Question 1

Find the next number in the series: 404, 415, 402, 413, 400, ?

Accepted Answer

Introduction / Context:This problem checks understanding of alternating operations in a number series. Instead of using a single subtraction or addition step throughout, many reasoning questions use a repeated pattern such as adding a number, then subtracting a different number, and so on. Here we must find the missing term that continues the alternating pattern in the given sequence of numbers starting from 404.Given Data / Assumptions:- Given series: 404, 415, 402, 413, 400, ?- Exactly one term is missing at the end of the series.- The pattern is expected to be consistent between consecutive terms, possibly involving alternation of two fixed operations.Concept / Approach:When a series moves up, then down, then up again, a very natural idea is that the operations alternate between addition and subtraction. To reveal the pattern, we compute the differences between consecutive terms and see if they repeat in a regular fashion. Once we identify the two-step cycle, we can apply it to the last known term to get the missing number.Step-by-Step Solution:- Difference from 404 to 415: 415 - 404 = 11 (an increase of 11).- Difference from 415 to 402: 415 - 402 = 13 (a decrease of 13).- Difference from 402 to 413: 413 - 402 = 11 (again an increase of 11).- Difference from 413 to 400: 413 - 400 = 13 (a decrease of 13).- We clearly see an alternating pattern: +11, -13, +11, -13, and so on.- To find the next term after 400, we continue the cycle. After a -13 step, the next step is +11.- Therefore, the missing term is 400 + 11 = 411.Verification / Alternative check:- Rewriting the complete series with the discovered pattern: 404 (+11) = 415, 415 (-13) = 402, 402 (+11) = 413, 413 (-13) = 400, 400 (+11) = 411.- The pattern of alternating increases and decreases is perfectly preserved when 411 is placed as the sixth term.- No other option allows such a neat and consistent alternation.Why Other Options Are Wrong:- 421, 417, 414 and 409 do not give a constant repeating pair of differences of +11 and -13 when substituted at the missing position.- For example, using 409 would give a difference of only +9 from 400, breaking the established pattern.Common Pitfalls:- Some test takers look only at approximate differences without checking the exact values and may misread 11 and 13 as the same or similar.- Another pitfall is to try fitting a single constant difference, which does not work because the series clearly moves both upward and downward.- Ignoring the alternation and focusing on more complicated formulas is unnecessary and wastes time in the exam.Final Answer:The series alternates between adding 11 and subtracting 13, so the missing number after 400 must be 400 + 11 = 411.

Question 2

Find the next number in the given number sequence: 4, 15, 37, 81, ?

Accepted Answer

Introduction / Context:This question tests recognition of a pattern where each term is obtained from the previous one by doubling and then adding a changing value. Many exam number series rely on such multiply and add structures where the additive part itself follows a simple pattern. Here, we must extend the sequence 4, 15, 37, 81 by one more term and identify it from the options.Given Data / Assumptions:- Given sequence: 4, 15, 37, 81, ?- Only the last term is missing.- The series is strictly increasing.- The pattern is likely to involve multiplication and addition rather than constant differences, because the gaps between numbers grow quickly.Concept / Approach:When the gaps between terms increase rapidly, it is natural to look for a rule of the form: next term = previous term * k + c, where k and c vary in a simple pattern. Checking the relationship between consecutive terms by reversing this operation often reveals a clear sequence of additive constants that helps to generalise the rule for the next step.Step-by-Step Solution:- From 4 to 15: 4 * 2 + 7 = 8 + 7 = 15.- From 15 to 37: 15 * 2 + 7 = 30 + 7 = 37.- From 37 to 81: 37 * 2 + 7 = 74 + 7 = 81.- We see a stable pattern: each term is twice the previous term plus 7.- To find the next term, apply the same rule to 81.- Calculation: 81 * 2 + 7 = 162 + 7 = 169.- So, the missing number in the series is 169.Verification / Alternative check:- We can confirm by recalculating each step: 4 → 15, 15 → 37, 37 → 81, and 81 → 169 all follow the rule previous term * 2 + 7.- The sequence of differences (11, 22, 44, 88) also shows a doubling pattern, which is consistent with the multiply by two structure.- No inconsistency appears when 169 is added, showing that the rule holds throughout.Why Other Options Are Wrong:- 196, 144, 121 and 225 do not satisfy the rule when placed as the fifth term; they cannot be written as 81 * 2 + 7.- Using these alternatives would break either the doubling pattern or the constant addition of 7.Common Pitfalls:- Candidates sometimes try to fit a pattern to the differences alone and may miss the more direct multiply and add relationship.- Another pitfall is assuming a quadratic formula or more complex function when a simple two step rule is sufficient.- Ignoring the repeated appearance of plus 7 and focusing only on the rapid growth of the numbers can also lead to confusion.Final Answer:Applying the clear rule next term = previous term * 2 + 7 to 81 gives 81 * 2 + 7 = 169, so 169 is the correct next number in the series.

Question 3

Find the next number in the given number series: 1, 3, 10, 41, 206, ?

