Question 1

In the following question on object classification, four items are listed (Mobile, Computer, Fountain Pen and Television). Three of these are electronic devices, while one is a non electronic writing instrument. Select the odd word from the given al…

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Introduction / Context:This question belongs to the general classification segment of verbal reasoning. The words given are Mobile, Computer, Fountain Pen and Television. Three of these represent modern electronic gadgets that operate using electricity or batteries, while one is a traditional writing tool that does not require electrical power. Identifying this basic technological difference will help you select the odd one out. Given Data / Assumptions: Mobile: handheld electronic communication device often called a mobile phone or smartphone. Computer: electronic device used for computing, processing data and running software. Fountain Pen: mechanical writing instrument using ink, not electricity. Television: electronic device used for receiving and displaying audio visual content. We categorise items as electronic devices versus non electronic tools. Concept / Approach:The concept is straightforward: check whether each item depends on electrical power to function. A mobile needs a battery and electronic circuits, a computer requires electricity, and a television needs an electrical power source. A fountain pen works entirely through mechanical flow of ink and hand movement, without any electronics or power supply. That makes the fountain pen fundamentally different from the other three devices. Step-by-Step Solution:Step 1: Consider Mobile.A Mobile phone is an electronic gadget that needs a battery charge or external power to operate. It is clearly an electronic device.Step 2: Consider Computer.A Computer operates using complex electronic components and must be plugged into a power source or powered by a battery. It is another electronic device.Step 3: Consider Television.A Television also needs electrical power to display images and sound. It is an electronic appliance used for entertainment and information.Step 4: Consider Fountain Pen.A Fountain Pen is a simple writing instrument that uses ink and mechanical pressure from the hand. It does not use electricity or electronic parts.Step 5: Identify the odd object.Since Mobile, Computer and Television are electronic devices, and Fountain Pen is a non electronic writing tool, Fountain Pen is the odd one out. Verification / Alternative check:You can also verify by asking which of these items must be plugged in, charged or switched on in order to function. The mobile phone, computer and television all require some form of electrical power. A fountain pen, on the other hand, simply needs ink and paper; it is ready to use without any power source. This clear difference in how they work reinforces the classification. Why Other Options Are Wrong:Mobile: Electronic device, belongs with Computer and Television. Computer: Electronic device, consistent with the same group. Television: Also an electronic device, therefore not the odd one. Common Pitfalls:This question is simple, but some learners may look for more refined categories such as communication devices versus non communication devices. While that distinction exists, the examiner has chosen a clearer, more obvious contrast: electronic gadgets versus a non electronic tool. In reasoning tests, always prioritise the simplest strong grouping that applies to most options before searching for more subtle differences. Final Answer:The odd word is Fountain Pen, because Mobile, Computer and Television are electronic devices, whereas a Fountain Pen is a non electronic writing instrument.

Question 2

In the following alphabet coding question, four letter pairs are given in the form AB – C: BN – P, GI – R, LM – Y and TA – U. In three of these, the single letter represents the sum of the positions of the two letters on the left, while one pair bre…

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Introduction / Context:This question belongs to the alphabet coding and analogy section. You are given four patterns of the form two letters followed by a single letter: BN – P, GI – R, LM – Y and TA – U. In such questions, the single letter is usually derived from some arithmetic operation on the positions of the two letters in the alphabet. Here, three pairs follow the rule that the position of the single letter equals the sum of the positions of the two letters on the left. One pair does not follow this rule and must be selected as the odd one out. Given Data / Assumptions: Pairs: BN – P, GI – R, LM – Y and TA – U. Alphabet positions: A = 1, B = 2, C = 3, ..., Z = 26. For each pair AB – C, we compute position(A) + position(B) and compare with position(C). Three pairs satisfy position(C) = position(A) + position(B). One pair does not satisfy this rule. Concept / Approach:The concept is to convert letters to numbers and perform addition. For example, in BN – P, we check if B (2) plus N (14) gives P (16). If this holds, then the pattern is consistent. We repeat this process for all four pairs. The pair where the sum of the first two letters does not equal the position of the third letter is the odd one out. This simple arithmetic based coding is very common in verbal reasoning tests. Step-by-Step Solution:Step 1: Analyse BN – P.B = 2 and N = 14. Sum = 2 + 14 = 16. P is the 16th letter of the alphabet. So BN – P satisfies the rule.Step 2: Analyse LM – Y.L = 12 and M = 13. Sum = 12 + 13 = 25. Y is the 25th letter of the alphabet. So LM – Y also satisfies the rule.Step 3: Analyse TA – U.T = 20 and A = 1. Sum = 20 + 1 = 21. U is the 21st letter of the alphabet. So TA – U again follows the rule.Step 4: Analyse GI – R.G = 7 and I = 9. Sum = 7 + 9 = 16. However, 16th letter is P, not R. R is the 18th letter, so GI – R does not satisfy the rule.Step 5: Identify the odd pair.BN – P, LM – Y and TA – U all match the sum of positions rule. GI – R is the only pair that does not, so it is the odd one out. Verification / Alternative check:You can verify quickly by writing down the alphabet with positions and checking each pair mentally. For GI – R, once you notice that G + I gives 16 (P) but the pair shows R, which is position 18, it is clear that the coding is inconsistent. Ensuring that all three other pairs work perfectly with the sum rule further confirms that GI – R is the unique exception. Why Other Options Are Wrong:BN – P: 2 + 14 = 16 and P is the 16th letter, so it follows the rule. LM – Y: 12 + 13 = 25 and Y is the 25th letter, so it is also consistent. TA – U: 20 + 1 = 21 and U is the 21st letter, so this pair belongs to the pattern. Common Pitfalls:A common error is to check only one or two pairs and assume all follow the same pattern, missing the incorrect one. Another pitfall is miscounting letter positions, especially in the second half of the alphabet. To avoid mistakes, it is useful to remember positions of a few key letters, such as J = 10, M = 13, P = 16, T = 20 and Z = 26, and use them as anchors when calculating others. Final Answer:The odd letter pair is GI – R, because it does not follow the rule that the position of the third letter equals the sum of the positions of the first two letters.

Question 3

In the following number relationship question, four number pairs are given: (143, 64), (232, 49), (719, 289) and (462, 169). In three pairs, the second number equals the square of the sum of the digits of the first number, while one pair does not sa…

