 107 also follows the same rule. 102 – 106 continues this pattern with an increment of 4. These three pairs are therefore similar in structure and cannot be labelled as odd-men-out. Only 104 – 106 violates the constant-difference rule, so the other three are not the answer. Common Pitfalls: A common mistake is to look at the parity of the numbers and become confused because all pairs involve numbers with the same parity. Another error is to just glance at the numbers without actually calculating the differences. In questions of this type, taking a few seconds to compute and compare differences is essential. This simple step quickly reveals the intended pattern and prevents guessing. Final Answer: The odd number pair is 104 – 106, because the difference between the two numbers is 2, whereas in all other pairs the difference is 4.

Question 2

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

Accepted Answer

Introduction / Context: This question is another alphabet-based odd-man-out problem. Each option consists of three letters. In three of the groups, the letters are equally spaced in the alphabet by a constant number of positions. In one group, the last step differs, so it does not maintain equal spacing. Your goal is to convert letters to their numerical positions and check how many positions separate consecutive letters. Given Data / Assumptions: Options: KQW, RXD, BHN and AGL. We use the standard order A = 1, B = 2, ..., Z = 26. We assume circular counting from Z to A is allowed when needed. Concept / Approach: The intended pattern is that the difference between the first and second letters, and between the second and third letters, is the same in three options. We will compute these differences for each group. In KQW, RXD and BHN, both steps are of size 6 (moving forward), while in AGL the first step is 6 but the second step is only 5. This mismatch in step size makes AGL the odd group. Step-by-Step Solution: Step 1: Convert letters in KQW to positions. K = 11, Q = 17 and W = 23. The differences are Q - K = 17 - 11 = 6 and W - Q = 23 - 17 = 6. So KQW has a pattern of +6, +6. Step 2: Convert letters in RXD. R = 18, X = 24 and D = 4. The difference from R to X is 24 - 18 = 6. To go from X to D using circular counting, we move forward from 24 by 6 positions: 24 + 6 = 30, and 30 - 26 = 4, which corresponds to D. Thus, the second step is effectively +6 as well, giving RXD a pattern of +6, +6. Step 3: Convert letters in BHN. B = 2, H = 8 and N = 14. The differences are H - B = 8 - 2 = 6 and N - H = 14 - 8 = 6. So BHN also follows +6, +6. Step 4: Convert letters in AGL. A = 1, G = 7 and L = 12. The difference from A to G is 7 - 1 = 6. The difference from G to L is 12 - 7 = 5. So the pattern is +6, +5, not +6, +6. Step 5: Summarise. Three groups have equal jumps of 6 positions each between consecutive letters, while one group has unequal jumps of 6 and 5. Step 6: Conclude that AGL is the odd group, because it breaks the equal-step pattern. Verification / Alternative check: We can visualise the letters on a number line or list the alphabet to verify the steps manually. Starting from K, count 6 steps forward to Q and another 6 to W. Similarly, from B to H to N and from R to X to D (using circular counting), we always move 6 steps. For AGL, after moving 6 steps from A to G, moving 6 steps again would land at M, not L. The fact that L is only 5 steps from G confirms that AGL deviates from the common pattern. Why Other Options Are Wrong: KQW is not odd because it uses a consistent +6 step between its letters. RXD also respects the +6 step size in a circular manner. BHN follows the same pattern. These three groups are therefore structurally identical under the equal-step rule and cannot be the odd-man-out. Only AGL has different step sizes and so does not belong with the others. Common Pitfalls: Some learners ignore circular counting from Z to A, which can make RXD look irregular at first sight. However, reasoning questions often assume that the alphabet can be treated cyclically. Another mistake is to test only one of the differences and not both. To be thorough, you must always check the step between first and second letters and between second and third letters. This reveals that AGL fails the equal-step condition and is the intended odd option. Final Answer: The odd group of letters is AGL, because in this group the letters are separated by +6 and +5 positions, whereas in the other groups they are separated consistently by +6 and +6 positions.

Question 3

In this three-number group odd-man-out question, select the group whose numbers do not form an arithmetic progression with the same common difference.

Accepted Answer

Introduction / Context: This is a number-sequence classification question involving groups of three numbers. In three of the groups, the numbers form an arithmetic progression with the same common difference. In one group, that pattern breaks because the third number does not follow the same step size. Recognising this pattern allows us to identify the odd-man-out quickly. Given Data / Assumptions: Groups given: (7, 14, 21), (5, 12, 19), (3, 10, 17) and (9, 16, 35). Each triple is ordered as (first, second, third). We are looking at the differences between consecutive terms in each triple. Concept / Approach: An arithmetic progression is a sequence of numbers where the difference between any two consecutive terms is constant. In this question, we check whether the second minus the first and the third minus the second give the same common difference within a triple, and also whether this common difference is the same across triples. We will see that three triples share a common difference of 7 throughout, while one triple deviates at the last step. Step-by-Step Solution: Step 1: Analyse (7, 14, 21). The differences are 14 - 7 = 7 and 21 - 14 = 7. This group forms an arithmetic progression with common difference 7. Step 2: Analyse (5, 12, 19). The differences are 12 - 5 = 7 and 19 - 12 = 7. This triple also has common difference 7. Step 3: Analyse (3, 10, 17). The differences are 10 - 3 = 7 and 17 - 10 = 7. This group again is an arithmetic progression with common difference 7. Step 4: Analyse (9, 16, 35). The differences are 16 - 9 = 7 and 35 - 16 = 19. The first step is 7, but the second step is 19, which is not equal to 7. So the numbers here do not form an arithmetic progression with constant difference. Step 5: Summarise. Three groups form arithmetic progressions with the same common difference of 7, while one group has a different second step. Step 6: Conclude that (9, 16, 35) is the odd group because it does not maintain the constant common difference of 7. Verification / Alternative check: We can also express the third term directly in terms of the first using the formula for an arithmetic progression: third = first + 2 * common difference. In the first three groups, third = first + 14. For example, 7 + 14 = 21, 5 + 14 = 19 and 3 + 14 = 17. In the last group, 9 + 14 = 23, but the third term is 35, not 23. This confirms that (9, 16, 35) does not follow the same progression and supports our conclusion from the difference method. Why Other Options Are Wrong: (7, 14, 21) is not odd because it is a clean arithmetic progression with common difference 7. (5, 12, 19) also has the same difference structure. (3, 10, 17) continues that pattern. Since these three triples all share the same arithmetic progression form with identical common difference, none of them can be the odd-man-out. Only (9, 16, 35) fails that rule by using a different second difference. Common Pitfalls: One common mistake is to just observe that 35 is far larger than the others and assume that size alone makes the triple odd, without actually verifying the pattern. While size hints that something may be different, the correct reasoning still depends on checking the differences systematically. Another error is to miscalculate the differences. To avoid such mistakes, always compute both steps carefully and compare them, rather than relying on approximate visual impressions. Final Answer: The odd group of numbers is (9, 16, 35), because it does not form an arithmetic progression with common difference 7, whereas all other groups do.