Accepted Answer

Introduction / Context:This question involves a non linear number series where each new term is generated from the previous term using both multiplication and addition. These higher order patterns are common in competitive exams and test whether candidates can observe relations that depend on the position of each term in the sequence. Our task is to extend the series 1, 3, 10, 41, 206 by one more term.Given Data / Assumptions:- Given series: 1, 3, 10, 41, 206, ?- The sequence is strictly increasing, with gaps growing rapidly.- Each term is expected to be generated from the previous one using a systematic rule that depends on the term position.Concept / Approach:In rapidly growing series, a good first step is to check products and then see if a small constant is added or subtracted. When the multiplication factor does not remain fixed, it often depends on the position of the term. So we try a rule of the form a(n+1) = a(n) * k(n) + c, where k(n) depends on n. By experimenting with small integer values of k(n) linked to the term index, we can uncover the correct pattern.Step-by-Step Solution:- Let the first term be a1 = 1.- From 1 to 3: 1 * 2 + 1 = 3. Here the multiplier is 2.- From 3 to 10: 3 * 3 + 1 = 10. Here the multiplier is 3.- From 10 to 41: 10 * 4 + 1 = 41. Here the multiplier is 4.- From 41 to 206: 41 * 5 + 1 = 206. Here the multiplier is 5.- We observe a clear pattern: a(n+1) = a(n) * (n + 1) + 1, starting with n = 1.- To find the next term a6, we use the same rule with multiplier 6: a6 = a5 * 6 + 1.- Calculation: a6 = 206 * 6 + 1 = 1236 + 1 = 1237.- Therefore, the missing number in the series is 1237.Verification / Alternative check:- Rebuild the series using the discovered rule: a1 = 1; a2 = 1 * 2 + 1 = 3; a3 = 3 * 3 + 1 = 10; a4 = 10 * 4 + 1 = 41; a5 = 41 * 5 + 1 = 206; a6 = 206 * 6 + 1 = 1237.- All steps are consistent with the rule a(n+1) = a(n) * (n + 1) + 1, with no mismatches.Why Other Options Are Wrong:- 897, 987, 1007 and 823 do not equal 206 * 6 + 1, and none fits a simple positional multiplier pattern.- Using any of these values would destroy the elegant link between term index and multiplication factor.Common Pitfalls:- A common mistake is to look only at differences (2, 7, 31, 165) and try to detect a pattern there, which is much less obvious.- Some candidates also assume a constant multiplication factor, which cannot explain the transition from 1 to 3 to 10 to 41 to 206.- Ignoring the idea that the multiplier might depend on the position n can prevent recognition of the true rule.Final Answer:The series follows the rule a(n+1) = a(n) * (n + 1) + 1, so the next term is 206 * 6 + 1 = 1237.

Question 4

What would be the next number in the sequence: 52, 56, 48, 64, 32, ?

Accepted Answer

Introduction / Context:This number series problem uses alternating addition and subtraction with differences whose magnitudes are doubling. Recognising alternating patterns is essential in reasoning tests because such series often look irregular at first glance. Our task is to determine the next number after 52, 56, 48, 64, 32.Given Data / Assumptions:- Sequence: 52, 56, 48, 64, 32, ?- The series alternates between increasing and decreasing values.- A simple numerical pattern involving addition and subtraction is expected.Concept / Approach:When a series moves up and down in value, a good strategy is to compute the differences between consecutive terms and see whether these differences themselves follow a pattern. Sometimes the differences may be constant, and at other times they may double or follow another progression. Here, we will calculate these differences and check for a doubling pattern in their magnitudes.Step-by-Step Solution:- From 52 to 56: 56 - 52 = +4 (increase of 4).- From 56 to 48: 48 - 56 = -8 (decrease of 8).- From 48 to 64: 64 - 48 = +16 (increase of 16).- From 64 to 32: 32 - 64 = -32 (decrease of 32).- The pattern is: +4, -8, +16, -32. The signs alternate, and the absolute values 4, 8, 16, 32 are doubling each time.- So the next difference should continue the pattern with a positive sign and double the previous magnitude: +64.- Therefore, the missing term is 32 + 64 = 96.Verification / Alternative check:- Rebuilding with this rule: 52 (+4) = 56, 56 (-8) = 48, 48 (+16) = 64, 64 (-32) = 32, 32 (+64) = 96.- The pattern of alternating signs with magnitudes 4, 8, 16, 32, 64 is consistent and neatly structured.Why Other Options Are Wrong:- 48, 54, 81 and 40 do not correspond to adding 64 to 32, nor do they maintain the doubling pattern of the absolute differences.- Substituting any of these numbers would break the systematic sequence of +4, -8, +16, -32, +64.Common Pitfalls:- Some candidates may look only at the differences 4, -8, 16, -32 without recognising that the absolute values are doubling.- Another mistake is to search for a single arithmetic operation instead of realising that the operations alternate between addition and subtraction.- Confusion is also possible if the sign pattern is ignored and attention is only on the sizes of the jumps.Final Answer:To continue the alternating doubling pattern, we add 64 to 32, giving 96 as the next number in the sequence.

Question 5

Choose the correct alternative that will continue the same pattern and replace x in the series: 1.5, 1.55, 1.65, 1.8, x

Accepted Answer

Introduction / Context:This series question involves decimal numbers and gradually increasing differences. Such problems test attention to fractional increments and the ability to see patterns in non integer changes. We are asked to determine which value of x continues the pattern in the sequence 1.5, 1.55, 1.65, 1.8, x.Given Data / Assumptions:- Sequence: 1.5, 1.55, 1.65, 1.8, x.- Only one term, x, is unknown.- Differences between terms are small and positive, suggesting an additive pattern.Concept / Approach:To solve such decimal series, the easiest method is to compute the difference between consecutive terms and see whether those differences follow their own simple pattern. Frequently, they increase or decrease by a constant amount. Recognising a pattern in the differences allows us to predict the next difference and hence the next term in the series.Step-by-Step Solution:- From 1.5 to 1.55: 1.55 - 1.5 = 0.05.- From 1.55 to 1.65: 1.65 - 1.55 = 0.10.- From 1.65 to 1.8: 1.8 - 1.65 = 0.15.- The differences are: 0.05, 0.10, 0.15. Each time, the increment increases by 0.05.- Therefore, the next difference should be 0.20.- So x = 1.8 + 0.20 = 2.0.Verification / Alternative check:- With x = 2.0, the sequence of differences becomes 0.05, 0.10, 0.15, 0.20, which is an arithmetic progression with common difference 0.05.- The resulting series 1.5, 1.55, 1.65, 1.8, 2.0 is smooth and consistent.Why Other Options Are Wrong:- 1.95, 1.85, 2.05 and 1.9 do not give a difference of 0.20 from 1.8, and they break the steadily increasing difference pattern.- For instance, 1.95 would give a difference of 0.15 again instead of 0.20, which fails to continue the growth in the increments.Common Pitfalls:- Misreading decimal values (for example mixing 0.05 and 0.5) can lead to incorrect differences.- Some candidates may stop after recognising that the series increases, without noticing that the increments themselves are increasing in a systematic way.- Rounding the values too roughly can hide the true underlying pattern.Final Answer:The next difference should be 0.20, so the missing term is 1.8 + 0.20 = 2.0.