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Introduction / Context:This is a number coding and odd one out question. You are given four ordered pairs: (143, 64), (232, 49), (719, 289) and (462, 169). In three of these pairs, the second number is directly related to the digits of the first number by a simple rule. One pair fails to follow this rule. Your task is to identify that exceptional pair as the odd number group. Given Data / Assumptions: Pairs: (143, 64), (232, 49), (719, 289) and (462, 169). We suspect a relation involving the sum of digits of the first number. Square of a sum is computed as (sum)^2. In three pairs, second number equals the square of the digit sum of the first number. Exactly one pair does not match this pattern. Concept / Approach:The natural approach when you see a three digit number paired with a two or three digit number is to try operations such as sum of digits, product of digits or difference between digits, then see if the second number is a square or cube of that result. Here, when we take the sum of digits of the first number in each pair and square it, we see an exact match with the second number in three cases. In the remaining pair, the square of the digit sum does not match the second number, revealing it as the odd one out. Step-by-Step Solution:Step 1: Analyse (143, 64).Sum of digits of 143: 1 + 4 + 3 = 8. Square of 8 is 8^2 = 64. This equals the second number, so the pair follows the rule.Step 2: Analyse (232, 49).Sum of digits of 232: 2 + 3 + 2 = 7. Square of 7 is 7^2 = 49. This matches the second number, so the pair again follows the rule.Step 3: Analyse (719, 289).Sum of digits of 719: 7 + 1 + 9 = 17. Square of 17 is 17^2 = 289. This equals the second number, so this pair also matches the pattern.Step 4: Analyse (462, 169).Sum of digits of 462: 4 + 6 + 2 = 12. Square of 12 is 12^2 = 144, not 169. The given second number 169 equals 13^2, not 12^2. Therefore this pair does not fit the rule.Step 5: Identify the odd group.Because (462, 169) is the only pair where the second number is not equal to the square of the sum of the digits of the first number, it is the odd one out. Verification / Alternative check:You can verify quickly by writing the sum of digits and the corresponding square alongside each pair. For 143 you get 8 and 64, for 232 you get 7 and 49, and for 719 you get 17 and 289. In all these cases the second number matches the square. For 462, however, the sum of digits is 12 but the second number is 169, which is 13^2. This mismatch confirms that the last pair breaks an otherwise perfect pattern, so it must be the odd group. Why Other Options Are Wrong:(143, 64): Follows the rule because 64 is equal to (1 + 4 + 3)^2. (232, 49): Follows the rule because 49 is equal to (2 + 3 + 2)^2. (719, 289): Follows the rule because 289 is equal to (7 + 1 + 9)^2. Common Pitfalls:Some candidates may search for relationships involving multiplication of digits or direct arithmetic between the two numbers, which can be more complicated and lead to confusion. Others may miscalculate the sum of digits or the square, especially under time pressure. To avoid errors, always perform sums and squares carefully and compare them clearly with the second number. Recognising common squares like 64, 49, 144 and 169 can also speed up your reasoning. Final Answer:The odd number group is (462, 169), because in this pair the second number is not equal to the square of the sum of the digits of the first number, whereas in all the other pairs it is.

Question 4

Four number pairs are given: 3 – 6, 5 – 10, 7 – 12 and 9 – 18. In each pair, the number on the left is related to the number on the right according to a specific rule. Three of the pairs follow the same rule, while one pair breaks the pattern. Based…

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Introduction / Context: This question belongs to the aptitude topic of odd one out and number relationships. You are given four number pairs and asked to identify which pair does not follow the same rule as the others. Such questions test your ability to detect numerical patterns, especially multiplication or proportional relationships between two numbers in each pair. Given Data / Assumptions: Given pairs: 3 – 6, 5 – 10, 7 – 12, 9 – 18. Each pair has a left number and a right number. Three pairs share a common rule; one pair violates that rule. We assume basic arithmetic rules like multiplication and division are to be checked first. Concept / Approach: In odd one out questions with number pairs, a very common pattern is that the second number is a multiple of the first. The simplest check is to see whether the right side is exactly double, triple, or follows some other easy multiplier of the left side. If three pairs share the same multiplier and one does not, that nonconforming pair is the odd one out. Step-by-Step Solution: Step 1: Check the pair 3 – 6. Here, 6 = 3 * 2. So the rule could be "right number is double the left number". Step 2: Check the pair 5 – 10. Here, 10 = 5 * 2, which matches the same doubling rule. Step 3: Check the pair 9 – 18. Here, 18 = 9 * 2, again following the same pattern. Step 4: Check the pair 7 – 12. If the same rule applied, we would expect 7 * 2 = 14. However, the given right number is 12, not 14, so this pair does not follow the doubling rule. Step 5: Since three pairs follow the exact relationship "right number = 2 * left number" and one does not, the nonmatching pair is the odd one out. Verification / Alternative check: Another way to verify is to compute right / left for each pair: 6 / 3 = 2, 10 / 5 = 2, 18 / 9 = 2, but 12 / 7 is not an integer and is approximately 1.71. Only three ratios are exactly 2, confirming that those three pairs share the same rule, and the remaining pair is different. This validates that our identified odd pair is correct. Why Other Options Are Wrong: 3 – 6 is correct according to the rule because 6 is exactly double 3. 5 – 10 is correct because 10 is exactly double 5. 9 – 18 is correct because 18 is exactly double 9. Only 7 – 12 fails the doubling condition, because 12 is not equal to 7 * 2. Common Pitfalls: Students sometimes look for complicated patterns, such as adding different constants or mixing multiplication and addition, when a simple and consistent rule like doubling is sufficient. Another mistake is to perform approximate mental calculations and assume that 12 is "close enough" to 14, which is not acceptable in precise aptitude reasoning. Always check exact operations and maintain consistency across all pairs. Final Answer: The number pair that does not follow the same rule and is therefore the odd one out is 7 – 12.

Question 5

In the following aptitude question, each option shows a pair of words where the first word may or may not belong to the general category expressed by the second word. Three word pairs show a correct category relationship between an individual colour…

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Introduction / Context: This verbal reasoning question asks you to identify the odd word pair based on logical category relationships. In three of the options, the first word is a specific colour and the second word is the general category "Colour". In one option, this clear category relationship does not hold in the same way. Recognising such classification patterns is common in general aptitude and competitive exams. Given Data / Assumptions: Word pairs given: White – Colour, Blue – Colour, Yellow – Orange, Black – Colour. We assume the second word in each pair is intended to be a category or related descriptor. We need to find the pair that does not fit the same relationship as the others. Basic knowledge of colours and their categories is assumed. Concept / Approach: The key concept here is category membership. For three options, the relationship is "X is a kind of Colour". White, Blue and Black are all basic colours, so each of those can be naturally followed by the category word "Colour". In a consistent pair, the second word should act as a broader class containing the first word. We simply check which pair does not show this same one-to-many category relationship. Step-by-Step Solution: Step 1: Examine "White – Colour". White is clearly a colour, so the relationship is "White is a Colour". This pair is logically correct. Step 2: Examine "Blue – Colour". Blue is also a basic colour, so "Blue is a Colour" is a valid category relationship. Step 3: Examine "Black – Colour". Black is again a basic colour, therefore the relationship "Black is a Colour" is also logically correct. Step 4: Examine "Yellow – Orange". Both Yellow and Orange are themselves names of individual colours. Here, the second word is not acting as a category that includes the first word. Instead, we simply have two different colours placed together without a clear "is a" category relationship. Step 5: Since three pairs follow the pattern "Specific Colour – Colour (category)" and one pair is "Colour – Colour" without a category link, the odd one out is "Yellow – Orange". Verification / Alternative check: You can recast each pair into a sentence: White is a Colour – correct. Blue is a Colour – correct. Black is a Colour – correct. Yellow is an Orange – incorrect, because Orange is not the broader category of Yellow. Only the fourth sentence is logically incorrect, confirming that Yellow – Orange does not fit the same pattern. Why Other Options Are Wrong: White – Colour is valid because White is a member of the category Colour. Blue – Colour is valid for exactly the same reason, Blue is also a Colour. Black – Colour is again valid, as Black is a recognised Colour. These three all share a clear "member–category" relationship, unlike Yellow – Orange. Common Pitfalls: A common confusion is to overthink the relationship between Yellow and Orange and imagine some hidden connection, such as both being warm colours. However, the test is not about similarity or contrast but about whether the second word is a category label for the first. Another pitfall is to assume that any pair of colours together forms a valid pattern, which is not the intended logic here. Final Answer: The pair that breaks the consistent category pattern and is therefore the odd one out is Yellow – Orange.

