Question 1

In the descending sequence of perfect squares 196, 169, 144, 121, 100, 81, what number should come next?

Accepted Answer

Introduction / Context: This problem checks your understanding of perfect squares and how they appear in number series. Each term here corresponds to the square of a natural number. Recognizing such square patterns is a core skill in aptitude questions dealing with sequences and series. Given Data / Assumptions: Sequence given: 196, 169, 144, 121, 100, 81, ? The numbers are arranged in decreasing order. We assume the sequence is built from perfect squares of consecutive integers. Concept / Approach: We recall that perfect squares are numbers of the form n^2 where n is a positive integer. The key idea is to express each term as a square and see how the base integers change. Once we identify the pattern in those base integers, predicting the next term is straightforward. Step-by-Step Solution: 196 can be written as 14 * 14, so 196 = 14^2.169 can be written as 13 * 13, so 169 = 13^2.144 can be written as 12 * 12, so 144 = 12^2.121 can be written as 11 * 11, so 121 = 11^2.100 can be written as 10 * 10, so 100 = 10^2.81 can be written as 9 * 9, so 81 = 9^2.We clearly see that the base integers are decreasing consecutively: 14, 13, 12, 11, 10, 9. Therefore, the next base integer is 8, and the next term is 8^2 = 64. Verification / Alternative check: If we continue the sequence of bases as 14, 13, 12, 11, 10, 9, 8 and square each, we get 196, 169, 144, 121, 100, 81 and 64, which is consistent. None of the other options produce a square that fits the pattern of consecutive integers. For example, 77, 74 and 67 are not perfect squares, while 49 would correspond to 7^2 which is the term after 64, not the immediate next one in this list. Why Other Options Are Wrong: 77, 74 and 67 are not perfect squares of integers, so they cannot continue a sequence clearly built from perfect squares. 49 is a perfect square (7^2), but it would be the term after 64 in the descending chain 14^2, 13^2, ..., 9^2, 8^2, 7^2. Since we only need the immediate next term, 49 is too far ahead. Common Pitfalls: Some students try to find differences between terms (27, 25, 23, 21, 19) and may get distracted. The differences themselves are decreasing by 2, which is another hint that these are squares of consecutive integers. However, focusing on the square structure is cleaner and less error prone. Forgetting standard squares such as 196, 169 or 144 can also slow you down. Final Answer: The next number in the sequence is 64.

Question 2

From the list Hawk, Parrot, Owl and Eagle, which one is the odd one out based on type of bird?

Accepted Answer

Introduction / Context: This verbal reasoning question tests your ability to categorize objects based on a shared property. Here, all the options are birds, but there is an important difference in their feeding habits and natural classification. Recognizing this hidden category is key to finding the odd one out. Given Data / Assumptions: The options are Hawk, Parrot, Owl and Eagle. We assume that three of them belong to a similar ecological or behavioral group and one does not. Basic general knowledge of common birds is expected. Concept / Approach: Hawk, Owl and Eagle are all birds of prey, also called raptors. They have strong talons, sharp hooked beaks and mainly hunt other animals for food. Parrots, on the other hand, are primarily seed and fruit eating birds with very different beaks and habits. The correct approach is to identify this predator versus non predator distinction. Step-by-Step Solution: Hawk: A hawk is a bird of prey that hunts small animals and has sharp talons and a hooked beak.Owl: An owl is also a bird of prey, usually nocturnal, with powerful talons and a strong beak used to hunt rodents and other small animals.Eagle: An eagle is another well known raptor, very strong, with keen eyesight and a carnivorous diet.Parrot: A parrot is generally not a bird of prey. It is typically herbivorous or omnivorous, feeding mostly on seeds, fruits and nuts, with a curved beak adapted for cracking rather than tearing flesh. Verification / Alternative check: If you classify the birds by category, Hawk, Owl and Eagle all fall under raptors or birds of prey. They share hunting behavior and similar physical adaptations. Parrots belong to a different group of birds. They are known for bright colors, ability to mimic sounds and a diet that does not primarily depend on hunting other animals. This strongly confirms that Parrot is the odd one out. Why Other Options Are Wrong: Hawk is clearly a bird of prey, so it fits with Owl and Eagle. Owl is also a bird of prey, especially adapted for night hunting, so it belongs in the same group. Eagle is a classic example of a large raptor and shares the same basic characteristics. These three therefore form a natural group, leaving Parrot as the one that does not belong. Common Pitfalls: Sometimes students get distracted by size or color instead of functional classification. They may think that Parrot is different because it is often brightly colored, but that is also consistent with the difference in lifestyle. The safe method is to think about the primary diet and hunting behavior rather than appearance alone. Understanding basic animal groups makes such questions easy. Final Answer: The odd one out is Parrot because it is not a bird of prey.

Question 3

In the number series 6, 3, 3, 6, 24, ?, what should be the next term that correctly continues the pattern?

