Question 1

A number series is given with one term missing. Identify the correct number that continues the pattern: 5, 8, 12, 17, 23, ?

Accepted Answer

Introduction / Context:This question is an example of a number series where the pattern is hidden in the differences between terms. Detecting such difference based patterns is a core skill in many reasoning and aptitude tests. Here, the numbers are increasing at a gradually changing rate, which signals that the differences themselves follow a simple rule.Given Data / Assumptions:We are given the series:5, 8, 12, 17, 23, ?We assume that consecutive terms are related by a regular increase that can be identified by examining the gaps between numbers.Concept / Approach:The standard approach is to compute the difference between each pair of consecutive terms and see if these differences form an arithmetic sequence or some other simple pattern. Often, for moderately increasing series, the differences themselves increase by 1 or by a fixed amount.Step-by-Step Solution:Step 1: Compute the differences.8 - 5 = 312 - 8 = 417 - 12 = 523 - 17 = 6Step 2: Observe the pattern in the differences: 3, 4, 5, 6. These are consecutive integers.Step 3: The next difference should logically be 7 if the pattern continues.Step 4: Add this next difference to the last known term.23 + 7 = 30.Verification / Alternative check:We can verify by reconstructing the series using the rule that each new difference is one more than the previous difference. Starting from 5, we add 3 to get 8, add 4 to get 12, add 5 to get 17, add 6 to get 23, and add 7 to reach 30. Everything is consistent and no contradictions occur, so the pattern is reliable.Why Other Options Are Wrong:Values like 72, 65, 48, or 27 break the clean difference pattern of 3, 4, 5, 6, 7. For example, if we choose 27, the last difference becomes 4, which repeats a previous gap and destroys the increasing sequence of differences. The other choices distort the series even more severely and therefore cannot be correct.Common Pitfalls:A common mistake is to assume a multiplicative pattern when numbers are only growing modestly. Another error is to miscalculate one of the differences, for instance computing 23 - 17 as 5 instead of 6, which leads to an incorrect continuation. Careful subtraction and systematic checking of the difference pattern avoid these issues.Final Answer:The correct number that completes the series is 30.

Question 2

A mixed number series is given with one missing term. Using the observed pattern, select the correct number to complete the sequence: 3, 9, 4, 16, 5, ?

Accepted Answer

Introduction / Context:This question presents a series that alternates between two related types of terms. Detecting alternating patterns is critical because many reasoning sequences are constructed by interleaving two simple series. Once you separate and analyze each subsequence, the overall pattern becomes clear.Given Data / Assumptions:The given series is:3, 9, 4, 16, 5, ?We assume that the first, third, and fifth terms form one pattern, while the second, fourth, and sixth terms form a related pattern. Our goal is to identify these patterns and then compute the missing value.Concept / Approach:Looking at the sequence, it suggests a relationship between each number and its square. For example, 3 and 9 are consecutive terms, and 9 is 3^2. Similarly, 4 and 16 follow, and 16 is 4^2. This strongly indicates that the series alternates between a base integer and its square. The same logic should then apply to the next base integer, which is 5.Step-by-Step Solution:Step 1: Group the terms in pairs: (3, 9), (4, 16), (5, ?).Step 2: Identify the pattern within each pair.For the first pair: 3 and 9, where 9 = 3^2.For the second pair: 4 and 16, where 16 = 4^2.Step 3: Apply the same logic to the third pair. If the first element is 5, the second should be 5^2.5^2 = 25.Step 4: Therefore, the missing term in the series is 25.Verification / Alternative check:Check the positions: the first, third, and fifth terms are 3, 4, and 5, which are consecutive integers. The second and fourth terms are 9 and 16, equal to 3^2 and 4^2. To maintain the integrity of the pattern, the sixth term must be 5^2. Any other value would break both the integer progression and the square relationship.Why Other Options Are Wrong:The options 6, 20, 18, and 30 do not equal 5^2 and do not create a perfect square when paired with 5. They also do not fit any consistent alternative pattern that respects the observed structure of the earlier terms. Therefore, they cannot be accepted as correct completions of the series.Common Pitfalls:Learners sometimes focus only on differences between consecutive terms and miss the alternating structure. Another mistake is to think the series is arbitrary and choose a number that is near 16 or 20 without any mathematical justification. Always look for relationships such as squares or cubes when numbers like 9 and 16 appear together in a series.Final Answer:The missing term that completes the alternating number and square pattern is 25.

Question 3

Consider the following number series with alternating operations: 100, 50, 52, 26, 28, ?, 16, 8. Choose the option that correctly replaces the missing term.