Question 4

Select the odd family relationship from the following alternatives based on blood relation versus relation by marriage.

Accepted Answer

Introduction / Context: This aptitude question tests your understanding of basic family relationships and how they are classified into blood relations and relations created through marriage. Such questions are common in reasoning sections of competitive exams and help to check how clearly you understand family trees and generational links. Given Data / Assumptions: Four relationship terms are given: Mother-in-law, Nephew, Grandson, Great grandfather. You are asked to select the relationship that is different from the other three. Assume standard definitions of family relations based on common usage in family trees. Concept / Approach: The key idea is to classify each option as either a blood relation or a relation by marriage. Blood relations are directly connected by birth, such as parent, child, or grandparent. A relation by marriage is created due to a spouse, such as mother-in-law, father-in-law, brother-in-law, and so on. Once we classify each option, we identify which one does not fit the majority pattern. Step-by-Step Solution: Step 1: Note that a nephew is the son of your brother or sister, so it is a blood relation. Step 2: A grandson is the son of your son or daughter, which is also a direct blood relation. Step 3: A great grandfather is the father of your grandfather or grandmother, which again is a direct blood relation that extends one more generation upward. Step 4: A mother-in-law, however, is the mother of your spouse, which is a relation created by marriage, not by direct blood. Step 5: Therefore, among the four, three are pure blood relations and one is a marriage-based relation. Verification / Alternative check: Another way to check is to imagine a family tree starting from yourself. Your nephew, grandson, and great grandfather can all be located by tracing up or down through parents and children only. Mother-in-law, on the other hand, appears only when you introduce a spouse into the family tree. This confirms that it is the only relation that is not purely blood based. Why Other Options Are Wrong: Nephew: This is a blood relation through your siblings, so it matches the pattern of blood relatives. Grandson: This is a direct blood relation to a younger generation, so it is similar to other blood relations. Great grandfather: This is also a direct blood relation but in an older generation, so it still fits the blood relationship pattern. Common Pitfalls: Many learners focus only on the generational difference and may think that great grandfather is different because it is farther away in the family tree. However, the question is about odd one out, and the stronger and more logical classification is blood relation versus relation by marriage. Overlooking this difference can lead to the wrong choice. Final Answer: Mother-in-law

Question 5

Select the odd letter group from the following alternatives based on the direction of the alphabetical sequence.

Accepted Answer

Introduction / Context: This reasoning question checks your understanding of alphabetical sequences and the direction in which letters progress. Such problems often appear in verbal reasoning and series questions where you must quickly recognize patterns of increasing or decreasing letters in the English alphabet. Given Data / Assumptions: The four letter groups given are: GHI, XYZ, VUT, and CDE. You are required to select the odd group based on the letter arrangement pattern. Assume standard English alphabet order with no wrapping beyond Z. Concept / Approach: The usual approach is to examine the order of letters in each group. You check whether each group follows increasing order (forward in the alphabet) or decreasing order (reverse in the alphabet). Once you know the direction of movement in each group, you can classify which one differs from the others. Step-by-Step Solution: Step 1: For GHI, the letters are G, H, and I. These are consecutive letters in forward order. Step 2: For XYZ, the letters X, Y, and Z are also consecutive and appear in forward alphabetical order. Step 3: For CDE, the letters C, D, and E again form a forward consecutive sequence. Step 4: For VUT, the letters are V, U, and T. Here, the sequence goes V to U to T, which is in reverse alphabetical order, not forward. Step 5: Therefore, three groups follow forward alphabetical order, while one group follows reverse order. Verification / Alternative check: You can also assign numerical positions to each letter. For example, G is 7, H is 8, I is 9 (increasing), X is 24, Y is 25, Z is 26 (increasing), C is 3, D is 4, E is 5 (increasing), but V is 22, U is 21, and T is 20 (decreasing). This numerical verification confirms that VUT is the only group in reverse order. Why Other Options Are Wrong: GHI: All letters are consecutive and arranged in forward alphabetical order, so it matches the main pattern. XYZ: This group also forms a forward sequence of consecutive letters, so it is not odd. CDE: Again, these letters create a forward consecutive alphabetical sequence, so they follow the same rule. Common Pitfalls: Students sometimes focus only on whether the letters are consecutive and overlook the direction of the sequence. Because V, U, and T are consecutive, it may look regular at first glance. However, the forward versus reverse direction is the key feature that distinguishes VUT from the others. Final Answer: VUT

Question 6

Select the odd number from the following alternatives based on whether it is prime or composite.

