Question 1

A number series is given with one term missing. Carefully examine the pattern in 5, 10, 13, 26, 29, 58, 61, ? and choose the correct alternative from the options that will complete the series.

Accepted Answer

Introduction / Context: This is a slightly more involved number series problem. The given sequence is 5, 10, 13, 26, 29, 58, 61, ?. The pattern is not a simple arithmetic or geometric progression. Instead, it alternates between two different operations. Such designs are common in exam questions where the examiner wants to test careful observation and the ability to detect a repeating cycle of operations. Given Data / Assumptions: Series: 5, 10, 13, 26, 29, 58, 61, ? Exactly one term is missing at the end of the series. The rule may involve alternating operations such as multiplication and addition. A single, consistent pattern should explain all transitions between terms. Concept / Approach: Looking at the series, we can try grouping the transitions in pairs. From 5 to 10 and 10 to 13, from 13 to 26 and 26 to 29, and so on. This suggests that one step may involve multiplication and the next a smaller addition. We look for a simple relationship like "multiply by 2, then add 3" repeated again and again. Such alternating two-step patterns are very common in number series questions. Step-by-Step Solution: From 5 to 10: 5 * 2 = 10. From 10 to 13: 10 + 3 = 13. From 13 to 26: 13 * 2 = 26. From 26 to 29: 26 + 3 = 29. From 29 to 58: 29 * 2 = 58. From 58 to 61: 58 + 3 = 61. Following the same pattern, the next step should be multiplication by 2 again. So, 61 * 2 = 122. Therefore, the missing term is 122. Verification / Alternative check: We verify by summarising the rule: multiply by 2, then add 3, and repeat. Applying this cyclic rule from the first term generates the entire series without any inconsistency. The final step, 61 * 2 = 122, continues the cycle perfectly. None of the other options maintain this simple and elegant pattern, which confirms that 122 is the correct answer. Why Other Options Are Wrong: Option B: 125 would require adding 64 instead of following the multiplication by 2 step, which is not supported by the previous terms. Option C: 128 is 2^7 and does not arise naturally from 61 under the observed rule of multiply by 2 then add 3 in alternation. Option D: 64 would correspond to adding only 3 to 61, while the pattern demands a multiplication at this stage. Option E: 118 does not fit either multiply by 2 or add 3, so it breaks the cycle. Common Pitfalls: Many candidates focus only on differences: 5, 3, 13, 3, 29, 3, which looks uneven and confusing. They may ignore the fact that some jumps are too large for simple addition and thus indicate multiplication. Recognising alternating operations is crucial. Another common mistake is to search for one single arithmetic progression instead of a repeated two-step pattern. Final Answer: The term that correctly completes the cycle of multiply by 2 and then add 3 is 122, so the correct option is 122.

Question 2

In the following number series, one term is wrong. Carefully analyse the pattern in 5, 10, 40, 80, 320, 550, 2560 and identify which term in the series is incorrect.

Accepted Answer

Introduction / Context: This question is a variation of the usual number series problems. Instead of finding a missing term, we are asked to find the wrong term in the series 5, 10, 40, 80, 320, 550, 2560. Detecting an incorrect term requires us to infer the intended pattern and then check which value does not fit that pattern. This tests both pattern recognition and error detection skills, which are important for competitive examinations. Given Data / Assumptions: Series: 5, 10, 40, 80, 320, 550, 2560. Exactly one term in this list is assumed to be wrong. There is an underlying rule that should connect the correct terms. We need to identify the term that violates this consistent rule. Concept / Approach: The numbers grow quite rapidly, which suggests a multiplicative pattern. We check how each term is obtained from the previous one using multiplication, possibly with a constant factor or an alternating factor. Observing the values, it looks natural to test a pattern like multiplying alternately by 2 and 4, a common exam trick. If this pattern holds, the term that does not respect it is the wrong one. Step-by-Step Solution: From 5 to 10: 5 * 2 = 10. From 10 to 40: 10 * 4 = 40. From 40 to 80: 40 * 2 = 80. From 80 to 320: 80 * 4 = 320. If we continue the same pattern, the next term should be 320 * 2 = 640. Continuing again: 640 * 4 = 2560 for the following term. Therefore, the correct series should be 5, 10, 40, 80, 320, 640, 2560. In the given series, 550 appears instead of 640, so 550 is the wrong term. Verification / Alternative check: We verify the intended pattern: multiply alternately by 2, 4, 2, 4, 2, 4. This reproduces 5, 10, 40, 80, 320, 640, 2560 perfectly. All terms except 550 fit smoothly into this rule when replaced by 640. Therefore 550 is the only term that does not conform to the consistent pattern, confirming that it is incorrect. Why Other Options Are Wrong: Option A: 80 fits the pattern as 40 * 2, so it is correct. Option B: 320 fits the pattern as 80 * 4, so it is also correct. Option D: 2560 fits the pattern as 640 * 4, where 640 is the expected term, so 2560 is not wrong. Option E: 10 is correctly generated as 5 * 2, so it is correct as well. Common Pitfalls: A frequent pitfall is to miscalculate one of the products and conclude that the wrong term is somewhere else. Another mistake is to look only for a single multiplier (for example, repeatedly doubling) and ignore the possibility of an alternating pattern such as multiply by 2 and then by 4. Exam questions often use such alternating multipliers precisely to mislead candidates who check only the first couple of steps. Final Answer: The only term that violates the consistent pattern of multiplying alternately by 2 and 4 is 550, so the correct option is 550.

Question 3

A number series is given with one term missing. Study the pattern in 1, 0.25, 1/9, ?, 0.04, 1/36 and choose the correct alternative that will complete the series.