Accepted Answer

Introduction / Context:This series combines two different operations that alternate as we move from one term to the next. Questions of this type test whether you can detect a repeated cycle of operations, such as halving followed by adding a constant. They are common in reasoning sections of competitive examinations.Given Data / Assumptions:The series is:100, 50, 52, 26, 28, ?, 16, 8We assume that a consistent two step process is being repeated across the entire series and that we need to identify and apply this cycle to find the missing term in the sixth position.Concept / Approach:A quick way to approach such questions is to compare every alternate term. Observe whether there is a pattern of dividing by a fixed number and then adding a constant. Here, the numbers move up and down in a way that suggests halving and then adding a small quantity repeatedly.Step-by-Step Solution:Step 1: Compare the first and second terms.100 to 50 is exactly half, so we apply division by 2.Step 2: Compare the second and third terms.50 to 52 is an increase of 2, so we add 2.Step 3: Apply the same pattern again.52 to 26 is a division by 2.26 to 28 is again an increase of 2.Step 4: Continue the established cycle.From 28, the next step in the pattern is division by 2, which gives 28 / 2 = 14.Step 5: Check with the next known term.From 14, we should add 2 to follow the cycle, giving 16, which matches the given term, and from 16, dividing by 2 gives 8, also matching the series.Verification / Alternative check:Write the operations explicitly: divide by 2, add 2, divide by 2, add 2, and so on. Applying this cycle from 100 gives 100, 50, 52, 26, 28, 14, 16, 8. Every step respects the same pair of alternating operations, and no inconsistencies appear, which strongly confirms the correctness of the missing term.Why Other Options Are Wrong:Values like 30, 32, 38, or 20 do not equal 28 divided by 2 and therefore break the halving step. For example, if we chose 30, then the move from 28 to 30 would be plus 2 rather than division by 2, which would disturb the alternating cycle and make it impossible to reach 16 and 8 correctly using the same pattern.Common Pitfalls:Some candidates try to force a single arithmetic progression or a constant difference when the series clearly alternates between two types of operations. Others may miscalculate half of 28 or forget to confirm that the next given term also fits the pattern. Always validate the pattern both forward and backward around the missing term.Final Answer:The correct number that should replace the missing term is 14.

Question 4

In the number series 256, ?, 190, 167, 148, 131, one term is missing. Using the underlying pattern, choose the correct value for the missing term.

Accepted Answer

Introduction / Context:This question involves a decreasing number series where the gaps between terms follow their own pattern. In many reasoning questions, the sequence is easier to understand when viewed either from left to right or right to left, especially when the differences themselves form a meaningful progression.Given Data / Assumptions:The given series is:256, ?, 190, 167, 148, 131We assume that there is a smooth mathematical pattern in the way numbers decrease and that the missing second term should maintain this pattern across the entire series.Concept / Approach:To solve this, we look at the differences between consecutive terms for the known portion of the series. Often the differences themselves form an increasing or decreasing sequence, and understanding that sequence allows us to work out missing numbers. Because the first gap is unknown, it is often helpful to examine the series starting from the rightmost terms where consecutive values are fully known.Step-by-Step Solution:Step 1: Compute the differences for the known rightmost segment.167 - 148 = 19190 - 167 = 23148 - 131 = 17Step 2: Reorder the series from right to left: 131, 148, 167, 190, ?, 256.Step 3: Compute the differences in this ascending order.148 - 131 = 17167 - 148 = 19190 - 167 = 23Step 4: Observe the pattern in the differences: 17, 19, 23. These are increasing by 2, then 4. The next increase can logically be 6, giving 23 + 6 = 29.Step 5: Add 29 to 190 to get the next term when moving upward.190 + 29 = 219.Step 6: The final gap from this new term to 256 should then be 256 - 219 = 37, which continues the increments of 2, 4, 6, 8 in the differences (17, 19, 23, 29, 37).Verification / Alternative check:Write the complete sequence in ascending order with the inferred term: 131, 148, 167, 190, 219, 256. The differences are 17, 19, 23, 29, and 37. The increments between these differences are 2, 4, 6, and 8, forming a clear and elegant pattern. This strongly supports that 219 is the correct missing value in the original decreasing series.Why Other Options Are Wrong:Values such as 165, 136, 216, or 200 do not generate a smooth pattern in the differences. For instance, if we used 216, the gap from 190 to 216 would be 26 and from 216 to 256 would be 40, which does not fit the controlled progression of difference increments. The same type of inconsistency occurs with the other options.Common Pitfalls:One frequent error is to search only for constant differences or to attempt direct ratios, which do not apply here. Another mistake is to work only from the left and ignore the useful structure visible on the right side of the series. Reversing the series and looking at differences can often reveal a hidden pattern more clearly.Final Answer:The missing term that maintains the structured pattern of differences is 219.

Question 5

In the following number sequence, one term is missing. Using the observed pattern, determine the number that should replace the question mark: 27, 29, 33, ?, 57.

Accepted Answer

Introduction / Context:This question tests understanding of number series where the differences between terms grow according to a simple rule. Rather than focusing directly on the terms, it is often easier to examine how much each term increases relative to the previous one. This is a common pattern in reasoning exams.Given Data / Assumptions:The sequence is:27, 29, 33, ?, 57We assume that the series obeys a consistent rule in the differences between terms, possibly involving doubling or another simple numeric relationship.Concept / Approach:The strategy is to compute the first differences between consecutive terms and see if these differences are themselves increasing according to a recognizable pattern. If the differences start small and then grow faster, doubling or a similar rule may be involved.Step-by-Step Solution:Step 1: Compute the known differences.29 - 27 = 233 - 29 = 4Step 2: Observe that the differences 2 and 4 appear to be doubling.Step 3: Continue this doubling pattern for the next two gaps.Next difference after 4 is 8.Next difference after 8 is 16.Step 4: Use these differences to find the missing term and confirm the last term.Unknown term = 33 + 8 = 41.Next term after that = 41 + 16 = 57, which matches the given final term.Verification / Alternative check:We can reconstruct the series using the rule that each difference doubles: starting from 27, we add 2 to get 29, add 4 to get 33, add 8 to get 41, and add 16 to reach 57. Since the resulting sequence matches all known terms and respects the doubling pattern at each step, the missing term must be 41. This confirms that there is no contradiction when 41 is chosen.Why Other Options Are Wrong:If we chose 30, 35, 39, or 40, the gap from 33 to the chosen number and then to 57 would not follow the exact pattern of doubling differences. For example, if we tried 39, the differences would become 2, 4, 6, and 18, which clearly breaks the neat doubling relationship and therefore cannot be correct.Common Pitfalls:Some candidates look for linear differences or average increments and fail to notice the doubling feature. Others may compute differences incorrectly or not check whether the final known term is still consistent with the assumed pattern. It is essential to verify both the missing and final terms once a pattern has been proposed.Final Answer:The number that correctly completes the series is 41.