Accepted Answer

Introduction / Context: This number reasoning question checks your understanding of prime and composite numbers. Prime numbers play a central role in number theory and frequently appear in aptitude questions, so being able to quickly separate primes from composites is a useful exam skill. Given Data / Assumptions: The four numbers given are: 43, 22, 13, and 41. You must select the number that does not share the same nature as the others. Assume standard definitions of prime and composite numbers. Concept / Approach: A prime number is a positive integer greater than 1 that has exactly two distinct positive factors: 1 and the number itself. A composite number has more than two factors. The standard method is to test each number for divisibility by smaller primes and identify which numbers are prime and which are composite. Step-by-Step Solution: Step 1: Check 43. It is not divisible by 2, 3, 5, or 7, and no smaller prime divides it. So 43 is a prime number. Step 2: Check 13. It is not divisible by 2, 3, or 5, and again it has no factors other than 1 and 13, so 13 is prime. Step 3: Check 41. It is not divisible by 2, 3, or 5, and there is no smaller divisor, so 41 is also a prime number. Step 4: Check 22. It is divisible by 2 and 11, so it has factors 1, 2, 11, and 22, meaning it is a composite number. Step 5: Three of the numbers are prime, and one number is composite. Therefore, the composite number is the odd one out. Verification / Alternative check: You can quickly verify your conclusion by checking divisibility rules. Any even number greater than 2 is automatically composite. Here, 22 is even, so it must be composite. The other numbers are odd and fail simple divisibility checks for small primes, which supports the conclusion that they are primes. This gives a fast alternative confirmation. Why Other Options Are Wrong: 43: This is a prime and shares the same property as 13 and 41, so it is not the odd number. 13: This is clearly a prime, so it matches the majority group. 41: This is another prime number, so it also belongs with the majority. Common Pitfalls: Sometimes learners quickly look at the size or parity of the numbers and may mistakenly treat all odd numbers as prime. However, not every odd number is prime, and not every even number is composite except 2. Here, paying attention to divisibility rules is essential, and recognizing that 22 is even immediately signals that it is composite. Final Answer: 22

Question 7

Select the odd word from the following alternatives based on whether it implies mixing or conflict.

Accepted Answer

Introduction / Context: This vocabulary based odd man out question examines your understanding of word meanings and how they group together semantically. Recognizing subtle differences in connotation and context is important in verbal aptitude sections and language based reasoning questions. Given Data / Assumptions: The options are: Blend, Mingle, Jumble, and Clash. You are asked to choose the one word that does not belong with the others. Assume normal dictionary meanings of all English words. Concept / Approach: The idea is to look for a common theme or action described by most of the words. Blend, mingle, and jumble all involve some sense of mixing or combining things together, although sometimes in a smooth way and sometimes in a disordered way. Clash, however, refers to disagreement, conflict, or strong opposition, which is a very different concept. Identifying this difference helps pinpoint the odd word. Step-by-Step Solution: Step 1: Blend means to mix different elements so that they combine smoothly. Step 2: Mingle means to mix or combine, often used for people or things coming together. Step 3: Jumble means to mix things in a confused or disordered manner, but still involves mixing. Step 4: Clash refers to conflict, disagreement, or a strong difference that leads to opposition, such as two people arguing or colors that do not go well together. Step 5: Since three words relate to mixing and one word relates to conflict, the one related to conflict is the odd one out. Verification / Alternative check: You can also group the words into themes. Blend, mingle, and jumble can be placed under the theme of combining or mixing things. In contrast, clash would be grouped under the theme of opposition or disagreement. Because it cannot fit naturally into the mixing group, it is clearly different. This alternative grouping method confirms the same answer. Why Other Options Are Wrong: Blend: This word fits the mixing theme perfectly and is similar in sense to mingle. Mingle: Again, this implies mixing and social or physical coming together, so it matches the main pattern. Jumble: Although it suggests disordered mixing, it still belongs to the overall mixing group, so it is not odd. Common Pitfalls: Some students may be misled by the slightly negative feeling of the word jumble and think it is the odd one out. However, the question focuses on the underlying action or idea, not just pleasant or unpleasant connotation. The real conceptual divide is between mixing and conflict, so clash is the correct odd term. Final Answer: Clash

Question 8

Select the odd word from the following alternatives based on alphabetical order of letters within the word.

Accepted Answer

Introduction / Context: This question explores your ability to notice internal patterns in words, specifically the order of letters according to the English alphabet. Such questions appear in logical reasoning sets where seemingly ordinary words hide a pattern that you must detect to choose the odd term. Given Data / Assumptions: The four options are the words or letter groups: ACE, ONE, EON, and RED. You are required to identify which word does not behave like the others when you look at the alphabetical order of its letters. Assume normal A to Z alphabetical positions for the letters. Concept / Approach: The key idea is to look at the relative order of letters within each word. If the letters proceed in strict alphabetical order from left to right, that word may be different from words where letters are jumbled. On the other hand, if three words have no internal alphabetical pattern and one has a neat pattern, the neat one becomes the odd member based on structure, not meaning. Step-by-Step Solution: Step 1: For ACE, the letters are A, C, and E. Their alphabetical positions are 1, 3, and 5. They increase in order and maintain a consistent step of +2, so ACE is in strict increasing alphabetical order. Step 2: For ONE, the letters O, N, and E appear in the order of positions 15, 14, and 5. These do not follow increasing order; in fact, the sequence decreases and then makes a large jump. Step 3: For EON, the letters E, O, and N correspond to 5, 15, and 14. Again, this is not a simple increasing or decreasing stepwise sequence. Step 4: For RED, the letters R, E, and D have positions 18, 5, and 4. This is also not a neat alphabetical progression. Step 5: Therefore, ACE is the only word whose letters appear in properly increasing alphabetical order from left to right. Verification / Alternative check: A quick verification is to write the letters of each word in alphabetical order and compare them with the original word. For ACE, sorting the letters still gives ACE, so it is already in alphabetical order. For ONE, sorted letters give ENO, which is different from ONE. For EON, sorted letters give ENO again, which is different from EON. For RED, sorted letters give DER, which differs from RED. This confirms that ACE alone is prearranged in alphabetical order and is therefore structurally distinct. Why Other Options Are Wrong: ONE: Its letters do not appear in alphabetical order, so it behaves like EON and RED and is not odd in this structural sense. EON: Although it is an anagram of ONE, its internal letter order is not alphabetical, so it fits with the general non ordered pattern. RED: The letters here are clearly jumbled with respect to alphabetical order and match the non pattern behavior seen in ONE and EON. Common Pitfalls: Candidates may focus on the meanings of the words instead of structural letter patterns. For instance, they might think ACE is special because it has a separate meaning related to excellence. However, the intended reasoning is purely alphabetical. Ignoring letter order and relying only on word meaning can easily lead to errors in such questions. Final Answer: ACE

Question 9

Select the odd number from the following alternatives based on whether it can be expressed as a product of three consecutive integers.