Accepted Answer

Introduction / Context: This number series uses reciprocals of perfect squares. The given sequence is 1, 0.25, 1/9, ?, 0.04, 1/36. Our task is to detect the pattern that links each term and then determine the missing value. Questions of this type test knowledge of basic squares and the ability to recognise when a series is built from them in decimal or fractional form. Given Data / Assumptions: Given series: 1, 0.25, 1/9, ?, 0.04, 1/36. Some terms are decimals, others are written as fractions. We assume the terms are related to each other by a simple mathematical formula. Exactly one of the provided options will match the required missing term. Concept / Approach: A sensible approach is to convert every term to a single representation, for example as reciprocals of squares. 1 can be written as 1/1^2, 0.25 as 1/4, which is 1/2^2, 1/9 is already in the form 1/3^2, 0.04 is 1/25, that is 1/5^2, and 1/36 is 1/6^2. This strongly suggests that the series is built from 1/(n^2) for n = 1, 2, 3, 4, 5, 6. Therefore, the missing term should be 1/4^2 = 1/16, written either as a fraction or as a decimal. Step-by-Step Solution: Express each term as 1/(n^2): 1 = 1/1^2. 0.25 = 1/4 = 1/2^2. 1/9 = 1/3^2. The missing term should be 1/4^2 = 1/16. 0.04 = 1/25 = 1/5^2. 1/36 = 1/6^2. 1/16 as a decimal is 0.0625. Hence, the missing term is 0.0625. Verification / Alternative check: We list the denominators of the reciprocals: 1^2, 2^2, 3^2, 4^2, 5^2, 6^2. The sequence of n values is 1, 2, 3, 4, 5, 6, so the series is clearly built from consecutive positive integers. All given terms match this rule except the missing one, which must correspond to n = 4. Therefore 1/16 or 0.0625 is the only value that fits the pattern seamlessly. Why Other Options Are Wrong: Option B: 0.025 equals 1/40 and does not correspond to 1/4^2 or any 1/n^2 with small integer n in this context. Option C: 1/8 is not the reciprocal of a perfect square but of 2^3, so it is inconsistent with the pattern. Option D: 1/6 is also not of the form 1/n^2 for n = 1 to 6 in this series. Option E: 0.01 equals 1/100, which would require n = 10, outside the small consecutive range implied here. Common Pitfalls: Students often overlook that decimals like 0.25 and 0.04 correspond to very clean fractional forms related to squares. Another pitfall is to search for an arithmetic progression in the decimal values instead of spotting the underlying 1/n^2 structure. Strong familiarity with squares from 1^2 up to at least 20^2 is extremely useful for quickly solving such problems in exams. Final Answer: The missing term that keeps the sequence of reciprocals of consecutive squares intact is 0.0625, so the correct option is 0.0625.

Question 4

A mixed fraction and decimal number series is given with one term missing. Examine the pattern in 3/5, 1.4, 11/5, ?, 19/5, 4.6 and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This series mixes fractions and decimals in a simple pattern. The given sequence is 3/5, 1.4, 11/5, ?, 19/5, 4.6. The challenge is to interpret all terms consistently and then identify the missing number using a clear arithmetic relationship. Such questions check whether candidates can recognise a basic progression even when the format of the numbers changes. Given Data / Assumptions: Series: 3/5, 1.4, 11/5, ?, 19/5, 4.6. The numbers can be converted between fraction and decimal forms. There should be a single arithmetic pattern, likely a constant increment. Only one option will preserve the pattern when placed in the missing position. Concept / Approach: We convert all terms to decimals so that increments become easier to spot. 3/5 is 0.6, 1.4 remains 1.4, 11/5 is 2.2, 19/5 is 3.8, and 4.6 stays 4.6. Now the series becomes 0.6, 1.4, 2.2, ?, 3.8, 4.6. This strongly suggests an arithmetic progression with a constant difference, which we can calculate by subtracting consecutive terms. Step-by-Step Solution: Write the sequence in decimals: 0.6, 1.4, 2.2, ?, 3.8, 4.6. Difference from 0.6 to 1.4: 1.4 - 0.6 = 0.8. Difference from 1.4 to 2.2: 2.2 - 1.4 = 0.8. The common difference is 0.8. Add 0.8 to 2.2 to find the missing term: 2.2 + 0.8 = 3.0. Next, 3.0 + 0.8 = 3.8 and 3.8 + 0.8 = 4.6, which match the later terms. Thus, the missing term is 3.0, or simply 3. Therefore, the correct answer is 3. Verification / Alternative check: We verify the full arithmetic progression: 0.6, 1.4, 2.2, 3.0, 3.8, 4.6. The difference is 0.8 at every step. Converting back to fractions, 3.0 is 3, consistent with the format of the series. No other candidate value maintains this uniform increment, which confirms that 3 is the only valid missing term. Why Other Options Are Wrong: Option A: 14/5 equals 2.8, which would create a difference of only 0.6 from 2.2 and 1.0 to 3.8, breaking the constant 0.8 increment. Option B: 3.2 gives a jump of 1.0 from 2.2 and 0.6 to 3.8, again inconsistent. Option C: 16/5 is 3.2 and has the same issue as 3.2 in terms of uneven differences. Option E: 17/5 equals 3.4, which does not maintain a uniform step size with neighbouring terms. Common Pitfalls: Candidates may be reluctant to convert between fractions and decimals, missing the simplicity of the underlying arithmetic progression. Others may attempt to see a more complex pattern instead of testing basic constant differences. Familiarity with common fraction to decimal conversions can save valuable time and reduce errors on such series questions. Final Answer: The term that keeps the constant increment of 0.8 throughout the series is 3, so the correct option is 3.

Question 5

In this simple number series question, one term is missing. Observe the pattern in 10, 12, 14, 16, 18, ? and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This is a straightforward number series problem. The given sequence is 10, 12, 14, 16, 18, ?. The aim is to identify the pattern connecting the terms and then determine the missing next value. Such questions commonly test quick recognition of basic arithmetic progressions in competitive exams and placement tests. Given Data / Assumptions: Series: 10, 12, 14, 16, 18, ? One term is missing at the end of the series. The sequence appears to be increasing steadily by a constant amount. Exactly one option will continue this simple pattern correctly. Concept / Approach: For small, regularly increasing series, we first check for an arithmetic progression. That means each term differs from the previous one by a fixed quantity. If the difference between consecutive terms is the same, we can easily extend the sequence by adding that common difference to the last known term. Step-by-Step Solution: Compute the differences: 12 - 10 = 2. Next: 14 - 12 = 2. Next: 16 - 14 = 2. Next: 18 - 16 = 2. The common difference between consecutive terms is 2 throughout. To find the missing term, add 2 to the last known term: 18 + 2 = 20. Therefore, the missing number is 20. Verification / Alternative check: Rewriting the series with the missing term included: 10, 12, 14, 16, 18, 20. This is a clear arithmetic progression starting at 10 with a common difference of 2. None of the other options gives such a smooth pattern. The sequence also corresponds to consecutive even numbers from 10 to 20, which further confirms the correctness of the answer. Why Other Options Are Wrong: Option A: 22 would correspond to 18 + 4, which breaks the constant difference of 2. Option B: 24 also does not follow the +2 rule and would skip several intermediate terms. Option D: 26 is even further away and clearly inconsistent with the basic progression. Option E: 28 is not the immediate successor in the pattern and would represent multiple missed steps. Common Pitfalls: This problem is simple, but under exam pressure candidates may overthink and search for a complicated rule. Another possible pitfall is misreading the final term and adding an incorrect difference. Always confirm that the same difference appears consistently between all consecutive terms before making a conclusion. Final Answer: The number that continues the pattern of adding 2 each time is 20, so the correct option is 20.