Question 6

In the following number series, one term is incorrect. Identify the wrong term: 3, 10, 27, 4, 16, 64, 5, 25, 125.

Accepted Answer

Introduction / Context:This problem requires identifying the term that breaks an underlying pattern in a structured series. The series is clearly grouped in sets of three numbers, and within each group there is a strong hint of powers, particularly cubes. Recognizing the pattern within each group is the key to discovering the incorrect term.Given Data / Assumptions:The series is:3, 10, 27, 4, 16, 64, 5, 25, 125We can naturally divide these into groups: (3, 10, 27), (4, 16, 64), and (5, 25, 125). We assume that each group should follow the same rule relating the three numbers, and we look for any group that does not fit that rule.Concept / Approach:The pattern suggests that each group may be based on a number and its powers. For example, 3 and 27 relate as 3^1 and 3^3, while 4 and 64 relate as 4^2 and 4^3, and similarly 5 and 125 correspond to 5^2 and 5^3. The middle number in each triplet should therefore match the square of the first element in that group. We test this idea for all three groups.Step-by-Step Solution:Step 1: Examine the second group: (4, 16, 64).Here, 4 is the base, 16 is equal to 4^2, and 64 is equal to 4^3. This group is perfectly consistent.Step 2: Examine the third group: (5, 25, 125).Here, 5 is the base, 25 is 5^2, and 125 is 5^3. This group is also correct.Step 3: Examine the first group: (3, 10, 27).Here, 3 is the base and 27 is 3^3, but 10 is not equal to 3^2. The correct square would be 9, not 10.Step 4: Therefore, 10 is the only term that fails to match the consistent rule observed in the other groups.Verification / Alternative check:Rewriting the series with the intended pattern gives us (3, 9, 27), (4, 16, 64), and (5, 25, 125), which shows a very clean structure: n, n^2, n^3 for n equal to 3, 4, and 5. Because only the middle number of the first triplet is wrong, the term 10 must be the one that does not belong in the original series.Why Other Options Are Wrong:The numbers 3, 4, 16, 27, 25, 64, and 125 all fit correctly into the n, n^2, n^3 pattern for n equal to 3, 4, or 5. Removing any of these would destroy the otherwise perfect structure. Only 10 fails to correspond to the correct square of 3 and thus stands out as incorrect.Common Pitfalls:Some students may look at the series as a single linear progression rather than as triplets based on powers. They might then focus on differences instead of the much clearer power relationship and become confused. Always consider grouping terms when a pattern appears to repeat every few numbers.Final Answer:The wrong term in the given series is 10.

Question 7

In the following number series, one term is missing. Using the observed pattern of multiplication, find the missing number: 19, 38, ?, 228, 684, 1368.

Accepted Answer

Introduction / Context:This question features a number series where each term is generated by multiplying the preceding term by a changing factor. Such alternating multiplication patterns, especially involving factors like 2 and 3, are very common in reasoning tests and need to be recognized quickly.Given Data / Assumptions:The series provided is:19, 38, ?, 228, 684, 1368Our assumption is that a multiplicative rule, possibly alternating between two factors, governs the transitions between terms. We need to identify this rule and use it to compute the missing third term.Concept / Approach:A natural first step is to check for simple multipliers. From 19 to 38, we see the clear factor of 2. Next, from 228 to 684 and from 684 to 1368, we can check their ratios and see if there is a pattern like multiplying by 2, then by 3, and so on. Once the pattern is clear at multiple positions, we can safely apply it where a term is missing.Step-by-Step Solution:Step 1: Check the ratio between known consecutive terms at the end of the series.228 to 684: 684 / 228 = 3, so this step multiplies by 3.684 to 1368: 1368 / 684 = 2, so this step multiplies by 2.Step 2: Observe that the series might alternate between multiplying by 2 and multiplying by 3.Step 3: Check the beginning of the series with this hypothesis.19 to 38 is multiplication by 2.Therefore, from 38 to the missing term we should multiply by 3.Step 4: Multiply 38 by 3 to find the missing term.38 * 3 = 114.Step 5: Confirm by continuing the pattern.From 114 to 228, we should multiply by 2, and indeed 114 * 2 = 228, which matches the series.Verification / Alternative check:Write the full pattern explicitly: start with 19, then multiply by 2 to get 38, multiply by 3 to get 114, multiply by 2 to get 228, multiply by 3 to get 684, and finally multiply by 2 to get 1368. This alternating multiplication by 2 and 3 perfectly fits all known terms and explains the entire series smoothly, which confirms that 114 is the correct missing value.Why Other Options Are Wrong:Numbers like 108, 113, 138, or 120 do not maintain the strict pattern of alternating factors. For example, if we chose 108, the ratio from 38 to 108 would not be 3, and the ratio from 108 to 228 would not be 2. Thus, the regular structure of the series would be broken, making these options invalid.Common Pitfalls:Students sometimes try to force an arithmetic pattern on such series or miscalculate one of the ratios, which sends them in the wrong direction. It is critical to compute ratios carefully and to check consistency across multiple segments of the series before confirming a rule.Final Answer:The missing term that preserves the alternating multiplication pattern is 114.