Question 6

Choose the correct alternative that will continue the same pattern and replace x in the series: 1, 2, 5, 10, 25, 50, x, 250

Accepted Answer

Introduction / Context:This number series question uses alternating multiplication factors and is typical of reasoning tests where candidates must detect a pattern in how each term is generated from the previous one. The sequence 1, 2, 5, 10, 25, 50, x, 250 shows smooth growth and suggests a combination of doubling and multiplying by a fraction like 2.5.Given Data / Assumptions:- Sequence: 1, 2, 5, 10, 25, 50, x, 250.- Only one term, x, is missing.- Each term is strictly greater than the previous term.Concept / Approach:A good approach is to compute ratios of successive terms. If the ratio alternates between two values, we can reconstruct the rule and extend the series. The presence of values like 5, 10, 25, 50 and 250 also hints at common factors of 2 and 5, guiding us toward multipliers such as 2 and 2.5.Step-by-Step Solution:- From 1 to 2: 2 / 1 = 2 (multiplied by 2).- From 2 to 5: 5 / 2 = 2.5 (multiplied by 2.5).- From 5 to 10: 10 / 5 = 2 (multiplied by 2).- From 10 to 25: 25 / 10 = 2.5 (multiplied by 2.5).- From 25 to 50: 50 / 25 = 2 (multiplied by 2).- We see the pattern: multiply alternately by 2 and 2.5.- After 50, we should apply the next factor, which is 2.5.- So x = 50 * 2.5 = 125.- After that, the next factor would be 2, giving 125 * 2 = 250, which matches the last term.Verification / Alternative check:- Rewriting the full pattern: 1 * 2 = 2, 2 * 2.5 = 5, 5 * 2 = 10, 10 * 2.5 = 25, 25 * 2 = 50, 50 * 2.5 = 125, 125 * 2 = 250.- The alternating factors 2 and 2.5 are confirmed throughout.Why Other Options Are Wrong:- 75, 150, 100 and 60 do not equal 50 multiplied by 2.5 and therefore fail to preserve the alternating pattern.- In particular, if x were 150 or 100, the final step to reach 250 would require a different multiplier, breaking the neat alternating rule.Common Pitfalls:- Some candidates only check differences (1, 3, 5, 15, 25, etc.), which look irregular and can hide the true multiplicative structure.- It is easy to overlook 2.5 as a multiplier because it is not an integer, even though it fits the ratio perfectly.- Trying to force a single constant ratio instead of considering alternating ratios can also cause confusion.Final Answer:Using the alternating pattern of multiplying by 2 and then by 2.5, the missing term is 50 * 2.5 = 125.

Question 7

Which number should come in place of the underline mark in the series: 3, 9, 21, ___, 93

Accepted Answer

Introduction / Context:This question presents a simple but elegant number series where each term is generated by multiplying the previous term and then adding a fixed constant. Such patterns are widely used in aptitude tests because they are straightforward once the core rule is spotted. We must determine which number fills the blank between 21 and 93 in the series 3, 9, 21, ___, 93.Given Data / Assumptions:- Sequence: 3, 9, 21, ?, 93.- Exactly one term is missing.- The series is strictly increasing.Concept / Approach:A good starting point is to check how each term relates to the previous one. If we can express each new term as previous term multiplied by a constant and then increased by a small number, we might reveal a rule such as a(n+1) = a(n) * k + c. We will test this hypothesis by working from left to right and verifying whether the same rule holds for every known transition.Step-by-Step Solution:- From 3 to 9: 3 * 2 + 3 = 6 + 3 = 9.- From 9 to 21: 9 * 2 + 3 = 18 + 3 = 21.- This suggests the rule: next term = previous term * 2 + 3.- Now apply it to find the missing term after 21: 21 * 2 + 3 = 42 + 3 = 45.- Apply it once more to confirm the last term: 45 * 2 + 3 = 90 + 3 = 93.- So the missing number in the series is 45.Verification / Alternative check:- Recomputed full series: 3, 9, 21, 45, 93.- Each step follows the same rule: multiply by 2 and then add 3.- No inconsistency appears, confirming 45 as the unique valid candidate.Why Other Options Are Wrong:- 39, 48, 51 and 57 do not satisfy the relation a(n+1) = a(n) * 2 + 3 when placed between 21 and 93.- For example, with 39 as the missing term, 39 * 2 + 3 = 81, which does not equal 93.Common Pitfalls:- Some candidates focus only on the differences (6, 12, 24, 48) and get lost in their rapid growth, instead of spotting the simpler multiply and add rule.- Another error is assuming a changing or alternating pattern when a single consistent rule actually works for the whole series.- Overcomplicating the relationship by looking for higher powers or factorials is unnecessary here.Final Answer:The series follows the rule next term = previous term * 2 + 3, so the missing number is 45.