Accepted Answer

Introduction / Context: This number series tests your ability to recognize patterns that involve repeated multiplication by changing factors. Instead of simple addition or subtraction, the pattern here is built from successive multipliers that follow a clear rule. Identifying such multiplier sequences is important for handling advanced series questions. Given Data / Assumptions: Given series: 6, 3, 3, 6, 24, ? The sequence is assumed to be consistent, with exactly one correct next term. Operations between terms may involve multiplication, division or both. Concept / Approach: We try to relate each term to the previous term by multiplication or division. From 6 to 3, there is a division by 2. From 3 to 3, there is an effective multiplication by 1. From 3 to 6, there is a multiplication by 2. From 6 to 24, there is a multiplication by 4. We notice that the multipliers follow a pattern: 1 divided by 2, then 1, then 2, then 4. This suggests the next multiplier may be 8, doubling each time after the neutral step. Step-by-Step Solution: Step 1: 6 to 3 is 6 * (1 / 2) = 3.Step 2: 3 to 3 is 3 * 1 = 3.Step 3: 3 to 6 is 3 * 2 = 6.Step 4: 6 to 24 is 6 * 4 = 24.Step 5: The multipliers after the first term are therefore 1 / 2, 1, 2, 4. These are successive terms multiplied by 2 after the neutral factor 1.Step 6: Continuing this pattern, the next multiplier should be 8. So the next term is 24 * 8 = 192. Verification / Alternative check: We can rewrite the pattern as repeated doubling of the multiplier: 1 / 2, 1, 2, 4, 8. Although the first factor is a division by 2, after that the pattern doubles the multiplier each time: 1 to 2 to 4 to 8. Applying 8 to the term 24 yields 192. None of the other options give a continuation that preserves this neat doubling pattern of multipliers. Why Other Options Are Wrong: 186, 182 and 194 are close to 192 but they do not correspond to multiplying 24 by a simple power of 2. They would require unnatural fractions as multipliers and break the clean pattern of doubling factors. The option 96 corresponds to multiplying 24 by 4, which repeats a multiplier already used and again breaks the established structure. Common Pitfalls: Candidates sometimes try to see only addition or subtraction patterns, which clearly do not work here. Others may only look at absolute differences (3, 0, 3, 18) which give no clear systematic rule. The correct strategy for such sequences is to check both multiplicative and divisive links between terms and look at how the multipliers themselves evolve. Final Answer: The next term in the series is 192.

Question 4

In the number series 1, 2, 8, 33, ?, find the next term that correctly continues the progression.

Accepted Answer

Introduction / Context: This series question involves a combination of multiplication and addition, where both operations change in a regular way. The pattern is slightly more complex than simple arithmetic or geometric progressions, making it a good test of pattern recognition and algebraic thinking in aptitude exams. Given Data / Assumptions: The series is: 1, 2, 8, 33, ? We need to find the single correct next term from the options. The rule is expected to be consistent and reasonably simple once identified. Concept / Approach: We look for a pattern that expresses each term from the previous one. A helpful idea is to see whether the multiplier and the added number are changing in a predictable way. By comparing how 1 becomes 2, 2 becomes 8 and 8 becomes 33, we can attempt to map a general rule that depends on the step number. Step-by-Step Solution: From 1 to 2: 1 * 1 + 1^2 = 1 + 1 = 2.From 2 to 8: 2 * 2 + 2^2 = 4 + 4 = 8.From 8 to 33: 8 * 3 + 3^2 = 24 + 9 = 33.We can see that at each step n, the operation is: next term = current term * n + n^2.For the next step, n = 4, so we use: next term = 33 * 4 + 4^2.Compute this: 33 * 4 = 132 and 4^2 = 16, so the next term = 132 + 16 = 148. Verification / Alternative check: To verify, we can generalize the formula: if T1 = 1, then T2 = T1 * 1 + 1^2, T3 = T2 * 2 + 2^2, T4 = T3 * 3 + 3^2 and so on. Plugging in the values sequentially reproduces the entire series: 1, 2, 8, 33 and then 148. No other option fits this rule without forcing a different and less natural formula. Why Other Options Are Wrong: 145, 143 and 141 are close to 148 but none matches the calculated value from the identified formula. Choosing any of them would break the consistent pattern of multiplying by n and adding n^2 at each step. 152 similarly does not satisfy this rule and therefore cannot be the correct continuation of the series. Common Pitfalls: Many candidates look only at differences (1, 6, 25) which do not form a simple arithmetic progression. Others may try constant multipliers, which also do not work. The key is to consider that both the multiplier and the added quantity can change based on the position in the sequence. Once that is tried, the pattern becomes clear and manageable. Final Answer: The next number in the series is 148.

Question 5

In the series 18, 97, 26, 91, ?, 83, find the missing number that correctly completes the pattern.

Accepted Answer

Introduction / Context: This question involves a number series where two interleaved sequences are hidden inside one combined list. Many exam level series questions use this technique, alternating between two simpler patterns placed in a single sequence. Being able to separate and analyze these subsequences is an important skill in quantitative aptitude. Given Data / Assumptions: The complete series is: 18, 97, 26, 91, ?, 83. We assume a single missing number that will make the pattern consistent. The series likely consists of two separate patterns, one in the odd positions and one in the even positions. Concept / Approach: We examine the numbers in odd positions and even positions separately. Often one subsequence is increasing in a simple way while the other decreases or changes with another rule. Here, 18, 26 and the missing term appear in the odd positions, while 97, 91 and 83 appear in the even positions. We will look at each subsequence independently. Step-by-Step Solution: Write odd positioned terms: 1st, 3rd and 5th terms are 18, 26 and ?.Write even positioned terms: 2nd, 4th and 6th terms are 97, 91 and 83.Consider the odd subsequence: 18, 26, ?. The difference between 26 and 18 is 8. A natural and simple pattern is to add 8 each time.So the next odd term would be 26 + 8 = 34.Consider the even subsequence: 97, 91, 83. Here the differences are 97 - 91 = 6 and 91 - 83 = 8. The decreases are 6 and then 8, which are increasing even numbers.This indicates that one subsequence increases by 8 while the other decreases by increasing even numbers, which is a reasonable and consistent structure. Verification / Alternative check: If we reconstruct the full series with the found value, we get: 18, 97, 26, 91, 34, 83. The odd subsequence 18, 26, 34 clearly grows by 8 each time. The even subsequence 97, 91, 83 decreases by 6 and then 8, forming a simple pattern of decreasing even differences. No other candidate among the options satisfies both subsequences as neatly. Why Other Options Are Wrong: 32, 30 and 28 do not maintain the odd subsequence as an arithmetic progression with difference 8. 36 makes the odd subsequence 18, 26, 36 which has differences 8 and 10 and breaks the simplest pattern. None of these alternatives gives such a clean structure in both subsequences as 34 does. Common Pitfalls: Some students try to connect consecutive numbers in the total series directly, which looks irregular and confusing. The key is to notice possible interleaving patterns. Once you separate positions into odd and even, the arithmetic progression for one subsequence and the controlled decrease in the other become much easier to see. Final Answer: The missing term in the series is 34.