Question 8

In the mixed number pattern 3, 4, 5, 4, 9, 10, 6, 16, 15, 9, 25, 20, 13, 36, ?, identify the missing number that completes the series.

Accepted Answer

Introduction / Context:This series is a more complex pattern in which the numbers are grouped in triplets, and different rules may apply to each position within the triplet. Recognizing such structured repetition is a key skill for solving higher level number series problems in reasoning tests.Given Data / Assumptions:The series is:3, 4, 5, 4, 9, 10, 6, 16, 15, 9, 25, 20, 13, 36, ?We can group the numbers into sets of three:(3, 4, 5), (4, 9, 10), (6, 16, 15), (9, 25, 20), (13, 36, ?).We assume that each position within a triplet follows its own consistent pattern across the sequence.Concept / Approach:First, examine the second term in each triplet: 4, 9, 16, 25, 36. These are clearly perfect squares of consecutive integers 2, 3, 4, 5, and 6. Next, examine the first terms and the third terms to see whether they follow simpler numeric progressions. Typically, in such questions, one subsequence may be based on squares, another on simple addition, and another on multiples of a constant like 5.Step-by-Step Solution:Step 1: Analyze the second terms of each triplet.They are 4, 9, 16, 25, 36 which equal 2^2, 3^2, 4^2, 5^2, 6^2. So second terms are consecutive squares.Step 2: Analyze the first terms of each triplet.They are 3, 4, 6, 9, 13. The differences are 1, 2, 3, and 4. Thus the increments themselves increase by 1.Step 3: Analyze the third terms of each triplet.They are 5, 10, 15, 20, ?. Each is a multiple of 5: 1*5, 2*5, 3*5, 4*5.Step 4: The next term in this subsequence should therefore be 5*5 = 25.Step 5: Hence, the missing term in the full series is 25.Verification / Alternative check:Rewriting the series with the observed patterns: the first terms increase with differences 1, 2, 3, and 4 (3, 4, 6, 9, 13), the second terms are squares 2^2 through 6^2, and the third terms are multiples of 5 from 5 to 25. The last triplet is then (13, 36, 25), which fits neatly into the established structure. No contradictions arise, confirming the solution.Why Other Options Are Wrong:Values like 17, 28, 31, or 22 are not multiples of 5 and therefore fail to continue the third term subsequence 5, 10, 15, 20. They do not fit the clean pattern where each third term is 5 times a consecutive integer. Only 25 satisfies this requirement.Common Pitfalls:Many learners try to treat the entire string of numbers as a single simple series and overlook the grouped structure. This leads to confusion because no straightforward pattern is visible when all numbers are considered together. Always look for repeating blocks or triplets in longer, more complex number sequences.Final Answer:The missing number that completes the given series is 25.

Question 9

Select the missing numbers from the given alternatives 8 21 4 27 ? 53

Accepted Answer

40

Question 10

In the following series, one term is missing. Using the observed pattern of sums, find the number that should replace the question mark: 19, 26, 45, 71, 116, ?

Accepted Answer

Introduction / Context:This series problem involves a pattern where each term after the first two appears to be related to the sum of earlier terms. Such Fibonacci style or additive sequences are frequently used in reasoning exams and require you to look beyond simple differences or ratios.Given Data / Assumptions:The series is:19, 26, 45, 71, 116, ?We assume that after the first two terms, each new term may be generated using a rule involving the previous terms, typically the sum of the last two numbers.Concept / Approach:A natural approach is to check whether each term from the third onward is equal to the sum of the two immediately preceding terms. If this holds for multiple consecutive terms, it is very likely that the pattern is additive. This idea is similar to the famous Fibonacci sequence, although here the starting values are different.Step-by-Step Solution:Step 1: Check the third term.19 + 26 = 45, which matches the third term.Step 2: Check the fourth term.26 + 45 = 71, which matches the fourth term.Step 3: Check the fifth term.45 + 71 = 116, which matches the fifth term.Step 4: Since the pattern holds consistently, we now compute the next term as the sum of the last two known terms.71 + 116 = 187.Thus, the missing term is 187.Verification / Alternative check:We can reconstruct the entire series from the first two terms under the assumption that each next term equals the sum of its predecessors. Starting from 19 and 26, we generate 45, 71, 116, and then 187. This perfectly matches the given terms and extends the pattern without any contradictions, so the rule is fully consistent across the series.Why Other Options Are Wrong:Numbers such as 166, 172, 184, or 160 do not equal 71 + 116. Using any of them would remove the clear additive relationship that exists between consecutive terms. For example, if we tried 184, the sum of 71 and 116 would no longer give the next term, which breaks the underlying structure of the sequence.Common Pitfalls:Some students focus on differences between consecutive terms, which vary and do not show a simple pattern here. Others may suspect multiplication or division where an additive rule is more appropriate. When differences do not produce a regular progression, always consider whether each term could be the sum of the previous two terms.Final Answer:The number that correctly completes the series is 187.

