Question 1

Find the missing number in the series: 2, 3, 8, ?, 112, 565

Accepted Answer

Introduction / Context:This number series grows very quickly and includes both multiplication and addition at each step. Such patterns often depend on the position of the term, with each step using the term index as a multiplier or an additive constant. The given sequence is 2, 3, 8, ?, 112, 565, and we must determine the missing value that makes the pattern consistent.Given Data / Assumptions:- Known terms: 2, 3, 8, ?, 112, 565.- One intermediate term between 8 and 112 is missing.- The series is strictly increasing with very rapid growth.- The rule likely involves multiplying by the step number and then adding that same step number.Concept / Approach:When numbers increase very fast, we check whether each term can be written as previous term * k + c. If k and c change in a simple way linked to the step index, we can reconstruct the rule. Here, we will test a pattern of the form a(n+1) = a(n) * n + n, where n increases as we move through the series.Step-by-Step Solution:- Label the terms: a1 = 2, a2 = 3, a3 = 8, a4 = ?, a5 = 112, a6 = 565.- From a1 to a2: 2 * 1 + 1 = 2 + 1 = 3.- From a2 to a3: 3 * 2 + 2 = 6 + 2 = 8.- This suggests the rule a(n+1) = a(n) * n + n.- For a4, use n = 3: a4 = a3 * 3 + 3 = 8 * 3 + 3 = 24 + 3 = 27.- For a5, use n = 4: a5 = a4 * 4 + 4 = 27 * 4 + 4 = 108 + 4 = 112.- For a6, use n = 5: a6 = a5 * 5 + 5 = 112 * 5 + 5 = 560 + 5 = 565.- All transitions match perfectly, confirming that the missing term is 27.Verification / Alternative check:- Reconstructed series: 2, 3, 8, 27, 112, 565.- At each step, we multiply by the current index and add the same index: times 1 plus 1, times 2 plus 2, times 3 plus 3, times 4 plus 4, times 5 plus 5.- No contradictions appear, so the rule is fully consistent.Why Other Options Are Wrong:- 565 and 112 are later terms in the series, not the missing intermediate value between 8 and 112.- 8 and 16 cannot satisfy the positional rule a(n+1) = a(n) * n + n when placed at the fourth position.- Using any value other than 27 breaks the multiplication and addition pattern tied to the term index.Common Pitfalls:- Some candidates look only at differences, which appear irregular here and do not reveal the pattern.- Ignoring the possibility that the step number itself enters the rule leads to incorrect attempts with constant multipliers.- Confusing the roles of multiplication and addition in the rule can cause calculation mistakes.Final Answer:The series follows a(n+1) = a(n) * n + n, so the missing term is 27.

Question 2

A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 72, 56, 42, 30, 20, ?

Accepted Answer

Introduction / Context:This series decreases in steps that themselves follow a simple pattern of even numbers. Many exam questions use decreasing sequences where the subtracted values form an arithmetic progression. The given series is 72, 56, 42, 30, 20, ?, and we must find the missing final term.Given Data / Assumptions:- Terms: 72, 56, 42, 30, 20, ?- Only the last term is missing.- The sequence is strictly decreasing.- The subtracted values appear to be consecutive even numbers.Concept / Approach:The first step is to compute the differences between consecutive terms. If these differences follow a simple pattern, such as -16, -14, -12, -10, -8, we can use that pattern to determine the missing number. This is a classic use of first differences in arithmetic series problems.Step-by-Step Solution:- From 72 to 56: 56 - 72 = -16.- From 56 to 42: 42 - 56 = -14.- From 42 to 30: 30 - 42 = -12.- From 30 to 20: 20 - 30 = -10.- The absolute values of the differences are 16, 14, 12, 10, which decrease by 2 each time.- Therefore, the next difference should be -8.- So the missing term is 20 - 8 = 12.Verification / Alternative check:- With 12 as the last term, the full sequence of differences is -16, -14, -12, -10, -8.- These differences form a clear arithmetic progression of even numbers decreasing by 2 each time.- No alternative value maintains this neat progression of step sizes.Why Other Options Are Wrong:- 22 and 20 would actually increase or keep the value constant relative to 20, which contradicts the decreasing trend.- 62 does not fit anywhere nearby and would produce a difference inconsistent with the pattern of even decrements.- Only 12 preserves both the direction and the structure of the decreasing differences.Common Pitfalls:- Forgetting to consider the sign of the differences and focusing only on magnitudes may cause confusion.- Some candidates attempt to find a multiplicative pattern where a simple subtraction pattern is sufficient.- Miscomputing one difference, such as reading -14 as -15, can hide the clear even number sequence.Final Answer:The differences decrease as -16, -14, -12, -10, -8, so the missing term is 12.

Question 3

A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 144, 256, 400, ?