Question 6

In the sequence 35, 48, 54, 63, 81, 105, which number is the odd one out?

Accepted Answer

Introduction / Context: This is a straightforward odd one out question based on divisibility. The task is to detect which number in the list does not share a common divisibility property with the others. Such questions are common in basic number system sections and are usually solved quickly with simple divisibility tests. Given Data / Assumptions: List of numbers: 35, 48, 54, 63, 81, 105. Exactly one number in this group behaves differently. Divisibility by 3 is often a useful property to check when many numbers are multiples of 3. Concept / Approach: A number is divisible by 3 if the sum of its digits is divisible by 3. Looking at the list, several numbers appear to be multiples of 3 at first glance. We apply the sum of digits test to each term and see which one fails this condition. The number that is not divisible by 3 while all others are will be the odd one out. Step-by-Step Solution: Check 35: Sum of digits = 3 + 5 = 8, which is not divisible by 3. So 35 is not a multiple of 3.Check 48: Sum of digits = 4 + 8 = 12, which is divisible by 3. So 48 is a multiple of 3.Check 54: Sum of digits = 5 + 4 = 9, which is divisible by 3. So 54 is a multiple of 3.Check 63: Sum of digits = 6 + 3 = 9, divisible by 3. So 63 is a multiple of 3.Check 81: Sum of digits = 8 + 1 = 9, divisible by 3. So 81 is a multiple of 3.Check 105: Sum of digits = 1 + 0 + 5 = 6, divisible by 3. So 105 is a multiple of 3. Verification / Alternative check: We can also divide each number directly by 3. We find that 48 divided by 3 is 16, 54 divided by 3 is 18, 63 divided by 3 is 21, 81 divided by 3 is 27 and 105 divided by 3 is 35, all exact integers. However, 35 divided by 3 gives a non integer result with remainder. This confirms that 35 alone is not divisible by 3, while all other numbers in the list are. Why Other Options Are Wrong: 48, 54, 63, 81 and 105 are all divisible by 3, so they share the common property and cannot be the odd one out. Only 35 fails the test for divisibility by 3, so it is the only number that does not belong to the group defined by this property. Common Pitfalls: Sometimes candidates look at prime factorizations or at divisibility by other numbers such as 5 or 7 and become confused. While 35 is divisible by 5 and 7, some of the others are also divisible by 3 and 5 or 3 and 7. The simplest and most consistent identifying feature here is divisibility by 3 for five of the numbers and lack of it for only one number. Final Answer: The odd one out in the sequence is 35.

Question 7

From the numbers 97, 233, 437 and 599, which one is the odd man out based on primality?

Accepted Answer

Introduction / Context: This question tests whether you can quickly distinguish between prime and composite numbers. Among the given options, three are prime while one is composite. Number theory and primality checks are frequent themes in aptitude tests, especially in odd man out and classification problems. Given Data / Assumptions: Given numbers: 97, 233, 437 and 599. We assume that three of these are prime numbers and one is not. We need to identify the composite number in the list. Concept / Approach: A prime number has exactly two distinct positive divisors, 1 and the number itself. A composite number has additional divisors. For each given number, we check divisibility by smaller primes up to its approximate square root. If we find a factor other than 1 and itself, the number is composite. Otherwise, it is prime. Step-by-Step Solution: Check 97: The approximate square root of 97 is less than 10. We test divisibility by 2, 3, 5 and 7. 97 is not divisible by any of these, so 97 is prime.Check 233: The square root of 233 is less than 16. We test divisibility by primes 2, 3, 5, 7, 11 and 13. None of these divide 233 exactly, so 233 is prime.Check 599: The square root of 599 is a little under 25. Try primes 2, 3, 5, 7, 11, 13, 17, 19 and 23. None of them divide 599 exactly, so 599 is prime.Check 437: We test divisibility by smaller primes. 437 divided by 19 equals 23 exactly, since 19 * 23 = 437. Therefore 437 has factors other than 1 and itself and is composite. Verification / Alternative check: After discovering that 437 = 19 * 23, we know with certainty it is not prime. For the other three numbers, any simple divisibility attempt fails for all primes up to their square roots, confirming they have no non trivial factors. Hence, 97, 233 and 599 behave alike as primes, while 437 stands apart as a composite number. Why Other Options Are Wrong: 97 is a prime number and therefore belongs to the group of primes. 233 is also prime and fits the same classification. 599 is prime as well, sharing the key property with 97 and 233. Since these three are primes, they cannot be the odd ones out in a set otherwise defined by primality. Common Pitfalls: Some students may assume that a number is composite simply because it is large or ends with certain digits. Without checking divisibility by small primes, such guesses can be very misleading. Others may not go up to the correct limit (square root) when testing factors. Carefully applying the divisibility checks up to the square root is the safest method to verify primality in exam conditions. Final Answer: The composite number and thus the odd one out is 437.

Question 8

In the series 5, 7, ?, 25, 45, 75, what number should replace the question mark to maintain the pattern?