Question 6

In the following number analogy question, 695 is related to 659 according to a specific pattern formed by rearranging its digits. Using the same rule, 839 will be related to which of the following numbers?

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Introduction / Context: This is a classic number analogy problem where you are given one pair of related numbers (695 : 659) and asked to find a number that relates to 839 in the same way. Such questions check your ability to spot patterns in the arrangement of digits rather than just arithmetic operations like addition, subtraction or multiplication. Given Data / Assumptions: Given analogy: 695 : 659. Target: 839 : ? Options: 392, 984, 931, 893. We assume the pattern involves rearranging or manipulating the digits of the original number. Concept / Approach: Instead of directly applying operations such as addition or subtraction to the entire number, it is often useful in analogy questions to look at the digits separately. We check whether the second number is formed by rearranging the digits of the first number in some fixed way. Once we identify the rule for 695 transforming into 659, we apply the same rule to 839 and see which option matches. Step-by-Step Solution: Step 1: Write the digits of 695 as 6, 9 and 5. Step 2: Observe the digits of 659: 6, 5 and 9. Step 3: Compare the two sequences. The first digit 6 remains the same in both numbers. The last two digits 9 and 5 in 695 have simply exchanged positions to become 5 and 9 in 659. Step 4: Thus, the rule appears to be: keep the first digit unchanged and swap the second and third digits of the original number. Step 5: Apply this rule to 839. The digits of 839 are 8, 3 and 9. Keeping the first digit 8 fixed and swapping the last two digits 3 and 9 gives 8, 9, 3. Step 6: The resulting number is 893. Check the options: 893 matches option D. Verification / Alternative check: To ensure the rule is consistent, verify that no other obvious pattern exists that would point to a different option. There is no simple arithmetic relation such as 695 minus a fixed value to get another option and then repeating the same for 839. Additionally, none of the other options 392, 984 or 931 arise from a simple swap of the last two digits of 839. This confirms that our digit rearrangement rule is both simple and unique. Why Other Options Are Wrong: 392 is formed by a different digit arrangement and does not keep the first digit of 839 fixed. 984 changes both the first digit and the order of the remaining digits, which does not follow the pattern from 695 to 659. 931 again does not keep the first digit unchanged and does not result from just swapping the last two digits of 839. Only 893 is obtained by preserving the first digit and interchanging the last two digits, which matches the original example. Common Pitfalls: Students sometimes jump to arithmetic operations such as subtracting or adding a fixed number, which can mislead them when the pattern is purely positional. Another common error is to overcomplicate the rule by combining digit sums and products when a simple swap is sufficient. Always start by checking the simplest possible pattern: digit rearrangement, reversal, or swapping. Final Answer: Using the same digit-swapping rule, the number related to 839 is 893.

Question 7

Four objects related to writing and reading are given as options: Book, Pen, Pencil and Wax Colours. Three of them are primarily writing or drawing instruments, while one is different in its main use. From the given alternatives, which word is the o…

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Introduction / Context: This question tests your ability to classify everyday objects based on their primary function. You are given four words that commonly appear in a study environment: Book, Pen, Pencil and Wax Colours. Your task is to identify which one does not belong to the same functional group as the others, making it the odd one out. Such questions are common in aptitude tests for developing logical grouping skills. Given Data / Assumptions: Options: Book, Pen, Pencil, Wax Colours. All four items are related to reading, writing or drawing in some way. We are looking for one item whose primary role is different from the other three. Basic real-life knowledge about stationeries and reading materials is assumed. Concept / Approach: The key idea is functional classification. We check how each item is mainly used: Pens, pencils and wax colours are tools used to produce writing or drawing marks. A book, however, is not a tool for writing; it is an object that already contains written or printed content for reading. By identifying which item does not function as a writing or colouring instrument, we can select the odd one out. Step-by-Step Solution: Step 1: Consider "Pen". A pen is a writing instrument used to put ink marks on paper. It is clearly a tool used for writing. Step 2: Consider "Pencil". A pencil is also a writing or drawing instrument, using graphite or colour lead to create lines and shapes on paper. Step 3: Consider "Wax Colours". Wax colours (crayons) are colouring tools used especially by children for drawing and shading. Step 4: Notice the similarity among Pen, Pencil and Wax Colours: all three are instruments used to create marks on a surface. Step 5: Consider "Book". A book is a collection of pages with printed or written text and images. Its primary role is to be read, not to be used as a writing or colouring tool. Step 6: Therefore, Book is functionally different from the other three items, which makes it the odd one out. Verification / Alternative check: One more way to verify your answer is to group the items by their rough category: Group 1: Writing and drawing instruments – Pen, Pencil, Wax Colours. Group 2: Reading material – Book. Because you can place three items in one functional group and only one item in another, the single member group is clearly the odd one out. Why Other Options Are Wrong: Pen is not odd because it belongs neatly to the category of writing instruments. Pencil is also a common writing and drawing tool, so it matches Pen and Wax Colours. Wax Colours are drawing tools used for colouring, sharing the same functional category as Pen and Pencil. Only Book does not act as an instrument; instead, it is an object to be read, so it is the different one. Common Pitfalls: Sometimes students overthink and consider that a book might indirectly be related to writing because authors use writing instruments to create its content. However, in reasoning questions, we consider the direct and primary use of each object. Another pitfall is focusing on physical appearance (for example, all items might be found on a study table) instead of actual function. Always focus on the central usage pattern. Final Answer: The word that differs in primary function and is therefore the odd one out is Book.

Question 8

In the following question, four groups of letters are given: AZF, LOQ, EVK and ZAC. In three of these groups, the sum of the alphabetical positions of the first and last letters is an odd number, whereas in one group it is even. Based on this hidden…