Accepted Answer

Introduction / Context:This question is built around perfect squares of specific integers. The series 144, 256, 400, ? consists of well known square numbers and tests whether candidates can recognise the pattern of squaring consecutive multiples of a fixed integer. We must determine the correct next square in this pattern.Given Data / Assumptions:- Known terms: 144, 256, 400.- One term is missing after 400.- All numbers are perfect squares.- The bases of these squares are likely to follow a simple pattern, such as equally spaced multiples.Concept / Approach:We rewrite each term as a square: n^2. By determining the sequence of n values, we can identify the next n and square it to get the missing term. Recognising common square values like 12^2, 16^2 and 20^2 is the key step here.Step-by-Step Solution:- 144 = 12^2.- 256 = 16^2.- 400 = 20^2.- The bases are 12, 16 and 20, which are multiples of 4: 4 * 3, 4 * 4 and 4 * 5.- These bases increase by 4 each time: 12, 16, 20, so the next base should be 24.- Compute 24^2: 24 * 24 = 576.- Therefore the missing term in the series is 576.Verification / Alternative check:- Sequence of square bases: 12, 16, 20, 24 are consecutive multiples of 4.- Their squares are 144, 256, 400, 576.- Thus the complete series of terms is 144, 256, 400, 576, which fits a clear and simple pattern.Why Other Options Are Wrong:- 441 = 21^2 and 289 = 17^2, which are not based on the multiples of 4 that we observe.- 625 = 25^2 and 512 is not a perfect square at all; both disrupt the neat sequence of square numbers of 12, 16, 20, 24.- None of these alternatives preserves the logic of using consecutive multiples of 4 as bases.Common Pitfalls:- Some candidates may focus only on differences between terms, which are 112 and 144, and fail to see the square pattern.- Mistaking 512 for a square number can lead to incorrect choices.- Forgetting standard square values such as 24^2 can result in unnecessary calculations or guesswork.Final Answer:The terms are squares of consecutive multiples of 4 (12, 16, 20, 24), so the missing number is 576.

Question 4

A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 5, 7.5, 12.5, 22.5, ?

Accepted Answer

Introduction / Context:This series uses decimal numbers and shows increasing differences between terms. The pattern is that the increment doubles at each step. Such problems test attention to decimal arithmetic and recognition of a simple relationship in the sequence of differences. The series is 5, 7.5, 12.5, 22.5, ?, and we must find the next term.Given Data / Assumptions:- Series: 5, 7.5, 12.5, 22.5, ?- The final term is missing.- All numbers are positive decimals.- Differences appear to grow rapidly, hinting at a doubling pattern.Concept / Approach:We compute consecutive differences between terms and examine how they change. If each difference is twice the previous one, then the next difference can be obtained by another doubling. This difference is then added to the last known term to obtain the missing number.Step-by-Step Solution:- Difference from 5 to 7.5: 7.5 - 5 = 2.5.- Difference from 7.5 to 12.5: 12.5 - 7.5 = 5.0.- Difference from 12.5 to 22.5: 22.5 - 12.5 = 10.0.- The differences are 2.5, 5, 10, which clearly double each time: 2.5 * 2 = 5, 5 * 2 = 10.- Therefore, the next difference should be 10 * 2 = 20.- Add this to the last known term: 22.5 + 20 = 42.5.- So the missing term is 42.5.Verification / Alternative check:- The full difference sequence becomes 2.5, 5, 10, 20, which is a geometric progression with ratio 2.- The reconstructed series 5, 7.5, 12.5, 22.5, 42.5 respects this doubling pattern exactly.- No alternative candidate preserves such a clean and simple progression of differences.Why Other Options Are Wrong:- 42, 44, 43.5 and 40.5 yield differences of 19.5, 21.5, 21 and 18 from 22.5, none of which equals 20, the expected next difference.- These values break the doubling rule for the increments and do not fit the geometric pattern in the differences.Common Pitfalls:- Rounding errors or misreading decimal points can cause miscalculation of differences like 2.5 or 10.- Some candidates look for a multiplicative rule for the main terms instead of examining differences, which is less natural in this particular series.- Ignoring the clear doubling pattern among differences may lead to random choice among the options.Final Answer:The differences double at each step (2.5, 5, 10, 20), so the missing term is 42.5.

Question 5

In the following question, select the missing number from the given series: 192, 186, 180, 174, ?, 162

Accepted Answer

Introduction / Context:This problem presents a simple decreasing arithmetic series. Each term is obtained by subtracting the same number from the previous term. Quick recognition of this constant difference is important in many competitive exams. The series given is 192, 186, 180, 174, ?, 162.Given Data / Assumptions:- Terms: 192, 186, 180, 174, ?, 162.- One term between 174 and 162 is missing.- The values decrease steadily with no abrupt changes.- A constant negative difference is the most likely pattern.Concept / Approach:We compute differences between consecutive known terms. If the same difference appears repeatedly, we can apply it to find the missing term. This is the standard approach for arithmetic sequences, which are among the simplest types of number series.Step-by-Step Solution:- From 192 to 186: 186 - 192 = -6.- From 186 to 180: 180 - 186 = -6.- From 180 to 174: 174 - 180 = -6.- Thus the series decreases by 6 at each step.- To find the next term after 174, subtract 6: 174 - 6 = 168.- Check the last term: 168 - 6 = 162, which matches the series.Verification / Alternative check:- With 168 inserted, the full sequence is 192, 186, 180, 174, 168, 162.- Every transition subtracts exactly 6, confirming an arithmetic series with common difference -6.- No other candidate preserves this constant step throughout the series.Why Other Options Are Wrong:- 166 and 170 would result in differences that are not equal to -6 at every step.- 164 and 172 either produce too large or too small a gap to lead on to 162 with the same difference.- Only 168 fits smoothly into the pattern of subtracting 6 each time.Common Pitfalls:- Miscalculations in subtraction can cause the common difference to be misread.- Some candidates might guess based purely on approximate closeness to 174 or 162 without checking all steps.- Overcomplicating the sequence with imagined higher order rules is unnecessary for such a simple arithmetic series.Final Answer:The series subtracts 6 at each step, so the missing term is 168.