Accepted Answer

Introduction / Context: This is a number series question where you must find the missing term. The pattern is based on the differences between consecutive terms and how those differences themselves change. Such problems test your ability to identify second level patterns and not just direct increments. Given Data / Assumptions: Given series: 5, 7, ?, 25, 45, 75. Exactly one number is missing. We assume the sequence is constructed in a consistent way based on simple arithmetic operations. Concept / Approach: To find the missing term, we look at the pattern of differences. We know the first term is 5 and the second is 7. The unknown third term must fit smoothly between 7 and 25 and then between 25 and 45 and 75. If the differences follow a regular rule like an arithmetic progression, we can use this to determine the missing number. Step-by-Step Solution: Let the missing term be x. Then the series becomes 5, 7, x, 25, 45, 75.Compute the known differences: 25 - x, 45 - 25 = 20, 75 - 45 = 30.We already know 7 - 5 = 2 and x - 7 is another difference we must determine.Look for a pattern where the differences themselves follow an arithmetic progression. Suppose the differences are 2, 6, 12, 20, 30.Check this: 5 + 2 = 7, 7 + 6 = 13, 13 + 12 = 25, 25 + 20 = 45, 45 + 30 = 75.This works perfectly and shows that the missing term must be 13. Verification / Alternative check: With the completed series 5, 7, 13, 25, 45, 75, the differences are 2, 6, 12, 20 and 30. The second differences are 4, 6, 8 and 10, which increase by 2 each time. This smooth and systematic behavior strongly indicates that 13 is the correct missing term. No other candidate will produce such a neat pattern in both first and second differences. Why Other Options Are Wrong: 11, 15, 17 and 19 all lead to irregular or messy patterns of differences that do not form a clear arithmetic progression or a simple structure in the second differences. For example, using 11 creates differences 2, 4, 14, 20 and 30, where second differences are not consistently increasing by a fixed amount. Common Pitfalls: Many test takers only check the visible part after the missing term and try to fit 25, 45 and 75 with the wrong value, which leads to random guessing. A systematic way is to express the unknown as x, compute differences and search for a reasonable pattern such as steadily increasing second differences. This structured reasoning avoids guesswork and improves accuracy. Final Answer: The missing number in the series is 13.

Question 9

In the series 1, 6, 27, 124, 650, which number is the odd man out that does not follow the same rule as the others?

Accepted Answer

Introduction / Context: This question asks you to identify the odd term in a series built using a mix of multiplication and addition. It is based on a pattern where each term is constructed from the previous one using a simple rule involving the position index. Spotting such a pattern is a common challenge in number series questions. Given Data / Assumptions: Sequence: 1, 6, 27, 124, 650. We assume that from the first few terms we can infer a rule. Exactly one term in the list breaks that rule. Concept / Approach: We look for a relation between each term and the next one. A useful idea is that the multiplier and the added quantity might depend on the step number. By comparing how 1 becomes 6, then 6 becomes 27 and 27 becomes 124, we can attempt to generalize the pattern and then test whether 650 fits or violates it. Step-by-Step Solution: From 1 to 6: 1 * 2 + 2^2 = 2 + 4 = 6.From 6 to 27: 6 * 3 + 3^2 = 18 + 9 = 27.From 27 to 124: 27 * 4 + 4^2 = 108 + 16 = 124.We see a clear rule: if Tn is the current term at step n, the next term is Tn * (n + 1) + (n + 1)^2.Following this rule, from 124 to the next term we should have: 124 * 5 + 5^2 = 620 + 25 = 645.The term in the series is 650, which does not match the required value 645. Therefore, 650 is inconsistent with the pattern. Verification / Alternative check: If we write the correct sequence according to the discovered rule, it becomes 1, 6, 27, 124, 645, and so on. All transitions follow the same formula using multipliers and squares of consecutive integers. Only 650 deviates from this regularity by being 5 units too large. This confirms it as the wrong term. Why Other Options Are Wrong: 1 is the starting value and fits naturally into the pattern. 6, 27 and 124 all satisfy the relation Tn+1 = Tn * (n + 1) + (n + 1)^2 exactly. Removing any one of these would destroy the internal consistency of the early part of the series, while the pattern up to 124 is perfectly smooth. Common Pitfalls: Some candidates may miscalculate one of the intermediate steps and conclude that an earlier term is wrong. Others might look only at rough magnitude growth and not check exact arithmetic. It is important to verify each step precisely and test whether a single formula works for all transitions. Once that formula is found, identifying the one term that breaks it becomes straightforward. Final Answer: The odd man out in the sequence is 650.

Question 10

In the series 7, 9, 19, 18, 31, 29, which number is the odd one out that does not fit the alternating pattern?

Accepted Answer

Introduction / Context: This is an odd one out question involving an alternating pattern. Numbers at odd and even positions often form separate arithmetic progressions or follow different rules. Recognizing such interleaved patterns is a powerful technique for solving series questions quickly and accurately. Given Data / Assumptions: The given sequence is 7, 9, 19, 18, 31, 29. Exactly one term is wrong or does not fit the pattern. We consider the possibility that odd and even positions form separate sub sequences. Concept / Approach: We separate the series into two subsequences: one consisting of numbers in odd positions and one of numbers in even positions. Often one is a simple arithmetic progression. If one subsequence is perfectly regular and the other is almost regular but has a single deviation, that deviation indicates the odd term. Step-by-Step Solution: Identify positions: 1st = 7, 2nd = 9, 3rd = 19, 4th = 18, 5th = 31, 6th = 29.Odd positioned terms: 7 (1st), 19 (3rd), 31 (5th).Even positioned terms: 9 (2nd), 18 (4th), 29 (6th).Check odd subsequence: 7, 19, 31. Differences are 19 - 7 = 12 and 31 - 19 = 12. So odd positions form an arithmetic progression with common difference 12.Check even subsequence: 9, 18, 29. Differences are 18 - 9 = 9 and 29 - 18 = 11. These are not equal and do not form a simple arithmetic progression.If we expect an arithmetic progression similar to the odd subsequence, we would want even differences to be consistent, for example 9 and then 9 or 11 and then 11. So one of the even terms is probably wrong.If we maintain the first two even terms 9 and 18 with difference 9, the third even term should be 18 + 9 = 27 instead of 29. That means 29 is the inconsistent number. Verification / Alternative check: Replace 29 with 27 to test the pattern. The full sequence becomes 7, 9, 19, 18, 31, 27. Now odd positions 7, 19, 31 form an arithmetic progression with difference 12, and even positions 9, 18, 27 form an arithmetic progression with difference 9. Both subsequences are clean and consistent, showing that 29 is the only value that breaks this two progression structure. Why Other Options Are Wrong: 7, 19 and 31 belong to the odd subsequence and already form a perfect arithmetic progression, so none of them can be wrong without destroying that structure. 9 and 18 are the first two terms of the even subsequence and set the difference as 9. Removing either of them would force a more complicated adjustment than simply correcting the last term. Common Pitfalls: Some test takers attempt to look at the entire series as a single pattern of successive differences, which gives irregular values and leads nowhere. The better strategy is to check whether terms in odd and even positions form separate patterns. Doing this often reveals clean arithmetic or geometric progressions that make identifying the odd term much easier. Final Answer: The odd number in the series is 29.