Question 8

Fill in the blanks to complete the letter pattern: bc _ b _ c _ b _ ccb

Accepted Answer

Introduction / Context:This verbal reasoning question deals with a letter series that hides a repeating block pattern. Candidates must carefully observe how short groups of letters recur and then insert the correct sequence into the blanks. Here the partially filled pattern is bc _ b _ c _ b _ ccb, and we must choose a four letter sequence to fill the blanks so that the whole series becomes consistent.Given Data / Assumptions:- Incomplete letter pattern: b c _ b _ c _ b _ c c b.- There are four blanks in total, and we must insert four letters in order.- Options give four letter groups such as cbcb, bbcb, cbbc and bcbc, which will be placed into the blanks from left to right.Concept / Approach:The best approach is to assume the pattern repeats some fixed block of letters. We test each option by substituting its letters into the blanks and then check whether the resulting full sequence can be partitioned into equal repeating blocks. The option which produces a perfect repetition throughout the length of the series is the correct answer.Step-by-Step Solution:- Write the pattern with placeholders: b c _ b _ c _ b _ c c b.- Now test option a: cbcb.- Fill the blanks in order with c, b, c, b.- The completed series becomes: b c c b b c c b b c c b.- Group the letters into blocks of four: (b c c b), (b c c b), (b c c b).- Each block is identical, giving a clean repetition of the pattern bccb.- This shows that option a creates a perfectly repeating structure across the entire string.Verification / Alternative check:- Test option b: bbcb. The resulting string does not break neatly into identical four letter blocks.- Test option c: cbbc and option d: bcbc similarly; each produces at least one block that differs from the others.- Only option a: cbcb yields three identical blocks bccb, confirming it as the unique correct choice.Why Other Options Are Wrong:- bbcb, cbbc and bcbc give patterns where some four letter segments differ from others, so the string cannot be described as a simple repetition of a single block.- This violates the usual expectation in such letter series questions where a short fixed pattern repeats.Common Pitfalls:- Candidates may try to reason only locally near each blank instead of observing the full repeated block.- It is easy to visually misread similar sequences like bccb and bcbc, leading to incorrect substitution.- Not grouping the letters into equal segments can make the repetition less obvious.Final Answer:Filling the blanks with the letters c, b, c, b gives a three time repetition of the block bccb, so the correct inserted group is cbcb.

Question 9

Find the next number in the series: 265, 269, 278, 284, ?

Accepted Answer

Introduction / Context:This question presents a number series whose differences do not remain constant but still follow a structured pattern. The aim is to recognise how the increments change from term to term and then apply the same logic to find the next number after 265, 269, 278 and 284.Given Data / Assumptions:- Series: 265, 269, 278, 284, ?- Exactly one term, the fifth term, is missing.- The pattern is expected to involve a regular change in the size of the increments.Concept / Approach:When differences are not constant, candidates should compute them and see whether they themselves follow a pattern. Often the increments alternate between two sequences that grow slowly. Here, we will analyse the step sizes and check whether they form two interleaved arithmetic progressions, one for odd steps and one for even steps.Step-by-Step Solution:- Compute differences between consecutive terms: • 269 - 265 = 4. • 278 - 269 = 9. • 284 - 278 = 6.- Now interpret these as part of two interleaved sequences of step sizes: • Odd numbered increments: 4, 6, ... (first, third, fifth step, etc.). • Even numbered increments: 9, 11, 13, ... (second, fourth, sixth step, etc.).- The odd increments increase by 2: 4, 6, 8 and so on.- The even increments also increase by 2: 9, 11, 13 and so on.- We already have the first three increments: 4 (odd), 9 (even), 6 (odd).- The next increment should be the second even increment, which is 11.- Therefore, the missing fifth term is 284 + 11 = 295.Verification / Alternative check:- We can list the step sizes explicitly as: +4, +9, +6, +11, +8, +13, ... where odd positions (1, 3, 5, ...) have values 4, 6, 8, ... and even positions (2, 4, 6, ...) have values 9, 11, 13, ...- The given series 265, 269, 278, 284 aligns with +4, +9 and +6, so the next step should indeed be +11, giving 295.- No other candidate continues both interleaved arithmetic progressions so neatly.Why Other Options Are Wrong:- 291, 299, 303 and 305 correspond to increments of 7, 15, 19 and 21 from 284.- None of these increments fit the required values 11 or 8 that would continue the structured double progression.- Using any of these alternatives would break the regular growth in the step sizes.Common Pitfalls:- Some candidates look for a simple quadratic or cubic form instead of analysing the differences directly.- It is easy to miss the idea that there can be two interleaved patterns operating simultaneously.- Guessing based only on approximate growth without calculating the exact increments often leads to wrong options like 291 or 299.Final Answer:Continuing the structured pattern of step sizes, the next term is 284 + 11 = 295.

Question 10

Find the next number in the given number sequence: 9, 19, 21, 43, 45, ...

Accepted Answer

Introduction / Context:This series question uses an alternating pattern of operations: one step multiplies and adds a constant, the next step simply adds a smaller constant. Such patterns are popular in reasoning tests because they appear irregular unless the candidate checks each consecutive pair carefully. We must find the next term after 9, 19, 21, 43, 45.Given Data / Assumptions:- Sequence: 9, 19, 21, 43, 45, ?- The series alternates between larger and smaller jumps.- The pattern is expected to use simple integer operations.Concept / Approach:We examine how each term is derived from the previous one. By computing both products and sums, we can detect whether there is a repeating two-step rule. In particular, we test whether there is a rule of multiplying by 2 and adding 1 in one step, and then adding 2 in the next step, which is a common kind of alternating pattern in exam series.Step-by-Step Solution:- From 9 to 19: 9 * 2 + 1 = 18 + 1 = 19.- From 19 to 21: 19 + 2 = 21.- From 21 to 43: 21 * 2 + 1 = 42 + 1 = 43.- From 43 to 45: 43 + 2 = 45.- We observe a stable repeating pattern: • Step 1: multiply by 2 and add 1. • Step 2: add 2.- To find the next term, we apply the next operation in the cycle, which is again multiply by 2 and add 1.- So the next term after 45 is: 45 * 2 + 1 = 90 + 1 = 91.Verification / Alternative check:- Rewriting the pattern: 9 → (9 * 2 + 1) = 19 → (19 + 2) = 21 → (21 * 2 + 1) = 43 → (43 + 2) = 45 → (45 * 2 + 1) = 91.- The two-step cycle is consistently preserved across all transitions, and 91 fits perfectly into this structure.Why Other Options Are Wrong:- 88, 54, 49 and 73 do not equal 45 * 2 + 1.- Substituting any of these values breaks the simple alternation between multiplying and adding fixed constants.Common Pitfalls:- Candidates may only look at differences (10, 2, 22, 2) without noticing that larger jumps are exactly double plus one of the previous term.- It is easy to overlook the alternating pattern and assume a more complex nonlinear relation that is not needed.- Guessing without verifying each step against a consistent rule can lead to plausible sounding but incorrect answers.Final Answer:The pattern alternates between multiplying by 2 and adding 1 and then adding 2, so the next term is 45 * 2 + 1 = 91.