Question 6

A letter series is given with one term missing. Observe the pattern in ALZ, CJV, EHR, GFN, ? and choose the correct group of letters that completes the series.

Accepted Answer

Introduction / Context: This is a letter series question from verbal reasoning. The series ALZ, CJV, EHR, GFN, ? contains three-letter groups, and one term is missing. The task is to analyse each position within the groups (first, second, and third letters) and recognise the alphabetical pattern followed, then find the group of letters that correctly completes the series. Such problems test familiarity with alphabetical positions and pattern recognition. Given Data / Assumptions: Given series: ALZ, CJV, EHR, GFN, ? Each term consists of three letters of the English alphabet. The pattern may apply separately to the first, second, and third letters. We assume that the same consistent rule extends to the missing term. Concept / Approach: The best strategy is to write down the alphabetical positions of each letter (A = 1, B = 2, ..., Z = 26) and then look at how these positions change from term to term in each of the three positions. Often the first letters follow one arithmetic sequence, the second letters follow another, and the third letters follow a third sequence, all operating independently. Step-by-Step Solution: First letters: A, C, E, G, ? Positions: A = 1, C = 3, E = 5, G = 7. Each time we add 2. So, next first letter: 7 + 2 = 9, which is I. Second letters: L, J, H, F, ? Positions: L = 12, J = 10, H = 8, F = 6. Each time we subtract 2. So, next second letter: 6 - 2 = 4, which is D. Third letters: Z, V, R, N, ? Positions: Z = 26, V = 22, R = 18, N = 14. Each time we subtract 4. So, next third letter: 14 - 4 = 10, which is J. Combining these, the missing group is I D J. Therefore, the correct term is IDJ. Verification / Alternative check: We can reconstruct the pattern: first letters increase by 2 (A, C, E, G, I), second letters decrease by 2 (L, J, H, F, D), and third letters decrease by 4 (Z, V, R, N, J). All transitions are perfectly consistent with simple arithmetic steps. IDJ is the only option that fits these three independent sequences at once. Why Other Options Are Wrong: Option A: JDJ has J as the first letter instead of I, breaking the +2 pattern in the first position. Option B: IEK has E as the third letter, which does not match the required decrease of 4 to J in the last position. Option D: JEK has incorrect letters in both the first and last positions compared with the established sequences. Option E: HFJ does not satisfy the incremental pattern in any of the positions consistently. Common Pitfalls: Many candidates try to interpret the groups as whole units rather than analysing each letter position separately. Another frequent mistake is to miscalculate alphabetical positions or skip letters when counting. Writing the alphabetical index of each letter explicitly and then applying simple addition or subtraction rules usually makes such patterns much easier to see and verify. Final Answer: The letter group that correctly completes the series is IDJ, so the correct option is IDJ.

Question 7

A number series is given with one term missing. Examine the pattern in 3, 4, 7, ?, 18, 29, 47 and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This number series problem is based on a pattern where each term is formed from the previous two. The given series is 3, 4, 7, ?, 18, 29, 47. We need to identify the rule that connects successive terms and then determine the missing value. Such series often use a relation similar to the Fibonacci pattern, where a term is the sum of two preceding terms. Given Data / Assumptions: Series: 3, 4, 7, ?, 18, 29, 47. One middle term is missing between 7 and 18. The pattern likely uses the sum of previous terms to generate the next one. The same rule should apply consistently after the missing term as well. Concept / Approach: We suspect that each term after the second is the sum of the previous two terms. This is because 3 + 4 = 7, which matches the third term exactly. If this holds, then the next term (the missing one) should be the sum of 4 and 7, the following term should be the sum of that missing term and 7, and so on. This gives us a clear way to reconstruct the entire series. Step-by-Step Solution: Check the relation for the third term: 3 + 4 = 7. Assume the pattern is: next term = sum of previous two terms. Missing term should be 4 + 7 = 11. Next term should be 7 + 11 = 18, which matches the given fifth term. Next: 11 + 18 = 29, which matches the sixth term. Next: 18 + 29 = 47, which matches the seventh term. Therefore, the missing term is 11. Verification / Alternative check: With the missing term filled in, the full series becomes 3, 4, 7, 11, 18, 29, 47. Every term from the third onward is the sum of the two immediately before it. This pattern is consistent and leaves no contradictions. No other candidate value yields such a smooth and fully consistent Fibonacci-style series when extended. Why Other Options Are Wrong: Option A: 8 would give 7 + 8 = 15, which does not match 18, breaking the pattern immediately. Option B: 9 would give 7 + 9 = 16, again inconsistent with the given 18. Option D: 12 yields 7 + 12 = 19, which does not equal 18, so the sequence fails. Option E: 15 would totally disrupt the later terms since 7 + 15 = 22, not 18. Common Pitfalls: Candidates sometimes focus on successive differences, which here are 1, 3, ?, 7, 11, 18, and may not immediately reveal a simple pattern. Another pitfall is to overlook the possibility that each term may depend on two earlier terms instead of just one. Recognising Fibonacci-type series is a crucial skill for many competitive exams. Final Answer: The value that maintains the sum-of-previous-two-terms pattern is 11, so the correct option is 11.