Question 11

In the series 12, 24, 26.5, 79.5, ?, 330, what number should replace the question mark to complete the pattern?

Accepted Answer

Introduction / Context: This number series mixes multiplication and addition in an alternating way. The multipliers and addends are changing, but in a controlled pattern. Being able to detect such alternating operations is very useful in medium difficulty series questions in aptitude exams. Given Data / Assumptions: Series: 12, 24, 26.5, 79.5, ?, 330. Exactly one missing term is to be found. The pattern likely alternates between multiplication and addition. Concept / Approach: We first compare consecutive terms to see whether there is multiplication or addition. The jump from 12 to 24 suggests multiplication by 2. The jump from 24 to 26.5 is a small increase, more likely addition. From 26.5 to 79.5 is a larger increase that fits multiplication by 3. This strongly suggests a pattern: multiply by a number, then add a related number, then multiply by the next number, and so on. Step-by-Step Solution: From 12 to 24: 12 * 2 = 24. So the first operation is multiplication by 2.From 24 to 26.5: 24 + 2.5 = 26.5. So the next operation is addition of 2.5.From 26.5 to 79.5: 26.5 * 3 = 79.5. So now we multiply by 3.This suggests a pattern: multiply by 2, add 2.5, multiply by 3, add 3, multiply by 4, add 4.5 and so on.From 79.5 to the missing term, we should add 3. So the missing term is 79.5 + 3 = 82.5.From 82.5 to 330, we check the next operation: 82.5 * 4 = 330, which fits perfectly. Verification / Alternative check: The full operations are therefore: 12 * 2 = 24, 24 + 2.5 = 26.5, 26.5 * 3 = 79.5, 79.5 + 3 = 82.5, 82.5 * 4 = 330. The multipliers increase as 2, 3 and 4 and the added numbers increase from 2.5 to 3 in a simple manner. This creates a clear, consistent pattern that uniquely picks 82.5 as the missing term. No other option gives a smooth alternation of multiplication and addition that matches the given numbers. Why Other Options Are Wrong: 211, 101.5, 99 and 90.5 do not satisfy the rule that from that term, multiplying by 4 gives exactly 330. They either break the add 3 step from 79.5 or do not allow a clean multiplication by 4 to reach 330. Any choice other than 82.5 forces an inconsistent or forced pattern. Common Pitfalls: Students sometimes try only constant multiplication or constant addition, both of which fail here. Others may misread 26.5 and 79.5 and not notice that 26.5 * 3 equals 79.5 exactly. The key idea is to suspect alternating operations when consecutive jumps change size drastically and then verify that by performing the calculations carefully. Final Answer: The missing term in the series is 82.5.

Question 12

A man saves Rs. 200 in each of the first three months of his service. In each subsequent month his saving increases by Rs. 40 more than the saving of the immediately previous month. After how many months will his total saving from the start of servi…

Accepted Answer

Introduction / Context: This question involves arithmetic progressions and cumulative sums. The man saves a fixed amount for the first few months, and then his monthly savings follow a pattern where they increase by a constant amount. You are asked to find the total number of months required to reach a given total saving. This is a classic application of arithmetic progression formulas in aptitude exams. Given Data / Assumptions: For the first three months he saves Rs. 200 per month. From the fourth month onward, each month he saves Rs. 40 more than the previous month. Total saving at some month is Rs. 11040. We must find the number of months from the start of service to reach this total. Concept / Approach: We split the problem into two parts: the first three months with constant savings, and the remaining months which form an arithmetic progression. The arithmetic progression has first term 240 and common difference 40. We then write the total saving as the sum of Rs. 600 from the first three months plus the sum of an arithmetic progression from month four onward. This leads to a quadratic equation in the number of additional months, which we solve to find the total time. Step-by-Step Solution: Step 1: Savings for first three months: 3 * 200 = 600.Step 2: Let the total number of months be n. Then the number of months after the first three is m = n - 3.Step 3: Savings from the fourth month form an arithmetic progression with first term a = 240 and common difference d = 40.Step 4: Sum of this arithmetic progression for m months is S = m / 2 * [2a + (m - 1) * d].Step 5: Substitute a = 240 and d = 40 to get S = m / 2 * [480 + 40m - 40] = m / 2 * (40m + 440) = 20m(m + 11).Step 6: Total saving is 600 + 20m(m + 11) = 11040.Step 7: So 20m(m + 11) = 11040 - 600 = 10440.Step 8: Divide both sides by 20 to get m(m + 11) = 522.Step 9: Solve m^2 + 11m - 522 = 0. The positive integer solution is m = 18 since 18 * 29 = 522.Step 10: Therefore n = m + 3 = 18 + 3 = 21 months. Verification / Alternative check: We can verify by calculating the sums directly. First three months contribute 600. The next 18 months form an arithmetic progression from 240 to 240 + 17 * 40 = 920. The sum is 18 / 2 * (240 + 920) = 9 * 1160 = 10440. Adding 600 gives 11040, which matches the required total. This confirms that 21 months is correct. Why Other Options Are Wrong: Using 19, 20 or 18 months leads to m values that do not satisfy the equation m(m + 11) = 522, and the total savings are either less than or greater than 11040. Similarly, 22 months would produce a total exceeding 11040. Only 21 months produces exactly the required total saving. Common Pitfalls: Some students forget to separate the constant saving phase and the arithmetic progression phase, and instead treat the entire period as one progression, which gives incorrect results. Others may make algebraic mistakes when forming or solving the quadratic equation. Carefully setting up the variables and using the standard sum formula for arithmetic progression avoids these issues. Final Answer: The man will have saved Rs. 11040 after 21 months from the start of his service.