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Introduction / Context: This question comes from the letter series and odd one out section of aptitude tests. You are provided with four three-letter groups: AZF, LOQ, EVK and ZAC. Your task is to identify which group does not follow the same positional pattern in the English alphabet as the others. Questions of this type test your ability to convert letters into their positions (A = 1, B = 2, ..., Z = 26) and to detect a consistent numerical relationship. Given Data / Assumptions: Letter groups: AZF, LOQ, EVK, ZAC. We use A = 1, B = 2, ..., Z = 26 as standard positions. We will compare the positions of the first and last letters in each group. We assume only one group breaks the otherwise consistent pattern. Concept / Approach: A useful approach in such problems is to convert letters into their numeric positions and then look for patterns based on sums, differences or parity (odd or even). Here, we examine the sum of the positions of the first and last letters of each group. If three sums have the same parity (all odd or all even) and one is different, that group becomes the odd one out. Step-by-Step Solution: Step 1: For AZF: A = 1, Z = 26, F = 6. Sum of first and last letters = 1 + 6 = 7, which is odd. Step 2: For LOQ: L = 12, O = 15, Q = 17. Sum of first and last letters = 12 + 17 = 29, which is odd. Step 3: For EVK: E = 5, V = 22, K = 11. Sum of first and last letters = 5 + 11 = 16, which is even. Step 4: For ZAC: Z = 26, A = 1, C = 3. Sum of first and last letters = 26 + 3 = 29, which is odd. Step 5: Compare parities: AZF gives 7 (odd), LOQ gives 29 (odd), ZAC gives 29 (odd), while EVK gives 16 (even). Step 6: Since exactly one group yields an even sum and the remaining three yield odd sums, EVK is the group that breaks the pattern. Verification / Alternative check: To verify, ensure no simpler pattern exists that would give a different answer. You can check differences between positions, vowel–consonant arrangements or alphabetical order, but none of these produce a consistent three-versus-one pattern as clearly as the sum parity rule. Because the odd-even difference is simple, unique and cleanly separates EVK from the others, this rule is a strong and reliable explanation. Why Other Options Are Wrong: AZF is not odd because 1 + 6 = 7, an odd sum, matching the overall odd-sum pattern. LOQ is not odd because 12 + 17 = 29, another odd sum consistent with the majority pattern. ZAC is not odd because 26 + 3 = 29, which is also odd and fits the same pattern. Only EVK, with 5 + 11 = 16, produces an even sum, making it different from the rest. Common Pitfalls: A common mistake is to overcomplicate the pattern by trying to relate all three letters in a more complex sequence or by forcing a rule that does not clearly separate one group. Another pitfall is to focus only on alphabetical ordering of letters rather than their numeric positions. When stuck, always try basic numeric operations on letter positions such as sums or differences and examine parities, because many exam questions are based on such simple yet effective patterns. Final Answer: The only letter group that breaks the odd-sum pattern is EVK, so it is the odd one out.

Question 9

In the following question, four number pairs are given: 41 – 22, 63 – 93, 82 – 44 and 83 – 64. In three of these pairs, the difference between the two numbers is a multiple of 19, while one pair does not follow this rule. Based on this relationship,…

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Introduction / Context: This question belongs to the number pair odd one out type in aptitude tests. You are given four pairs of numbers and asked to find which pair does not follow the same numerical rule as the others. Here, the key idea is to look at the difference between the two numbers in each pair and identify a consistent pattern, especially involving a specific factor such as 19. Given Data / Assumptions: Number pairs: 41 – 22, 63 – 93, 82 – 44, 83 – 64. We will compute the difference between the two numbers in each pair. We are searching for a common factor, particularly 19, in three of the four differences. One pair is expected to break this pattern and will be the odd one out. Concept / Approach: Odd one out questions on number pairs often use relationships such as sums, products, or differences. A neat and common trick is to check whether the differences between the pair members are multiples of a specific number. If three differences are multiples of a certain integer and one is not, the corresponding pair is the odd one out. We will apply this method using basic subtraction and divisibility checks. Step-by-Step Solution: Step 1: For 41 – 22: Difference = 41 - 22 = 19. 19 is clearly a multiple of 19 (19 * 1). Step 2: For 82 – 44: Difference = 82 - 44 = 38. 38 is 19 * 2, so it is also a multiple of 19. Step 3: For 83 – 64: Difference = 83 - 64 = 19. Again, 19 is exactly 19 * 1, a multiple of 19. Step 4: For 63 – 93: Difference = 63 - 93 = -30. For odd one out purposes, we can consider the magnitude, which is 30. Step 5: Check whether 30 is a multiple of 19. Since 19 * 1 = 19 and 19 * 2 = 38, 30 lies between these and is not a multiple of 19. Step 6: We see that three pairs (41 – 22, 82 – 44 and 83 – 64) have differences that are multiples of 19, while the pair 63 – 93 does not. Verification / Alternative check: As an alternative, you can simply list the absolute differences: |41 - 22| = 19 |82 - 44| = 38 |83 - 64| = 19 |63 - 93| = 30 Then check divisibility: 19 / 19 = 1 (exact multiple), 38 / 19 = 2 (exact multiple), 19 / 19 = 1 (exact multiple), but 30 / 19 is not an integer. Since only 30 is not a multiple of 19, the pair 63 – 93 clearly breaks the common rule. Why Other Options Are Wrong: 41 – 22 is not odd because its difference 19 is exactly 19 * 1. 82 – 44 is not odd because its difference 38 is 19 * 2. 83 – 64 is not odd because its difference 19 is again 19 * 1. Only 63 – 93 produces a difference 30 that is not divisible by 19, making it special. Common Pitfalls: A common mistake is to focus on the sum of the numbers in each pair or to look for more complex patterns such as squares or cubes, which are not needed here. Another pitfall is to ignore negative signs and get confused. In odd one out problems, it is usually safe to consider the absolute difference between the numbers. Keeping the reasoning simple and checking multiples carefully avoids such errors. Final Answer: The pair that does not have a difference which is a multiple of 19 and is therefore the odd one out is 63 – 93.

Question 10

In the following question, four three-letter groups are given: FHJ, LNQ, JLN and NPR. In three of these groups, the letters progress through the alphabet with equal jumps of two positions each, while one group does not follow this pattern. Which let…

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Introduction / Context: This question belongs to the letter series and odd one out category in aptitude tests. You are given four groups of letters and asked to identify which group does not follow the same alphabetical pattern as the others. These questions test your skills in mapping letters to their positions in the English alphabet and recognising consistent step sizes between them. Given Data / Assumptions: Letter groups: FHJ, LNQ, JLN, NPR. We use the standard positions: A = 1, B = 2, ..., Z = 26. We will examine the step difference between consecutive letters in each group. We assume that exactly one group will break the established pattern. Concept / Approach: In many letter pattern questions, the difference in alphabetical positions between letters is constant. For example, a sequence might move +2 positions each time. Here, we will calculate the position difference between the first and second letters, and between the second and third letters, for each group. If three groups share the same pattern (for example, +2 and +2) and one group does not, that group is the odd one out. Step-by-Step Solution: Step 1: For FHJ: F = 6, H = 8, J = 10. Differences: H - F = 8 - 6 = 2, J - H = 10 - 8 = 2. So the pattern here is +2, +2. Step 2: For JLN: J = 10, L = 12, N = 14. Differences: L - J = 12 - 10 = 2, N - L = 14 - 12 = 2. This also follows a +2, +2 pattern. Step 3: For NPR: N = 14, P = 16, R = 18. Differences: P - N = 16 - 14 = 2, R - P = 18 - 16 = 2. Again, the pattern is +2, +2. Step 4: For LNQ: L = 12, N = 14, Q = 17. Differences: N - L = 14 - 12 = 2, Q - N = 17 - 14 = 3. Step 5: Here, LNQ has step sizes +2 and +3, while all the other groups strictly have +2 and +2. Step 6: Therefore, LNQ is the only letter group that does not follow the same equal-jump pattern and is the odd one out. Verification / Alternative check: To verify quickly, you can mentally check if each sequence looks like equally spaced letters. FHJ, JLN and NPR all look like evenly spaced letters in the alphabet. In contrast, LNQ appears slightly stretched, especially in the jump from N to Q. This quick alphabet check confirms our detailed numeric analysis. Why Other Options Are Wrong: FHJ is not odd because both jumps, F to H and H to J, are exactly 2 letters apart. JLN is not odd because both jumps, J to L and L to N, are also 2 letters apart. NPR is not odd because N to P and P to R both involve a jump of 2 letters. Only LNQ, with jumps of +2 then +3, breaks the equal step pattern. Common Pitfalls: A common mistake is to miscount the number of steps between letters, especially when doing it quickly in your head. Another pitfall is focusing only on whether the letters are generally moving forward without checking if the distances are consistent. Always convert letters to numbers and compute exact differences to avoid such errors in letter reasoning questions. Final Answer: The letter group that does not maintain equal jumps of two positions and is therefore the odd one out is LNQ.