Question 11

In the number series 9, 11, 14, 18, 23, ?, one term is missing. Based on the pattern in the differences, choose the correct number to complete the series.

Accepted Answer

Introduction / Context:This problem features a straightforward number series where the increments between consecutive terms themselves follow a simple increasing pattern. Identifying and continuing this pattern of differences is a fundamental skill in solving many reasoning questions.Given Data / Assumptions:The series is:9, 11, 14, 18, 23, ?We assume that the differences between consecutive terms are not constant but increase in a predictable way from one step to the next.Concept / Approach:The main approach is to compute the difference between each pair of neighboring terms and then see whether these differences form an arithmetic pattern or some other simple progression. When numbers increase but not at a fixed rate, the differences often increase by 1 each time.Step-by-Step Solution:Step 1: Compute the differences.11 - 9 = 214 - 11 = 318 - 14 = 423 - 18 = 5Step 2: Observe that the differences are consecutive integers: 2, 3, 4, 5.Step 3: Following the pattern, the next difference should be 6.Step 4: Add this difference to the last known term.23 + 6 = 29.Verification / Alternative check:Rebuild the series using the rule that each difference is one more than the previous difference. Start at 9, add 2 to get 11, add 3 to get 14, add 4 to get 18, add 5 to reach 23, and finally add 6 to arrive at 29. The sequence now appears smooth and consistent, confirming that 29 is the correct missing term.Why Other Options Are Wrong:Values such as 27, 31, 33, or 26 would break this simple pattern of differences. For example, if we chose 27, the last difference would be 4, not 6, and the progression 2, 3, 4, 5, 4 would no longer be strictly increasing. Only 29 maintains the clean sequence of consecutive differences from 2 to 6.Common Pitfalls:A frequent mistake is to look for multiplicative relationships where none exist, or to miscalculate one of the differences, such as computing 23 - 18 incorrectly. This can mislead you into thinking the series is irregular. Accurate subtraction and a careful look at the difference pattern are essential for success on such problems.Final Answer:The missing term that continues the pattern is 29.

Question 12

In the number series 11, 19, 40, 87, 173, ?, one term is missing. By analyzing the pattern in the differences, determine the correct value for the missing term.

Accepted Answer

Introduction / Context:This question involves a number series with differences that grow according to a secondary pattern. Instead of the terms themselves following a simple rule, the increments between them increase in a structured way. Recognizing patterns in differences and even differences of differences is an important reasoning skill.Given Data / Assumptions:The series given is:11, 19, 40, 87, 173, ?We assume that the differences between consecutive terms follow a progression that can be identified and used to compute the next term.Concept / Approach:First, we calculate the differences between consecutive terms. Then we inspect how these differences themselves change. If these second level changes follow a simple pattern, such as increasing by a constant amount, we can use that to extend the series consistently.Step-by-Step Solution:Step 1: Compute first differences between consecutive terms.19 - 11 = 840 - 19 = 2187 - 40 = 47173 - 87 = 86Step 2: List these first differences: 8, 21, 47, 86.Step 3: Compute second differences between these first differences.21 - 8 = 1347 - 21 = 2686 - 47 = 39Step 4: Notice that these second differences are multiples of 13 and increase by 13 each time: 13, 26, 39. The next second difference should therefore be 39 + 13 = 52.Step 5: The next first difference will be the last existing first difference plus this new second difference: 86 + 52 = 138.Step 6: Add this next first difference to the last term of the original series.173 + 138 = 311.Verification / Alternative check:We can check the extended difference pattern: starting with first differences 8, 21, 47, 86, and the new one 138. The second differences are 13, 26, 39, and 52, which are 13 multiplied by 1, 2, 3, and 4. This is a smooth and logical progression. Adding 138 to 173 to get 311 preserves this structure, confirming that 311 is the correct next term.Why Other Options Are Wrong:Values such as 301, 304, 294, or 320 would imply different first differences that do not create the clean series of second differences in steps of 13. For example, if the next term were 301, the last first difference would be 301 - 173 = 128, which does not extend the existing pattern of 8, 21, 47, and 86 in a way that fits the 13 based progression.Common Pitfalls:Some test takers focus only on the first differences and fail to see a pattern because those values themselves look irregular. Others may attempt to apply a linear or multiplicative rule on the main series, which does not work here. When first differences appear uneven but structured, always check second differences for a simple progression.Final Answer:The correct value that completes the number series is 311.

Question 13

In the number series 54, 51, 48, 45, 42, ?, one term is missing. Choose the correct number that should come next in the sequence.

