Question 1

In the alphabet series Z, U, Q, ?, L, which letter should replace the question mark to continue the pattern correctly?

Accepted Answer

Introduction / Context: This question is based on an alphabet series with decreasing letter positions. Such problems test your familiarity with alphabetical order and your ability to detect arithmetic progressions on letter positions rather than on numbers directly. Once you map letters to their numeric positions, the pattern becomes straightforward. Given Data / Assumptions: - The given sequence of letters is: Z, U, Q, ?, L.- We use the standard English alphabet: A = 1, B = 2, ..., Z = 26.- We assume a consistent rule is used for moving from one letter to the next. Concept / Approach: Alphabet series questions are easily handled by converting each letter to its numeric position. Once we have the numerical form, we can look for addition or subtraction patterns, often involving constant differences. After identifying the pattern, we convert the result back into the corresponding letter for the final answer. Step-by-Step Solution: - Convert letters to numbers: Z = 26, U = 21, Q = 17, L = 12.- Compute differences: 26 to 21 is -5, 21 to 17 is -4.- We suspect the differences may follow a pattern of decreasing negative steps: -5, -4, -3, -2.- Apply the next step: 17 - 3 = 14.- The number 14 corresponds to the letter N.- From 14 to 12 is a difference of -2, which matches the expected next step and leads to L as given. Verification / Alternative check: - Check the full pattern of positions: 26, 21, 17, 14, 12.- Differences are: -5, -4, -3, -2, which is a clear and consistent progression.- This confirms that N (position 14) is the only letter that fits between Q and L. Why Other Options Are Wrong: - M (13) and K (11) do not maintain the required difference sequence of -5, -4, -3, -2.- I (9) is even further away and completely breaks the pattern of stepwise decreasing negative differences.- Only N keeps the clean numerical progression when letters are converted to positions. Common Pitfalls: Candidates sometimes guess based on approximate alphabetical location without calculating exact positions, which often leads to wrong choices. Another pitfall is assuming a constant step size, while this question uses a gradually changing step size. Always translate letters to numbers and examine the differences carefully for alphabet series problems. Final Answer: The missing letter in the series is N, so the correct option is N.

Question 2

In the sequence AB, DEF, HIJK, ?, STUVWX, which group of letters should replace the question mark to continue the pattern?

Accepted Answer

Introduction / Context: This question involves a pattern of letter blocks in the English alphabet where both the starting letter and the length of each block change in a systematic way. It checks your ability to work with sequences of letters, not just single-letter jumps, which is a common theme in verbal reasoning tests. Given Data / Assumptions: - The given groups are: AB, DEF, HIJK, ?, STUVWX.- Each group consists of consecutive letters without gaps inside the group.- Both starting letters and group lengths appear to follow patterns. Concept / Approach: We should examine two things: the starting letter of each group and the number of letters in each group. Frequently, such series increase the group length step by step and shift the starting letter forward according to a separate rule. By understanding both patterns, we can accurately determine the missing group of letters. Step-by-Step Solution: - Count letters: AB has 2 letters, DEF has 3 letters, HIJK has 4 letters, and STUVWX has 6 letters.- The missing group should therefore have 5 letters to keep a gradual increase of 2, 3, 4, 5, 6 letters.- Look at starting letters: AB starts at A (1), DEF at D (4), HIJK at H (8).- Differences in starting positions: A to D is +3, D to H is +4, so the next difference should be +5.- H is position 8, so the next start is 8 + 5 = 13, which is M.- A 5-letter block from M is: M, N, O, P, Q giving MNOPQ.- Finally, 6-letter block from S gives STUVWX as in the question, so the pattern is consistent. Verification / Alternative check: - Confirm lengths: 2, 3, 4, 5, 6 form a clear increasing sequence.- Confirm starts: A (1), D (4), H (8), M (13), S (19) have increments of +3, +4, +5, +6.- These two coordinated patterns clearly identify MNOPQ as the only valid missing group. Why Other Options Are Wrong: - QRSTU starts at Q, not at M, and does not maintain the correct increment for the starting letters.- LMNO has only 4 letters, so it violates the required group length of 5.- LMNOP starts at L instead of M, so it breaks the start-position pattern, even though it has 5 letters.- Only MNOPQ satisfies both the starting position and group length patterns simultaneously. Common Pitfalls: Students often focus only on the number of letters and ignore the starting letter pattern, or vice versa. Another mistake is to pick the group that looks alphabetically closest without verifying both conditions. Always check both the starting position and the length of each block when dealing with such letter-series questions. Final Answer: The missing group of letters is MNOPQ, so the correct option is MNOPQ.

Question 3

In the letter series BAZ, DCY, FEX, ?, which group of letters should replace the question mark to continue the pattern?

Accepted Answer

Introduction / Context: This is a three-letter alphabet series question where each position in the group follows its own pattern. Such problems are designed to test your ability to track multiple simultaneous patterns across the first, second, and third letters independently and then combine them to find the missing term. Given Data / Assumptions: - The given groups are: BAZ, DCY, FEX, ?- Each group has exactly three letters.- We assume that each letter position follows a simple pattern when considered separately. Concept / Approach: A standard technique for multi-letter series is to split the sequence into three independent sequences: one formed by the first letters, one by the second letters, and one by the third letters. By mapping each letter to its position in the alphabet and then observing differences, you can usually discover simple arithmetic rules and apply them to find the missing term. Step-by-Step Solution: - First letters: B, D, F correspond to 2, 4, 6 in the alphabet.- This is an arithmetic progression with a common difference of +2, so the next first letter is 8, which is H.- Second letters: A, C, E correspond to 1, 3, 5, again forming an arithmetic progression with common difference +2.- The next second letter is 7, which corresponds to G.- Third letters: Z, Y, X correspond to 26, 25, 24, a sequence decreasing by 1 each time.- The next third letter is 23, which is W.- Combining these results, the missing group should be H (first), G (second), W (third), giving HGW. Verification / Alternative check: - Check all positions: first letters 2, 4, 6, 8; second letters 1, 3, 5, 7; third letters 26, 25, 24, 23.- Each position clearly follows its own arithmetic pattern, so the combined term HGW is fully consistent.- No other option maintains all three independent patterns at once. Why Other Options Are Wrong: - FXW and FEX do not have the correct first and second letters according to the +2 pattern.- FEY introduces a third letter Y which does not continue the -1 progression from Z to Y to X to W.- Only HGW correctly follows +2 for the first letters, +2 for the second letters, and -1 for the third letters. Common Pitfalls: Some candidates only look at the first letters and guess based on that partial pattern, ignoring the second and third letters. Others try to treat the three-letter groups as a whole without decomposing them, which makes the pattern difficult to see. The safest approach is to treat each position separately and then recombine the results. Final Answer: The correct group of letters that completes the pattern is HGW, so the correct option is HGW.