Question 11

In the following question, select the odd number pair from the given alternatives: 11 – 121, 13 – 169, 19 – 391 and 21 – 441. In three of these pairs, the second number is the exact square of the first number, while in one pair this square relations…

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Introduction / Context: This question is an odd one out problem involving number pairs and perfect squares. You are given four pairs of numbers and must identify which pair does not follow the same square relationship as the others. Recognising squares and square relationships is very common in quantitative aptitude tests and helps in quickly classifying numerical patterns. Given Data / Assumptions: Number pairs: 11 – 121, 13 – 169, 19 – 391, 21 – 441. We suspect that a square relationship might exist because numbers like 121, 169 and 441 are familiar squares. We will check whether the second number in each pair equals the square of the first number. One pair will fail this test and will be the odd one out. Concept / Approach: The basic concept is that of perfect squares: n^2 means n multiplied by itself. For each pair (a, b), we check whether b = a^2. If three of the pairs satisfy this exact square relation and one does not, the nonconforming pair is the odd one out. This approach uses straightforward arithmetic and basic knowledge of square numbers. Step-by-Step Solution: Step 1: For 11 – 121: Compute 11^2 = 11 * 11 = 121. So the second number is exactly the square of the first. Step 2: For 13 – 169: Compute 13^2 = 13 * 13 = 169. Again, the second number is the square of the first. Step 3: For 21 – 441: Compute 21^2 = 21 * 21 = 441. The second number is exactly equal to 21^2. Step 4: For 19 – 391: Compute 19^2 = 19 * 19 = 361. However, the second number given is 391, which is not equal to 361. Step 5: Because 391 does not equal 19^2, the pair 19 – 391 does not follow the square relationship shared by the other three pairs. Verification / Alternative check: You can also check by factorisation: 121 = 11 * 11, therefore a perfect square. 169 = 13 * 13, again a perfect square. 441 = 21 * 21, also a perfect square. 391, however, can be factorised as 17 * 23, which is not of the form n * n. Thus 391 is not a perfect square, confirming that 19 – 391 is structurally different from the other pairs. Why Other Options Are Wrong: 11 – 121 is not odd because 121 is the perfect square of 11. 13 – 169 is not odd because 169 is the perfect square of 13. 21 – 441 is not odd because 441 is the perfect square of 21. Only 19 – 391 breaks the rule as 391 is not equal to 19^2. Common Pitfalls: A frequent mistake is miscalculating the square of 19 or confusing 391 with 361 due to similar digits. Some students might also attempt to relate the numbers using arbitrary multiplication or addition instead of checking the simplest and most obvious square relationship. Always calculate squares carefully and, when in doubt, verify by factorisation. Final Answer: The pair that does not follow the square relationship and is therefore the odd one out is 19 – 391.

Question 12

In the following question about indoor and outdoor games, four games are listed: Cricket, Carrom, Table Tennis and Chess. Three of these games are typically played indoors on a board or table, while one is mainly played outdoors on a large ground. F…

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Introduction / Context: This is a classification-based odd one out question from the general aptitude section. You are given four popular games: Cricket, Carrom, Table Tennis and Chess. While all of them are well known, they differ in where and how they are usually played. Your job is to identify which game does not belong with the other three in terms of being an indoor versus outdoor game. Given Data / Assumptions: Games listed: Cricket, Carrom, Table Tennis, Chess. We assume their usual playing environment: indoor or outdoor. Carrom, Table Tennis and Chess are generally played indoors on a small surface. Cricket is mainly played outdoors on a larger ground. Concept / Approach: The concept here is to classify games based on their typical playing venue and equipment: Indoor games are usually played inside a room on tables or boards. Outdoor games generally require large open grounds or fields. By identifying which game does not fit the indoor category, we can select the odd one out. This approach uses simple real-life knowledge rather than complex calculations. Step-by-Step Solution: Step 1: Consider Carrom. Carrom is a board game that is almost always played indoors on a carrom board placed on a table or stand. Step 2: Consider Table Tennis. Table Tennis is played on a table with a net in the middle and is typically played indoors in halls or sports rooms. Step 3: Consider Chess. Chess is a strategic board game that is played indoors on a chessboard placed on a table. Step 4: Note the commonality: Carrom, Table Tennis and Chess are all indoor games played on compact surfaces. Step 5: Consider Cricket. Cricket is normally played outdoors on a large ground or stadium, with a pitch in the centre and fielders spread out across the field. Step 6: Because Cricket clearly differs in its outdoor nature and large playing area, it is the odd one out among these games. Verification / Alternative check: Another way to verify is to imagine the equipment and venue required: Indoor board or table-based equipment: Carrom board, Table Tennis table, Chess board. Outdoor field and pitch-based equipment: Cricket bat, ball and large ground. Only Cricket demands a large outdoor field as an essential part of the game. This classification confirms that Cricket is different from the others. Why Other Options Are Wrong: Carrom is not odd because it is a typical indoor board game. Table Tennis is not odd because it is primarily played indoors on a table. Chess is not odd because it is also an indoor, table-top board game. Cricket alone is mainly an outdoor sport played on a field, making it the outlier. Common Pitfalls: Some students may think that Table Tennis can also be played outdoors, but standard competitive and organised Table Tennis is predominantly an indoor sport. Another pitfall is focusing on the popularity of the game instead of the place where it is played. For aptitude classification questions, always focus on the main defining characteristic, not side details. Final Answer: The game that is mainly outdoor and therefore the odd one out is Cricket.

Question 13

In the following question, four letter groups are given: IMX, DHS, GWK and KOZ. In three of these groups, the letters follow the pattern of jumping +4 positions and then +11 positions in the English alphabet, while one group does not follow this pat…