Question 11

Next number in the number sequence is: 22, 11, 33, 16.5, 49.5, ?

Accepted Answer

Introduction / Context:This series alternates between division and multiplication. It is a classic pattern in reasoning exams where one step halves the number and the next step triples it. We need to find the next term after 22, 11, 33, 16.5, 49.5.Given Data / Assumptions:- Sequence: 22, 11, 33, 16.5, 49.5, ?- The series alternates between larger and smaller values.- A simple fractional operator such as division by 2 and multiplication by 3 is expected.Concept / Approach:Observe the relation between every pair of consecutive terms. The presence of exact halves and clean decimal values such as 16.5 is a strong hint of division by 2. Similarly, jumps like 11 to 33 and 16.5 to 49.5 suggest multiplication by 3. Once we confirm this alternation, we can confidently compute the missing term.Step-by-Step Solution:- From 22 to 11: 22 / 2 = 11 (division by 2).- From 11 to 33: 11 * 3 = 33 (multiplication by 3).- From 33 to 16.5: 33 / 2 = 16.5 (division by 2).- From 16.5 to 49.5: 16.5 * 3 = 49.5 (multiplication by 3).- The pattern is: divide by 2, then multiply by 3, and repeat.- After 49.5, the next operation in the cycle is division by 2.- So the next term is 49.5 / 2 = 24.75.Verification / Alternative check:- Rewriting with the identified rule: 22 ÷ 2 = 11, 11 × 3 = 33, 33 ÷ 2 = 16.5, 16.5 × 3 = 49.5, 49.5 ÷ 2 = 24.75.- The alternating division and multiplication operations are applied consistently, and 24.75 fits perfectly.Why Other Options Are Wrong:- 41, 33.5, 26.75 and 29.75 are not equal to 49.5 divided by 2 and do not preserve the strict divide by 2 then multiply by 3 cycle.- Using any of these values would force a different operation at one of the earlier steps, breaking the neat alternation.Common Pitfalls:- Some candidates look only at differences rather than ratios and may fail to notice that the pattern is based on division and multiplication.- Rounding errors with decimals can mislead if 16.5 or 24.75 is not handled carefully.- Forgetting to continue the same cycle of operations and inventing a new rule at the end can lead to wrong answers.Final Answer:The series alternates between dividing by 2 and multiplying by 3, so the next term after 49.5 is 49.5 ÷ 2 = 24.75.

Question 12

Complete the number series: 11, 12.2, 14.6, 18.2, ?

Accepted Answer

Introduction / Context:This decimal number series features differences that themselves form a simple arithmetic progression. Candidates are expected to recognise the changing increments and use them to compute the next term. The given sequence is 11, 12.2, 14.6, 18.2, and we must find the next number.Given Data / Assumptions:- Sequence: 11, 12.2, 14.6, 18.2, ?- Values are positive decimal numbers.- Only one term at the end is missing.Concept / Approach:We begin by computing the differences between consecutive terms and then check whether those differences themselves form a simple pattern. Here, because we are working with tenths, we expect differences like 1.2, 2.4 and 3.6, which might form a clear arithmetic progression. Once that progression is identified, extending it by one more step will give the next difference and the next term in the series.Step-by-Step Solution:- From 11 to 12.2: 12.2 - 11 = 1.2.- From 12.2 to 14.6: 14.6 - 12.2 = 2.4.- From 14.6 to 18.2: 18.2 - 14.6 = 3.6.- Thus, the consecutive differences are 1.2, 2.4, 3.6.- These values form an arithmetic progression with common difference 1.2.- Therefore, the next difference should be 3.6 + 1.2 = 4.8.- The next term is then 18.2 + 4.8 = 23.0.- So, the required number is 23.Verification / Alternative check:- Reconstruct the sequence with the identified rule: 11 (+1.2) = 12.2, (+2.4) = 14.6, (+3.6) = 18.2, (+4.8) = 23.- The series of differences, 1.2, 2.4, 3.6, 4.8, is perfectly regular and supports our answer.Why Other Options Are Wrong:- 21.8, 24.6, 25 and 22.8 do not correspond to adding 4.8 to 18.2.- Using any of them would break the neat arithmetic progression in the differences.Common Pitfalls:- Miscalculating decimal differences and confusing 1.2 with 1.02 or 0.12.- Assuming a constant difference and stopping after noticing that the differences are not the same, rather than checking how they change.- Rounding intermediate steps carelessly can distort the underlying pattern.Final Answer:The differences increase by 1.2 each time, so the next difference is 4.8 and the next term is 18.2 + 4.8 = 23.