Accepted Answer

Introduction / Context: This numerical reasoning question examines your ability to recognize hidden factorization patterns, specifically numbers that can be written as the product of three consecutive integers. Such patterns are useful in algebra, number theory, and competitive exam questions involving special forms of integers. Given Data / Assumptions: The four given numbers are: 1716, 2730, 3360, and 4086. You must select the number that does not fit the common factorization pattern of the other three. Assume all numbers are positive integers. Concept / Approach: The approach is to test whether each number can be expressed in the form n * (n + 1) * (n + 2), where n, n + 1, and n + 2 are three consecutive integers. If three numbers share this property and one does not, that one is the odd term. This may require trial factorization or spotting familiar products. Step-by-Step Solution: Step 1: Factor 1716. One way is to check 11 * 12 * 13. Multiplying 11 * 12 gives 132, and 132 * 13 gives 1716, so 1716 equals 11 * 12 * 13, a product of three consecutive integers. Step 2: Consider 2730. Try 13 * 14 * 15. Multiplying 13 * 14 gives 182, and 182 * 15 gives 2730, so 2730 equals 13 * 14 * 15, which again is a product of three consecutive integers. Step 3: Check 3360. Try 14 * 15 * 16. Multiplying 14 * 15 gives 210, and 210 * 16 gives 3360, so 3360 equals 14 * 15 * 16, also a product of three consecutive integers. Step 4: Now test 4086. No simple choice of n gives n * (n + 1) * (n + 2) equal to 4086. If we try 15 * 16 * 17, we get 4080, which is close but not equal. Trying 16 * 17 * 18 gives a much larger value. Therefore, 4086 cannot be written as a product of three consecutive integers in the same neat way. Step 5: Since 1716, 2730, and 3360 all share this factorization property and 4086 does not, 4086 is the odd number. Verification / Alternative check: You can also factor each number into primes. For example, 1716 factors into 2 * 2 * 3 * 11 * 13, which can be regrouped as 11 * 12 * 13. Similarly, 2730 and 3360 admit groupings that correspond to 13 * 14 * 15 and 14 * 15 * 16. However, 4086 factors into 2 * 3 * 3 * 227 and does not rearrange into three consecutive integers. This prime factorization view confirms that 4086 breaks the pattern. Why Other Options Are Wrong: 1716: Equal to 11 * 12 * 13, so it clearly fits the special product pattern. 2730: Equal to 13 * 14 * 15, so it also has the required product form. 3360: Equal to 14 * 15 * 16, so it conforms perfectly to the pattern of consecutive integer products. Common Pitfalls: Many students focus only on divisibility by small primes or number size and miss the specific product pattern. Another trap is to stop checking after spotting a partial pattern, such as divisibility by 3 or 5. The correct approach here is not just divisibility but matching the exact form n * (n + 1) * (n + 2). Ignoring the structure can lead to an incorrect choice. Final Answer: 4086

Question 10

Select the odd number from the following alternatives based on whether it is a prime or a composite number.

Accepted Answer

Introduction / Context: This question checks your ability to recognize prime and composite numbers among larger three digit values. Prime recognition is a frequent topic in quantitative aptitude and number system questions, so quick and accurate identification is very useful. Given Data / Assumptions: The four numbers provided are: 211, 287, 283, and 277. You must select the number that does not share the same prime or composite status as the others. Use the standard definition that a prime number has exactly two distinct positive factors. Concept / Approach: The plan is to classify each number as prime or composite. A composite number can be factored into smaller positive integers, whereas a prime number cannot be split in this way except as 1 and itself. By applying divisibility tests and checking possible factors up to the approximate square root, you can identify which numbers are prime and which are not. Step-by-Step Solution: Step 1: For 211, test divisibility by small primes like 2, 3, 5, 7, 11, and 13. It is not divisible by any of these, so 211 is a prime number. Step 2: Check 283. Again test divisibility by 2, 3, 5, 7, 11, and 13. None of these divide 283 exactly, so 283 is also a prime number. Step 3: Check 277 in the same way. It is not divisible by 2, 3, 5, 7, 11, or 13, so 277 is also a prime. Step 4: Now analyze 287. It is not even, so it is not divisible by 2. However, 287 divided by 7 equals 41, so 287 equals 7 * 41 and clearly has more than two factors. Thus, 287 is a composite number. Step 5: Since three numbers are prime and one is composite, the composite number 287 is the odd one out. Verification / Alternative check: You can quickly verify by using digit sum checks and basic divisibility rules. For example, 287 has a digit sum of 2 + 8 + 7 = 17, so it is not divisible by 3, but trial division by 7 reveals that 7 * 41 equals 287. In contrast, trial division of 211, 283, and 277 by primes up to their square roots does not yield any exact factors. This confirms that these three are primes and 287 is composite. Why Other Options Are Wrong: 211: Since it has no divisor other than 1 and 211, it is prime and thus similar to 283 and 277. 283: This is another prime number and matches the majority pattern. 277: This is also a prime number and therefore not the odd choice. Common Pitfalls: Some learners avoid checking divisibility beyond a couple of small primes and may misclassify a number. Others might assume that a three digit number is probably composite without verification. Systematic checking, at least for primes like 2, 3, 5, 7, 11, and 13, is essential for accuracy in exam conditions. Final Answer: 287

Question 11

Choose the odd colour from the following alternatives based on the visible spectrum of light.