Question 8

A number series is given with one term missing. Observe the sequence 1, 2, 4, 7, ?, 16 and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This problem presents a number series with gradually increasing terms. The given sequence is 1, 2, 4, 7, ?, 16. Our job is to determine the missing middle term by uncovering the pattern that describes how each term is generated from the previous one. Many such series are based on increasing differences that follow a simple rule. Given Data / Assumptions: Series: 1, 2, 4, 7, ?, 16. One term is missing between 7 and 16. The pattern likely uses increasing differences rather than a constant increment. Exactly one option will make the differences follow a simple sequence. Concept / Approach: To solve this, we analyse the differences between consecutive terms. If the differences themselves follow a simple pattern, such as consecutive integers (1, 2, 3, 4, 5, ...), we can extend that pattern to identify the missing term. This type of structure is very common in exam questions and is an important pattern to recognise quickly. Step-by-Step Solution: Compute differences between known terms. From 1 to 2: difference = 1. From 2 to 4: difference = 2. From 4 to 7: difference = 3. The differences so far are 1, 2, and 3, which are consecutive integers. Next difference should be 4, so the missing term is 7 + 4 = 11. After that, the difference should be 5, giving 11 + 5 = 16, which matches the last term. Hence, the missing term is 11. Verification / Alternative check: With the missing term filled in, the series becomes 1, 2, 4, 7, 11, 16. The differences are 1, 2, 3, 4, 5, which form a perfect sequence of consecutive natural numbers. This is a very standard pattern and provides strong confirmation that 11 is the correct answer. Why Other Options Are Wrong: Option A: 14 would give a difference of 7 from 7 and only 2 to 16, which does not follow the consecutive differences pattern. Option B: 8 gives a difference of 1 from 7 and then 8 to 16, destroying the 1, 2, 3, 4, 5 structure. Option D: 15 results in differences 8 and 1, which are highly irregular. Option E: 9 gives differences of 2 and 7, again inconsistent with the simple gradual increase in differences. Common Pitfalls: Some candidates may guess based on the approximate size of the missing term rather than systematically working out the differences. Others may try to fit a multiplicative rule where none is needed. In many reasoning questions, increasing difference patterns like 1, 2, 3, 4, and so on appear very frequently. Recognising them quickly can save time and improve accuracy. Final Answer: The number that maintains the sequence of differences as 1, 2, 3, 4, 5 is 11, so the correct option is 11.

Question 9

A number series is given with one term missing. Study the pattern in 5, 11, 24, 51, 106, ? and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This number series question is more challenging and is suitable for higher-level competitive exams. The sequence is 5, 11, 24, 51, 106, ?, and we must determine the next term. The growth rate is faster than simple addition but not strictly geometric, suggesting that the differences between terms themselves follow a pattern. Understanding such second-level patterns is crucial for advanced number series problems. Given Data / Assumptions: Series: 5, 11, 24, 51, 106, ? Exactly one term is missing at the end of the series. The sequence increases rapidly, hinting at multiplication or doubling within the pattern of differences. We assume a single consistent rule connects each term to the next. Concept / Approach: First, we calculate the differences between consecutive terms to see whether those differences form a recognisable sequence. If those differences themselves roughly double or follow a simple recurrence, we can extend that pattern to calculate the next difference and therefore the next term. This is a typical approach for complex series where the original numbers grow quickly. Step-by-Step Solution: Compute first-level differences. 11 - 5 = 6. 24 - 11 = 13. 51 - 24 = 27. 106 - 51 = 55. Now observe the pattern in the differences: 6, 13, 27, 55. Each difference is nearly double the previous one plus 1. 6 * 2 + 1 = 13, 13 * 2 + 1 = 27, 27 * 2 + 1 = 55. Applying the same rule: next difference = 55 * 2 + 1 = 111. Add this to the last term: 106 + 111 = 217. Thus, the missing term is 217. Verification / Alternative check: We summarise the pattern as: difference(n) = difference(n - 1) * 2 + 1. Starting from 6, this generates 6, 13, 27, 55, 111. Adding these differences successively to the initial term 5 recreates the series: 5, 11, 24, 51, 106, 217. This structure is smooth, systematic, and typical of higher difficulty exam questions, which confirms the validity of 217 as the next term. Why Other Options Are Wrong: Option A: 122 gives a last difference of only 16, which does not fit the doubling plus 1 pattern for differences. Option C: 120 gives a difference of 14, again inconsistent with the rapidly growing differences 6, 13, 27, 55. Option D: 153 gives a difference of 47, which does not match any simple transformation of 55 such as doubling plus 1. Option E: 211 gives a difference of 105, still not equal to 55 * 2 + 1. Common Pitfalls: One pitfall is to search for a direct multiplicative relation between each pair of terms rather than looking at the pattern in the differences. Another mistake is to assume a fixed difference or ratio when the series clearly grows faster than that. For tougher number series, it is vital to explore second-level patterns such as how the differences themselves change from step to step. Final Answer: The next term, based on the pattern where each difference is double the previous difference plus one, is 217, so the correct option is 217.

Question 10

Which number comes next in the following number series? Carefully observe the pattern in 1, 5, 2, 6, 3, 7, ? and choose the correct alternative from the options.

Accepted Answer

Introduction / Context: This question features an alternating number series. The given sequence is 1, 5, 2, 6, 3, 7, ?, and we must find the next term. Such series often consist of two independent subsequences interwoven together. Identifying those subsequences is a key technique in verbal reasoning questions involving numbers. Given Data / Assumptions: Series: 1, 5, 2, 6, 3, 7, ? There is one missing term at the end of the series. The numbers seem to alternate between two distinct patterns. The same rule should apply consistently within each subsequence. Concept / Approach: We list the terms along with their positions and separate the series into odd and even positions. Often, one subsequence will be increasing slowly (for example, 1, 2, 3, 4, ...) while the other also increases but perhaps from a different starting value. In this series, the first, third, and fifth terms form one subsequence, and the second, fourth, and sixth terms form another. Step-by-Step Solution: Write the series with positions: 1st: 1, 2nd: 5, 3rd: 2, 4th: 6, 5th: 3, 6th: 7, 7th: ?. Odd-position terms: 1, 2, 3, ?. Even-position terms: 5, 6, 7. Odd positions clearly follow: 1, 2, 3, 4 (consecutive natural numbers). Even positions follow: 5, 6, 7, 8 (also consecutive natural numbers), although 8 has not yet appeared. The missing term is at the 7th position, which is an odd position. So the next odd-position term after 3 is 4. Therefore, the missing number is 4. Verification / Alternative check: Reconstruct the extended series: odd positions as 1, 2, 3, 4 and even positions as 5, 6, 7, 8. Interleaving them gives 1, 5, 2, 6, 3, 7, 4, 8, and so on. This is a completely regular pattern of two increasing sequences interwoven together. The seventh term must therefore be 4, and none of the other options fits this structure. Why Other Options Are Wrong: Option A: 6 belongs to the even-position subsequence and has already appeared, so it cannot be the next odd-position term. Option B: 5 is also part of the even-position subsequence and repeats an earlier value, breaking the smooth pattern. Option D: 3 has already appeared at the fifth position and does not continue the odd-position sequence 1, 2, 3, 4. Option E: 8 would be the next even-position term, not the next odd-position term, so it is misplaced here. Common Pitfalls: A common mistake is to treat the series as a single progression and search for one complex pattern rather than two simple alternating ones. Another pitfall is to ignore the importance of positions and focus only on the values themselves. In many reasoning questions, carefully separating odd and even positions quickly reveals the underlying rule. Final Answer: The number that correctly completes the alternating pattern is 4, so the correct option is 4.