Accepted Answer

Introduction / Context:This problem presents a simple decreasing number series where the terms appear to fall at a steady pace. Many exam questions use such sequences to quickly test whether a candidate can recognize a constant difference between consecutive numbers and extend the pattern accordingly.Given Data / Assumptions:The series is:54, 51, 48, 45, 42, ?We assume that the pattern is governed by a constant subtraction at each step, and our task is to identify that constant and apply it to find the next term.Concept / Approach:The key idea is to calculate the difference between each pair of consecutive terms and check whether this difference stays the same throughout the series. When all differences are identical, the series is a simple arithmetic progression, and extending it becomes straightforward.Step-by-Step Solution:Step 1: Compute the consecutive differences.51 - 54 = -348 - 51 = -345 - 48 = -342 - 45 = -3Step 2: Observe that each term is 3 less than the previous term, so the constant difference is -3.Step 3: Apply this difference to the last known term.42 - 3 = 39.Verification / Alternative check:We can reconstruct the series from the first term using the rule that each next term equals the previous term minus 3. Starting from 54, we get 51, 48, 45, 42, and then 39. The pattern remains perfectly consistent, confirming that subtraction of 3 at each step is indeed the governing rule of the sequence.Why Other Options Are Wrong:Values such as 38, 36, 40, or 41 do not fit the rule of subtracting 3 each time. For example, 38 would represent a difference of -4 from 42, while 40 would represent a difference of -2, both of which break the uniform step size. Only 39 maintains the constant decrease of 3 that characterizes the entire series.Common Pitfalls:Sometimes test takers miscalculate one of the differences, especially when working quickly, and then infer a wrong rule. Another mistake is to overcomplicate a clearly simple pattern by looking for multiplicative or alternating operations when none are needed. Always check for a constant difference first in regularly spaced sequences.Final Answer:The next number in the series that maintains the pattern is 39.

Question 14

In the number series 9, 18, 72, 576, ?, the terms grow rapidly. By identifying the pattern in the multipliers, choose the correct number to complete the series.

Accepted Answer

Introduction / Context:This question presents a rapidly increasing number series, which typically indicates a multiplicative pattern rather than one based on small differences. Your task is to recognize the pattern in the multipliers applied at each step and then extend that pattern to determine the next term in the sequence.Given Data / Assumptions:The series is:9, 18, 72, 576, ?We assume that each term is generated by multiplying the previous term by a certain factor, and that these factors themselves follow a simple progression, often involving powers of 2 or another small integer.Concept / Approach:We start by examining the ratio between consecutive terms in the series. When those ratios show a clear and predictable pattern, such as doubling, tripling, or following powers of a particular number, we can use that pattern to find the missing term. The presence of values like 72 and 576 suggests strong multiplicative behavior.Step-by-Step Solution:Step 1: Compute the ratios between consecutive terms.18 / 9 = 272 / 18 = 4576 / 72 = 8Step 2: Observe that the multipliers are 2, 4, and 8, which are powers of 2: 2^1, 2^2, and 2^3.Step 3: The pattern suggests that the next multiplier should be the next power of 2 in this sequence, namely 2^4 = 16.Step 4: Multiply the last known term by 16.576 * 16 = 9216.Verification / Alternative check:We can describe the series generation rule as follows: start with 9, then multiply by 2 to get 18, multiply by 4 to get 72, multiply by 8 to get 576, and finally multiply by 16 to obtain the missing term. This yields 9, 18, 72, 576, 9216. The sequence of multipliers is 2, 4, 8, 16, clearly following powers of 2, which confirms that the pattern is correct and the computed term is consistent.Why Other Options Are Wrong:The alternative values 8116, 8216, 9016, or 9600 do not equal 576 multiplied by 16 and do not fit any simple extension of the powers of 2 pattern. For instance, if we attempted to use 9016, the ratio 9016 / 576 would not be a power of 2 and would break the elegant structure of the multipliers that define the series.Common Pitfalls:Some candidates may mistakenly look at differences between terms, which become very large and irregular in multiplicative series, making that approach ineffective. Others might miscalculate one of the products, especially 576 times 16, which requires careful multiplication. Always confirm the multipliers carefully and verify that they form a simple and consistent progression.Final Answer:The next term in the series, obtained by multiplying 576 by 16, is 9216.

Question 15

A series is given with one number missing. Choose the correct alternative from the given options that will complete the series: 49, 64, ?, 100, 121

Accepted Answer

Introduction / Context:This problem tests recognition of perfect squares in a simple number series. Many verbal reasoning questions use well known patterns such as square numbers of consecutive integers. The series is 49, 64, ?, 100, 121, and we must identify the missing term that preserves this structure.Given Data / Assumptions:- Series terms: 49, 64, ?, 100, 121.- Exactly one number is missing in the central position.- The other four terms are assumed to be correct and to follow a common pattern.- All values are positive integers and reasonably small, which is typical for square or cube patterns.Concept / Approach:The key observation is that 49, 64, 100 and 121 are familiar square numbers. If we express each term as n^2, we can see whether they correspond to consecutive values of n. Once we detect that, the missing number should simply be the square that belongs between the known consecutive squares.Step-by-Step Solution:- 49 = 7^2.- 64 = 8^2.- 100 = 10^2.- 121 = 11^2.- The sequence of bases is 7, 8, ?, 10, 11, which clearly should be consecutive integers 7, 8, 9, 10, 11.- Therefore, the missing base is 9, and the missing term is 9^2.- Compute 9^2 = 81.- So the completed series is 49, 64, 81, 100, 121.Verification / Alternative check:- Consecutive squares from 7 to 11 are: 7^2 = 49, 8^2 = 64, 9^2 = 81, 10^2 = 100, 11^2 = 121.- This matches the given pattern exactly once 81 is inserted in the missing position.- No other integer placed in the middle would preserve the idea of consecutive square numbers.Why Other Options Are Wrong:- 74, 75, 80 and 96 are not perfect squares, so they break the consecutive square structure.- In particular, none of these values can be written as n^2 with n an integer between 7 and 11.Common Pitfalls:- Some candidates focus on the differences (15, ?, 19, 21) and try to find a pattern in them, which is less natural here.- Forgetting standard square values, especially 9^2 = 81, can cause confusion.- Overcomplicating the series with advanced formulas is unnecessary for this straightforward square pattern.Final Answer:The series lists consecutive perfect squares from 7^2 to 11^2, so the missing term is 81.