Accepted Answer

Introduction / Context: This general aptitude question tests your knowledge of colours in the visible spectrum of light. Many school level science lessons describe the rainbow using the familiar pattern of seven colours. Recognizing which colours belong to this spectrum helps you solve this type of odd one out question quickly. Given Data / Assumptions: The options are: Violet, Blue, Indigo, and White. You are asked to choose the colour that does not belong with the others based on the standard visible spectrum. Assume the typical VIBGYOR (Violet, Indigo, Blue, Green, Yellow, Orange, Red) ordering for rainbow colours. Concept / Approach: The visible spectrum consists of seven main colours often memorized by the acronym VIBGYOR. Violet, Indigo, and Blue are all part of this list. White, however, is not a single spectral colour; instead, it is a combination of all visible wavelengths. Therefore, by identifying which colours are basic spectrum components, you can find the odd one. Step-by-Step Solution: Step 1: Note that Violet is explicitly listed as the first colour in the VIBGYOR sequence. Step 2: Indigo is the second colour in the VIBGYOR sequence and is also a pure spectral colour. Step 3: Blue is the third colour in the visible spectrum sequence and is again a basic spectral colour. Step 4: White is not a single spectral colour. It is produced when light contains a balanced combination of all the spectral colours or when the eye perceives multiple wavelengths together. Step 5: Since the first three options are individual spectral colours and the last is a mixture, White is the odd colour. Verification / Alternative check: You can also think about a simple prism experiment from basic physics. When white light passes through a glass prism, it splits into seven colours: Violet, Indigo, Blue, Green, Yellow, Orange, and Red. This clearly shows that Violet, Indigo, and Blue are components of white light, while white itself is the combined result of all those wavelengths. This experiment based mental picture confirms that White is different from the three spectral colours listed. Why Other Options Are Wrong: Violet: A distinct spectral colour and part of the standard VIBGYOR list, so it belongs with Indigo and Blue. Blue: Another major spectral colour that appears in the rainbow, so it is not odd. Indigo: Also one of the seven colours in the visible spectrum and similar in nature to Violet and Blue. Common Pitfalls: Some learners may think that Indigo is odd because it is less frequently mentioned in everyday life compared to Blue or Violet. Others may confuse the classification by thinking in terms of favourite colours rather than scientific spectrum colours. The correct reasoning must rely on the standard physics based definition of the visible spectrum, which clearly separates White from the other options. Final Answer: White

Question 12

Choose the odd group of letters from the following alternatives based on the alphabetical step pattern.

Accepted Answer

Introduction / Context: This question checks your ability to recognize patterns in letter sequences, especially fixed steps in the alphabet. Such questions appear frequently in series and coding decoding sections of aptitude tests and help examine your comfort with alphabet positions and jumps. Given Data / Assumptions: The given letter groups are: MPS, WZC, FHJ, and ADG. You must select the group that does not follow the same step pattern as the others. Assume standard English alphabet order with A as 1 and Z as 26. Concept / Approach: The approach is to convert each letter to its numerical position in the alphabet, then examine differences between consecutive letters within each group. If three groups share an identical difference pattern, the remaining group is the odd one out. This method is systematic and avoids guesswork based purely on appearance. Step-by-Step Solution: Step 1: For MPS, the letters are M, P, and S. Their positions are 13, 16, and 19. The difference from M to P is +3, and from P to S is also +3. Step 2: For WZC, interpret Z as 26 and C as 3. The positions are 23, 26, and 3. From W to Z is +3 (23 to 26). From Z to C, if you consider alphabetical cycling, the step is also effectively +3 when counted modulo 26. Step 3: For ADG, the letters A, D, and G have positions 1, 4, and 7. From A to D is +3, and from D to G is +3, so the pattern is again a consistent +3 step. Step 4: For FHJ, the letters F, H, and J have positions 6, 8, and 10. From F to H is +2, and from H to J is +2, not +3. Step 5: Therefore, three groups show a step pattern of +3 between letters, whereas FHJ shows a pattern of +2. Hence FHJ is the odd group. Verification / Alternative check: An alternative check is to rewrite each group as a triple (first letter, middle letter, last letter) and see if the middle letter seems equidistant from the first and last. In MPS, P is the midpoint with equal distance to M and S using a step of three. Similarly, in ADG and WZC, the middle letter can be seen as evenly spaced. In FHJ, H is only two steps from F and two steps from J. This reinforces the conclusion that FHJ follows a different jumping rule. Why Other Options Are Wrong: MPS: Follows the pattern of equal +3 steps between consecutive letters, so it matches the main rule. WZC: Despite wrapping around the alphabet, it still follows a consistent +3 step pattern, so it is not odd. ADG: Displays clear +3 gaps between letters and therefore fits the same pattern as MPS and WZC. Common Pitfalls: Sometimes learners are distracted by the wraparound from Z back to C in WZC and incorrectly treat it as irregular. Others may not convert letters into numerical positions and miss the uniform step sizes. Remember that cyclic patterns around the alphabet are common in aptitude questions, and you must account for them when analyzing differences. Final Answer: FHJ

Question 13

Choose the odd number from the following alternatives based on divisibility by 3.