Question 13

Find the odd word among the following animal-related terms: Horse, Ewe, Hind, and Bitch.

Accepted Answer

Introduction / Context: This verbal reasoning question asks you to find the odd word among a group of animal-related terms. Such questions test basic general knowledge about animals and also check whether you notice subtle categorical differences, for example between generic animal names and specific gender names for animals. Given Data / Assumptions: We are given four words: Horse, Ewe, Hind, and Bitch. All four are related to animals in some way. Exactly one option should be categorised as different from the others on a clear logical basis. Concept / Approach: A standard approach for odd word out questions is to look for a category that three items clearly share but the fourth does not. Here the natural category is whether each word represents a specific female of a species, or whether it is a general animal name that does not specify gender. Step-by-Step Solution: Step 1: Ewe refers to an adult female sheep. Step 2: Hind is a term used for a female deer, especially a female red deer. Step 3: Bitch is the common term for a female dog. Step 4: Horse, on the other hand, is a general term for the animal species. The male is called a stallion and the female is called a mare, so horse itself is not specifically female. Verification / Alternative check: If we group the words based on whether they are female specific, we get one group with Ewe, Hind, and Bitch which all unambiguously indicate female animals. Horse does not fit this pattern because it denotes the animal in general and can refer to either male or female unless further specified. Therefore, Horse is the unique odd member in the list. Why Other Options Are Wrong: Ewe is clearly a female sheep, so it matches the category of female animals. Hind is the female of the deer species and therefore also fits the same group. Bitch is the standard word for a female dog, again matching the female category. None of these can be considered the odd one out when compared with the others. Common Pitfalls: Many learners mistakenly focus on the type of animal (farm animal, pet, wild animal) instead of the grammatical or biological category. Others may misremember that horse is a gender neutral term and think that it is male only. Always recall that stallion and mare are gendered terms, while horse is general. For odd word out questions, try multiple angles such as gender, usage, category, and meaning before deciding. Final Answer: Thus, the only word that does not denote a specifically female animal is Horse, so it is the odd word out.

Question 14

In the number series 6, 78, 858, 7722, 54055, 270270, which term is incorrect?

Accepted Answer

Introduction / Context: This is an odd term in a number series question. The task is to detect the underlying pattern that generates the series and then check which term violates that pattern. These questions are common in competitive exams because they test pattern recognition, logic, and comfort with multiplication. Given Data / Assumptions: Series given: 6, 78, 858, 7722, 54055, 270270. Exactly one term is wrong, all others follow a consistent rule. All numbers are positive integers. Concept / Approach: For rapidly increasing series, a sensible approach is to check multiplicative patterns. We can try to express each term as the previous term multiplied by some factor, possibly a sequence of related factors such as descending odd numbers or a regular progression. Step-by-Step Solution: Step 1: Calculate ratios using multiplication: 6 to 78 can be checked as 6 * 13 = 78. Step 2: From 78 to 858: 78 * 11 = 858. Step 3: From 858 to 7722: 858 * 9 = 7722. Step 4: From 7722 to 54055 as written: 7722 * 7 = 54054, but the term in the series is 54055, which is one more than 54054. Step 5: From 54054 to 270270: 54054 * 5 = 270270, which matches the last term exactly. Verification / Alternative check: We see that the pattern is: multiply successively by 13, 11, 9, 7, 5. If we generate the correct series using this rule we obtain 6, 78, 858, 7722, 54054, 270270. Therefore every step except the fourth is consistent with this rule, and the correct fourth product is 54054, not 54055. Since only a single term is allowed to be incorrect, 54055 is the odd term. Why Other Options Are Wrong: 270270 is correct as 54054 * 5. The term 7722 is correct as 858 * 9. The term 858 is also correct as 78 * 11. None of these deviates from the pattern of multiplying by descending odd numbers. Only 54055 fails to equal 7722 multiplied by 7. Common Pitfalls: Learners sometimes divide adjacent terms and round ratios, which can obscure an exact integer pattern. Another pitfall is looking only at digit patterns instead of full multiplication. For fast growing series, always first check whether each term is an exact product of the previous term and a simple integer factor like 2, 3, 5, or a sequence such as 13, 11, 9, 7, 5. Final Answer: The term that does not follow the correct multiplication pattern is 54055.

Question 15

In the series 311, 230, 294, ?, 281, 256, what number should replace the question mark?

Accepted Answer

Introduction / Context: This question is a number series completion problem. The key skill required is to recognise a hidden pattern, often in the differences between consecutive terms, and then use that pattern to fill the missing value so that the sequence remains consistent. Given Data / Assumptions: Series: 311, 230, 294, ?, 281, 256. Exactly one number is missing and must be determined. The sequence is assumed to follow a single logical pattern throughout. Concept / Approach: When the numbers do not show simple multiplication or division, the next strategy is to examine first-level differences. If these differences form a recognisable pattern, such as squares, cubes, or another arithmetic progression, we can leverage that to find the missing term. Step-by-Step Solution: Step 1: Find the difference between the first two terms: 311 − 230 = 81. Step 2: Difference between the second and third terms: 294 − 230 = 64. Step 3: Let the missing term be X. Then the difference from 294 to X and from X to 281 must fit a pattern. Check the later known pair: 281 − 256 = 25. Step 4: Observe the known differences: 81, 64, ?, ?, 25. Note that 81 = 9^2, 64 = 8^2, and 25 = 5^2. It suggests a sequence of decreasing perfect squares. Step 5: Continue the pattern of square differences: 9^2, 8^2, 7^2, 6^2, 5^2 which are 81, 64, 49, 36, 25. Step 6: From 294, subtract 49 (7^2) to get the missing term: X = 294 − 49 = 245. Step 7: Now check the next difference: 281 − 245 = 36, which is 6^2. This fits the square pattern perfectly. Verification / Alternative check: The completed series is 311, 230, 294, 245, 281, 256. The differences are 81, 64, 49, 36, 25 which are 9^2, 8^2, 7^2, 6^2, 5^2. The pattern of consecutive squares in decreasing order is clear and consistent for all terms, so 245 is uniquely correct. Why Other Options Are Wrong: If we insert 240, 244, or 246, the differences would not form a perfect square sequence. Either the square pattern breaks or one of the required square differences is lost. Only 245 maintains the ordered squares 9^2, 8^2, 7^2, 6^2, 5^2. Common Pitfalls: A common mistake is to look only at the numbers themselves rather than at their differences. Another error is to treat this as a random combination of operations, which leads to forced and inconsistent patterns. In exam series questions, perfect squares and cubes often appear in the differences, so you should actively check for them. Final Answer: The missing term that preserves the decreasing square difference pattern is 245.