Question 4

In the alphanumerical series D-4, F-6, H-8, J-10, ?, ?, which two terms should replace the question marks to continue the pattern?

Accepted Answer

Introduction / Context: This question presents an alphanumerical series, meaning each term is made up of a letter and a number tied together by a consistent rule. You must identify the pattern in both the letter part and the number part to determine the missing entries. Such series are typical in reasoning sections of many competitive exams. Given Data / Assumptions: - The given terms are: D-4, F-6, H-8, J-10, ?, ?- Each term combines a capital letter with an even number.- We assume the letter progression and number progression each follow simple arithmetic patterns. Concept / Approach: To solve alphanumerical series, separate the two components: the letter sequence and the number sequence. Treat each as its own series, identify the pattern independently, and then pair the appropriate letter and number to form the missing terms. In many such questions, letters move in fixed steps and numbers increase by a constant amount. Step-by-Step Solution: - For letters: D, F, H, J correspond to positions 4, 6, 8, 10 in the alphabet.- The pattern is an arithmetic progression with a common difference of +2.- Therefore, the next two letters after J (10) are: 12 (L) and 14 (N).- For numbers: 4, 6, 8, 10 form another arithmetic progression with a difference of +2.- The next two numbers will be 12 and 14.- Pairing these results gives the missing terms: L-12 and N-14. Verification / Alternative check: - Check full combined series: D-4, F-6, H-8, J-10, L-12, N-14.- Letters move by +2 positions each time (D, F, H, J, L, N).- Numbers also increase by +2 each step (4, 6, 8, 10, 12, 14).- The pattern is perfectly consistent throughout the sequence. Why Other Options Are Wrong: - K-12 or K-14 would come from position 11, which does not match the +2 pattern starting from D (4).- Any combination not using L and N breaks the arithmetic sequence in the letters.- Number pairs like 12, 14 are correct, but they must be attached to the correct letter sequence.- Only L-12, N-14 preserves both the letter and number patterns simultaneously. Common Pitfalls: Candidates sometimes focus solely on the numerical part and ignore the letter logic, or vice versa. Others miscalculate alphabet positions, particularly if they do not mentally index the letters from A to Z. Writing down positions explicitly (A = 1, B = 2, ..., Z = 26) can prevent such mistakes. Final Answer: The two missing terms in the series are L-12 and N-14, so the correct option is L-12, N-14.

Question 5

In the series A2BC, ?, ABC4, A5BC, which term should replace the question mark so that the pattern in the position of the digit 2, 3, 4, 5 is maintained?

Accepted Answer

Introduction / Context: This problem uses an alphanumeric pattern involving the letters A, B, C and digits 2, 3, 4, 5 placed in different positions. The goal is to identify not only the correct digit to insert but also the exact position in which it must appear so that the overall sequence respects a hidden positional rule. Given Data / Assumptions: - The visible terms are: A2BC, ?, ABC4, A5BC.- Digits 2, 3, 4, 5 appear one by one across these terms.- The sequence suggests that both the digit value and its position in the four character pattern are important. Concept / Approach: We first list the structure of each term and track where the digit is placed. For A2BC and A5BC, the digit appears in the second position, while in ABC4 it appears at the end. This indicates that the position of the digit is not fixed and may be moving in a systematic way. We must find a placement for the digit 3 that bridges the pattern between A2BC and ABC4 logically. Step-by-Step Solution: - The set of digits involved is 2, 3, 4, 5, which should all appear exactly once.- A2BC already uses digit 2, ABC4 uses digit 4, and A5BC uses digit 5, so the missing term must use digit 3.- Consider positions: A2BC has digit at second position, ABC4 has digit at fourth position, A5BC again at second position.- A natural pattern is to let the digit move gradually across the middle positions while preserving A, B, C in the remaining places.- Placing 3 in the third position gives AB3C, which fits smoothly between A2BC and ABC4 as the digit shifts towards the end.- Hence AB3C is a consistent and systematic choice for the missing term. Verification / Alternative check: - Check that each digit 2, 3, 4, 5 appears exactly once across the four terms.- Confirm that A, B, C always occupy three of the four positions and that the digit occupies the remaining one.- The progression A2BC, AB3C, ABC4, A5BC gives a natural shifting of the digit position from earlier to later positions and back, while covering all digits. Why Other Options Are Wrong: - A3BC keeps the digit in the second position, offering no positional change between A2BC and the next term.- ABC3 places the digit at the end like ABC4, making the two middle terms too similar in structure.- A2B3C4 introduces extra digits and completely breaks the intended one-digit-per-term pattern.- Only AB3C uses digit 3 exactly once and provides a logical positional transition. Common Pitfalls: Many candidates focus only on which digit is missing and ignore the positional structure, leading them to choose any option containing 3. Some also overlook that each term should contain only one digit. Always check both which symbol is used and where it is placed in pattern-based alphanumeric series. Final Answer: The correct term that should replace the question mark is AB3C, so the correct option is AB3C.

