Question 1

In the series 8, 14, 24, 40, ?, find the next term that correctly continues the numeric pattern.

Accepted Answer

Introduction / Context: This is a number series completion problem where the next term must be deduced from the pattern formed by the given numbers. The series does not grow by a constant difference, so we examine how the differences themselves change from one step to the next. Given Data / Assumptions: Series: 8, 14, 24, 40, ? All numbers are positive integers. We assume a single consistent rule that generates each term from its predecessors. Concept / Approach: The usual strategy when the differences are not constant is to compute first level differences and then second level differences. If the second level differences show a simple pattern, we treat the series as a second order arithmetic progression, which is quite common in exam questions. Step-by-Step Solution: Step 1: Compute first differences: 14 - 8 = 6, 24 - 14 = 10, 40 - 24 = 16.Step 2: The first differences are 6, 10 and 16, which are not constant.Step 3: Compute second differences: 10 - 6 = 4 and 16 - 10 = 6. We see the second differences increasing.Step 4: The increase from 4 to 6 suggests the next second difference will be 8, following a pattern that grows by 2 each time.Step 5: The next first difference is therefore 16 + 8 = 24.Step 6: Add this to the last term: 40 + 24 = 64. Verification / Alternative check: We can view the first differences directly as 6, 10, 16, 24. The increases between them are 4, 6 and then logically 8. These are themselves simple even numbers increasing by 2. Since this structure is smooth and natural, 64 is strongly supported as the next term. No other candidate maintains this precise second difference pattern. Why Other Options Are Wrong: Values such as 52, 56, 72 or 80 give rise to first or second differences that do not follow a simple numeric structure. They produce jumps that break the increasing even second differences pattern of 4, 6, 8 and so on. Only 64 keeps the differences in a clean numeric progression. Common Pitfalls: Learners sometimes stop after checking only first differences and assume there is no pattern. Many exam series are designed as second order progressions, where second differences form the regular pattern. It is also a mistake to guess based only on rough growth without calculating differences. Final Answer: The next term that correctly continues the series is 64.

Question 2

In the sequence 11, 17, 39, 85, ?, determine the next number that correctly continues the pattern.

Accepted Answer

Introduction / Context: This number series problem involves non constant differences, so it requires examining both first and second differences. The pattern is based on differences that themselves increase in a regular way, a common technique used in competitive exam series questions. Given Data / Assumptions: Series: 11, 17, 39, 85, ? All terms are whole numbers. We assume there is a single hidden rule that governs the entire series. Concept / Approach: We start by finding the difference between successive terms. If these differences do not form a constant pattern, we then look at differences of those differences. When second differences show a simple arithmetic progression, we can extend that pattern to find the missing term in the original series. Step-by-Step Solution: Step 1: Compute first differences: 17 - 11 = 6, 39 - 17 = 22, 85 - 39 = 46.Step 2: The first differences are 6, 22 and 46, which again do not form a simple sequence at first glance.Step 3: Compute second differences: 22 - 6 = 16 and 46 - 22 = 24.Step 4: The second differences 16 and 24 show a pattern: they differ by 8. It suggests that the next second difference should be 32, continuing the addition of 8.Step 5: The next first difference is then 46 + 32 = 78.Step 6: Add this to the last known term: 85 + 78 = 163. Verification / Alternative check: Write the full structure: first differences 6, 22, 46, 78 and second differences 16, 24, 32. The second differences increase steadily by 8, which is exactly what we extended. No other option, such as 133, 143, 153 or 173, produces this neat combination of first and second difference patterns. Hence 163 is uniquely consistent. Why Other Options Are Wrong: Substituting 133, 143, 153 or 173 gives first and second differences that become irregular and do not follow the observed pattern of second differences increasing by 8. These choices break the smooth growth that the series exhibits, so they must be rejected. Common Pitfalls: Many learners stop after trying only simple operations like constant addition or multiplication and then guess. For higher level series, exam setters often rely on second differences. Failing to compute them leads to confusion and incorrect answers. Final Answer: The next number that correctly continues the given series is 163.