Question 13

Find out the wrong term in the series: 83, 92, 85, 90, 85, 88

Accepted Answer

Introduction / Context:This question asks for the wrong term in a series where the differences between consecutive terms follow a particular alternating pattern. One of the values does not fit the intended series and must be identified. The given sequence is 83, 92, 85, 90, 85, 88.Given Data / Assumptions:- Series: 83, 92, 85, 90, 85, 88.- Exactly one term is incorrect.- The correct terms are assumed to follow a simple, regular pattern in their differences.Concept / Approach:When asked to find a wrong term, we usually compute the differences between consecutive numbers and see if most of them follow a clear rule. Any single term that makes one step violate the rule can be considered wrong. Here we will attempt to identify a pattern of alternating addition and subtraction with changing odd differences and then see which term breaks this structure.Step-by-Step Solution:- Compute differences between consecutive terms: • 92 - 83 = +9. • 85 - 92 = -7. • 90 - 85 = +5. • 85 - 90 = -5. • 88 - 85 = +3.- Notice the sequence of differences: +9, -7, +5, -5, +3.- A natural intended pattern is: +9, -7, +5, -3, +1, where the absolute values are decreasing odd numbers: 9, 7, 5, 3, 1, with alternating signs.- Let us build the ideal series using this rule starting from 83: • 83 + 9 = 92. • 92 - 7 = 85. • 85 + 5 = 90. • 90 - 3 = 87. • 87 + 1 = 88.- So the correct series should be 83, 92, 85, 90, 87, 88.- The term at the fifth position should be 87, but the given series has 85 instead.Verification / Alternative check:- Except for the step from 90 to 85, all other steps can be matched to a decreasing odd difference pattern.- Replacing the fifth term 85 by 87 restores the smooth pattern of consecutive odd differences 9, 7, 5, 3, 1 with alternating signs.- Therefore, the value 85 at the fifth position is the wrong term.Why Other Options Are Wrong:- 83, 92, 85 (third term) and 90 can all be part of the corrected series 83, 92, 85, 90, 87, 88.- 88 is also consistent as the final value when we follow the pattern of adding 1 after subtracting 3.- Only the value 85 in the fifth position conflicts with the intended progression.Common Pitfalls:- Some candidates may be confused because the number 85 appears twice in the series and may think that both occurrences are suspicious.- It is important to check which occurrence of 85 actually breaks the pattern rather than simply counting frequency.- Failing to recognise the decreasing odd sequence in the differences can lead to random guessing instead of logical reasoning.Final Answer:The term that violates the regular pattern of decreasing odd differences is the fifth value, which is 85, so 85 is the wrong term in the series.

Question 14

In the following question, various terms of an alphabet series are given with one or more terms missing as shown by (?). Choose the missing term: Y, B, T, G, O, ?

Accepted Answer

Introduction / Context:This alphabet series question involves two interleaved sequences, one using letters that move backward along the alphabet and the other using letters that move forward. Candidates must separate these two hidden series and fill the missing term. The given sequence is Y, B, T, G, O, ?.Given Data / Assumptions:- Series: Y, B, T, G, O, ?- Letters are in the English alphabet, where A is 1 and Z is 26.- Every alternate term may belong to a separate subsequence.Concept / Approach:For alphabet series, a good technique is to separate the terms at odd and even positions and study them as two independent sequences. Often, one subsequence will show a clear progression forward, while the other may move backward with a fixed step. After figuring out both subsequences, we can identify the missing term at the appropriate position.Step-by-Step Solution:- Write positions explicitly: 1st = Y, 2nd = B, 3rd = T, 4th = G, 5th = O, 6th = ?- Consider the letters at odd positions: 1st Y, 3rd T, 5th O.- Convert them to numerical positions: Y = 25, T = 20, O = 15.- Differences: 25 → 20 is -5, 20 → 15 is -5. So the odd position series decreases by 5 each time.- Now consider the letters at even positions: 2nd B, 4th G, 6th ?.- Convert to numeric: B = 2, G = 7.- Difference: 2 → 7 is +5. So the even position series increases by 5 each time.- Next even term should be 7 + 5 = 12, which corresponds to the 12th letter of the alphabet.- The 12th letter is L.- Therefore, the missing term at the 6th position is L.Verification / Alternative check:- Reconstruct odd positions: 25 (Y), 20 (T), 15 (O) are obtained by repeatedly subtracting 5.- Reconstruct even positions: 2 (B), 7 (G), 12 (L) are obtained by repeatedly adding 5.- Combining them gives the final series: Y, B, T, G, O, L, which is fully consistent.Why Other Options Are Wrong:- N, M, K and J do not correspond to the expected numeric position 12.- Choosing any of these letters would break the consistent step of plus 5 in the even position subsequence.Common Pitfalls:- Not separating the series into odd and even positions causes confusion because the combined sequence appears irregular.- Some candidates may try to measure differences between consecutive letters directly, which does not reveal a simple pattern here.- Miscounting alphabet positions can also lead to wrong answers even after spotting the correct step size.Final Answer:The even position subsequence increases by 5 in alphabet positions, so the missing letter is the 12th letter, L.

Question 15

In each of the following questions a letter-series is given, in which some letters are missing. The missing letters are given in the proper sequence as one of the alternatives. Choose the correct alternative: _ op _ mo _ n _ _ pnmop _

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Introduction / Context:This letter series question involves completing a string so that it becomes a repetition of a short block of letters. Candidates must determine which sequence of letters, when inserted into the blanks, produces a perfectly regular repeating pattern. The incomplete string is _ op _ mo _ n _ _ pnmop _.Given Data / Assumptions:- Incomplete series: _ o p _ m o _ n _ _ p n m o p _.- There are six blanks in total.- Each option supplies exactly six letters to fill the blanks from left to right.- We expect the final completed string to show a neat repetition of a fixed letter block.Concept / Approach:The usual pattern in such questions is that the final series becomes a repetition of a short word or block of letters. We can test each option by inserting its letters into the blanks and then checking whether the resulting series can be split into equal sized, identical segments. The option that produces a perfectly repeating pattern is the correct answer.Step-by-Step Solution:- Represent the pattern with underscores for blanks: _ o p _ m o _ n _ _ p n m o p _.- Insert the letters of option a: m n p m o n into the blanks, in order.- The resulting complete series is: m o p n m o p n m o p n m o p n.- Now group this string into blocks of four letters: (m o p n), (m o p n), (m o p n), (m o p n).- Each block is exactly the same, showing a clean repetition of the block mopn.Verification / Alternative check:- Test option b: filling with m p n m o p does not yield a series that breaks into identical fixed blocks.- Similarly, filling with options c or d results in strings where at least one four letter group differs from the others.- Only option a gives a continuous mopn mopn mopn mopn structure, confirming that mnpmon is the correct sequence to insert.Why Other Options Are Wrong:- Options b, c and d cannot be split into repeating identical blocks after substitution, so they fail the standard expectation of a repeated letter pattern.- Option e is not consistent with the required mapping of each blank and also breaks the repetition.Common Pitfalls:- Trying to reason letter by letter without checking for a repeating block can make the pattern seem more complex than it is.- Misplacing letters from an option or inserting them in the wrong order can lead to incorrect rejection of the correct alternative.- Not grouping the completed series into equal segments hides the repetitive structure.Final Answer:Substituting the letters m n p m o n (option a) produces the perfectly repeating pattern mopn, so the correct sequence to fill the blanks is mnpmon.