Question 6

In the letter series JAK, KBL, LCM, MDN, ?, which three-letter group should replace the question mark to continue the pattern?

Accepted Answer

Introduction / Context: This letter series question uses three-letter groups where each position follows a simple rule. Your task is to identify patterns in the first, second, and third letters separately and then combine those patterns to find the correct missing group. Such structured patterns are common in exam series questions. Given Data / Assumptions: - The given groups are: JAK, KBL, LCM, MDN, ?- Each term consists of three capital letters.- The pattern is likely to be consistent and based on alphabet positions. Concept / Approach: The best strategy is to treat each letter position independently. Map each letter to its alphabetical index (A = 1, B = 2, ..., Z = 26) and then check how the indices change from term to term. Most such series show constant increments or decrements, making it easier to extend the pattern to find the missing term. Step-by-Step Solution: - First letters: J, K, L, M correspond to 10, 11, 12, 13.- This is a simple +1 sequence, so the next first letter should be 14, which is N.- Second letters: A, B, C, D correspond to 1, 2, 3, 4.- This is also a +1 sequence, so the next second letter should be 5, which is E.- Third letters: K, L, M, N correspond to 11, 12, 13, 14.- Continuing the +1 pattern, the next third letter is 15, which is O.- Combining these, the missing term is N (first), E (second), O (third), giving NEO. Verification / Alternative check: - Check the full extended series: JAK, KBL, LCM, MDN, NEO.- All three positions follow a +1 progression through the alphabet.- Since the logic is consistent and simple, NEO is confirmed as the correct continuation. Why Other Options Are Wrong: - MEN, NEM, OEP all violate at least one of the three positional patterns.- MEN would require the first letter to jump from M to M again, breaking the +1 rule.- NEM and OEP disrupt the clearly increasing second and third letter sequences.- Only NEO matches the +1 increment in each of the three positions. Common Pitfalls: Some test takers try to treat each three-letter block as a whole and attempt to guess the answer by visual similarity alone. Others may miscount alphabet positions or forget to check every position. Always convert letters to numbers and verify each column of letters separately for such questions. Final Answer: The correct three-letter group that completes the series is NEO, so the correct option is NEO.

Question 7

In the number series 2, 3, 7, 16, 32, ?, which number should replace the question mark so that the pattern is preserved?

Accepted Answer

Introduction / Context: This question is based on a number series where the difference between consecutive terms is not constant but follows a recognisable pattern. Identifying the correct pattern in these differences is crucial to determining the missing number and is a common type of challenge in quantitative reasoning sections. Given Data / Assumptions: - The series is: 2, 3, 7, 16, 32, ?- All terms are positive and increasing.- The pattern appears to involve changing differences rather than simple multiplication. Concept / Approach: To solve such series, first compute the differences between consecutive terms. If the differences themselves form a structured pattern, such as squares, cubes, or another arithmetic sequence, you can extend that pattern to find the next difference and consequently the next term in the original series. Step-by-Step Solution: - Calculate differences: 3 - 2 = 1, 7 - 3 = 4, 16 - 7 = 9, 32 - 16 = 16.- The difference sequence is: 1, 4, 9, 16.- These are perfect squares: 1^2, 2^2, 3^2, 4^2.- Naturally, the next difference in this pattern should be 5^2 = 25.- Add this next difference to the last known term: 32 + 25 = 57.- Therefore, the missing term in the series is 57. Verification / Alternative check: - Rebuild the series using the rule: start from 2 and add 1^2, 2^2, 3^2, 4^2, 5^2.- 2 + 1 = 3, 3 + 4 = 7, 7 + 9 = 16, 16 + 16 = 32, 32 + 25 = 57.- Every step matches the given series and yields 57 as the next term, confirming the logic. Why Other Options Are Wrong: - 49, 52, and 54 do not satisfy the pattern of adding consecutive square numbers.- Using any of these alternatives would break the neat square-difference sequence and result in inconsistent future terms.- Only 57 can be expressed as 32 plus 5^2 in line with the established rule. Common Pitfalls: One common mistake is to look for multiplication or simple constant differences and give up when none is found. Another pitfall is noticing that the differences increase but not recognising that they are perfect squares. When the series grows steadily but not explosively, always check whether the differences themselves form a classic sequence like squares or cubes. Final Answer: The number that correctly completes the series is 57, so the correct option is 57.

Question 8

In the series 9, 81, ?, 6561, 59049, which number should replace the question mark to maintain the pattern?

Accepted Answer

Introduction / Context: This number series clearly grows very rapidly, suggesting that it is based on exponentiation rather than simple addition or subtraction. Many exam questions use powers of a small integer like 2, 3, or 5 in such contexts. Recognising powers and their exponents is the key idea here. Given Data / Assumptions: - The series given is: 9, 81, ?, 6561, 59049.- All terms are large powers of some base, likely 3 or 9.- We assume the exponents increase in a simple, consistent pattern. Concept / Approach: We start by factorising each known term into prime powers. If we see a repeated base with changing exponents, we can examine how these exponents progress. Once we identify the base and the exponent sequence, inserting the missing term is straightforward, as it must follow exactly the same exponential rule. Step-by-Step Solution: - Rewrite each term as a power of 3.- 9 = 3^2, 81 = 3^4, 6561 = 3^8, 59049 = 3^10.- The exponents we see are 2, 4, ?, 8, 10.- The pattern of exponents increases by 2 each step: 2, 4, 6, 8, 10.- Therefore, the missing exponent must be 6.- 3^6 = 729.- So, the missing term in the series is 729. Verification / Alternative check: - Build the complete exponent sequence: 3^2, 3^4, 3^6, 3^8, 3^10.- This yields exactly: 9, 81, 729, 6561, 59049.- All these values fit perfectly into the original series, confirming that 729 is correct. Why Other Options Are Wrong: - 3561 and 4213 are not integer powers of 3 with exponent 6 and do not fit the exponential pattern.- If any of these replaced the missing term, the sequence of exponents would be broken and the growth would become inconsistent.- Thus, only 729 matches the established rule of powers of 3 with exponents forming 2, 4, 6, 8, 10. Common Pitfalls: Students may try to apply multiplication by a constant ratio; however, the ratio itself changes, causing confusion. Another error is not recognising familiar powers of 3 and instead attempting lengthy trial and error with arbitrary multipliers. Learning common powers of small integers up to reasonable exponents is very helpful for such questions. Final Answer: The number that correctly completes the series is 729, so the correct option is 729.