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Introduction / Context: This question comes from the letter series and odd one out section of aptitude tests. You are given four three-letter groups and must identify which one does not follow the same pattern in terms of letter positions in the English alphabet. Such questions strengthen your skill in translating letters to numbers (A = 1 to Z = 26) and spotting arithmetic patterns in the jumps between letters. Given Data / Assumptions: Letter groups: IMX, DHS, GWK, KOZ. Alphabet positions: A = 1, B = 2, ..., Z = 26. We will check the position differences between consecutive letters in each group. We expect three groups to share a common pattern and one group to differ. Concept / Approach: A standard approach is to compute the difference in positions between the first and second letters, and between the second and third letters. When a clear pattern such as +4, +11 appears repeatedly, we can classify groups that follow this pattern together and then identify the one that does not. The group breaking the pattern is the odd one out. Step-by-Step Solution: Step 1: For IMX: I = 9, M = 13, X = 24. Differences: M - I = 13 - 9 = 4, X - M = 24 - 13 = 11. So the pattern is +4, then +11. Step 2: For DHS: D = 4, H = 8, S = 19. Differences: H - D = 8 - 4 = 4, S - H = 19 - 8 = 11. Again, the pattern is +4, then +11. Step 3: For KOZ: K = 11, O = 15, Z = 26. Differences: O - K = 15 - 11 = 4, Z - O = 26 - 15 = 11. This also follows the +4, then +11 pattern. Step 4: For GWK: G = 7, W = 23, K = 11. Differences: W - G = 23 - 7 = 16, K - W = 11 - 23 = -12. Step 5: The pattern in GWK, with jumps of +16 and -12, clearly does not match the neat +4, +11 pattern of the other three letter groups. Step 6: Therefore, GWK is the odd one out. Verification / Alternative check: As a quicker check, you can visually inspect whether the letters look evenly spaced in the alphabet. IMX, DHS and KOZ all show moderately spaced jumps that are consistent in size, while GWK contains a very large jump from G to W and then backwards from W to K. This visual irregularity indicates GWK behaves differently, confirming our detailed numeric analysis. Why Other Options Are Wrong: IMX is not odd because the differences between its letters are +4 and +11, matching the common pattern. DHS is not odd because it also follows +4 and +11 between consecutive letters. KOZ is not odd because it continues the exact same +4 and +11 jump pattern. Only GWK fails to follow this jump pattern, showing irregular jumps of +16 and -12. Common Pitfalls: Students sometimes miscalculate letter positions or forget that Z corresponds to 26, leading to incorrect differences. Another pitfall is looking only at increasing or decreasing sequences without checking actual jump sizes. To avoid such mistakes, always write down the position numbers and perform basic subtraction carefully. Final Answer: The letter group that does not follow the +4, then +11 pattern and is therefore the odd one out is GWK.

Question 14

In the following question, four letter groups are given: CEF, LNO, RTU and GIK. In three of these groups, the second and third letters are obtained by adding +2 and then +1 positions to the first letter in the English alphabet, while one group does …

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Introduction / Context: This question is part of the letter series and odd one out type in aptitude exams. You are given four three-letter groups and must determine which group does not follow the same consistent alphabetic pattern as the others. These questions evaluate how well you can map letters to their numerical positions in the alphabet and spot fixed step-size patterns. Given Data / Assumptions: Letter groups: CEF, LNO, RTU, GIK. Alphabet positions: A = 1, B = 2, ..., Z = 26. We will examine the differences in positions between consecutive letters in each group. We expect a common pattern in three groups, and one group will differ. Concept / Approach: Many letter group questions follow a pattern where each subsequent letter is obtained by adding a fixed number to the position of the previous letter. Here, we will: Compute the difference between the first and second letters. Compute the difference between the second and third letters. If three groups follow a +2, then +1 pattern and one does not, the nonconforming group is the odd one out. Step-by-Step Solution: Step 1: For CEF: C = 3, E = 5, F = 6. Differences: E - C = 5 - 3 = 2, F - E = 6 - 5 = 1. Pattern: +2, then +1. Step 2: For LNO: L = 12, N = 14, O = 15. Differences: N - L = 14 - 12 = 2, O - N = 15 - 14 = 1. Pattern: +2, then +1. Step 3: For RTU: R = 18, T = 20, U = 21. Differences: T - R = 20 - 18 = 2, U - T = 21 - 20 = 1. Pattern: +2, then +1. Step 4: For GIK: G = 7, I = 9, K = 11. Differences: I - G = 9 - 7 = 2, K - I = 11 - 9 = 2. Pattern: +2, then +2. Step 5: While CEF, LNO and RTU all follow a +2, +1 pattern, GIK follows +2, +2 and thus does not fit the same rule. Step 6: Therefore, GIK is the odd one out. Verification / Alternative check: Visually, you can see that in CEF, LNO and RTU, the first and second letters are separated by two letters, while the second and third letters are adjacent in the alphabet. In GIK, however, there is always a gap of one letter between each pair of letters (G to I and I to K), which is a different pattern. This supports our numeric analysis. Why Other Options Are Wrong: CEF is not odd because it clearly follows the +2, then +1 pattern. LNO is not odd because its letters also move forward by +2, then +1 positions. RTU is not odd because it continues the same +2, then +1 step pattern. Only GIK uses +2, then +2, breaking the consistent pattern followed by the others. Common Pitfalls: A typical mistake is to glance at the letters quickly and assume all sequences look similar without checking the exact distances between them. Another pitfall is miscalculating the letter positions or forgetting that H is 8, I is 9 and so on. Always translate letters to their numeric positions and perform exact subtraction to avoid careless errors. Final Answer: The letter group that does not follow the +2, then +1 pattern and is therefore the odd one out is GIK.

Question 15

In the following question, four number pairs are given: 49 – 64, 576 – 729, 441 – 484 and 100 – 121. In three of these pairs, the numbers are perfect squares of consecutive integers, while one pair does not follow this consecutive-square relationshi…

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Introduction / Context: This question is based on recognising perfect squares and patterns between them. You are given four number pairs and must determine which pair does not follow the same relationship as the others. Specifically, three pairs consist of perfect squares of consecutive integers, while one pair has a different gap between the square roots of the two numbers. Such questions help test your familiarity with square numbers and your ability to detect simple numerical patterns. Given Data / Assumptions: Number pairs: 49 – 64, 576 – 729, 441 – 484, 100 – 121. We will express each number as a square of some integer. We then examine the difference between the square roots in each pair. Three pairs are expected to have consecutive integer square roots, and one pair will not. Concept / Approach: The method is straightforward: Write each number as n^2 if possible. For each pair (a, b), find integers m and n such that a = m^2 and b = n^2. Check whether n = m + 1, meaning that the second number is the square of the next consecutive integer. The pair where this relationship does not hold is the odd one out. Step-by-Step Solution: Step 1: For 49 – 64: 49 = 7^2 and 64 = 8^2. The square roots are 7 and 8, which are consecutive integers. Step 2: For 441 – 484: 441 = 21^2 and 484 = 22^2. The square roots are 21 and 22, again consecutive integers. Step 3: For 100 – 121: 100 = 10^2 and 121 = 11^2. The square roots are 10 and 11, which are consecutive. Step 4: For 576 – 729: 576 = 24^2 and 729 = 27^2. The square roots are 24 and 27, which are not consecutive (there is 25 and 26 in between). Step 5: Therefore, in three pairs the square roots differ by 1, and in one pair they differ by 3. The pair 576 – 729 breaks the consecutive square pattern. Verification / Alternative check: You can also check the differences between the square roots: 49 – 64: roots 7 and 8, difference = 1. 441 – 484: roots 21 and 22, difference = 1. 100 – 121: roots 10 and 11, difference = 1. 576 – 729: roots 24 and 27, difference = 3. Since only the pair 576 – 729 shows a larger gap between the square roots, it is clearly distinct from the others. Why Other Options Are Wrong: 49 – 64 is not odd because it is formed by squares of consecutive integers 7 and 8. 441 – 484 is not odd because it uses consecutive roots 21 and 22. 100 – 121 is not odd because its roots 10 and 11 are consecutive. Only 576 – 729 uses roots 24 and 27, which are not consecutive, making it different. Common Pitfalls: A common mistake is to look only at the numeric differences between the pair members instead of focusing on square roots. Another error is misremembering squares such as 24^2 and 27^2. To avoid confusion, carefully compute or recall key squares and focus on the relationship between their roots, not just the raw numbers. Final Answer: The pair that does not consist of squares of consecutive integers and is therefore the odd one out is 576 – 729.