Accepted Answer

Introduction / Context: This question evaluates your familiarity with simple divisibility rules, particularly divisibility by 3. Recognizing such patterns quickly is extremely helpful in number series, simplification, and odd one out tasks in competitive exams. Given Data / Assumptions: The numbers presented are: 165, 792, 852, and 671. You must determine which number does not follow the same divisibility pattern as the others. Use the standard rule that a number is divisible by 3 if the sum of its digits is divisible by 3. Concept / Approach: The divisibility rule for 3 is simple and fast. You add the digits of a number. If the resulting sum is a multiple of 3, then the original number is divisible by 3. By applying this rule to each option, you can quickly group numbers into those divisible by 3 and those that are not, then choose the odd one out. Step-by-Step Solution: Step 1: For 165, add the digits: 1 + 6 + 5 = 12. Since 12 is divisible by 3, 165 is divisible by 3. Step 2: For 792, add the digits: 7 + 9 + 2 = 18. Since 18 is divisible by 3, 792 is divisible by 3. Step 3: For 852, add the digits: 8 + 5 + 2 = 15. Since 15 is divisible by 3, 852 is divisible by 3. Step 4: For 671, add the digits: 6 + 7 + 1 = 14. Since 14 is not divisible by 3, 671 is not divisible by 3. Step 5: Three numbers are divisible by 3, and one number is not, so the one that is not divisible by 3 is the odd one out. Verification / Alternative check: You can verify the conclusion by performing quick mental division. For example, 165 divided by 3 gives 55, 792 divided by 3 gives 264, and 852 divided by 3 gives 284, all of which are exact integers. For 671, dividing by 3 results in a non integer value. This cross check confirms the result obtained from the digit sum method. Why Other Options Are Wrong: 165: Divisible by 3 based on the digit sum of 12, so it matches the main pattern. 792: Clearly divisible by 3 as the digit sum 18 is a multiple of 3. 852: Also divisible by 3 since the digit sum 15 is a multiple of 3. Common Pitfalls: Students sometimes attempt long division for each number, which is time consuming and can lead to mistakes under exam pressure. Another mistake is to assume that any number ending in 5 or 0 is special only with respect to 5 or 10, but here the relevant property is divisibility by 3. Using the digit sum rule makes the solution faster and more reliable. Final Answer: 671

Question 14

Find the odd number from the following alternatives based on divisibility by 5.

Accepted Answer

Introduction / Context: This odd one out question checks your understanding of divisibility by 5, a very common rule in arithmetic and number theory. Having these rules at your fingertips helps in speed based exams where quick elimination of options is essential. Given Data / Assumptions: The four numbers provided are: 82, 75, 64, and 31. You are required to pick the number that does not behave like the others with respect to divisibility by 5. Use the standard rule that a number divisible by 5 ends in 0 or 5. Concept / Approach: The divisibility rule for 5 is straightforward. If the last digit (units digit) of a number is either 0 or 5, the number is divisible by 5. If the last digit is anything else, the number is not divisible by 5. Applying this rule to all four options lets you group them accordingly and identify the odd number based on which group is smaller. Step-by-Step Solution: Step 1: Look at 82. Its last digit is 2, so 82 is not divisible by 5. Step 2: Look at 64. Its last digit is 4, so 64 is not divisible by 5. Step 3: Look at 31. Its last digit is 1, so 31 is also not divisible by 5. Step 4: Look at 75. Its last digit is 5, so 75 is divisible by 5. Step 5: Three numbers are not divisible by 5, and only one number is divisible by 5, so the divisible number is the odd one out. Verification / Alternative check: You can verify this by actual division. Dividing 75 by 5 gives exactly 15, which is an integer. If you try 82 divided by 5, you get 16.4, which is not an integer. Similarly, 64 divided by 5 and 31 divided by 5 yield non integer results. This confirms that 75 is the only number divisible by 5 among the four options. Why Other Options Are Wrong: 82: Ends with 2 and is not divisible by 5, similar to 64 and 31. 64: Ends with 4 and therefore does not satisfy the divisibility rule for 5. 31: Ends with 1 and also is not divisible by 5, so it follows the same pattern as 82 and 64. Common Pitfalls: A common mistake is to look for patterns like even or odd numbers and ignore the more relevant divisibility rule. Here, parity does not separate one number clearly from the others because there are both even and odd numbers in the options. Focusing on the last digit and recalling the rule for divisibility by 5 leads to a faster and more accurate solution. Final Answer: 75

Question 15

Find the odd number from the following alternatives based on whether it is a perfect cube.

Accepted Answer

Introduction / Context: This question focuses on recognizing perfect cubes among given numbers. Perfect powers such as squares and cubes are very important in arithmetic and frequently appear in reasoning and number system questions in competitive exams. Given Data / Assumptions: The numbers given are: 512, 100, 125, and 216. You must choose the number that is not a perfect cube, while the others are. Assume cube values of small integers are known or can be recalled, such as 5^3, 6^3, 8^3, and so on. Concept / Approach: A perfect cube is a number that can be written as n^3, where n is an integer. The straightforward approach is to recall common cubes of small integers and check whether each given number matches one of those values. If three numbers are perfect cubes and one is not, then the non cube is the odd one out. Step-by-Step Solution: Step 1: Check 512. We know that 8^3 equals 8 * 8 * 8, which is 512, so 512 is a perfect cube. Step 2: Check 125. We know that 5^3 equals 5 * 5 * 5, which is 125, so 125 is a perfect cube. Step 3: Check 216. We know that 6^3 equals 6 * 6 * 6, which is 216, so 216 is also a perfect cube. Step 4: Now check 100. There is no integer n such that n^3 equals 100. Cubes near 100 are 4^3 = 64 and 5^3 = 125, so 100 falls between these and is not a perfect cube. Step 5: Therefore, 100 is the only number that is not a perfect cube, making it the odd one out. Verification / Alternative check: You can also confirm by prime factorization. For a number to be a perfect cube, the exponent of each prime factor must be a multiple of 3. For example, 125 is 5^3, 216 is 2^3 * 3^3, and 512 is 2^9, which is (2^3)^3. In contrast, 100 factors as 2^2 * 5^2, where the exponents are not multiples of 3. This discrepancy confirms that 100 cannot be expressed as an integer cube. Why Other Options Are Wrong: 512: Equal to 8^3, so it clearly fits the perfect cube property. 125: Equal to 5^3, and therefore a standard perfect cube. 216: Equal to 6^3, which is another well known perfect cube and matches the majority pattern. Common Pitfalls: Some learners may confuse squares and cubes or rely only on approximate mental estimation. Confusing 10^2 and 10^3 or mixing up 4^3 and 5^3 can lead to incorrect conclusions. A systematic approach using either a memorized cube table or prime factorization avoids such mistakes and ensures accurate identification of perfect cubes. Final Answer: 100

Question 16

Find the odd animal from the following alternatives based on biological family classification.