Question 9

In the number series 9, 11, 15, 17, 21, 23, ?, which number should replace the question mark so that the alternating pattern is preserved?

Accepted Answer

Introduction / Context: This series uses an alternating pattern where numbers increase in pairs. Many reasoning questions adopt such paired structures to test whether candidates can observe and extend simple but slightly disguised patterns. Identifying the structure of these pairs is the main task here. Given Data / Assumptions: - The given series is: 9, 11, 15, 17, 21, 23, ?- Terms appear to be arranged in pairs: (9,11), (15,17), (21,23).- We suspect a consistent rule for pair construction and movement between pairs. Concept / Approach: When a series appears to form natural pairs, it is useful to treat each pair as a unit and examine how those pairs are generated. In this series, each pair consists of two numbers that are very close to each other, and there is a fixed gap between the first elements of consecutive pairs. Once the pattern in the first elements is known, we simply add the constant internal difference to get the second element of the next pair. Step-by-Step Solution: - Group the terms: (9, 11), (15, 17), (21, 23).- Within each pair, the second number is the first plus 2: 9 + 2 = 11, 15 + 2 = 17, 21 + 2 = 23.- Consider the first numbers of each pair: 9, 15, 21.- Differences between these first terms: 15 - 9 = 6, 21 - 15 = 6.- So the first number of each pair increases by 6.- The next first term should therefore be 21 + 6 = 27.- Hence the next pair is (27, 29), and we only need the first missing number 27 for the series. Verification / Alternative check: - Reconstruct the logical pairs: (9, 11), (15, 17), (21, 23), (27, 29).- First elements follow: 9, 15, 21, 27 with constant difference 6.- Second elements follow: first element + 2, which matches every pair.- This confirms that 27 is the missing term in the original series. Why Other Options Are Wrong: - 29 and 30 would shift the internal or external differences and break either the pair structure or the 6-step progression.- 28 does not fit naturally into any consistent pattern of first terms increasing by 6 and internal pair difference of 2.- Only 27 preserves both the pairwise difference and the inter-pair movement. Common Pitfalls: Many candidates try to treat each term individually rather than as part of a pair and end up searching for a single-step arithmetic or geometric rule. Others might miscalculate the differences or misidentify the pair boundaries. Always look for natural groupings when you see repeated small gaps like +2 appearing regularly. Final Answer: The correct number to replace the question mark is 27, so the correct option is 27.

Question 10

In the series 1, 3, 6, 11, 18, ?, which number should replace the question mark so that the pattern continues correctly?

Accepted Answer

Introduction / Context: This number series grows moderately, suggesting an additive pattern with changing differences rather than an aggressive exponential or purely multiplicative rule. Many reasoning questions use differences based on prime numbers or similar simple sequences. Recognising the structure in these differences is the key here. Given Data / Assumptions: - The series is: 1, 3, 6, 11, 18, ?- All terms are positive integers.- The pattern appears to involve increasing additive steps. Concept / Approach: We first calculate the differences between consecutive terms. If these differences form a recognisable pattern, such as successive prime numbers or another classic sequence, we extend that pattern to find the next difference and thus the missing term. This is a very standard and efficient technique for this style of question. Step-by-Step Solution: - Compute differences: 3 - 1 = 2, 6 - 3 = 3, 11 - 6 = 5, 18 - 11 = 7.- The difference sequence is: 2, 3, 5, 7.- These numbers are the first four prime numbers in order.- The next difference should naturally be the next prime, which is 11.- Add this to the last known term: 18 + 11 = 29.- Therefore, the missing term is 29. Verification / Alternative check: - Rebuild the series from 1 using prime differences: 1 + 2 = 3, 3 + 3 = 6, 6 + 5 = 11, 11 + 7 = 18, 18 + 11 = 29.- Every step fits the pattern of adding consecutive primes: 2, 3, 5, 7, 11.- This confirms that 29 is the only correct value for the missing term. Why Other Options Are Wrong: - 27, 28, and 31 cannot be obtained by adding the next prime number 11 to 18.- Using any of these alternatives would break the clean prime difference pattern and lead to inconsistency.- Only 29 preserves the structure of consecutive prime increments. Common Pitfalls: Students may attempt to fit an arbitrary quadratic or multiplicative rule instead of checking simple difference patterns. Others may overlook that 2, 3, 5, 7 are prime numbers and miss the opportunity to extend the prime sequence. Always inspect the difference sequence for familiar number families such as primes, squares, or cubes. Final Answer: The correct number to complete the series is 29, so the correct option is 29.

Question 11

In the series 13, 27, 56, 115, ?, which number should replace the question mark so that the pattern remains consistent?