Question 16

A series is given with one number missing. Choose the correct alternative from the given options that will complete the series: 400, -200, 100, ?, 25, -12.5

Accepted Answer

Introduction / Context:This question involves a geometric type number series in which each term is obtained from the previous one by multiplying by a constant factor. The presence of alternating positive and negative values, together with decreasing magnitudes, strongly suggests multiplication by a negative fraction. Our task is to find the missing term in the sequence 400, -200, 100, ?, 25, -12.5.Given Data / Assumptions:- Series terms: 400, -200, 100, ?, 25, -12.5.- Exactly one central term is missing.- Signs alternate positive and negative as we move along the series.- Magnitudes appear to be halving with each step.Concept / Approach:For geometric series, we examine the ratio of each term to the previous one. If the ratio remains constant, we can use it to generate missing terms. The alternating signs indicate that the common ratio is negative. The consistent halving of magnitudes suggests that the numerical value of the ratio is 1/2.Step-by-Step Solution:- From 400 to -200: ratio = -200 / 400 = -1/2.- From -200 to 100: ratio = 100 / (-200) = -1/2.- Thus the common ratio for the series is -1/2.- To find the missing term after 100, multiply 100 by -1/2.- 100 * (-1/2) = -50.- Check the remaining terms: -50 * (-1/2) = 25 and 25 * (-1/2) = -12.5, which matches the given series.Verification / Alternative check:- Rewriting the complete series using the ratio -1/2: 400, -200, 100, -50, 25, -12.5.- Each step multiplies the previous term by -1/2, so the pattern holds throughout.- There is no inconsistency once -50 is inserted, confirming it as the correct term.Why Other Options Are Wrong:- 50, 75, -75 and 25 do not satisfy the constant ratio -1/2 when placed between 100 and 25.- For example, if the missing term were 50, then 50 / 100 = 1/2 (not -1/2), and 25 / 50 = 1/2, breaking both the sign alternation and the geometric pattern.Common Pitfalls:- Some candidates check only differences instead of ratios, which is misleading in geometric series.- Ignoring the alternating signs can lead to a mistaken ratio of 1/2 instead of -1/2.- Confusion between division and multiplication by a fraction may cause computational errors.Final Answer:Each term is obtained by multiplying the previous one by -1/2, so the missing term is -50.

Question 17

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

Accepted Answer

Introduction / Context:This number series tests the ability to spot a simple alternating pattern in the differences between terms. The sequence 11, 13, 16, 18, 21, ? appears to grow in small steps, suggesting that fixed increments are being added in a repeating cycle. Recognising this cycle quickly is a key skill in reasoning exams.Given Data / Assumptions:- Series: 11, 13, 16, 18, 21, ?- Exactly one term, the sixth term, is missing.- All existing terms are positive integers.- The pattern is expected to involve simple additions of small whole numbers.Concept / Approach:The standard method is to compute consecutive differences and check whether they repeat. If there is a clear short cycle, such as +2, +3, +2, +3, then we can extend the cycle to find the missing term. We do not need any complex formula; only careful observation of increments is required.Step-by-Step Solution:- From 11 to 13: difference = 13 - 11 = 2.- From 13 to 16: difference = 16 - 13 = 3.- From 16 to 18: difference = 18 - 16 = 2.- From 18 to 21: difference = 21 - 18 = 3.- The differences clearly alternate: +2, +3, +2, +3.- The next step should continue this pattern with a difference of +2.- Therefore, the missing term is 21 + 2 = 23.Verification / Alternative check:- With the missing term as 23, the full difference sequence becomes 2, 3, 2, 3, 2.- The alternating pattern +2, +3 repeats perfectly throughout the series.- No other candidate produces such a clean and consistent alternation of differences.Why Other Options Are Wrong:- 25, 27, 29 and 31 lead to differences that disrupt the neat repeating cycle of +2 and +3.- For example, choosing 25 would add a difference of +4 at the end, which does not match the established pattern.Common Pitfalls:- Candidates sometimes miscalculate small differences, especially when working quickly under exam pressure.- It is easy to overthink and search for complex rules when a simple alternating pattern is sufficient.- Ignoring the idea of repetition and treating each difference as unrelated can make the sequence look irregular when it is not.Final Answer:The series alternates between adding 2 and adding 3, so the missing term is 23.

Question 18

In the following question, select the missing number from the given series: 59, 68, 78, 89, 101, ?