Question 16

In the sequence 4, 8, 14, 22, ?, find the next term.

Accepted Answer

Introduction / Context: This is a basic number series question that checks comfort with arithmetic progressions of differences. Instead of a simple arithmetic sequence, the sequence of differences itself forms a simple pattern, which is a very common style in aptitude tests. Given Data / Assumptions: Given sequence: 4, 8, 14, 22, ? All terms are integers. There is exactly one correct next term which continues the same rule. Concept / Approach: When the jump between consecutive terms is not constant, it is natural to look at the differences between the terms. If those differences follow a regular pattern, such as an arithmetic sequence, we can extend the pattern to find the next difference and hence the next term. Step-by-Step Solution: Step 1: Compute the differences: 8 − 4 = 4, 14 − 8 = 6, 22 − 14 = 8. Step 2: The differences are 4, 6, and 8. These are consecutive even numbers increasing by 2 each time. Step 3: Following this pattern, the next difference should be 10. Step 4: Add this new difference to the last known term: 22 + 10 = 32. Verification / Alternative check: With the candidate term 32, the full series becomes 4, 8, 14, 22, 32. The differences are then 4, 6, 8, 10 which clearly forms an arithmetic progression of even numbers with common difference 2. This confirms that the rule is consistent across all positions, and the value 32 is correct. Why Other Options Are Wrong: If we choose 28, the difference from 22 would be 6, and the sequence of differences would be 4, 6, 8, 6 which no longer shows a simple pattern. Similarly, choosing 36 or 46 leads to sequences of differences that do not follow the smooth progression of adding 2 each time. Therefore those values do not preserve the intended rule. Common Pitfalls: Students sometimes attempt to guess the next term by estimation instead of checking the exact numerical pattern. Another pitfall is to try multiplication patterns first when the series is actually governed by changing differences. Always compute the first-level differences; it is often the fastest and most reliable approach in such problems. Final Answer: The next term that correctly continues the pattern of increasing even differences is 32.

Question 17

Find the sum of the first 36 terms of the arithmetic progression 2, 5, 8, 11, ... .

Accepted Answer

Introduction / Context: This problem is a standard arithmetic progression (A P) question where you need to find the sum of a specified number of terms. Mastering such questions is essential for aptitude exams because they combine formula recall with careful substitution and arithmetic. Given Data / Assumptions: The A P has first term a = 2. Common difference d = 5 − 2 = 3. Number of terms n = 36. We must compute the sum of the first 36 terms, denoted by S. Concept / Approach: For an arithmetic progression, the nth term is given by a_n = a + (n − 1) * d. The sum of the first n terms is S_n = n * (a + a_n) / 2. So we first find the 36th term using the nth term formula and then apply the sum formula. Step-by-Step Solution: Step 1: Compute the 36th term a_36. a_36 = a + (n − 1) * d = 2 + (36 − 1) * 3 = 2 + 35 * 3. Step 2: Evaluate 35 * 3 = 105, so a_36 = 2 + 105 = 107. Step 3: Use the sum formula S_36 = n * (a + a_36) / 2. S_36 = 36 * (2 + 107) / 2 = 36 * 109 / 2. Step 4: Simplify: 36 / 2 = 18, so S_36 = 18 * 109. Step 5: Multiply 18 * 109 = 18 * 100 + 18 * 9 = 1800 + 162 = 1962. Verification / Alternative check: As a quick check, observe that the average of the first and last terms is (2 + 107) / 2 = 54.5. In any A P the average term equals this midpoint value. The sum of 36 terms is then 36 * 54.5, which again gives 1962. This cross check confirms that the calculation is consistent. Why Other Options Are Wrong: The other options 3924, 1684, and 1452 come from typical mistakes such as forgetting to divide by 2 in the sum formula, miscomputing the 36th term, or using an incorrect value for n. None of them match the correctly derived sum of 1962. Common Pitfalls: Candidates sometimes mix up the formulas for the nth term and the sum, or they use n instead of (n − 1) when computing a_n. Another common error is arithmetic slipping when multiplying larger numbers. Writing each step clearly and simplifying fractions early reduces the chance of mistakes. Final Answer: The sum of the first 36 terms of the progression 2, 5, 8, 11, ... is 1962.

Question 18

Find the next term in the series 143, 143, 136, 110, ?.