Accepted Answer

Introduction / Context: This number series grows quite rapidly, indicating that the differences between consecutive terms are themselves increasing. The question tests whether you can detect a pattern in these differences and then extend that pattern to find the missing term logically and accurately. Given Data / Assumptions: - The series is: 13, 27, 56, 115, ?- All terms are positive integers.- The pattern likely involves a rule on the differences between consecutive terms. Concept / Approach: We will compute the successive differences between the terms and check whether these differences follow a simple relation such as doubling, adding a constant, or another simple recurrence. Once we find such a rule, we can apply it to the last known difference to obtain the next difference and thus the missing term in the original series. Step-by-Step Solution: - First difference: 27 - 13 = 14.- Second difference: 56 - 27 = 29.- Third difference: 115 - 56 = 59.- The differences are: 14, 29, 59.- Observe the pattern: 14 * 2 + 1 = 29, and 29 * 2 + 1 = 59.- So each new difference is obtained by doubling the previous difference and then adding 1.- Apply this rule to get the next difference: 59 * 2 + 1 = 119.- Add this next difference to the last known term: 115 + 119 = 234.- Therefore, the missing term in the series is 234. Verification / Alternative check: - Reconstruct the series using the difference rule: start with 13, then add 14, 29, 59, 119.- 13 + 14 = 27, 27 + 29 = 56, 56 + 59 = 115, 115 + 119 = 234.- All terms match the given series and the newly found term, confirming the pattern and the answer. Why Other Options Are Wrong: - 224, 231, and 233 do not equal 115 plus 119, and none of them preserves the rule difference(n+1) = 2 * difference(n) + 1.- Choosing any of these would break the internal structure of the difference sequence and make future extensions inconsistent.- Only 234 fits perfectly with the difference pattern discovered. Common Pitfalls: A common mistake is to look only for a direct multiplicative relation between consecutive terms and miss the elegant pattern in the differences. Another pitfall is to spot that the differences are increasing but fail to test a simple recurrence like doubling plus one. Always examine difference patterns and test simple recurrences on them before concluding that no pattern exists. Final Answer: The number that correctly completes the series is 234, so the correct option is 234.

Question 12

In the number series 8, 15, 28, 53, ?, which term should replace the question mark to continue the pattern?

Accepted Answer

Introduction / Context: This series grows faster than a simple arithmetic progression but not as fast as a pure geometric progression. This often indicates that the differences between terms themselves follow a multiplicative or doubling based pattern. Identifying this pattern allows us to calculate the missing term accurately. Given Data / Assumptions: - The series is: 8, 15, 28, 53, ?- All terms are positive integers.- The differences between terms appear to be increasing. Concept / Approach: We start by calculating the differences between consecutive terms. If these differences follow a recognisable recurrence, such as doubling minus a constant, we extend that rule to find the next difference. Adding that next difference to the last known term then yields the missing number in the original series. Step-by-Step Solution: - Compute differences: 15 - 8 = 7, 28 - 15 = 13, 53 - 28 = 25.- So the differences are: 7, 13, 25.- Examine the pattern: 7 * 2 - 1 = 13, and 13 * 2 - 1 = 25.- This suggests the rule difference(n+1) = 2 * difference(n) - 1.- Apply the rule to find the next difference: 25 * 2 - 1 = 50 - 1 = 49.- Add this next difference to the last term: 53 + 49 = 102.- Therefore, the missing term is 102. Verification / Alternative check: - Reconstruct using the rule starting from first difference 7: differences become 7, 13, 25, 49.- Build the series: 8 + 7 = 15, 15 + 13 = 28, 28 + 25 = 53, 53 + 49 = 102.- These values match the given terms and the newly computed term, confirming the pattern. Why Other Options Are Wrong: - 106, 100, and 108 cannot be obtained from 53 by adding a difference that fits the recurrence difference(n+1) = 2 * difference(n) - 1.- Substituting any of these would break the coherent pattern in the differences and yield inconsistent future terms.- Only 102 aligns perfectly with the discovered rule. Common Pitfalls: Sometimes candidates attempt to find a single formula that maps term position directly to term value without first checking the much simpler difference pattern. Others miscalculate the double minus one relation and end up with incorrect intermediate differences. Carefully compute each step and always verify by reconstructing the entire series. Final Answer: The correct term that should replace the question mark is 102, so the correct option is 102.

Question 13

In the number series 19, 25, 32, 38, 45, 51, ?, which number should come next to maintain the existing pattern?

Accepted Answer

Introduction / Context: This series increases steadily with moderately sized steps. The key idea is to inspect the differences between consecutive terms and see whether these differences themselves follow a simple repeating pattern. Such alternating-difference sequences are very common in competitive exams. Given Data / Assumptions: - The series is: 19, 25, 32, 38, 45, 51, ?- All terms are positive integers increasing by small amounts.- The differences appear to alternate between two nearby values. Concept / Approach: We calculate the differences between consecutive terms and look for repetition or alternation. If the differences alternate between two constants, we simply continue that alternation to find the next difference and thus the next term. This approach quickly exposes the underlying rule in such series questions. Step-by-Step Solution: - Compute consecutive differences: 25 - 19 = 6 32 - 25 = 7 38 - 32 = 6 45 - 38 = 7 51 - 45 = 6- So the differences form the pattern: 6, 7, 6, 7, 6.- The next difference should continue this pattern, so it must be 7.- Add this difference to the last term: 51 + 7 = 58.- Therefore, the missing term is 58. Verification / Alternative check: - Rebuild the series using alternating differences 6 and 7: 19 + 6 = 25, 25 + 7 = 32, 32 + 6 = 38, 38 + 7 = 45, 45 + 6 = 51, 51 + 7 = 58.- Every term matches the original series, and the newly obtained term fits perfectly at the end. Why Other Options Are Wrong: - 59, 62, and 64 do not correspond to adding 7 to 51.- Adopting any of these options would break the neat alternating 6, 7 difference pattern.- Only 58 preserves the exact alternation structure and remains consistent with all previous terms. Common Pitfalls: Some candidates overlook the alternating nature of the differences and look for a single constant step or more complicated formula. Others miscalculate one of the differences and fail to see the 6, 7, 6, 7 pattern. Carefully computing and writing out each difference can quickly reveal such alternating structures. Final Answer: The number that should come next in the series is 58, so the correct option is 58.