Question 3

In the sequence 101, 98, 93, 86, 75, ?, find the next number that continues the pattern.

Accepted Answer

Introduction / Context: This series is strictly decreasing, and the drops between terms are not constant. Many such sequences are based on subtracting successive prime numbers or odd numbers. Identifying that pattern is the key to finding the next term. Given Data / Assumptions: Series: 101, 98, 93, 86, 75, ? The terms are decreasing. We assume there is a single clean rule based on subtraction. Concept / Approach: When a sequence is decreasing with irregular steps, we usually investigate whether the differences correspond to a familiar sequence such as prime numbers, odd numbers or multiples of a constant. Once we see a familiar pattern, we extend it to calculate the next difference and therefore the next term. Step-by-Step Solution: Step 1: Calculate the differences: 101 - 98 = 3, 98 - 93 = 5, 93 - 86 = 7, 86 - 75 = 11.Step 2: The differences are 3, 5, 7 and 11.Step 3: These are prime numbers, but not starting from 2. The visible primes here are 3, 5, 7 and 11.Step 4: The next prime number after 11 is 13.Step 5: Subtract 13 from the last term: 75 - 13 = 62. Verification / Alternative check: Listing the primes in order: 2, 3, 5, 7, 11, 13 and so on. The sequence uses 3, 5, 7 and 11. Even though 2 is skipped, the pattern after that is consistent, so using 13 next is natural. If we use any other subtraction value, such as 12 or 14, the pattern ceases to align with prime numbers. Why Other Options Are Wrong: Values such as 68, 71 or 73 correspond to subtracting 7, 4 or 2 from 75, which does not follow the prime sequence after 11. Only 62 is obtained by subtracting 13, the next prime after 11, so the alternatives must be rejected. Common Pitfalls: Learners sometimes look for differences that increase by a constant amount, which does not work here. Another pitfall is assuming that the series must start with the very first prime, whereas exam questions may start from a prime in the middle of the list. Focusing on the visible pattern rather than expectations is essential. Final Answer: The next term in the series, obtained by subtracting the next prime number 13 from 75, is 62.

Question 4

In the series 33, 40, 37, 44, x, determine the value of x that continues the pattern.

Accepted Answer

Introduction / Context: This question features a short numeric sequence with alternating increases and decreases. Very often such patterns have two operations applied alternately, for example adding a fixed number and then subtracting another fixed number. The task is to discover the alternating rule and use it to find x. Given Data / Assumptions: Series: 33, 40, 37, 44, x. We expect a regular pattern using simple addition or subtraction. The unknown x must keep that pattern consistent. Concept / Approach: When a series moves up and down, it is often best to examine the differences between adjacent terms and check if these differences alternate between two fixed values. Once this alternating pattern is detected, extending it to the next step becomes straightforward. Step-by-Step Solution: Step 1: Compute the differences: 40 - 33 = 7, 37 - 40 = -3, 44 - 37 = 7.Step 2: We see an alternating pattern: +7, -3, +7.Step 3: The natural continuation of this alternating rule is another -3 after the last +7.Step 4: Starting from 44, subtract 3 to get x: 44 - 3 = 41. Verification / Alternative check: Write the pattern explicitly: 33 + 7 = 40, 40 - 3 = 37, 37 + 7 = 44, 44 - 3 = 41. Every step now consistently follows the rule of adding 7 and then subtracting 3 in alternation. No other value for x maintains this simple and clear pattern. Why Other Options Are Wrong: Values like 31, 42, 39 or 45 would correspond to subtractions or additions that do not match the established alternation of +7 and -3. For example, 42 gives a difference of -2 from 44, which contradicts the required -3 step. Common Pitfalls: Some learners try to force a single uniform pattern such as always adding or always subtracting, which does not match the observed behaviour here. It is important to notice alternation, particularly in shorter series where simple alternating rules are very common. Final Answer: The value of x that correctly continues the alternating pattern is 41.

Question 5

In the series 31, 45, 35, 47, 39, x, 43, 51, 47, 53, find the value of x that maintains the pattern.