Question 11

A number series is given with one term missing. Observe the sequence 19, 28, 39, 52, ?, 84 and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This question presents a steadily increasing number series. The given sequence is 19, 28, 39, 52, ?, 84. Our goal is to determine the missing middle term by analysing the pattern of increases between consecutive numbers. Many such series are built using differences that themselves form a simple sequence, often of consecutive odd or even numbers. Given Data / Assumptions: Series: 19, 28, 39, 52, ?, 84. One term is missing between 52 and 84. The series increases in a non-linear but regular way. We assume that the differences between terms themselves follow a clear pattern. Concept / Approach: We calculate the differences between consecutive known terms to see whether these differences form a recognizable sequence. In many exam problems, differences are consecutive odd numbers or follow a simple arithmetic progression. Once we identify the pattern in the differences, we can apply it to find the missing term and verify the result. Step-by-Step Solution: Compute differences between known terms. 28 - 19 = 9. 39 - 28 = 11. 52 - 39 = 13. The differences so far are 9, 11, and 13, which are consecutive odd numbers. So, the next difference should be 15, followed by 17. Add 15 to 52: 52 + 15 = 67. Add 17 to 67: 67 + 17 = 84, which matches the last term in the series. Therefore, the missing term is 67. Verification / Alternative check: With the missing term inserted, the full series becomes 19, 28, 39, 52, 67, 84. The differences are 9, 11, 13, 15, 17, which form a perfect sequence of consecutive odd numbers. This type of structure is common in reasoning questions and confirms that the observed pattern is deliberate and correct. Why Other Options Are Wrong: Option A: 39 simply repeats a previous term and breaks the smooth upward trend of the series. Option B: 52 is already part of the series and cannot appear again as the missing term. Option D: 84 is the last term and not the missing middle term, so it cannot be correct here. Option E: 71 would require a difference of 19 from 52 and 13 from 71 to 84, which fails to maintain the consistent pattern of consecutive odd differences. Common Pitfalls: Candidates might initially look for a direct multiplicative relation or assume a fixed difference. Others may miscalculate one of the differences and miss the simple odd-number sequence. It is always advisable to carefully compute all differences and look for familiar sequences, especially involving consecutive odd or even numbers. Final Answer: The number that maintains the consecutive odd differences pattern is 67, so the correct option is 67.

Question 12

A number series is given with one term missing. Examine the alternating pattern in 68, 72, 65, 69, 62, 66, ? and choose the correct alternative that completes the series.

Accepted Answer

Introduction / Context: This number series question involves an alternating pattern of increases and decreases. The given sequence is 68, 72, 65, 69, 62, 66, ?, and we must find the missing last term. Such series commonly use two alternating operations, for example adding a fixed number and then subtracting another fixed number in a repeating cycle. Given Data / Assumptions: Series: 68, 72, 65, 69, 62, 66, ? One term is missing at the end of the series. The sequence appears to alternate between an increase and a decrease. We assume a simple repeating pattern governs the entire series. Concept / Approach: We calculate consecutive differences and look for repetition. If we see, for example, +4, -7, +4, -7, and so on, we can extrapolate the pattern. This type of alternating addition and subtraction is a very common structure in verbal reasoning number series questions and should be checked early. Step-by-Step Solution: Compute the differences between consecutive terms. 72 - 68 = 4 (increase of 4). 65 - 72 = -7 (decrease of 7). 69 - 65 = 4 (increase of 4). 62 - 69 = -7 (decrease of 7). 66 - 62 = 4 (increase of 4). The pattern of differences is +4, -7, +4, -7, +4, ... Following this alternating pattern, the next difference should be -7. So, the missing term is 66 - 7 = 59. Therefore, the correct answer is 59. Verification / Alternative check: Reconstruct the extended sequence: 68, 72, 65, 69, 62, 66, 59. The differences are +4, -7, +4, -7, +4, -7, which shows a perfectly consistent alternating pattern. No other option creates such a clean alternation of +4 and -7, so 59 is the only valid choice. Why Other Options Are Wrong: Option A: 61 would give a difference of -5 from 66, which does not match the recurring -7 change. Option C: 68 would mean a difference of +2, breaking the established +4 and -7 cycle. Option D: 75 results in a difference of +9, which is inconsistent with earlier steps. Option E: 63 gives a difference of -3, again violating the repeating pattern of -7 after each +4. Common Pitfalls: One common error is to look for a single arithmetic progression rather than noticing the alternation of adding and subtracting. Another pitfall is to miscalculate one of the differences and then search for an incorrect pattern based on that error. Carefully computing all differences and checking for a simple repeating cycle can greatly simplify many number series questions. Final Answer: The term that maintains the alternating pattern of +4 and -7 is 59, so the correct option is 59.

Question 13

In the following number series with one term missing, choose the correct alternative that will complete the series: 41, 43, 47, 53, ?