Question 14

In the series 111, 107.5, 104, ?, 97, 93.5, which number should replace the question mark to preserve the pattern?

Accepted Answer

Introduction / Context: This question features a decreasing number series with fractional values. The pattern is actually very simple: a constant negative difference is applied at each step. The task is to identify this constant difference and then use it to compute the missing value in the middle of the sequence. Given Data / Assumptions: - The series is: 111, 107.5, 104, ?, 97, 93.5.- Values are decreasing but by the same amount each time.- The common difference appears to be a decimal number. Concept / Approach: We compute the difference between consecutive known terms and check whether it remains constant. If it does, we apply the same difference between 104 and the missing term, and between the missing term and 97, to maintain a perfect arithmetic progression. This straightforward approach handles both integer and decimal progressions effectively. Step-by-Step Solution: - Difference from 111 to 107.5: 111 - 107.5 = 3.5.- Difference from 107.5 to 104: 107.5 - 104 = 3.5.- So the common difference is -3.5 at each step.- Apply the same difference to find the missing term after 104.- 104 - 3.5 = 100.5.- Now check from 100.5 to 97: 100.5 - 97 = 3.5, which is consistent.- 97 - 3.5 = 93.5, which matches the last term in the series. Verification / Alternative check: - Write the full arithmetic progression: 111, 107.5, 104, 100.5, 97, 93.5.- Confirm that each step decreases by exactly 3.5.- Since the pattern is uniform and consistent, 100.5 must be the missing term. Why Other Options Are Wrong: - 100 or 99 would create differences of 4 or 5 with neighbouring terms, breaking the constant -3.5 step.- 99.5 would also produce inconsistent differences between 104 and the missing term, and between the missing term and 97.- Only 100.5 maintains a uniform difference of -3.5 throughout the series. Common Pitfalls: Some candidates miscalculate decimal differences or assume that the series must involve more complex operations. Others may attempt to use multiplication even when the changes are small and consistent. For such sequences, always test for a simple arithmetic progression first, even when the numbers are decimals. Final Answer: The correct number to fill the blank is 100.5, so the correct option is 100.5.

Question 15

In the series 28, 30, 36, 48, ?, 98, 140, which number should replace the question mark to continue the pattern?

Accepted Answer

Introduction / Context: This number series grows in a way that suggests increasing differences rather than constant steps or simple multiplication. The question tests your ability to detect a pattern in the differences and how those differences change from one step to the next, which is a common reasoning skill in aptitude exams. Given Data / Assumptions: - The series is: 28, 30, 36, 48, ?, 98, 140.- All terms are positive integers.- The differences between consecutive terms seem to grow according to a secondary pattern. Concept / Approach: We start by computing the first-level differences between consecutive terms. Then, we examine how these differences themselves change. If these second-level changes follow a predictable structure, such as consecutive even numbers, we can extend the pattern to determine the missing first-level difference and hence the missing term in the series. Step-by-Step Solution: - Compute consecutive differences: 30 - 28 = 2 36 - 30 = 6 48 - 36 = 12 ? - 48 = ? 98 - ? = ? 140 - 98 = 42- We know the first known differences are 2, 6, 12 and the last known is 42.- Observe that 2, 6, 12 can be seen as 2, 2 + 4, 2 + 4 + 6.- The sequence of differences between these differences is: 6 - 2 = 4, 12 - 6 = 6.- This suggests that the increments between differences are 4, 6, 8, 10, 12, etc.- So the next difference should be 12 + 8 = 20, then 20 + 10 = 30, and finally 30 + 12 = 42 matches the last gap.- Therefore the missing differences are 20 between 48 and the next term, and 30 between that term and 98.- Compute the missing term: 48 + 20 = 68, and 68 + 30 = 98 which matches the given series. Verification / Alternative check: - The complete difference sequence becomes 2, 6, 12, 20, 30, 42.- Differences between these are 4, 6, 8, 10, 12: a neat pattern of consecutive even numbers.- Rebuilding the series using these differences gives exactly 28, 30, 36, 48, 68, 98, 140. Why Other Options Are Wrong: - 65, 67, and 72 do not allow the differences to follow the 2, 6, 12, 20, 30, 42 pattern with second-level differences of 4, 6, 8, 10, 12.- Substituting any of these alternatives breaks the smooth progression in the differences and makes the later terms inconsistent.- Only 68 preserves the elegant double-layered pattern in the series. Common Pitfalls: Some candidates stop after noticing that the differences are 2, 6, 12 and assume some arbitrary continuation like 18 or 24 without checking second-level differences. Others miscalculate one of the intermediate differences and miss the simple even-number progression. Always go one layer deeper if the first level differences themselves are not constant. Final Answer: The number that should replace the question mark in the series is 68, so the correct option is 68.

Question 16

In the following question, select the missing number that continues the pattern in the series: 12, 15, 19, 24, 30, ?