Accepted Answer

Introduction / Context: This question illustrates a series where two separate number patterns are interleaved. The odd and even positions each follow their own simple rule. To find x, we must separate these two subsequences and study them individually. Given Data / Assumptions: Series: 31, 45, 35, 47, 39, x, 43, 51, 47, 53. x appears in the 6th position. We assume that the sequence is organised into two interleaved arithmetic progressions. Concept / Approach: In interleaved series, the numbers in odd positions (1st, 3rd, 5th and so on) and even positions (2nd, 4th, 6th and so on) often form two independent arithmetic sequences. We extract these subsequences and examine their patterns separately, then recombine the results to identify the missing term. Step-by-Step Solution: Step 1: Write down the odd position terms: 31 (1st), 35 (3rd), 39 (5th), 43 (7th), 47 (9th).Step 2: Observe that 31, 35, 39, 43, 47 form an arithmetic sequence with a common difference of +4.Step 3: Now write down the even position terms: 45 (2nd), 47 (4th), x (6th), 51 (8th), 53 (10th).Step 4: The even subsequence starts 45, 47, ?, 51, 53. The differences 47 - 45 = 2 and 51 - 47 = 4 suggest a constant difference of +2 between every adjacent pair.Step 5: Continue this pattern: after 47, the next even term should be 47 + 2 = 49, and then 49 + 2 = 51, which matches the given term.Step 6: Therefore x must be 49. Verification / Alternative check: Check the two subsequences completely: odd terms 31, 35, 39, 43, 47 all differ by 4, and even terms 45, 47, 49, 51, 53 all differ by 2. This confirms that we have correctly identified the rule for both positions and that 49 is the only choice that preserves both arithmetic progressions. Why Other Options Are Wrong: Any other value for x such as 48, 36, 38 or 46 breaks the constant difference of 2 in the even subsequence. For example, if x were 48 then the difference from 47 would be 1, and from 48 to 51 would be 3, which is not consistent. Common Pitfalls: A frequent mistake is to treat the whole list as one single sequence and search for complex patterns, rather than noticing that odd and even positions behave differently. Recognising interleaving is crucial for solving many reasoning series questions efficiently. Final Answer: The value of x that maintains both interleaved arithmetic patterns is 49.

Question 6

In the number series 4, 8, 15, 25, 36, 54, one term is incorrect. Which number from the options should replace the wrong term so that the series follows a consistent pattern?

Accepted Answer

Introduction / Context: This question does not ask for the next term but instead asks for a correction to one of the existing terms. One term in the middle of the series is wrong, and we must decide which replacement value from the options produces a consistent numeric pattern throughout the series. Given Data / Assumptions: Original series: 4, 8, 15, 25, 36, 54. Exactly one term is incorrect. We must replace the wrong term with one of the given alternatives to create a regular pattern. Concept / Approach: The strategy is to look for a simple rule that links the first few terms and then see where that rule fails. Often such series are based on increasing differences that themselves follow a simple arithmetic sequence. Once we identify the intended rule, we can determine what number should occupy the incorrect position. Step-by-Step Solution: Step 1: Consider the given terms: 4, 8, 15, 25, 36, 54 and compute differences: 8 - 4 = 4, 15 - 8 = 7, 25 - 15 = 10, 36 - 25 = 11, 54 - 36 = 18.Step 2: The differences 4, 7, 10 suggest an intended pattern where each difference increases by 3: 4, 7, 10, 13, 16 and so on.Step 3: If we continue this pattern, after 25 the next difference should be 13, so the next term should be 25 + 13 = 38, not 36.Step 4: Continuing further, the next difference should be 16, giving 38 + 16 = 54, which matches the last term.Step 5: This shows that the correct series is 4, 8, 15, 25, 38, 54, and 36 is the wrong term.Step 6: Therefore the number that should replace the wrong term is 38. Verification / Alternative check: If we adopt 38 as the replacement, the full difference pattern becomes 4, 7, 10, 13, 16, which increases regularly by 3. Trying any other suggested replacement, such as 28, 30, 40 or 48, fails to produce this smooth increment pattern and leads to irregular jumps. Why Other Options Are Wrong: Replacing 36 with 28, 30, 40 or 48 results in difference sequences that are inconsistent and lack a simple formal rule. None of these choices create a steady increase of 3 in the differences, so they cannot represent the intended series. Common Pitfalls: One pitfall is to treat the last term as suspicious because it is largest, rather than carefully examining the difference pattern. Another error is to look only at a part of the series and overlook that the later terms can confirm or refute a hypothesised rule. Final Answer: The number that should replace the incorrect term in the series is 38.