Question 16

In the following questions a letter-series is given, in which some letters are missing. The missing letters are given in the proper sequence as one of the alternatives. Choose the correct alternative: _ nmmn _ mmnn _ mnnm _

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Introduction / Context:This letter series involves a simple repetition of a short four letter block. Some letters are missing and must be filled so that the completed string exhibits exact repetition. The incomplete pattern is _ nmmn _ mmnn _ mnnm _. We must decide which sequence of four letters, when placed into the blanks, yields a neat repeating structure.Given Data / Assumptions:- Incomplete series: _ n m m n _ m m n n _ m n n m _.- There are four blanks in total.- Each option gives a four letter sequence to be inserted from left to right.- The completed series is expected to consist of identical four letter blocks repeated several times.Concept / Approach:We test each option by inserting its four letters into the blanks and then examine whether the resulting letter string can be broken into equal blocks of four letters, all of which are exactly the same. This is a typical pattern in such alphabet series questions. The option that produces a clean repetition is the correct answer.Step-by-Step Solution:- Represent the pattern with underscores: _ n m m n _ m m n n _ m n n m _.- Insert option d: nnmm into the blanks in order.- The completed series is: n n m m n n m m n n m m n n m m.- Group this string into four letter blocks: (n n m m), (n n m m), (n n m m), (n n m m).- All blocks are identical, so the pattern is a perfect repetition of nnmm.Verification / Alternative check:- Try option a: mnnm; after substitution, the resulting groups of four letters are not all the same.- Similar inconsistency appears with options b, c and e; each leaves us with at least one block that differs from the others.- Only option d produces four identical segments, confirming it as the valid choice.Why Other Options Are Wrong:- mnnm, nmmn, nmnm and mnmn all yield mixed blocks after substitution, so the final series cannot be described as a repetition of a single fixed four letter pattern.- This contradicts the typical design of such letter series questions where a neat repeating word underlies the entire string.Common Pitfalls:- Not checking the entire completed string and judging only by local matches can lead to wrong choices.- It is easy to confuse similar looking sequences like nnmm and nmmn when scanning quickly.- Failing to group letters into fixed size blocks hides the underlying repetition.Final Answer:Filling the blanks with nnmm produces four identical blocks nnmm, nnmm, nnmm, nnmm, so the correct sequence is nnmm.

Question 17

In the alphanumeric series A/2, B/4, C/6, D/8, ?, ?, identify the pair of missing terms that correctly continues the pattern.

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Introduction / Context:This problem is based on an alphanumeric series where both the letters and the numbers follow simple, regular patterns. The task is to identify how each part of the term changes from one position to the next and then apply that rule to find the missing pair of terms.Given Data / Assumptions:The given series is A/2, B/4, C/6, D/8, ?, ?Letters in the numerators appear in the order A, B, C and D.Denominators are the even numbers 2, 4, 6 and 8.We assume the same pattern continues in a consistent way for the missing terms.Concept / Approach:We treat letters and numbers as two independent but linked sequences. The numerator letters are expected to move forward in the English alphabet with a constant step, and the denominators are expected to increase using a simple arithmetic pattern. Once these two separate patterns are identified, we combine them to obtain each full term in the series.Step-by-Step Solution:Step 1: Look at the letters: A, B, C, D. Each letter moves one step forward in the alphabet.Step 2: The next letters after D are E and F. So the missing numerators are E and F.Step 3: Look at the denominators: 2, 4, 6, 8. This is an arithmetic sequence with a common difference of 2.Step 4: Continuing this pattern, the next denominators are 10 and 12.Step 5: Combine the numerator and denominator patterns to get the missing terms: E/10 and F/12.Verification / Alternative check:Check the pattern once more. For the letters: A to B to C to D to E to F is a simple +1 step in the alphabet. For the denominators: 2, 4, 6, 8, 10 and 12 is a simple +2 arithmetic sequence. There are no breaks or inconsistencies, so E/10 and F/12 are fully consistent with all earlier terms.Why Other Options Are Wrong:Options like D/10, E/10 or E/8, F/10 either repeat a previous letter or break the constant step size in the alphabet or the even-number pattern in the denominators. Options that use C/10 or B/6 also move backwards in the alphabet, which does not match the strictly forward progression seen in the series.Common Pitfalls:A common mistake is to focus only on numbers or only on letters and ignore that both must follow a regular rule at the same time. Another error is to assume the step size changes midway. For standard exam series questions like this, step sizes are usually constant unless clearly indicated otherwise.Final Answer:The pair of missing terms that correctly continues the given alphanumeric pattern is E/10, F/12.

Question 18

In the alphabet series C, E, G, J, M, Q, ?, choose the letter that correctly completes the pattern.