Accepted Answer

Introduction / Context: This question is a straightforward number series problem from verbal reasoning. The aim is to identify the missing term by observing how each number in the series changes to produce the next one. Such problems check your comfort with differences between consecutive terms and your ability to spot simple arithmetic patterns quickly in examinations. Given Data / Assumptions: Series given: 12, 15, 19, 24, 30, ? Exactly one number is missing at the end of the series. The rule is expected to be simple and consistent, usually based on addition or subtraction. Concept / Approach: For most basic number series, the first step is to calculate the differences between consecutive terms. If these differences themselves form a simple pattern, such as increasing by 1 or by a fixed amount each time, then we can extend that pattern to find the missing number. This idea of working with first differences is the simplest and most effective strategy here. Step-by-Step Solution: Step 1: Find the differences between consecutive terms. 15 - 12 = 3. 19 - 15 = 4. 24 - 19 = 5. 30 - 24 = 6. Step 2: Observe the pattern in the differences: 3, 4, 5, 6. Step 3: The differences are increasing by 1 each time. The next difference in this pattern should therefore be 7. Step 4: Add this next difference to the last known term: 30 + 7 = 37. Step 5: So the missing number in the series is 37. Verification / Alternative check: Rewrite the series including the missing term: 12, 15, 19, 24, 30, 37. Now recompute the differences: 3, 4, 5, 6, 7. This clearly shows a simple chain where each difference increases by 1. There are no contradictions or irregular jumps, which confirms that 37 is fully consistent with the intended pattern of the series. Why Other Options Are Wrong: Options 38, 39, and 40 would give difference patterns 3, 4, 5, 6, 8 or 3, 4, 5, 6, 9 or 3, 4, 5, 6, 10. In all these cases, the difference sequence suddenly jumps, breaking the smooth progression of plus 1 each time. Since exam series are designed with neat regular rules, any choice that disturbs this pattern cannot be correct. Common Pitfalls: Some learners guess based on the approximate size of the next number without checking the exact pattern in the differences. Others look for unnecessary complex rules when a simple pattern is present. Always compute consecutive differences carefully and check if they form an obvious sequence before considering more complicated ideas. Final Answer: The missing number that correctly completes the series is 37.

Question 17

A series is given with one term missing. Select the correct alternative that will complete the series: 4, 9, 25, 64, 169, ?

Accepted Answer

Introduction / Context: This question involves a number series based on perfect squares. However, the interesting twist is that the bases of these squares themselves follow a well known pattern. Questions like this test your ability to recognize both square numbers and familiar sequences such as the Fibonacci series, which is common in aptitude and competitive exams. Given Data / Assumptions: Series: 4, 9, 25, 64, 169, ? Exactly one term is missing at the end. Each visible term appears to be a perfect square. Concept / Approach: First, identify whether the given numbers are perfect squares. If they are, then look at the square roots and see if those roots follow a simpler sequence. In this question, those roots form a variant of the Fibonacci sequence. Once that underlying pattern is recognised, you can square the next base term to obtain the missing number in the original series. Step-by-Step Solution: Step 1: Write each number as a square if possible. 4 = 2^2. 9 = 3^2. 25 = 5^2. 64 = 8^2. 169 = 13^2. Step 2: Collect the square roots: 2, 3, 5, 8, 13. Step 3: Notice that these roots follow a Fibonacci type rule, where each term is approximately the sum of the previous two: 2, 3, 5, 8, 13, 21, ... Step 4: The next base should therefore be 21, the next Fibonacci number after 13. Step 5: Square this base: 21^2 = 441. Verification / Alternative check: Extend the list of squares using the Fibonacci based roots: 2^2 = 4, 3^2 = 9, 5^2 = 25, 8^2 = 64, 13^2 = 169, 21^2 = 441. This exactly matches the given series and adds the missing term. There is no simpler alternative that connects all the given numbers as elegantly as this Fibonacci squared pattern, so the result is strongly validated. Why Other Options Are Wrong: 225 is 15^2 and 256 is 16^2, while 289 is 17^2. None of the bases 15, 16, or 17 fit into the Fibonacci root pattern 2, 3, 5, 8, 13, 21. Choosing any of these would break the relationship where each new base is formed from the sum of the two previous bases, which is the key idea behind this question. Common Pitfalls: Many candidates stop after noticing that the numbers are squares and then try to find a pattern directly among 4, 9, 25, 64, 169 without looking at the roots. Others may try to impose a complicated difference pattern. The more reliable strategy is to move one level down to the square roots and check whether they follow a familiar sequence like the Fibonacci series. Final Answer: The missing term in the series is 441.

Question 18

Choose the correct alternative that will continue the same pattern and replace x in the series: 6, 18, 42, 78, x.

Accepted Answer

Introduction / Context: This is a standard number series question where the differences between consecutive terms are not constant but increase in a systematic way. You are required to determine the next number in the sequence by identifying how these differences grow. Problems like this are common in reasoning sections because they test your ability to recognise simple arithmetic progressions at the level of differences rather than the original terms. Given Data / Assumptions: Series: 6, 18, 42, 78, x. Exactly one term x is missing at the end. The rule is expected to be straightforward, based on differences between terms. Concept / Approach: When the numbers increase fairly quickly and not in a fixed step, the first thing to check is the difference between consecutive terms. If those differences themselves form a simple arithmetic sequence, then you can extend that sequence to find the next difference and hence the missing term. This approach uses first differences and sometimes second differences if needed. Step-by-Step Solution: Step 1: Compute the successive differences. 18 - 6 = 12. 42 - 18 = 24. 78 - 42 = 36. Step 2: Collect these differences: 12, 24, 36. Step 3: Observe that the differences form a sequence where each step increases by 12: 12, 24, 36. Step 4: The next difference in this pattern should be 36 + 12 = 48. Step 5: Add this difference to the last known term of the original series: 78 + 48 = 126. Verification / Alternative check: Write the extended series with the found value: 6, 18, 42, 78, 126. Now recompute: 18 - 6 = 12, 42 - 18 = 24, 78 - 42 = 36, 126 - 78 = 48. The first differences 12, 24, 36, 48 clearly form an arithmetic progression with common difference 12. This symmetry strongly confirms that 126 is the correct next term. Why Other Options Are Wrong: Values like 84, 96, or 108 would produce difference sets that no longer follow the pattern of adding 12 each time. For example, if x were 96, then the last difference would be 96 - 78 = 18, which does not fit into the difference sequence 12, 24, 36. Since the question is built on a clear increasing difference pattern, any option that breaks this structure must be rejected. Common Pitfalls: One frequent mistake is to search for multiplicative relationships such as ratios between terms when a simple additive pattern is sufficient. Another is to guess based only on rough growth without checking the exact difference sequence. Always calculate and examine differences carefully, especially in series questions where numbers grow at a changing rate. Final Answer: The value of x that correctly completes the series is 126.