Question 6

A series is given with one term missing. Choose the meaningful number from the given responses that will complete the series: 206, 221, 251, 296, ?, 431

Accepted Answer

Introduction / Context:This problem shows a series in which the differences between consecutive terms are multiples of a fixed number. Here the increments appear to grow in a regular way, suggesting that each step adds 15 times a simple sequence of integers. The series is 206, 221, 251, 296, ?, 431, and we must find the missing term that keeps this structure intact.Given Data / Assumptions:- Given series: 206, 221, 251, 296, ?, 431.- Only the fifth term is missing.- The values are increasing.- Differences are likely to be multiples of 15 following a simple pattern.Concept / Approach:We compute successive differences and then see whether those differences form a simple pattern, such as 15, 30, 45, 60, 75. Once we recognise that pattern, we can add the appropriate difference to find the missing term and confirm that the last step also fits the rule.Step-by-Step Solution:- From 206 to 221: 221 - 206 = 15.- From 221 to 251: 251 - 221 = 30.- From 251 to 296: 296 - 251 = 45.- The differences are 15, 30, 45, which are 15 * 1, 15 * 2, 15 * 3.- The next two differences should be 15 * 4 = 60 and 15 * 5 = 75.- Therefore, the missing term after 296 is 296 + 60 = 356.- Check the last term: 356 + 75 = 431, which matches the final value in the series.Verification / Alternative check:- With 356 inserted, the full difference sequence becomes 15, 30, 45, 60, 75.- This is an arithmetic progression in the differences with common difference 15.- No other candidate produces such a neat multiple of 15 structure extending to 431.Why Other Options Are Wrong:- 326, 311 and 341 lead to differences that are not 60 and 75 at the fourth and fifth steps.- 371 would give a last difference of 60 to reach 431, which does not continue the intended sequence 15, 30, 45, 60, 75.- Only 356 maintains the consistent growth of differences by 15 each time.Common Pitfalls:- Focusing only on the main numbers without analysing differences can hide the multiple of 15 pattern.- Miscalculating a single difference, such as confusing 296 - 251, can disturb recognition of the sequence.- Guessing based solely on approximate size, rather than verifying the full pattern, can lead to incorrect options.Final Answer:The differences are 15, 30, 45, 60, 75, so the missing term between 296 and 431 is 356.

Question 7

A series is given with one number missing. Choose the correct alternative from the given options that will complete the series: 2, 5, 10, 17, ?, 37

Accepted Answer

Introduction / Context:This series grows by adding consecutive odd numbers. Number series of this form are very common in aptitude tests because they are simple yet require close attention to small differences. The given series is 2, 5, 10, 17, ?, 37 and we must find the missing term that fits the pattern of odd increments.Given Data / Assumptions:- Series: 2, 5, 10, 17, ?, 37.- The second last term is missing.- All terms are positive integers.- Differences appear to increase slowly, hinting at consecutive odd numbers such as 3, 5, 7, 9, 11.Concept / Approach:The method is to calculate consecutive differences between terms. If those differences are odd and increase by 2 each time, then we can extend this sequence of differences and use it to fill the missing value. This is a standard pattern of additive growth using odd numbers.Step-by-Step Solution:- From 2 to 5: 5 - 2 = 3.- From 5 to 10: 10 - 5 = 5.- From 10 to 17: 17 - 10 = 7.- The differences so far are 3, 5, 7, which are consecutive odd numbers increasing by 2.- The next differences in this sequence should be 9 and then 11.- Therefore, the next term after 17 is 17 + 9 = 26.- The final term should then be 26 + 11 = 37, which matches the given last term.Verification / Alternative check:- With 26 inserted, the full sequence is 2, 5, 10, 17, 26, 37.- The complete list of differences is 3, 5, 7, 9, 11, confirming the consecutive odd number pattern.- No other candidate produces this smooth progression of differences.Why Other Options Are Wrong:- 24, 30, 32 and 28 yield differences that do not match the required series 3, 5, 7, 9, 11.- For instance, 24 would give a difference of 7 from 17 and 13 from 24 to 37, breaking the consecutive odd step of 9 and 11.Common Pitfalls:- Some candidates may miscalculate one of the differences, making the pattern appear irregular.- Failing to recognise the standard sequence of odd numbers can lead to overcomplicated attempts using squares or cubes.- Guessing based on proximity to 37 without checking the full pattern can result in wrong choices like 30 or 32.Final Answer:The differences form the odd number sequence 3, 5, 7, 9, 11, so the missing term is 26.

Question 8

In the following question, select the missing number from the given series: 11, 13, 16, 18, 21, ?

Accepted Answer

Introduction / Context:This series repeats the same pattern of alternating increments as a previous example. The numbers 11, 13, 16, 18, 21, ? increase in small steps that follow a cycle of adding 2 and then adding 3. The task is to identify the correct continuation of this simple alternation.Given Data / Assumptions:- Series: 11, 13, 16, 18, 21, ?- The sixth term is missing.- All terms are positive integers.- Increments appear to switch between two small values.Concept / Approach:We compute differences between consecutive terms and look for a repeating cycle. If the pattern is +2, +3, +2, +3 and so on, then we continue that cycle to obtain the missing number. This is a classic example of an alternating difference sequence.Step-by-Step Solution:- From 11 to 13: 13 - 11 = 2.- From 13 to 16: 16 - 13 = 3.- From 16 to 18: 18 - 16 = 2.- From 18 to 21: 21 - 18 = 3.- The differences follow the repeating pattern +2, +3, +2, +3.- The next step should again be +2.- Therefore, the missing term is 21 + 2 = 23.Verification / Alternative check:- With 23 as the last term, the full list of differences becomes 2, 3, 2, 3, 2.- This matches the established cycle and confirms the consistency of the pattern across the series.- No other option continues the alternating increments correctly.Why Other Options Are Wrong:- 25, 27, 29 and 31 correspond to differences of 4, 6, 8 and 10 from 21, which do not match the expected increment of 2.- Using any of these alternatives would break the neat alternating pattern +2, +3.Common Pitfalls:- Careless subtraction can cause the pattern to be misread as something more complicated.- Some candidates may truncate the series and look only at a part of it, missing the full cycle of changes.- Overthinking a simple alternation can lead to unnecessary trial and error with the options.Final Answer:The series keeps adding 2 and then 3 alternately, so the missing term is 23.