Accepted Answer

Introduction / Context: This number series question involves recognising a pattern in the differences between consecutive terms. The pattern is slightly non obvious, using values related to cubes, which makes this a moderately challenging mental maths problem. Given Data / Assumptions: Series: 143, 143, 136, 110, ? Exactly one next term is required. The same rule governs all transitions between neighbouring terms. Concept / Approach: When the numbers do not appear to follow a simple multiplication pattern, the next step is to look at the differences between terms. If those differences themselves fit a clean formula, such as n^3 − 1 or a similar expression, we can extend that pattern to find the next difference and thus the missing term. Step-by-Step Solution: Step 1: Compute the differences: 143 − 143 = 0, 143 − 136 = 7, 136 − 110 = 26. Step 2: Consider the absolute values of the differences: 0, 7, 26. Notice that 0 = 1^3 − 1, 7 = 2^3 − 1, 26 = 3^3 − 1. Step 3: This suggests the pattern of subtracting successive numbers of the form n^3 − 1 where n increases by 1 each time: 1^3 − 1, 2^3 − 1, 3^3 − 1, 4^3 − 1, and so on. Step 4: The next difference should therefore be 4^3 − 1 = 64 − 1 = 63. Step 5: Subtract this difference from the last known term: 110 − 63 = 47. Verification / Alternative check: The completed series with the candidate term is 143, 143, 136, 110, 47. The absolute differences become 0, 7, 26, 63 which correspond to 1^3 − 1, 2^3 − 1, 3^3 − 1, 4^3 − 1. The pattern is consistent for each step, confirming that 47 is the correct next term. Why Other Options Are Wrong: Options 91, 35, and 69 produce differences that do not match the required cube minus one pattern. For example, if the term were 69, the last difference would be 110 − 69 = 41, which is not of the form n^3 − 1 for any integer n. Only 47 leads to the correct sequence of differences. Common Pitfalls: A common mistake is to look for simple linear or geometric patterns and give up when they are not found. Another error is to ignore the absolute value of the first difference, which here neatly fits the same formula as the others. When dealing with unusual series, always test for relationships involving squares or cubes of small integers. Final Answer: The next term in the series following the cube minus one pattern is 47.

Question 19

In the series 3, 10.5, 36.75, 128.625, ?, find the next number.

Accepted Answer

Introduction / Context: This question presents a geometric type number series where each term is obtained from the previous one by multiplying with a constant factor. The values involve decimals, so careful multiplication is required to avoid rounding mistakes. Given Data / Assumptions: Series: 3, 10.5, 36.75, 128.625, ? All terms are real numbers, not necessarily integers. The pattern is expected to be consistent multiplicative growth. Concept / Approach: For series involving decimals that increase rapidly, it is natural to suspect a geometric progression or a simple multiplication factor. We can determine the multiplier by dividing consecutive terms and checking if the ratio remains constant. Step-by-Step Solution: Step 1: Compute the ratio of the second term to the first: 10.5 / 3 = 3.5. Step 2: Check the next ratio: 36.75 / 10.5 = 3.5, which confirms the same factor. Step 3: Check the third ratio: 128.625 / 36.75 = 3.5 again. Step 4: Therefore, each term is obtained by multiplying the previous term by 3.5. Step 5: Compute the next term: 128.625 * 3.5. Step 6: 128.625 * 3 = 385.875 and 128.625 * 0.5 = 64.3125. So 128.625 * 3.5 = 385.875 + 64.3125 = 450.1875. Step 7: Rounded to three decimal places, this is approximately 450.187, which matches option A. Verification / Alternative check: We can reconstruct the series using the rule term_{n+1} = term_n * 3.5. Starting from 3 we obtain 3, 10.5, 36.75, 128.625, 450.1875. The values up to the fourth term match perfectly, and the fifth term matches the given option when rounded, so the rule is confirmed as correct. Why Other Options Are Wrong: Values such as 442.151, 441.231, and 456.852 correspond to ratios that are slightly lower or higher than 3.5 when divided by 128.625. They do not maintain the exact constant multiplier across the series, so they break the geometric pattern. Common Pitfalls: A common pitfall is to approximate the ratio visually and assume some other factor like 3.4 or 3.6 without checking precisely. Another error is to round intermediate products too early, which can drift away from the correct option. Always keep enough decimal places during multiplication and only round when comparing with the options. Final Answer: The next term in the series, based on multiplication by 3.5, is 450.187.

Question 20

In the series 90, 72, 56, 42, 36, 20, which term is the odd one out?

Accepted Answer

Introduction / Context: This is an odd man out question in a decreasing number series. The objective is to detect a simple arithmetic rule that most terms satisfy and then identify the term that does not follow that rule. Given Data / Assumptions: Series: 90, 72, 56, 42, 36, 20. Exactly one term is incorrect or does not fit the intended pattern. The pattern is expected to involve simple subtraction. Concept / Approach: For decreasing sequences, it is natural to check the differences between consecutive terms. If most of those differences follow an orderly pattern, such as subtracting even numbers in a consistent fashion, we can then check which term breaks that logic. Step-by-Step Solution: Step 1: Compute differences between consecutive terms: 72 − 90 = −18, 56 − 72 = −16, 42 − 56 = −14, 36 − 42 = −6, 20 − 36 = −16. Step 2: Look at the absolute differences: 18, 16, 14, 6, 16. Step 3: A natural pattern to expect is subtracting consecutive even numbers: 18, 16, 14, 12, 10, and so on. Step 4: If we follow this ideal pattern from 90, we get: 90 − 18 = 72, 72 − 16 = 56, 56 − 14 = 42, 42 − 12 = 30, 30 − 10 = 20. Step 5: The corrected series should therefore be 90, 72, 56, 42, 30, 20. Step 6: The term 36 in the given sequence is in place of the expected 30, so 36 breaks the pattern. Verification / Alternative check: Once we adjust the fifth term to 30, the consecutive differences are 18, 16, 14, 12, 10 in absolute value. This is a smooth decreasing sequence of even numbers subtracting 2 each time. The intended pattern is therefore clear, and 36 is the only term that does not fit. Why Other Options Are Wrong: The terms 20, 42, and 56 fit perfectly into the adjusted series. Removing any of them would destroy the consistent subtraction by 18, 16, 14, 12, and 10. Only 36 prevents that pattern from appearing, which makes it the true odd man out. Common Pitfalls: Some learners focus on divisibility or factors instead of differences and may incorrectly pick a term that looks less structured, such as 20. However, the most systematic way to solve such series is to examine differences first. Overlooking the idea of consecutive even subtractions is another typical mistake. Final Answer: The term that does not follow the decreasing even difference pattern is 36.

Odd Man Out and Series Questions