Question 19

Choose the correct alternative that will continue the same pattern and replace x in the series: 3, 12, 27, 48, 75, x, 147.

Accepted Answer

Introduction / Context: This number series problem is based on a simple formula involving squares of natural numbers. Each term follows a regular pattern that can be expressed as a multiple of the square of its position in the series. Recognising when numbers relate to squares or cubes is a key skill in quantitative aptitude questions. Given Data / Assumptions: Series: 3, 12, 27, 48, 75, x, 147. One term x is missing before the final given term. The pattern is likely related to squares or another familiar function of the position in the series. Concept / Approach: When terms increase at a rate that roughly follows n^2, n^3, or similar growth, it is useful to check if each term can be written in terms of those powers. Here, every term can be expressed as 3 times a perfect square. Once this pattern is confirmed, we can generate the missing term by applying the same rule to the next position in the sequence. Step-by-Step Solution: Step 1: Label the positions of the series terms: position 1 has value 3, position 2 has 12, position 3 has 27, position 4 has 48, position 5 has 75, position 6 is x, and position 7 has 147. Step 2: Express each known term in terms of its position. At position 1: 3 = 3 * 1^2. At position 2: 12 = 3 * 2^2. At position 3: 27 = 3 * 3^2. At position 4: 48 = 3 * 4^2. At position 5: 75 = 3 * 5^2. At position 7: 147 = 3 * 7^2. Step 3: The pattern is clearly term(n) = 3 * n^2. Step 4: For position 6, compute term(6) = 3 * 6^2 = 3 * 36 = 108. Verification / Alternative check: List the full series using the formula term(n) = 3 * n^2: for n = 1 to 7, we have 3, 12, 27, 48, 75, 108, 147. This exactly reproduces all the given terms and fills in the missing one. There are no inconsistencies, which confirms that the rule is correct and that the missing value must be 108. Why Other Options Are Wrong: Values 127, 112, or 85 are not equal to 3 times any perfect square. For example, 127 is not 3 * k^2 for an integer k. Substituting any of these numbers would break the neat formula that holds for all other terms in the series. Therefore these options cannot be correct under the identified pattern term(n) = 3 * n^2. Common Pitfalls: Some candidates try to work with differences between consecutive terms, which here are 9, 15, 21, 27, ... and also follow a pattern, but this can be slightly more cumbersome. Recognising the connection to squares often provides a faster route. Another common mistake is to assume a random rule based only on the first few terms without checking the entire series including the last fixed term, which is crucial here. Final Answer: The value of x that correctly completes the series is 108.

Question 20

In the following alphabet series, various terms are given with one term missing as shown by (?). Choose the missing term from the given alternatives: BF, CH, ?, HO, LT.

Accepted Answer

Introduction / Context: This question involves an alphabet series in which each term consists of two letters. You are given several terms with a missing pair in the middle. The task is to determine the missing pair by analysing the pattern in how both the first letters and the second letters move through the alphabet. Such questions assess your skill in mapping letters to positions and tracking regular jumps in value across several steps. Given Data / Assumptions: Given series of letter pairs: BF, CH, ?, HO, LT. Exactly one two letter term is missing in the third position. The English alphabet has positions A = 1, B = 2, ..., Z = 26. The pattern is expected to apply separately to the first letters and the second letters of each pair. Concept / Approach: For such series, it is best to separate the pattern for the first letters (B, C, ?, H, L) and for the second letters (F, H, ?, O, T). Convert letters into their numeric positions and examine the differences. Often, each subsequence (first letters and second letters) forms its own arithmetic progression, possibly with a different step size. The missing pair must respect both of these progressions at the same time. Step-by-Step Solution: Step 1: Consider the first letters: B, C, ?, H, L. Their positions are: B = 2, C = 3, H = 8, L = 12. Step 2: Look for a pattern. A natural sequence with these values is 2, 3, 5, 8, 12 where the missing first letter is at position 5. Step 3: Position 5 corresponds to the letter E. So the first letter of the missing pair is E. Step 4: Now consider the second letters: F, H, ?, O, T. Their positions are: F = 6, H = 8, O = 15, T = 20. Step 5: Differences: 8 - 6 = 2, 15 - 11 = 4, 20 - 15 = 5 suggests we want a progression 6, 8, 11, 15, 20 with steps +2, +3, +4, +5. Step 6: The missing second letter should therefore be position 11, which is K. Step 7: Combining both parts, the missing pair must be EK. Verification / Alternative check: Write the completed sequence using EK: BF, CH, EK, HO, LT. First letters in positions: B(2), C(3), E(5), H(8), L(12) follow increments of +1, +2, +3, +4. Second letters F(6), H(8), K(11), O(15), T(20) follow increments of +2, +3, +4, +5. This double arithmetic pattern is clean, simple, and consistent, strongly confirming EK as the correct missing term. Why Other Options Are Wrong: DN, EL, and EM do not satisfy both progressions at the same time. If we insert any of them, then either the first letters or the second letters will fail to follow a regular sequence of increasing differences. For example, using EL produces second letters F, H, L, O, T which break the pattern of differences +2, +3, +4, +5. Hence these options are inconsistent with the underlying structure of the series. Common Pitfalls: Some learners focus on letter shapes or try to guess based on partial observations without converting letters to positions. This often hides the simple arithmetic pattern. Another mistake is to treat the pair as a whole and search for complex transformations instead of separating the first and second letters into two clean subsequences. Always analyse each column of letters independently in such problems. Final Answer: The missing term that completes the alphabet series is EK.

Number Series Questions