Question 9

In the following question, select the missing number from the given series: 57, 69, 81, 93, ?, 117

Accepted Answer

Introduction / Context:This problem is based on a simple arithmetic series with a constant positive difference. Each term increases by the same amount. The series is 57, 69, 81, 93, ?, 117, and we are required to identify the missing number that keeps the increments uniform.Given Data / Assumptions:- Series: 57, 69, 81, 93, ?, 117.- The fifth term is missing.- The sequence increases steadily.- The simplest and most likely pattern is addition of a fixed number at each step.Concept / Approach:We calculate the differences between consecutive known terms. If the difference is the same between several pairs, we can assume an arithmetic progression and apply that difference to find the missing term. This is among the most basic types of series used in reasoning tests.Step-by-Step Solution:- From 57 to 69: 69 - 57 = 12.- From 69 to 81: 81 - 69 = 12.- From 81 to 93: 93 - 81 = 12.- Thus, the common difference is +12.- To find the next term after 93, add 12: 93 + 12 = 105.- Check the final term: 105 + 12 = 117, which matches the series.Verification / Alternative check:- With 105 added, the complete sequence is 57, 69, 81, 93, 105, 117.- Each transition adds exactly 12, confirming an arithmetic progression.- No alternative value maintains this constant difference throughout.Why Other Options Are Wrong:- 104, 111, 108 and 99 lead to differences that are not all equal to 12.- For example, if 108 were chosen, then 108 - 93 = 15 and 117 - 108 = 9, breaking the constant step pattern.Common Pitfalls:- Some candidates fail to check all steps and may select a value that fits one gap but not the entire series.- Miscalculations in adding 12 can lead to incorrect answers such as 104 or 108.- Overcomplicating an obviously linear series with higher order reasoning is unnecessary and time consuming.Final Answer:The series is an arithmetic progression with common difference 12, so the missing term is 105.

Question 10

A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 8, 24, 12, ?, 18, 54

Accepted Answer

Introduction / Context:This series alternates between multiplication and division by fixed numbers. Recognising such alternating operation patterns is important in number series questions. The sequence is 8, 24, 12, ?, 18, 54, and we must determine the missing fourth term so that the alternating pattern remains consistent.Given Data / Assumptions:- Series: 8, 24, 12, ?, 18, 54.- Exactly one intermediate term is missing.- Values rise, then fall, then rise again, suggesting alternating multiplication and division.- The operations likely use simple integers such as 3 and 2.Concept / Approach:We analyse how each term is derived from the previous one. Many exam series use a repeating two-step pattern like multiply by 3, then divide by 2, and so on. If that fits the known terms, we can apply the same rule to identify the missing value.Step-by-Step Solution:- From 8 to 24: 24 = 8 * 3 (multiplied by 3).- From 24 to 12: 12 = 24 / 2 (divided by 2).- This suggests a two step cycle: multiply by 3, then divide by 2.- Apply this rule to find the missing term after 12.- From 12 to the next term: 12 * 3 = 36.- From this term to 18: 18 = 36 / 2, which perfectly fits the divide by 2 step.- Finally, 18 to 54 also follows multiply by 3: 18 * 3 = 54.- Therefore, the missing number must be 36.Verification / Alternative check:- Reconstruct the series with the pattern: • 8 * 3 = 24. • 24 / 2 = 12. • 12 * 3 = 36. • 36 / 2 = 18. • 18 * 3 = 54.- The operations times 3, divide by 2 repeat throughout, confirming that 36 is correct.Why Other Options Are Wrong:- 48, 29, 21 and 24 do not support the consistent multiply by 3 then divide by 2 cycle when inserted between 12 and 18.- For example, if 24 were chosen, the step 24 to 18 would not be a division by 2, and 18 to 54 would not continue the established pattern correctly.Common Pitfalls:- Focusing only on the main numbers without listing operations can hide the alternating pattern.- Assuming a single operation such as a fixed difference or ratio does not work here and can mislead candidates.- Miscomputing a division or multiplication step, especially in the middle of the sequence, can obscure the regularity of the pattern.Final Answer:The series alternates between multiplying by 3 and dividing by 2, so the missing term is 36.