Question 16

Arrange the following words in the order in which they would appear in a standard English dictionary: Waste, Wrong, Witty, Worcester and Warlike. The options show different numerical sequences representing the correct alphabetical order. Which seque…

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Introduction / Context: This question tests your understanding of dictionary or alphabetical order for English words. You are given five words and asked to arrange them as they would appear in a dictionary. The options use numbers to represent the positions of the words in the original list, and you must choose the correct sequence. Such questions help build careful attention to spelling and letter-by-letter comparison. Given Data / Assumptions: Words with their numbers: 1. Waste 2. Wrong 3. Witty 4. Worcester 5. Warlike We assume standard English alphabetical order. We need to compare the words letter by letter starting from the left. The correct option will encode the order of words using their given numbers. Concept / Approach: In dictionary ordering: First compare the first letter of all words. If the first letter is the same, compare the second letter, and so on. The moment a difference is found, the word with the earlier alphabet letter comes first. Here, all words start with "W", so we move to successive letters until we can determine their relative order. Step-by-Step Solution: Step 1: Write the words: Waste (1), Wrong (2), Witty (3), Worcester (4), Warlike (5). Step 2: Compare second letters: Waste (a), Wrong (r), Witty (i), Worcester (o), Warlike (a). Step 3: In alphabetical order, the second letters rank as: a, a, i, o, r. Step 4: So words starting with "Wa" will come before "Wi", which will come before "Wo", which then comes before "Wr". Step 5: Among "Wa" words, we have Waste (1) and Warlike (5). Now compare further: Warlike: W A R... Waste: W A S... At the third letter, r comes before s, so Warlike (5) comes before Waste (1). Step 6: After the "Wa" words, we have Witty (3) (Wi...), then Worcester (4) (Wo...), then Wrong (2) (Wr...). Within these, i comes before o, and o comes before r, so the order Witty (3), Worcester (4), Wrong (2) is correct. Step 7: Combining all, the complete dictionary order is: 5. Warlike 1. Waste 3. Witty 4. Worcester 2. Wrong This corresponds to the sequence 51342. Verification / Alternative check: You can verify by listing them in order: Warlike Waste Witty Worcester Wrong Now check the option codes: 51342 exactly matches this order, confirming it as correct. Why Other Options Are Wrong: Option 51324 misplaces Worcester and Wrong at the end. Option 13452 starts with Waste instead of Warlike, which is incorrect because "War..." comes before "Was...". Option 15342 has the same problem, placing Waste before Warlike. Only option 51342 aligns with the correct alphabetical sequencing of all five words. Common Pitfalls: Students sometimes compare only the first two letters and ignore later letters when they are crucial for ordering words like Waste and Warlike. Another common error is to assume that more familiar or frequently used words come first, which is not how dictionary order works. Always compare letters strictly from left to right, moving to the next letter only when the previous letters are identical. Final Answer: The correct dictionary order corresponds to the sequence 51342.

Question 17

In the following question, select the odd number from the given alternatives: 133, 253, 231 and 209. Three of these numbers are divisible by 11, while one number is not divisible by 11. Based on this divisibility property, which number is the odd on…

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Introduction / Context: This question checks your understanding of divisibility rules and prime factorisation. You are given four numbers and asked to select the one that does not share a particular divisibility property with the others. Here, three of the numbers are divisible by 11, while one number is not. Identifying such patterns is common in odd one out questions in quantitative aptitude exams. Given Data / Assumptions: Given numbers: 133, 253, 231, 209. We will use divisibility checks and factorisation. We suspect a common factor, specifically 11, in three of the numbers. One number will not be divisible by 11 and thus be the odd one out. Concept / Approach: The approach is to check each number for divisibility by 11: Use either the difference-of-sums rule for 11 or straightforward factorisation. If 11 divides three numbers but not the fourth, the undivided number is the odd one out. You can also factor each number directly to confirm which ones contain 11 as a factor. Step-by-Step Solution: Step 1: Check 253. Try dividing by 11: 11 * 23 = 253, so 253 is divisible by 11. Step 2: Check 231. Try dividing by 11: 11 * 21 = 231, so 231 is divisible by 11. Step 3: Check 209. Try dividing by 11: 11 * 19 = 209, so 209 is also divisible by 11. Step 4: Check 133. Try dividing by 11: 11 * 12 = 132, and 11 * 13 = 143, so 133 lies between these and is not a multiple of 11. Step 5: Alternatively, factor 133: Try 7: 7 * 19 = 133, so 133 = 7 * 19 and contains no factor 11. Step 6: Therefore, 253, 231 and 209 are all divisible by 11, while 133 is not. Hence 133 is the odd one out. Verification / Alternative check: You can also use the divisibility rule for 11, which says: If the difference between the sum of the digits in odd places and the sum of the digits in even places is a multiple of 11 (including 0), then the number is divisible by 11. Apply this: For 253: (2 + 3) - 5 = 5 - 5 = 0 → divisible by 11. For 231: (2 + 1) - 3 = 3 - 3 = 0 → divisible by 11. For 209: (2 + 9) - 0 = 11 - 0 = 11 → divisible by 11. For 133: (1 + 3) - 3 = 4 - 3 = 1, which is not a multiple of 11 → not divisible by 11. This confirms that 133 is the only number not divisible by 11. Why Other Options Are Wrong: 253 is not odd because it clearly equals 11 * 23 and is divisible by 11. 231 is not odd because it equals 11 * 21 and is divisible by 11. 209 is not odd because it equals 11 * 19 and is divisible by 11. 133 is the only number that lacks 11 as a factor, making it the odd one out. Common Pitfalls: Students sometimes rely on rough mental estimation instead of precise multiplication and may incorrectly assume 133 is 11 * 11 or 11 * 12. Another pitfall is to look for patterns in the sum of digits or parity (odd or even) instead of focusing on the intended divisibility property. Using the proper divisibility rule for 11 or exact factorisation prevents these errors. Final Answer: The number that is not divisible by 11 and is therefore the odd one out is 133.

Question 18

In the following question, four number pairs are given: 10 – 121, 12 – 169, 14 – 225 and 16 – 279. In three of these pairs, the second number is the square of an odd integer that is exactly one greater than the first number, while in one pair this s…