Accepted Answer

Introduction / Context:This question checks the ability to recognise a pattern in the positions of letters in the English alphabet. The letters do not increase with a constant step size, so we must look carefully at how the gaps between successive letters change as the series progresses.Given Data / Assumptions:Series given: C, E, G, J, M, Q, ?C is the 3rd letter, E is the 5th, G is the 7th, J is the 10th, M is the 13th, Q is the 17th.We assume the same hidden rule that generates earlier terms also generates the missing term.Concept / Approach:The key idea is to convert each letter into its numerical position in the alphabet and then inspect the differences between successive positions. Once a pattern of differences is found, we extend it to find the position of the missing letter and then convert that back to an alphabetic character.Step-by-Step Solution:Step 1: Replace letters by positions: C=3, E=5, G=7, J=10, M=13, Q=17.Step 2: Find the differences between consecutive terms: 5 - 3 = 2, 7 - 5 = 2, 10 - 7 = 3, 13 - 10 = 3, 17 - 13 = 4.Step 3: The differences follow the pattern 2, 2, 3, 3, 4, so the next difference should again be 4.Step 4: Add 4 to the last known position: 17 + 4 = 21.Step 5: The 21st letter of the alphabet is U, so the missing term is U.Verification / Alternative check:Write the sequence of differences explicitly as pairs: two 2s, then two 3s, then 4. It suggests a pattern of repeating each step size twice before increasing it by 1. Extending that logic gives another 4, which leads exactly to position 21 and thus to the letter U. This confirms internal consistency.Why Other Options Are Wrong:Letters like T, P, V or S do not correspond to adding the correct difference of 4 to the last position. For example, T is position 20 (difference 3), and V is position 22 (difference 5). These break the observed repeated difference pattern and therefore cannot be correct.Common Pitfalls:Some learners only look for a single constant step, such as adding 2 or adding 3, and conclude that no clear pattern exists. In alphabet series questions, step sizes can themselves follow a pattern, such as repeating or gradually increasing. Ignoring this second layer leads to wrong answers.Final Answer:The letter that correctly completes the series is U.

Question 19

In the alphabet series QAR, RAS, SAT, TAU, ?, find the next three letter group that completes the pattern.

Accepted Answer

Introduction / Context:This problem involves recognising a pattern within three letter alphabetic groups. Each position within the group can follow its own sequence. The task is to track how the first, second and third letters progress and then combine those patterns to determine the missing term.Given Data / Assumptions:Given groups: QAR, RAS, SAT, TAU, ?We treat each group as three independent letter positions.The rule that generates earlier groups is assumed to continue in the same way.Concept / Approach:For such series, the best strategy is to write each group in vertical columns: first letters together, second letters together and third letters together. Then we inspect how each column changes across the series. Normally we see simple alphabetic sequences such as increments by one position.Step-by-Step Solution:Step 1: First letters: Q, R, S, T. These are consecutive letters in forward order, so the next first letter is U.Step 2: Second letters: A, A, A, A. The second position remains fixed at A for every group, so the next second letter is also A.Step 3: Third letters: R, S, T, U. These are also consecutive letters moving forward by one each time, so the next third letter is V.Step 4: Combining all three positions, the missing group is U A V, written as UAV.Verification / Alternative check:If we rewrite the pattern clearly, we get: first column Q R S T U, second column A A A A A, third column R S T U V. Both the first and third columns form straightforward alphabetical sequences. There is no sign of any other consistent pattern that contradicts UAV, so the answer is stable.Why Other Options Are Wrong:UAT, UAS and UTS all preserve U as the first letter, but their third letters break the simple forward sequence R, S, T, U, V. Any option that does not use V as the third letter fails the observed pattern. TAV changes multiple positions at once and is inconsistent with all three columns examined together.Common Pitfalls:Learners sometimes try to treat each three letter group as a single unit and search for complex transformations, instead of separating the positions into columns. For many exam questions of this type, breaking the series into columns reveals three very simple sequences, which is the case here.Final Answer:The three letter group that correctly completes the series is UAV.

Question 20

In the number series 21, 24, 33, 49, 74, one term does not fit a consistent pattern. Identify the odd number out.

Accepted Answer

Introduction / Context:This question asks for the odd term out in a numeric sequence. The usual idea is that most of the numbers follow a clear rule, while one of them breaks that rule. Our job is to detect the underlying pattern that links the majority of the terms and then remove the term that does not match it.Given Data / Assumptions:Given series: 21, 24, 33, 49, 74.We are to treat exactly one number as inconsistent.We look for a pattern that fits at least four numbers strongly, rather than forcing a weak rule through all five.Concept / Approach:An effective way to tackle such problems is to consider consecutive differences between terms. If we find that a neat pattern emerges for most of the sequence once one element is removed, that singled out term is usually the odd one out. Here the key is to look at the differences between 24, 33, 49 and 74.Step-by-Step Solution:Step 1: Consider the subsequence 24, 33, 49, 74 and compute differences: 33 - 24 = 9, 49 - 33 = 16, 74 - 49 = 25.Step 2: The differences 9, 16 and 25 are perfect squares: 3^2, 4^2 and 5^2.Step 3: This shows a very clean pattern among 24, 33, 49 and 74 with differences following consecutive square numbers.Step 4: The number 21 does not participate in this square difference structure, because 24 - 21 = 3, which is not a perfect square and does not align with the 3^2, 4^2, 5^2 pattern.Step 5: Therefore 21 is the number that breaks the most consistent pattern in the sequence.Verification / Alternative check:If we attempt to include 21 in a pattern with perfect square differences, we fail to obtain consistent squares from the beginning. On the other hand, if we simply drop 21, the remaining four terms follow the neat difference pattern of 9, 16 and 25, which strongly supports the conclusion that 21 is the odd one out.Why Other Options Are Wrong:Numbers such as 24, 33, 49 and 74 are linked by differences that are perfect squares. Removing any of them would break this clear rule. For example, dropping 24 would give 21, 33, 49, 74, where the differences no longer follow any simple or smooth numeric pattern.Common Pitfalls:One common error is to try to fit all five numbers into a single pattern, which can lead to overly complicated reasoning. Another pitfall is ignoring the power and simplicity of square numbers in difference sequences. Many exam setters deliberately hide square difference patterns inside such series questions.Final Answer:The number that does not fit the consistent perfect square difference pattern is 21.

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