Question 11

Which number will complete the series? 11, 13, 17, 19, 23, 25, _____

Accepted Answer

Introduction / Context:This series question relies on a simple pattern of alternating increments. The numbers 11, 13, 17, 19, 23, 25, _____ increase by 2 and 4 in turn. Candidates must detect this pattern and extend it by one more step to find the missing term.Given Data / Assumptions:- Terms: 11, 13, 17, 19, 23, 25, ?- One final term is missing.- All values are positive integers.- The increments between terms appear to alternate between two fixed small numbers.Concept / Approach:The standard technique is to compute consecutive differences and observe any repeating cycle. If we see a pattern like +2, +4, +2, +4, then we know the next difference must continue this cycle. That difference is then added to the last known term to obtain the missing number.Step-by-Step Solution:- Difference from 11 to 13: 13 - 11 = 2.- Difference from 13 to 17: 17 - 13 = 4.- Difference from 17 to 19: 19 - 17 = 2.- Difference from 19 to 23: 23 - 19 = 4.- Difference from 23 to 25: 25 - 23 = 2.- The pattern is a repeating cycle of +2, +4, +2, +4, +2.- Therefore, the next difference should be +4.- Add this to the last term: 25 + 4 = 29.- Thus, the missing term is 29.Verification / Alternative check:- With 29 included, the complete difference list is 2, 4, 2, 4, 2, 4.- This perfectly preserves the alternating increment pattern throughout the series.- No other candidate value allows this clean repetition.Why Other Options Are Wrong:- 25 is already present and would not be a new term in the series.- 27 and 31 correspond to differences of 2 and 6 from 25, breaking the established cycle of +4 after +2.- 33 would lead to an increment of 8, which also does not fit the pattern.Common Pitfalls:- Some candidates may notice that many of the numbers are prime and assume a prime pattern, but 25 is not prime, so this is not the correct basis.- Failing to compute all differences accurately may hide the alternating nature of the increments.- Guessing based on the idea of the next prime number, for example 29 or 31, without verifying the difference pattern can lead to partial reasoning instead of complete justification.Final Answer:The series alternates between adding 2 and adding 4, so the missing term is 29.

Question 12

Find the missing number in the series: 75, 96, 116, 135, 153, ?

Accepted Answer

Introduction / Context:This series uses decreasing differences between consecutive terms. The pattern is that the increment reduces by 1 at each step. Reasoning questions often employ such smoothly changing differences because they are easy to see once carefully computed. The series is 75, 96, 116, 135, 153, ?, and we must identify the next number.Given Data / Assumptions:- Series: 75, 96, 116, 135, 153, ?- One final term is missing.- All terms are positive integers and increase steadily.- Differences appear to form a simple pattern, probably decreasing by 1 each time.Concept / Approach:We calculate the differences between successive terms and then study how those differences change. If they follow an arithmetic progression, such as 21, 20, 19, 18, 17, we can use this to compute the next increment and hence the missing term.Step-by-Step Solution:- From 75 to 96: 96 - 75 = 21.- From 96 to 116: 116 - 96 = 20.- From 116 to 135: 135 - 116 = 19.- From 135 to 153: 153 - 135 = 18.- The differences are 21, 20, 19, 18, decreasing by 1 each time.- The next difference should therefore be 17.- Add this to the last term: 153 + 17 = 170.- So the missing term is 170.Verification / Alternative check:- With 170 added, the complete difference sequence is 21, 20, 19, 18, 17.- These differences form a neat arithmetic progression with common difference -1.- No other candidate among the options preserves this exact decreasing pattern.Why Other Options Are Wrong:- 173, 178 and 175 correspond to differences of 20, 25 and 22 from 153, which do not continue the -1 step in the increments.- 168 would produce a difference of 15, also breaking the regular sequence of 21, 20, 19, 18, 17.Common Pitfalls:- Candidates sometimes assume a constant difference without checking all gaps and get confused when they see variation.- Miscomputing any single difference, such as 135 to 153, can obscure the linear decrease by 1.- Guessing based purely on approximate size of the final term without checking the full pattern may lead to incorrect answers.Final Answer:The increments decrease by 1 each time (21, 20, 19, 18, 17), so the missing term is 170.

Question 13

A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 6, 10, 18, 34, ?, 130

Accepted Answer

Introduction / Context:This series uses differences that double at each step. The numbers 6, 10, 18, 34, ?, 130 grow increasingly quickly, and the pattern lies not in the terms themselves but in the differences between them. Recognising this structure is important for handling more advanced number series questions.Given Data / Assumptions:- Series: 6, 10, 18, 34, ?, 130.- One term between 34 and 130 is missing.- All terms are positive integers and increase rapidly.- Differences appear to double each time.Concept / Approach:The approach is to compute first differences and then examine whether these differences form a geometric sequence. If each difference is twice the previous one, we can generate the next difference by doubling again and use that to find the missing term. This is similar to working with exponential growth in the step sizes.Step-by-Step Solution:- From 6 to 10: 10 - 6 = 4.- From 10 to 18: 18 - 10 = 8.- From 18 to 34: 34 - 18 = 16.- The differences are 4, 8, 16, which double each time.- The next difference should be 16 * 2 = 32.- Therefore, the missing term after 34 is 34 + 32 = 66.- To reach 130, the next difference should double again: 32 * 2 = 64.- Check: 66 + 64 = 130, which matches the given final term.Verification / Alternative check:- With 66 inserted, the complete difference sequence is 4, 8, 16, 32, 64.- Each difference is exactly twice the previous one, confirming a geometric pattern in the increments.- No other candidate produces this clean doubling sequence.Why Other Options Are Wrong:- 52, 78, 94 and 82 lead to final differences that do not follow the doubling pattern from 4 to 64.- For example, if 78 were used, then 78 - 34 = 44 and 130 - 78 = 52, and the differences 4, 8, 16, 44, 52 do not maintain a consistent rule.Common Pitfalls:- Failing to compute all differences can cause candidates to miss the clear doubling trend.- Some might search for a complex formula for the main terms instead of noticing the simpler structure in the differences.- Quick guessing based on approximate position between 34 and 130, rather than pattern verification, often leads to wrong answers.Final Answer:The differences double at each step (4, 8, 16, 32, 64), so the missing term is 66.