Accepted Answer

Introduction / Context: This verbal reasoning question tests your ability to analyse a simple number series and identify the underlying pattern in the differences between consecutive terms. Such problems appear frequently in banking, SSC and other competitive examinations to measure basic numerical pattern recognition skills. Given Data / Assumptions: - The given number series is 41, 43, 47, 53, ?.- Exactly one term is missing, and it must be chosen from the options.- The pattern is assumed to be consistent through the entire series. Concept / Approach: The standard approach is to compute the differences between consecutive numbers. In many aptitude questions, these differences themselves form a simple arithmetic sequence or a predictable pattern. Once the pattern in the differences is identified, we extend it to find the missing term. This is often faster and more reliable than trying to see the pattern in the original numbers directly. Step-by-Step Solution: Step 1: Find the difference between the second and first terms: 43 - 41 = 2.Step 2: Find the difference between the third and second terms: 47 - 43 = 4.Step 3: Find the difference between the fourth and third terms: 53 - 47 = 6.Step 4: The differences are 2, 4 and 6, which form an increasing pattern where each difference increases by 2.Step 5: Following this rule, the next difference should be 6 + 2 = 8.Step 6: Add this next difference to the last known term: 53 + 8 = 61.Step 7: Therefore the missing term that completes the series is 61. Verification / Alternative check: Write the completed series as 41, 43, 47, 53, 61. Now recompute all gaps: 43 - 41 = 2, 47 - 43 = 4, 53 - 47 = 6 and 61 - 53 = 8. The differences are 2, 4, 6, 8, which clearly form an arithmetic progression with common difference 2. Since the rule holds across the entire sequence, the value 61 is fully consistent. Why Other Options Are Wrong: If we choose 59, the last difference becomes 59 - 53 = 6, breaking the increasing pattern. If we choose 63 or 65, the last difference becomes 10 or 12, which jumps too far and does not fit the smooth progression of differences 2, 4, 6, 8. Hence these options do not preserve a single simple rule for all the terms in the series. Common Pitfalls: Many students guess based on the rough size of the numbers or check only one or two gaps and then stop. Another common mistake is to try complicated operations like squares or cubes before checking simple differences. In exam conditions, always start with the most basic idea: look at the consecutive differences and see if they themselves follow an easy pattern. Final Answer: The missing term that correctly completes the series is 61.

Question 14

The missing number in the following series is: 15 (105) 14, 13 (?) 12. Choose the correct alternative that fits the same pattern as the first bracketed number.

Accepted Answer

Introduction / Context: This question checks your understanding of number relationships using brackets. You are given one complete pattern, 15 (105) 14, and then asked to apply the same hidden rule to a second case, 13 (?) 12. Such questions appear regularly in reasoning sections to test how quickly you can discover and transfer a numerical rule. Given Data / Assumptions: - First pattern: 15 (105) 14.- Second pattern: 13 (?) 12.- The same rule must connect the outer numbers to the middle number in both cases. Concept / Approach: When numbers appear outside and inside brackets like this, a common idea is that the middle number is derived from combining the two outer numbers using multiplication, addition, or a fraction of their product. Here, the outer numbers in the first pattern are 15 and 14, so it is natural to try operations involving 15 * 14 or 15 + 14 and see what yields 105. Step-by-Step Solution: Step 1: Multiply the outer numbers in the first pattern: 15 * 14 = 210.Step 2: Observe that 105 is exactly half of 210, so 105 = (15 * 14) / 2.Step 3: Thus, the rule is: middle number = (first outer number * second outer number) / 2.Step 4: Apply the same rule to the second pattern. Multiply the outer numbers: 13 * 12 = 156.Step 5: Divide by 2 to match the discovered pattern: 156 / 2 = 78.Step 6: Therefore, the missing number in the second pattern is 78. Verification / Alternative check: Check the rule once more for the first pattern: (15 * 14) / 2 = 210 / 2 = 105, which is correct. Then check the second pattern: (13 * 12) / 2 = 156 / 2 = 78, which matches our result. Since the same relationship holds for both cases, the rule is consistent and reliable. Why Other Options Are Wrong: Option 91 does not equal (13 * 12) / 2, because 91 is not half of 156. Option 65 is smaller than half of 156, and option 68 is also not equal to 78. None of these values can be obtained using the same rule that produced 105 from 15 and 14, so they break the pattern. Common Pitfalls: Students sometimes try arbitrary operations like adding a fixed number or squaring individual terms without checking whether the same idea works consistently across all given patterns. Another mistake is to focus on only one of the outer numbers rather than using both together. Always verify that the rule you propose explains every example provided in the question. Final Answer: The missing number that completes the second pattern is 78.

Question 15

In the following simple arithmetic number series, choose the missing term that will correctly complete the series: 5, 9, 13, 17, ?, 25.

Accepted Answer

Introduction / Context: This is a straightforward arithmetic number series question. You are given several consecutive terms and asked to identify the missing term that maintains the pattern. Such problems are common in aptitude tests because they quickly reveal how comfortable a candidate is with recognising simple numerical progressions. Given Data / Assumptions: - The series is 5, 9, 13, 17, ?, 25.- Exactly one term is missing.- The pattern is assumed to be uniform throughout. Concept / Approach: For a series where numbers increase smoothly, the first thing to test is whether it is an arithmetic progression, meaning that we add a constant value each time. To check this, we calculate the difference between each pair of consecutive numbers and see if the difference is constant or follows a simple rule. Step-by-Step Solution: Step 1: Compute the difference between the second and first terms: 9 - 5 = 4.Step 2: Compute the difference between the third and second terms: 13 - 9 = 4.Step 3: Compute the difference between the fourth and third terms: 17 - 13 = 4.Step 4: Since all differences are equal to 4, the series is an arithmetic progression with common difference 4.Step 5: To get the next term after 17, add the common difference: 17 + 4 = 21.Step 6: Now check consistency with the last given term: 21 + 4 = 25, which matches the series. Verification / Alternative check: The completed series becomes 5, 9, 13, 17, 21, 25. All consecutive differences are 4, confirming that the arithmetic progression rule is upheld across the entire sequence. Therefore, 21 fits perfectly and there is no need for a more complicated explanation. Why Other Options Are Wrong: Option 27 produces a difference of 10 from 17, which breaks the constant gap of 4. Option 23 creates differences of 6 and 2 near the end, so it does not maintain a steady pattern. Option 19 would reduce the difference between 17 and the missing term to 2, again violating the rule that every step increases by 4. Hence these options cannot be correct. Common Pitfalls: A common mistake is to look at the overall range from 5 to 25 and then guess the middle value without checking each step. Another error is to consider complicated operations like multiplication or division when a simple constant addition works perfectly. Always check differences first before trying more complex patterns. Final Answer: The missing term that completes the arithmetic series is 21.