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Introduction / Context: This is an odd one out question involving number pairs and square relationships. Each pair consists of a smaller first number and a larger second number. In three pairs, the second number is the square of an odd number that is exactly one greater than the first number. In one case, this pattern breaks. Recognising squares and understanding such structured relationships is common in aptitude tests. Given Data / Assumptions: Number pairs: 10 – 121, 12 – 169, 14 – 225, 16 – 279. We will compare the first number with the square root of the second number. We suspect that the second number is intended to be (first number + 1)^2 for three of the pairs. One pair will not fit this formula and will be the odd one out. Concept / Approach: We use the idea of perfect squares and simple algebraic relations: If a pair is of the form (n, m), we check if m = (n + 1)^2. Since the first numbers 10, 12, 14 and 16 are even, the next integers 11, 13, 15 and 17 are odd, and their squares may appear as the second numbers. We will compute (n + 1)^2 for each first number and see which pair does not match. Step-by-Step Solution: Step 1: For the pair 10 – 121: First number n = 10, so n + 1 = 11. Compute (n + 1)^2 = 11^2 = 121. The second number is 121, which matches. Step 2: For the pair 12 – 169: n = 12, so n + 1 = 13. Compute (n + 1)^2 = 13^2 = 169. The second number is 169, which matches. Step 3: For the pair 14 – 225: n = 14, so n + 1 = 15. Compute (n + 1)^2 = 15^2 = 225. The second number is 225, which matches. Step 4: For the pair 16 – 279: n = 16, so n + 1 = 17. Compute (n + 1)^2 = 17^2 = 289. Step 5: The given second number is 279, but the correct square should be 289, so this pair does not satisfy the same relation. Step 6: Therefore, 16 – 279 is the only number pair that fails the pattern m = (n + 1)^2 and is the odd one out. Verification / Alternative check: List the intended pattern: 10 → 11^2 = 121 ✔ 12 → 13^2 = 169 ✔ 14 → 15^2 = 225 ✔ 16 → 17^2 = 289 ✘ (but given as 279) The first three pairs follow the formula perfectly, while the last pair uses an incorrect second value, confirming that the pair 16 – 279 breaks the pattern. Why Other Options Are Wrong: 10 – 121 is not odd because 121 equals 11^2, following m = (n + 1)^2. 12 – 169 is not odd because 169 equals 13^2, again following the pattern. 14 – 225 is not odd because 225 equals 15^2 and fits the rule. Only 16 – 279 violates the rule since 279 is not equal to 17^2. Common Pitfalls: Students might miscalculate 17^2 and think it is 279 instead of 289, leading to the wrong conclusion that all pairs follow the pattern. Another pitfall is to attempt more complex relationships, such as mixing multiplication and addition, instead of checking the simple square form first. Carefully computing squares for small integers helps avoid such mistakes. Final Answer: The number pair that does not satisfy the square-of-next-odd-number rule and is therefore the odd one out is 16 – 279.

Question 19

In the following question, select the odd word/letters/number/number pair from the given alternatives: 794, 576, 668 and 992. Three of these numbers are not perfect squares, while one number is a perfect square. Based on this property, which number …

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Introduction / Context: This question is a numerical odd one out problem, where you must select the number that differs from the others based on an important mathematical property. Here, three numbers are non-perfect squares, while one is a perfect square. Recognising perfect squares quickly is very useful in quantitative aptitude and number system questions. Given Data / Assumptions: Numbers: 794, 576, 668, 992. We will check whether each number can be expressed as n^2 for some integer n. A number that is exactly the square of an integer is called a perfect square. Three numbers will not be perfect squares; one will be, and that will be the odd one out. Concept / Approach: The idea is to factorise or recall squares around the approximate square roots: Find the nearest integer square roots. Check whether squaring those integers gives the exact number. If the number equals some integer squared, it is a perfect square; otherwise, it is not. We then identify which number stands out due to this property. Step-by-Step Solution: Step 1: Check 576. We know 24 * 24 = 576. So 576 = 24^2, which is a perfect square. Step 2: Check 794. Find nearby squares: 28^2 = 784, 29^2 = 841. 794 lies between 784 and 841 and is not equal to either, so 794 is not a perfect square. Step 3: Check 668. Nearby squares: 25^2 = 625, 26^2 = 676. 668 lies between 625 and 676 and is not equal to 676, so 668 is not a perfect square. Step 4: Check 992. Nearby squares: 31^2 = 961, 32^2 = 1024. 992 lies between 961 and 1024 and is not equal to either, so 992 is not a perfect square. Step 5: Therefore, among the four given numbers, only 576 is a perfect square, while 794, 668 and 992 are not. Verification / Alternative check: To verify, you can factor 576 completely: 576 = 2 * 2 * 2 * 2 * 2 * 2 * 3 * 3. Grouping equal factors: 576 = (2 * 2 * 2 * 3) * (2 * 2 * 2 * 3) = 24 * 24 = 24^2. For the other numbers, no such clean pairing into identical groups of factors is possible without producing fractional factors. This confirms that only 576 has the structure of a perfect square. Why Other Options Are Wrong: 794 is not special because it is not a perfect square; it lies between 784 and 841. 668 is not special because it lies between 625 and 676 and is not equal to 676, so it is not a square. 992 is not special because it lies between 961 and 1024 and does not equal any perfect square. 576 stands out because it exactly equals 24^2. Common Pitfalls: A typical pitfall is to rely purely on digit patterns or divisibility instead of checking whether the number is a perfect square. Some students may confuse 576 with nearby values or misremember its square root. Another mistake is to factor partially and stop early, missing the perfect square structure. Systematic checking using known squares around each number avoids this problem. Final Answer: The only perfect square in the list and therefore the odd one out is 576.

Question 20

In the following question, select the odd word from the given alternatives: Hills, Valleys, Trees and Mountains. Three of these words describe landforms or natural elevations and depressions of the earth's surface, while one refers to vegetation. Wh…

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Introduction / Context: This is a verbal classification and odd one out question. You are given four common words that describe parts of the natural environment: Hills, Valleys, Trees and Mountains. Three of these refer to types of landforms, while one refers to vegetation. Your task is to identify which word does not belong to the same category as the others. Given Data / Assumptions: Words: Hills, Valleys, Trees, Mountains. We assume basic knowledge of geographical features and vegetation. Hills, Valleys and Mountains describe the shape and height of the earth's surface. Trees describe living plants, not landform shapes. Concept / Approach: The main idea is category classification: Landforms: physical features formed by the earth's surface, such as hills, valleys and mountains. Vegetation: plant life such as trees, shrubs and grasses. By checking which word refers to plant life rather than to a landform, we can identify the odd one out. Step-by-Step Solution: Step 1: Consider Hills. Hills are elevated landforms that rise above the surrounding terrain but are usually lower and less steep than mountains. Step 2: Consider Valleys. Valleys are low areas between hills or mountains, often with a river or stream flowing through them, and they are landform depressions. Step 3: Consider Mountains. Mountains are large natural elevations of the earth's surface, generally higher and steeper than hills. Step 4: Observe the similarity: Hills, Valleys and Mountains all describe landforms, that is, shapes of the terrain. Step 5: Consider Trees. Trees are tall, woody plants that are part of the earth's vegetation, not a shape or elevation of the ground itself. Step 6: Since Trees do not belong to the category of landforms but rather to vegetation, Trees is the odd one out. Verification / Alternative check: You can group the words into categories: Landforms: Hills, Valleys, Mountains. Vegetation: Trees. There is a clear 3-versus-1 separation, where three words share one category and one word belongs to another, confirming Trees as different. Why Other Options Are Wrong: Hills is not odd because it describes a type of landform. Valleys is not odd because it also describes a landform, specifically a low area between higher ground. Mountains is not odd because it is another kind of elevated landform. Trees stands apart as it refers to living plants, not to the shape or height of the earth's surface. Common Pitfalls: A common mistake is to focus only on whether the words are plural or singular or on their general association with nature, rather than on their precise category. All four words relate to nature, which can be misleading. However, the test here is to distinguish between geographical features and vegetation, so attention to category specifics is crucial. Final Answer: The word that refers to vegetation rather than a landform and is therefore the odd one out is Trees.

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