Accepted Answer

Introduction / Context: This general knowledge and reasoning question examines your understanding of basic animal classification, especially at the level of biological families. Such questions often appear in the general aptitude or general awareness sections of competitive exams. Given Data / Assumptions: The options are four animals: Tiger, Jaguar, Leopard, and Fox. You must choose the one animal that does not belong to the same family as the others. Assume standard zoological classification based on biological families. Concept / Approach: Tiger, jaguar, and leopard are all big cats, and they belong to the family Felidae. They share many characteristics such as retractile claws, cat like body structure, and similar hunting patterns. The fox, on the other hand, is a canid and belongs to the family Canidae, which also includes wolves and dogs. This difference in family classification helps identify the odd animal. Step-by-Step Solution: Step 1: Recognize that the tiger is a large cat and is scientifically classified under the family Felidae. Step 2: Note that the jaguar is also a big cat from the same Felidae family, found primarily in the Americas. Step 3: Observe that the leopard is another big cat species from the Felidae family, commonly found in parts of Africa and Asia. Step 4: Identify that the fox is not a cat but a member of the dog family. It belongs to the family Canidae and has different physical and behavioral traits from big cats. Step 5: Since three animals are big cats from the same biological family and one is a canid, the fox becomes the odd animal. Verification / Alternative check: An alternative way to see this is to compare typical physical features and hunting styles. Tigers, jaguars, and leopards share characteristics such as retractile claws, similar skull shapes, and predatory behavior that relies on stealth and pouncing. Foxes, however, resemble dogs in limb structure, facial features, and general movement, and their hunting style is more like that of smaller canids. This difference in behavior and appearance further confirms the classification difference. Why Other Options Are Wrong: Tiger: A well known big cat belonging to the family Felidae, so it is similar to jaguar and leopard. Jaguar: Another big cat from the same family and therefore not the odd one out. Leopard: Also a big cat species in the family Felidae and matches the pattern of the other two big cats. Common Pitfalls: Some candidates may focus only on whether the animals are wild predators and miss the deeper classification into biological families. Since all four are carnivorous mammals, that criterion does not help distinguish them. Understanding that big cats are grouped together in one family and foxes in another allows you to make the correct choice consistently. Final Answer: Fox

Question 17

Find the odd group of letters from the following alternatives based on whether the letters appear in reverse alphabetical order.

Accepted Answer

Introduction / Context: This question tests your ability to detect whether a sequence of letters runs in forward or reverse alphabetical order. Recognizing such direction based patterns is essential in many reasoning questions that involve letter series and coding decoding. Given Data / Assumptions: The letter groups provided are: YXW, LKJ, RQP, and MNO. You must choose the group that does not follow the same alphabetical direction pattern as the others. Assume standard English alphabet order where A comes before B and so on. Concept / Approach: The approach is to check whether each group shows letters arranged in forward order (A to Z) or in reverse order (Z to A). If three groups show decreasing or reverse ordering and one shows increasing or forward ordering, the forward sequence becomes the odd one out. Step-by-Step Solution: Step 1: For YXW, the letters are Y, X, and W. In the alphabet, Y comes before X and X comes before W when read backward from Z, so this is a reverse alphabetical sequence. Step 2: For LKJ, the letters L, K, and J appear consecutively when you move from L backward, so LKJ is also in reverse order. Step 3: For RQP, the letters R, Q, and P again form a clear reverse alphabetical sequence. Step 4: For MNO, the letters M, N, and O move in forward order, not reverse. M is followed by N, and N is followed by O when moving forward through the alphabet. Step 5: Since three groups follow reverse alphabetical order and one group follows forward order, the forward order group is the odd one out. Verification / Alternative check: You can confirm this conclusion by assigning numerical positions to the letters. For YXW, the positions are 25, 24, and 23. For LKJ, they are 12, 11, and 10. For RQP, they are 18, 17, and 16. All these sequences show decreasing values. For MNO, the positions are 13, 14, and 15, which clearly increase. This numerical approach verifies the same pattern difference. Why Other Options Are Wrong: YXW: A correctly ordered reverse sequence and so fits with LKJ and RQP. LKJ: Another perfect reverse alphabetical run that matches the main pattern. RQP: Also shows letters in reverse order and therefore is not the odd group. Common Pitfalls: Some learners may only check whether the letters are consecutive without paying attention to direction. Since all four groups contain consecutive letters of the alphabet, this can be confusing. The essential difference is direction: three are decreasing sequences and one is an increasing sequence. Ignoring direction often leads to the wrong answer. Final Answer: MNO

Question 18

In the analogy 7 : 50 :: 9 : ?, find the missing number that continues the same numerical pattern.

Accepted Answer

Introduction / Context: This question is an analogy based number problem in the odd man out and series category. Instead of simply choosing a different number, you are asked to complete a pattern defined by the first pair. Recognizing the underlying rule between the numbers is the core challenge. Given Data / Assumptions: You are given the pair 7 : 50 and asked to extend the pattern to 9 : ?. The answer must be chosen from the options 37, 82, 17, and 90. Assume a consistent mathematical relationship connects the first number in each pair with the second. Concept / Approach: The usual technique in such questions is to search for a simple relation like addition, subtraction, multiplication, squaring, or a combination of these. Since 50 is close to 7 squared, we can suspect a pattern involving n^2 plus or minus a constant. Once you find a rule that fits the first pair neatly, you apply it to the second first number and see which option matches. Step-by-Step Solution: Step 1: Consider the first pair 7 and 50. Compute 7^2, which is 49. Notice that 49 + 1 equals 50, so 50 can be expressed as 7^2 + 1. Step 2: This suggests a rule of the form second number = first number squared plus 1, written as n^2 + 1. Step 3: Apply this rule to the second first number, which is 9. Compute 9^2, which is 81. Step 4: Add 1 to get 81 + 1 = 82. Step 5: Compare this result with the available options. The value 82 appears among the options, so 82 is the required missing number. Verification / Alternative check: You can also test whether any other simple relation fits the pair 7 and 50. For example, 7 * 7 + 1 equals 50, but forms like 7 * 8 or 7 * 6 plus constants do not match as cleanly and would not generalize well to 9. When you apply 9^2 + 1, the resulting 82 fits exactly one of the choices. No other option can be generated by applying the same squared based rule to 9, which confirms that 82 is the correct answer and the pattern is consistent. Why Other Options Are Wrong: 37: This does not equal 9^2 + 1 or follow from any simple extension of the rule used for 7 and 50. 17: Very far from 9^2, so it does not satisfy a squared plus constant pattern. 90: Also not equal to 9^2 + 1 and lacks a simple relation with the first term that would match the 7 : 50 pair. Common Pitfalls: Some students may attempt random arithmetic operations or guess based on closeness in value without properly identifying the rule. Others may overcomplicate the relationship by involving multiple steps when a simple squared pattern already fits perfectly. In analogy questions, always try to find the simplest consistent rule for the first pair before testing your options. Final Answer: 82