Question 16

A series is given with one number missing. Choose the correct alternative that will complete the decimal number series: 4, 5.2, 6.4, ?, 8.8.

Accepted Answer

Introduction / Context: This question involves a number series with decimal values. The aim is to identify the pattern by which each term is obtained from the previous one and then use that rule to find the missing term. Decimal series questions test both comfort with fractions and the ability to notice small, consistent changes between terms. Given Data / Assumptions: - The given series is 4, 5.2, 6.4, ?, 8.8.- One term is missing between 6.4 and 8.8.- The same rule is applied throughout the series. Concept / Approach: Because the numbers are close together and increase smoothly, the most likely rule is that we add a constant decimal value to each term. Therefore, we should compute the differences between the given adjacent terms. If those differences are equal or follow a simple pattern, we can apply that difference to obtain the missing term. Step-by-Step Solution: Step 1: Calculate the difference between the second and first terms: 5.2 - 4 = 1.2.Step 2: Calculate the difference between the third and second terms: 6.4 - 5.2 = 1.2.Step 3: So far, the common difference is 1.2.Step 4: Assume the same difference continues. The missing term after 6.4 should be 6.4 + 1.2 = 7.6.Step 5: Check the last gap using this value: 8.8 - 7.6 = 1.2, which matches the same difference.Step 6: Therefore the missing term that keeps a constant increment of 1.2 is 7.6. Verification / Alternative check: The completed series becomes 4, 5.2, 6.4, 7.6, 8.8. Now check each difference: 5.2 - 4 = 1.2, 6.4 - 5.2 = 1.2, 7.6 - 6.4 = 1.2 and 8.8 - 7.6 = 1.2. Since the common difference is uniform throughout, this confirms that our answer is consistent and correct. Why Other Options Are Wrong: If we choose 7, the difference from 6.4 is 0.6 and from 7 to 8.8 is 1.8, which does not preserve a constant increase. Option 8 gives differences of 1.6 and 0.8, also inconsistent. Option 8.25 creates uneven jumps as well. Thus, none of these values can form a simple arithmetic progression in decimals, so they must be rejected. Common Pitfalls: Some test takers become nervous when they see decimals and try to convert them to fractions or use unnecessary calculations. The key idea is that the method of looking at differences remains the same whether the numbers are integers or decimals. Focus on the pattern, not on the type of numbers used. Final Answer: The missing decimal number that completes the series is 7.6.

Question 17

A series is given with one number missing. Choose the correct alternative from the given options that will complete the geometric number series: 6, 18, 54, ?, 486, 1458.

Accepted Answer

Introduction / Context: This is a geometric progression type number series, where each term is obtained by multiplying the previous term by a fixed factor. You are asked to identify the missing term. Such questions are frequently used to test recognition of multiplicative patterns rather than additive patterns. Given Data / Assumptions: - The series is 6, 18, 54, ?, 486, 1458.- One term between 54 and 486 is missing.- The pattern is consistent for the entire sequence. Concept / Approach: When numbers grow very quickly, we should suspect multiplication rather than addition. To detect a geometric pattern, divide each term by the previous one and see if the ratio is constant. If a constant ratio exists, the series is a geometric progression, and we can find missing terms by multiplying or dividing by this ratio. Step-by-Step Solution: Step 1: Compute the ratio between the second and first terms: 18 / 6 = 3.Step 2: Compute the ratio between the third and second terms: 54 / 18 = 3.Step 3: So the common ratio is 3.Step 4: Apply this ratio to find the missing term after 54: 54 * 3 = 162.Step 5: Verify the next term using the same ratio: 162 * 3 = 486, which matches the series.Step 6: Finally, check the last term: 486 * 3 = 1458, confirming that the ratio 3 holds throughout. Verification / Alternative check: After inserting 162, the completed series is 6, 18, 54, 162, 486, 1458. To verify, check each ratio: 18 / 6 = 3, 54 / 18 = 3, 162 / 54 = 3, 486 / 162 = 3 and 1458 / 486 = 3. The consistent ratio shows that this is a perfect geometric progression with common ratio 3, and 162 is therefore correct. Why Other Options Are Wrong: Options 160, 164 and 168 are all close to 162 but none of them produce a constant ratio of 3 when used in the series. For example, if we put 160, then 160 * 3 = 480, which does not equal 486. Any small deviation from 162 breaks the clean multiplication pattern of the entire series, so these values cannot be correct. Common Pitfalls: Some students try to look at differences instead of ratios in a rapidly increasing series. While difference methods work for arithmetic progressions, they are inefficient for geometric progressions. When numbers are tripling or doubling, always check for a constant ratio first, as that usually reveals the underlying rule immediately. Final Answer: The missing term that completes the geometric number series is 162.

Question 18

A series is given, with one number missing. Choose the correct alternative that will complete the series of reciprocals of perfect cubes: 1, 0.125, 1/27, 1/64, ?, 1/216.