Question 14

A series is given with one number missing. Choose the correct alternative from the given options that will complete the series: 1/4, 0.65, ?, 29/20, 1.85

Accepted Answer

Introduction / Context:This series mixes fractions and decimals but follows a very simple additive pattern. The idea is that each term is obtained by adding a fixed decimal value to the previous term. The sequence is 1/4, 0.65, ?, 29/20, 1.85, and we must express the missing term in a form consistent with the others.Given Data / Assumptions:- Terms: 1/4, 0.65, ?, 29/20, 1.85.- Fractions and decimals represent the same kinds of real numbers.- One middle term is missing.- The pattern appears to involve addition of a constant decimal amount.Concept / Approach:To analyse the pattern, it is convenient to convert all fractions to decimal form. Then we inspect the differences between consecutive terms. If we find a constant difference, we can use it to compute the missing value and then convert that value back to a simple fraction if needed.Step-by-Step Solution:- Convert 1/4 to decimal: 1/4 = 0.25.- The second term is 0.65.- Difference between first and second terms: 0.65 - 0.25 = 0.40.- Express 29/20 as a decimal: 29/20 = 1.45.- The fifth term is 1.85.- Difference between fourth and fifth terms: 1.85 - 1.45 = 0.40.- This shows that consecutive terms differ by 0.40.- Apply this rule to find the missing third term: 0.65 + 0.40 = 1.05.- Convert 1.05 back into a simple fraction: 1.05 = 105/100 = 21/20.- Thus, the missing term is 21/20.Verification / Alternative check:- Write the series entirely in decimals using the discovered pattern: 0.25, 0.65, 1.05, 1.45, 1.85.- Each step adds exactly 0.40.- Converting back to mixed fraction and decimal notations: 1/4, 0.65, 21/20, 29/20, 1.85.- The pattern holds consistently across the series.Why Other Options Are Wrong:- 1.1, 19/20, 1.2 and 23/20 correspond to decimal values 1.10, 0.95, 1.20 and 1.15, respectively.- None of these values are exactly 0.40 greater than 0.65 and 0.40 less than 1.45 at the same time.- Hence they do not preserve the constant difference of 0.40 between consecutive terms.Common Pitfalls:- Mixing up fractions and decimals without converting them can make the pattern hard to see.- Rounding errors when working with decimals may lead to an incorrect difference value.- Some candidates may try to impose a multiplicative pattern, which does not fit the consistent additive increase observed here.Final Answer:The series adds 0.40 at each step, so the missing term is 21/20.

Question 15

A number series is given below with one missing term. Choose the correct alternative from the given options that will complete the series. -0.5, -0.35, -0.2, -0.05, ?, 0.25

Accepted Answer

Introduction / Context: This question tests understanding of simple arithmetic progressions in decimal form within a number series. The learner has to observe how each term changes and then use that pattern to find the missing value in a sequence that moves from negative decimals toward a positive value. Such items are very common in reasoning examinations because they check pattern recognition and accuracy with decimal calculations. Given Data / Assumptions: - The given series is: -0.5, -0.35, -0.2, -0.05, ?, 0.25. - There is one missing term in the fifth position. - The pattern is expected to be consistent across consecutive terms. Concept / Approach: The idea is to compute the difference between each pair of consecutive terms and see whether these differences follow a simple arithmetic pattern. If the same constant value is added each time, then the series is an arithmetic progression, only written with decimal numbers. Once the constant difference is identified, the missing term can be found by adding this difference to the previous term, or by working backward from later terms. Step-by-Step Solution: Step 1: Find the difference between the first and second term: -0.35 - (-0.5) = -0.35 + 0.5 = 0.15. Step 2: Find the difference between the second and third term: -0.2 - (-0.35) = -0.2 + 0.35 = 0.15. Step 3: Find the difference between the third and fourth term: -0.05 - (-0.2) = -0.05 + 0.2 = 0.15. Step 4: The series therefore increases by 0.15 at every step. Step 5: The missing fifth term equals the fourth term plus 0.15: -0.05 + 0.15 = 0.10. Step 6: The sixth term also fits this rule: 0.10 + 0.15 = 0.25. Verification / Alternative check: To verify, start from the first term and repeatedly add 0.15. You obtain -0.5, -0.35, -0.2, -0.05, 0.10, 0.25. This exactly matches the given series when the missing term is taken as 0.1. The uniform increase of 0.15 confirms that the pattern is a simple arithmetic progression in decimal form with constant difference 0.15. Why Other Options Are Wrong: - Option -0.1 would create a difference of 0.1 from -0.05, which breaks the constant step of 0.15. - Option 0.15 would create a difference of 0.2 from -0.05, again not equal to 0.15. - Option -0.15 moves the series backward and would not move the sequence toward the given positive value 0.25. Common Pitfalls: Many learners focus only on the signs and may confuse negative values, leading them to subtract instead of adding the common difference. Another frequent mistake is to approximate or round differences too early instead of computing them exactly. Always compute the exact decimal difference between consecutive terms before deciding on the pattern. Final Answer: The missing term in the series is 0.1, so the correct option is 0.1.