Question 19

In the analogy 23 : 8 :: 62 : ?, find the missing number that follows the same exponent based pattern.

Accepted Answer

Introduction / Context: This is another analogy style number question where you must find the hidden mathematical rule connecting the first number in a pair to the second. Such problems often use exponents or digit based operations to create a neat pattern. Given Data / Assumptions: The first pair given is 23 : 8. You need to determine the missing term in 62 : ?. The options available are 8, 36, 12, and 40. Concept / Approach: The digits of the first number may be used as a base and an exponent to produce the second number. For example, in the pair 23 : 8, you can interpret 23 as the digits 2 and 3, and observe that 2^3 equals 8. Extending this idea, for 62 you might interpret the digits as 6 and 2 and consider 6^2. If this yields one of the options, then you have found a consistent and elegant rule. Step-by-Step Solution: Step 1: Examine the pair 23 and 8. Take the digits 2 and 3 from 23. Step 2: Compute 2^3, which is 2 * 2 * 2 = 8. This matches the second number in the first pair, so the rule looks like a digit based exponent: left digit raised to the power of right digit. Step 3: Apply the same idea to 62. The digits are 6 and 2. Step 4: Compute 6^2, which is 6 * 6 = 36. Step 5: Check the options. The number 36 appears as one of the choices, so it is the logical continuation of the same pattern. Verification / Alternative check: You can test other possible patterns to be sure this exponent based rule is the most consistent. For example, you might try adding the digits or multiplying them, but 2 + 3 equals 5 and 2 * 3 equals 6, neither of which equals 8, so those rules do not work. Similarly, for 62, digit sums or products do not match 36. Only the exponent rule 2^3 = 8 and 6^2 = 36 matches both pairs cleanly and provides a direct link between the given numbers and the answer option. Why Other Options Are Wrong: 8: This value comes from the first pair and does not represent the result of 6^2, so it cannot complete the second pair in the same way. 12: No simple exponent rule using digits 6 and 2 yields 12, and it does not fit consistently with the first pair. 40: Also not obtained through the 6^2 pattern, and it does not match any natural extension of the 23 : 8 relationship. Common Pitfalls: One common mistake is to treat 23 and 62 as entire numbers and search for a direct arithmetic relation, such as adding or subtracting constants. However, this approach often fails in digit based analogy questions. Instead, focusing on the positional role of digits and considering exponentiation leads to a simple and elegant rule that accurately explains the given pair and predicts the missing number. Final Answer: 36

Question 20

Find the odd item from the following alternatives based on whether it is used primarily as a vegetable or a spice.

Accepted Answer

Introduction / Context: This question belongs to the general awareness and reasoning category, focusing on everyday food items. It tests whether you can distinguish between items commonly used as vegetables and items mainly used as spices or flavoring agents in cooking. Given Data / Assumptions: The options are: Potato, Tomato, Ginger, and Carrot. You must identify the item whose primary culinary role differs from the others. Assume typical usage patterns in regular cooking rather than strict botanical definitions. Concept / Approach: In most cuisines, potatoes, tomatoes, and carrots are commonly treated as vegetables and used as main ingredients in dishes. Ginger, though it can be eaten, is primarily used as a spice or flavoring agent in small quantities. Therefore, instead of classifying by plant structure, this question aims at everyday culinary classification and usage patterns. Step-by-Step Solution: Step 1: Potato is generally used as a vegetable. It can be the main ingredient in many dishes such as fries, curries, and mashed potato. Step 2: Tomato is also widely used as a vegetable in cooking, forming the base of gravies, sauces, and salads, even though botanically it is a fruit. Step 3: Carrot is another vegetable that is used in salads, curries, soups, and various cooked dishes as a primary ingredient. Step 4: Ginger, on the other hand, is not typically used as a vegetable. It is added in small amounts to impart strong flavor and aroma to dishes, and is therefore better classified as a spice or condiment. Step 5: Since three items are broadly used as vegetables and one is mainly used as a spice, ginger stands out as the odd item. Verification / Alternative check: You can also think about how you purchase and store these ingredients. Potatoes, tomatoes, and carrots are often bought in larger quantities and used in bulk as part of a meal. Ginger is usually bought in smaller pieces and used sparingly. Additionally, cookbook recipes frequently list ginger among spices or aromatics along with garlic and chilies rather than among core vegetables. This practical perspective supports the classification of ginger as different from the other three. Why Other Options Are Wrong: Potato: Commonly treated as a vegetable and often forms a major component of the dish, matching the pattern of tomato and carrot. Tomato: Also used as a vegetable in cooking and not primarily as a spice, so it fits with potato and carrot. Carrot: Clearly used as a vegetable, whether raw or cooked, and thus not the odd one. Common Pitfalls: Some learners may overthink botanical definitions and consider tomato a fruit, which is scientifically correct. However, aptitude questions of this type usually rely on everyday culinary usage, not strict botanical classification. Keeping the exam context in mind and thinking practically about how the ingredients are used in cooking leads to the correct answer. Final Answer: Ginger

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