Accepted Answer

Introduction / Context: This number series involves both fractions and decimal representations of reciprocals. The goal is to detect the pattern of denominators and identify the missing term. Such questions test familiarity with cubes and their reciprocals, as well as the ability to recognise equivalences between decimals and fractions. Given Data / Assumptions: - The given series is 1, 0.125, 1/27, 1/64, ?, 1/216.- 0.125 is equal to 1/8 in fractional form.- The missing term is between 1/64 and 1/216. Concept / Approach: The denominators 1, 8, 27, 64 and 216 are all familiar perfect cubes: 1^3, 2^3, 3^3, 4^3 and 6^3. It is natural to suspect that the series lists reciprocals of consecutive cubes. If that is the rule, the missing term should correspond to the cube that lies between 4^3 and 6^3, which is 5^3. We must then match the reciprocal of 5^3 with one of the options, possibly in decimal form. Step-by-Step Solution: Step 1: Rewrite the numbers in fractional form where needed. 1 = 1/1 and 0.125 = 1/8.Step 2: Identify denominators: 1, 8, 27, 64, ?, 216.Step 3: Recognise that 1 = 1^3, 8 = 2^3, 27 = 3^3, 64 = 4^3 and 216 = 6^3.Step 4: The sequence of cube bases is 1, 2, 3, 4, ?, 6, so the missing base is 5.Step 5: Compute 5^3 = 125, so the missing term should be 1/125.Step 6: Convert 1/125 to decimal form: 1 / 125 = 0.008.Step 7: Therefore, the missing term is 0.008, which represents 1/125. Verification / Alternative check: List the full series in a uniform form: 1/1, 1/8, 1/27, 1/64, 1/125, 1/216. The denominators now are clearly 1^3, 2^3, 3^3, 4^3, 5^3 and 6^3. This proves that we have reciprocals of consecutive cubes from 1 to 6, confirming that 1/125 or 0.008 is the correct missing term. Why Other Options Are Wrong: Option 0.025 equals 1/40, which is not a cube denominator. Option 1/8 repeats the earlier term and breaks the pattern of distinct denominators. Option 1/128 uses 128, which is not the cube of an integer. Hence none of these values fit the rule of reciprocals of consecutive perfect cubes. Common Pitfalls: Candidates sometimes focus only on the decimal values and miss the underlying structure in the denominators. Another common mistake is to treat 0.125 and 0.008 as unrelated decimals instead of converting them to fractions. When a series involves fractions or decimals, always check whether the denominators form a simple pattern like consecutive squares or cubes. Final Answer: The missing number that correctly completes the series is 0.008 (which equals 1/125).

Question 19

In the following question, select the missing number from the given decreasing series: 47, 44, 40, 37, ?, 30.

Accepted Answer

Introduction / Context: This question presents a decreasing number series where one term is missing. The purpose is to identify the pattern of subtraction that connects each term and then find the missing number. Such problems are common in verbal reasoning sections because they require quick observation rather than heavy calculation. Given Data / Assumptions: - The given series is 47, 44, 40, 37, ?, 30.- The numbers are decreasing overall.- Exactly one term between 37 and 30 is missing. Concept / Approach: For decreasing sequences, we usually look at how much is being subtracted each time. If the decreases are not constant, they may follow an alternating pattern such as subtracting two different fixed numbers in turn. Once we recognise the cycle of subtractions, we can extend it to determine the missing term. Step-by-Step Solution: Step 1: Find the difference between the second and first terms: 47 - 44 = 3.Step 2: Find the difference between the third and second terms: 44 - 40 = 4.Step 3: Find the difference between the fourth and third terms: 40 - 37 = 3.Step 4: So the pattern in differences is -3, -4, -3, and it is natural to expect the next difference to be -4 again, continuing the alternation of subtracting 3 and 4.Step 5: Subtract 4 from 37 to get the missing term: 37 - 4 = 33.Step 6: Finally, check the last difference: 33 - 30 = 3, which returns to subtracting 3. Verification / Alternative check: With the missing value inserted, the series becomes 47, 44, 40, 37, 33, 30. Now check all differences: 47 - 44 = 3, 44 - 40 = 4, 40 - 37 = 3, 37 - 33 = 4, 33 - 30 = 3. The pattern is clearly subtract 3, subtract 4, subtract 3, subtract 4, subtract 3, confirming that 33 is correct. Why Other Options Are Wrong: If we choose 32, the differences 40 - 37 = 3, 37 - 32 = 5 and 32 - 30 = 2 do not follow any simple alternating pattern. For 34, the gaps become 3, 4, 3, 3 and 4, which again breaks the clear alternating structure. Option 31 also fails to produce a neat repeat of the subtract 3, subtract 4 pattern. Therefore these values are inconsistent with the rule of the series. Common Pitfalls: Students sometimes try to fit a complicated formula or see prime numbers without first checking basic differences. Another mistake is to treat the decreasing series as if it had a single constant difference, when in fact an alternating pattern is present. Always list all the differences to see whether they themselves form a simple sequence. Final Answer: The missing number in the series is 33.

Question 20

A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 9, 1331, 18, 121, 27, ?

Accepted Answer

Introduction / Context: This is a mixed pattern series that alternates between two different kinds of numbers. One subsequence involves multiples of a base number, and the other subsequence involves powers of another base. You must identify both patterns and then apply them to find the missing term. Such questions test your ability to separate an interleaved series into simpler components. Given Data / Assumptions: - The series given is 9, 1331, 18, 121, 27, ?.- Terms in odd positions are 9, 18, 27.- Terms in even positions are 1331, 121 and the missing value. Concept / Approach: When a series appears irregular, it is often formed by two independent subseries interwoven. Here, looking at the odd-position terms and even-position terms separately helps. The odd terms 9, 18 and 27 suggest a simple multiple pattern, while the even terms 1331 and 121 seem like familiar powers of 11. Once we identify both patterns, we can determine the missing even-position term. Step-by-Step Solution: Step 1: Consider the odd-position terms: 9 (first), 18 (third), 27 (fifth).Step 2: Recognise that 9 = 9 * 1, 18 = 9 * 2 and 27 = 9 * 3, so the odd terms are multiples of 9 in increasing order.Step 3: Now look at the even-position terms: 1331 (second) and 121 (fourth).Step 4: Note that 1331 = 11^3 and 121 = 11^2, both powers of 11.Step 5: It is natural to continue this pattern with the next lower power 11^1 = 11.Step 6: Therefore, the missing sixth term in the series should be 11. Verification / Alternative check: Rewrite the series as two separate subseries. Odd positions: 9, 18, 27 form 9 * 1, 9 * 2, 9 * 3. Even positions: 1331, 121, 11 form 11^3, 11^2, 11^1. When we interleave them, the series is 9, 1331, 18, 121, 27, 11, which perfectly matches both identified patterns. This verifies that 11 is the correct missing term. Why Other Options Are Wrong: The options 13, 17 and 19 are prime numbers but they do not fit the descending power pattern of 11^3, 11^2, 11^1. Using any of these values would disrupt the smooth sequence of powers of 11 in the even positions, so they cannot be correct. Only 11 maintains the consistent rule across the series. Common Pitfalls: Many candidates try to find a single rule relating each term to the next, which becomes very messy here. The key insight is to separate odd and even positions when the overall sequence looks irregular. Once you notice both the multiples of 9 and the powers of 11, the missing term becomes easy to identify. Final Answer: The missing number that completes the series is 11.

Number Series Questions