Accepted Answer

Introduction / Context:This question checks recognition of a series where the differences between consecutive terms increase in a simple arithmetic fashion. The series 59, 68, 78, 89, 101, ? grows steadily, but not by a fixed amount. Instead, the increment itself increases by 1 each time, which is a common pattern in number series questions.Given Data / Assumptions:- Terms: 59, 68, 78, 89, 101, ?- One final term is missing.- The sequence is strictly increasing.- We expect a regular pattern in the step sizes between terms.Concept / Approach:The natural method is to compute consecutive differences, then examine how those differences themselves change. If the differences form an arithmetic progression, we can extend that smaller progression to get the next difference and thus the next term in the main series.Step-by-Step Solution:- Difference from 59 to 68: 68 - 59 = 9.- Difference from 68 to 78: 78 - 68 = 10.- Difference from 78 to 89: 89 - 78 = 11.- Difference from 89 to 101: 101 - 89 = 12.- The differences 9, 10, 11, 12 form an arithmetic progression with common difference 1.- The next difference should therefore be 13.- Add this to the last known term: 101 + 13 = 114.- So the missing term is 114.Verification / Alternative check:- Reconstructing with the identified pattern: 59 (+9) = 68, (+10) = 78, (+11) = 89, (+12) = 101, (+13) = 114.- The full sequence of differences 9, 10, 11, 12, 13 is perfectly regular.- No other candidate value gives this clean progression.Why Other Options Are Wrong:- 116, 118, 120 and 112 correspond to differences of 15, 17, 19 and 11 from 101, which do not continue the pattern of increasing by 1 at each step.- In particular, 112 repeats a difference of 11, while the pattern clearly demands 13 after 12.Common Pitfalls:- Some candidates mistakenly assume a constant difference and, when they see this is not true, abandon the difference method altogether.- Miscalculating one difference can hide the underlying arithmetic progression in the step sizes.- Jumping directly to options without checking the full pattern of differences often leads to incorrect guesses.Final Answer:The differences increase by 1 each time (9, 10, 11, 12, 13), so the missing term is 114.

Question 19

In the following question, select the missing number from the given series: 470, 465, 460, 455, ?, 445

Accepted Answer

Introduction / Context:This is a straightforward arithmetic series where each term decreases by a fixed amount. Such questions test quick recognition of constant differences between consecutive terms. The given sequence is 470, 465, 460, 455, ?, 445, and we are asked to supply the missing number.Given Data / Assumptions:- Terms: 470, 465, 460, 455, ?, 445.- Only the fifth term is missing.- The numbers are close together and appear to follow a simple linear pattern.- The most likely rule is subtraction of the same value at each step.Concept / Approach:To identify an arithmetic series, we compute successive differences and see if they are constant. If the pattern holds across several steps, we then apply the same difference to find any missing term. Here the series appears to decrease smoothly, so we expect a constant negative difference.Step-by-Step Solution:- Difference from 470 to 465: 465 - 470 = -5.- Difference from 465 to 460: 460 - 465 = -5.- Difference from 460 to 455: 455 - 460 = -5.- The pattern is a constant decrease of 5.- Therefore, the next term after 455 is 455 - 5 = 450.- Check the final term: 450 - 5 = 445, which matches the series.Verification / Alternative check:- With the missing term as 450, the series becomes 470, 465, 460, 455, 450, 445.- Every step from left to right subtracts exactly 5.- No other candidate preserves this perfectly constant difference.Why Other Options Are Wrong:- 448, 440 and 452 would give differences that are not equal to -5 and would disrupt the regular pattern.- 460 is already present in the series as the third term and does not fit between 455 and 445 when we enforce a constant step of -5.Common Pitfalls:- Failing to compute differences carefully and misreading the steps as -4 or -10 can lead to incorrect answers.- Overthinking a very simple linear pattern sometimes causes candidates to search for needless complexity.- Ignoring the consistency of differences from multiple positions can result in choosing a value that fits locally but not globally.Final Answer:The series decreases by 5 at each step, so the missing term is 450.

Question 20

A series is given with one term missing. Choose the correct alternative from the given options that will complete the series: 2, 10, 30, 68, ?

Accepted Answer

Introduction / Context:This number series grows quickly, and the jumps between terms themselves change in a regular way. Such questions typically involve second differences that form an arithmetic progression. The series is 2, 10, 30, 68, ?, and we must deduce the next term from the pattern hidden in the differences.Given Data / Assumptions:- Series terms: 2, 10, 30, 68, ?- One term, the fifth, is missing.- The series is strictly increasing and accelerates as it grows.- The pattern is likely based on changing differences rather than a single multiplication factor.Concept / Approach:When the growth between terms increases, it is helpful to compute first differences and then second differences. If second differences follow a simple arithmetic rule (for example, increasing by a fixed amount), we can extend that rule forward. This method is similar to working with quadratic sequences in algebra.Step-by-Step Solution:- Compute first differences: • From 2 to 10: 10 - 2 = 8. • From 10 to 30: 30 - 10 = 20. • From 30 to 68: 68 - 30 = 38.- First differences are 8, 20, 38.- Compute second differences: • 20 - 8 = 12. • 38 - 20 = 18.- Second differences are 12 and 18, which increase by 6.- Continue this pattern: next second difference = 18 + 6 = 24.- Therefore the next first difference = 38 + 24 = 62.- Add this to the last known term: 68 + 62 = 130.- So the missing term is 130.Verification / Alternative check:- With the missing term as 130, the first differences become 8, 20, 38, 62.- The second differences are then 12, 18, 24, which clearly form an arithmetic progression with common difference 6.- This confirms that 130 is consistent with the underlying rule.Why Other Options Are Wrong:- 135, 140, 120 and 150 do not produce first and second differences that continue the sequence 12, 18, 24 in the second differences.- For example, using 135 would give the last first difference as 67, leading to a second difference of 29, which breaks the pattern.Common Pitfalls:- Some candidates try to fit a single multiplication factor like times 3 or times 2 plus a constant, which does not work cleanly here.- Failing to compute second differences causes the regularity in the pattern to be missed.- Random guessing based only on approximate growth often leads to values that do not preserve the structured second differences.Final Answer:The second differences form an arithmetic progression 12, 18, 24, so the next term in the series is 130.

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