Question 16

A number series is given below with one missing term. Choose the correct alternative from the given options that will complete the series. 100, -20, 4, ?, 0.16, -0.032

Accepted Answer

Introduction / Context: This item checks understanding of geometric type number series where each term is obtained by multiplying the previous term by a constant factor. In this case the factor is a negative fraction, which changes both the sign and magnitude of each term. Such questions train the learner to recognise multiplication patterns beyond simple integers. Given Data / Assumptions: - The series provided is: 100, -20, 4, ?, 0.16, -0.032. - The fourth term is missing and needs to be determined. - The pattern is expected to be consistent across all consecutive terms. Concept / Approach: Number series that alternate in sign and decrease in magnitude often follow a multiplication rule with a negative fraction. To solve, compute the ratio of consecutive terms. If this ratio is constant, the series is geometric. The same ratio is then applied to move forward or backward in the sequence to find the missing term. Step-by-Step Solution: Step 1: Compute the ratio from the first term to the second term: -20 / 100 = -0.2. Step 2: Compute the ratio from the second term to the third term: 4 / (-20) = -0.2. Step 3: Since the ratio is constant and equal to -0.2, the series is geometric with common ratio -0.2. Step 4: To get the missing fourth term, multiply the third term by the common ratio: 4 * (-0.2) = -0.8. Step 5: Verify using the remaining terms. Multiply -0.8 by -0.2 to get 0.16, then multiply 0.16 by -0.2 to get -0.032. This matches the given fifth and sixth terms. Verification / Alternative check: An alternative check is to start from the known later term and work backward. For example, -0.032 divided by -0.2 gives 0.16, and 0.16 divided by -0.2 gives -0.8, which confirms the missing value and validates the common ratio -0.2 in both directions. Why Other Options Are Wrong: - Option 0.8 has the wrong sign, and 0.8 * (-0.2) would not give 0.16, so it breaks the pattern. - Option 1 cannot be obtained by multiplying 4 by -0.2 and does not lead correctly to 0.16. - Option -1 does not produce 0.16 when multiplied by -0.2 and therefore does not maintain the constant ratio. Common Pitfalls: Learners sometimes ignore the sign of the ratio and treat the pattern as if it had a positive common ratio. Others may compute the ratio with rounding or inexact division, which can hide a clear fractional value such as -0.2. It is important to handle negative signs carefully and to test the pattern across more than one pair of terms. Final Answer: The missing term that completes the geometric pattern is -0.8, so the correct option is -0.8.

Question 17

In the following question, a number series is given with one missing term. Select the correct number from the given options that will complete the series. 9, 10, 13, 22, 49, ?

Accepted Answer

Introduction / Context: This question involves a number series where the gaps between successive terms increase according to a pattern. The learner must study the differences between consecutive terms and identify a rule that can be extended to compute the missing value. Recognising structured growth in the differences is a core skill in number series reasoning. Given Data / Assumptions: - Given series: 9, 10, 13, 22, 49, ? - The sixth term is missing. - The pattern is expected to depend on differences between terms. Concept / Approach: Many number series use a pattern in the first differences or even second differences. Here, we inspect the differences between consecutive terms. If the differences themselves form a recognisable pattern, such as powers of a number or multiples with a fixed ratio, that pattern can be extended to find the next term in the original series. Step-by-Step Solution: Step 1: Compute differences: 10 - 9 = 1, 13 - 10 = 3, 22 - 13 = 9, 49 - 22 = 27. Step 2: Observe that these differences are 1, 3, 9, and 27. Step 3: Notice that 1, 3, 9, 27 are consecutive powers of 3: 3^0 = 1, 3^1 = 3, 3^2 = 9, 3^3 = 27. Step 4: The next difference should naturally continue this pattern as 3^4 = 81. Step 5: Add 81 to the last known term to get the missing value: 49 + 81 = 130. Verification / Alternative check: Verify by reconstructing the series from the starting term. Begin with 9, then add 1, 3, 9, 27, and finally 81. This generates 9, 10, 13, 22, 49, 130, which matches the given sequence and confirms that 130 is the correct missing term. Why Other Options Are Wrong: - Option 117 implies a final difference of 68, which does not fit the powers of three pattern. - Option 126 gives a last difference of 77, which again does not match any power of three. - Option 115 gives a difference of 66 and breaks the systematic pattern in the consecutive differences. Common Pitfalls: Some learners look only for linear patterns, such as constant or steadily increasing differences, and may miss that the differences themselves follow an exponential rule. Others might try to fit an arbitrary formula directly to the terms instead of first analysing the simpler sequence of differences. A clear and methodical approach to differences greatly simplifies such questions. Final Answer: The missing term in the series is 130, so the correct option is 130.

Question 18

A number series is given below with one term missing. Choose the correct alternative from the given options that will complete the series. 72, 65.7, ?, 53.1, 46.8

Accepted Answer

Introduction / Context: This series question tests the understanding of a simple arithmetic progression with a constant negative difference that involves decimal values. The learner needs to identify how much each term decreases and then apply that decrease to determine the missing term. Such questions improve comfort with decimal subtraction and pattern recognition. Given Data / Assumptions: - Given series: 72, 65.7, ?, 53.1, 46.8. - The third term is missing. - The pattern is expected to be a constant step between terms. Concept / Approach: In an arithmetic progression, each term is obtained by adding or subtracting a fixed value called the common difference. By using the first and last terms and the number of steps between them, or by computing successive differences between adjacent known terms, this common difference can be discovered. Once the difference is known, every missing term can be filled in. Step-by-Step Solution: Step 1: Observe the first and last given terms: 72 and 46.8, with four steps between them. Step 2: Compute the total change: 46.8 - 72 = -25.2. Step 3: Divide this change by four steps to find the common difference: -25.2 / 4 = -6.3. Step 4: Check between the first two terms: 72 - 6.3 = 65.7, which matches the series. Step 5: Apply the same difference from the second term to find the missing value: 65.7 - 6.3 = 59.4. Step 6: Continue to verify: 59.4 - 6.3 = 53.1, and 53.1 - 6.3 = 46.8, which confirms the consistency. Verification / Alternative check: An alternative method is to compute the difference directly between known adjacent terms: 65.7 to 53.1 is a change of -12.6 over two steps, so the step per term is -12.6 / 2 = -6.3. The same difference connects 53.1 to 46.8. This again confirms that each step is a reduction of 6.3 and confirms 59.4 as the missing value. Why Other Options Are Wrong: - Option 60.4 does not maintain a constant difference of -6.3 and would break the smooth progression. - Option 59.3 introduces a small discrepancy and would not give exact equal steps across the series. - Option 60.3 also fails to match a consistent difference when checked against the neighbouring terms. Common Pitfalls: Learners may approximate differences mentally and accept near values instead of exact ones, which leads to minor errors that completely break the arithmetic pattern. It is important to carry out calculations accurately, especially with decimal values, and confirm that the same difference works between every pair of adjacent terms. Final Answer: The missing term in the series is 59.4, so the correct option is 59.4.

Question 19

A number series is given with one term missing. Choose the correct alternative from the given options that will complete the series. 7, 49, 343, ?

Accepted Answer

Introduction / Context: This question involves a geometric style series where each term is obtained by multiplying the previous term by the same integer. In this example, the base number is seven, so the series progresses through powers of seven. Identifying such power patterns is a useful skill in many competitive examinations. Given Data / Assumptions: - Series: 7, 49, 343, ? - One term is missing in the fourth position. - Terms appear to grow rapidly, suggesting multiplication by a fixed number. Concept / Approach: When each term is obtained by multiplying the previous term by a constant factor, the series is geometric. Here, the factor appears to be 7. Recognising that 7, 49, and 343 are 7^1, 7^2, and 7^3 helps to project the next term as 7^4. This power based understanding gives a fast and reliable method for finding the missing value. Step-by-Step Solution: Step 1: Express each term as a power of seven: 7 = 7^1, 49 = 7^2, 343 = 7^3. Step 2: Observe that exponents increase by one at each step: 1, 2, 3. Step 3: The next exponent should be 4, so the next term is 7^4. Step 4: Compute 7^4 as 7 * 7 * 7 * 7 = 49 * 49 = 2401. Step 5: Therefore, the missing term equals 2401. Verification / Alternative check: Another way is to check the ratio between consecutive terms. 49 / 7 = 7 and 343 / 49 = 7. Thus, the common ratio is 7. Multiplying the third term by this ratio gives 343 * 7 = 2401, which confirms the result and the geometric nature of the series. Why Other Options Are Wrong: - Option 3087 is not a power of seven and does not follow the repeated multiplication rule with factor 7. - Option 1029 is 343 * 3, so it uses the wrong multiplier and breaks the geometric pattern. - Option 1091 has no simple relation to the previous term under the constant ratio rule. Common Pitfalls: Some learners may attempt to apply addition or subtraction instead of multiplicative reasoning, which will not work for rapidly growing series like this. Others may miscalculate powers of seven, especially 7^4. It helps to remember key powers for small primes, such as 2, 3, 5, and 7, for quick recognition in exams. Final Answer: The missing term is 2401, so the correct option is 2401.

Question 20

In the following question, a number series is given with one missing term. Select the correct alternative from the options that will complete the series. 43, 44, 46, 47, 49, 49, 50, ?

Accepted Answer

Introduction / Context: This number series question requires the learner to recognise an alternating pattern in the differences between consecutive terms. Instead of a single constant difference, the series uses a repeating sequence of differences. Identifying this repeating pattern makes it possible to determine the missing term. Given Data / Assumptions: - Series: 43, 44, 46, 47, 49, 49, 50, ? - The eighth term is missing. - Differences between terms are not constant but appear to cycle. Concept / Approach: When the gap between successive terms is not constant, it can still follow a repeating or structured sequence. The method is to compute each difference and then look for repetition, for example a pattern like 1, 2, 1, 2, 0, and so on. After establishing this sequence, it can be extended to find the next difference and therefore the next term in the original series. Step-by-Step Solution: Step 1: Compute consecutive differences. 43 to 44: difference = 1. 44 to 46: difference = 2. 46 to 47: difference = 1. 47 to 49: difference = 2. 49 to 49: difference = 0. 49 to 50: difference = 1. Step 2: The differences form the pattern 1, 2, 1, 2, 0, 1. Step 3: It is natural to continue this pattern with the next difference equal to 2. Step 4: Add this difference to the last known term: 50 + 2 = 52. Verification / Alternative check: We can confirm the pattern by grouping the differences into a cycle: (1, 2), (1, 2), (0, 1, 2). The appearance of 0 and then 1 suggests the sequence 1, 2 repeats with a slight delay. Extending the pattern gives the final required difference 2, which leads consistently to 52 as the next term without any contradiction in the series. Why Other Options Are Wrong: - Option 54 would require a difference of 4 from 50, which does not align with the existing difference cycle. - Option 53 would need a difference of 3, again not present in the pattern. - Option 51 would use a difference of 1, but the established pattern after 1 is 2, not another 1. Common Pitfalls: Learners sometimes assume a fixed difference without actually calculating all gaps, causing them to miss subtle alternating structures. Another common error is to stop after inspecting only two or three differences. In many reasoning questions, the full pattern becomes clear only after examining all given terms carefully. Final Answer: The missing term in the series is 52, so the correct option is 52.

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