Question 7

In the alphabet series CMW, HRB, ?, RBL, WGQ, BLV, choose the missing three letter group that continues the pattern.

Accepted Answer

Introduction / Context: This is an alphabetic series involving three letter groups. Each letter position appears to follow its own pattern. The key idea is to observe how each group changes from one step to the next and to deduce the transformation rule that applies to all three letters simultaneously. Given Data / Assumptions: Series: CMW, HRB, ?, RBL, WGQ, BLV. Each group consists of three letters. The missing group must fit a consistent transformation observed between neighbouring groups. Concept / Approach: An efficient approach is to treat each three letter group as a vector of letter positions. We then compare consecutive groups to see how each letter is shifted inside the alphabet. If the same positional shift is applied to all three letters, we can extend that rule to find the unknown group. Step-by-Step Solution: Step 1: Convert CMW and HRB into positions: C=3, M=13, W=23 and H=8, R=18, B=2.Step 2: Compute shifts from the first to the second group: 3 to 8 is +5, 13 to 18 is +5, 23 to 2 is +5 modulo 26.Step 3: Therefore, the transformation rule from one group to the next is adding 5 positions to each letter in the alphabet, wrapping around after Z.Step 4: Apply this rule to HRB to get the missing third group: H(8)+5=13 (M), R(18)+5=23 (W), B(2)+5=7 (G). So the missing group is MWG.Step 5: Verify the rule forward: MWG plus 5 gives RBL, and RBL plus 5 gives WGQ, and WGQ plus 5 gives BLV, all matching the given series. Verification / Alternative check: Writing out the full chain with the +5 rule shows no contradictions: CMW → HRB → MWG → RBL → WGQ → BLV. Every step obeys the same shift, so the pattern is highly consistent. Any group that does not arise from repeated +5 shifts is incompatible with the series. Why Other Options Are Wrong: Groups such as WMX, LVF, LWG or NVH do not produce a constant +5 progression between all neighbouring terms. When we attempt to apply a single uniform shift to or from these options, we quickly find that at least one letter breaks the pattern, so they cannot represent the missing group. Common Pitfalls: Some learners try to assign different rules to each letter position, which complicates the series unnecessarily. In many exam questions, a single constant shift is applied to all letters. Recognising modular arithmetic on letters is an important skill for these series. Final Answer: The three letter group that correctly completes the sequence is MWG.

Question 8

In the mixed alphabet series A, B, N, C, D, O, E, F, P, ?, ?, ?, find the three letters that should replace the question marks.

Accepted Answer

Introduction / Context: This series interleaves triples of letters. Each set of three letters appears to follow a similar pattern, and the task is to recognise how the first two letters in each triple relate to the third one. Once that pattern is clear, we can generate the next triple and thus fill in the missing letters. Given Data / Assumptions: Series: A, B, N, C, D, O, E, F, P, ?, ?, ? We can group these as triples: (A, B, N), (C, D, O), (E, F, P), (? , ?, ?). The same structural rule applies to each triple. Concept / Approach: Within each triple, the first two letters are consecutive in the alphabet, while the third letter is some fixed number of positions ahead of the second letter. Observing how far the third letter is from the second letter in each triple allows us to project the rule onto the next triple and determine the missing letters. Step-by-Step Solution: Step 1: Look at the first triple: A, B, N. Positions are A=1, B=2, N=14. The jump from B to N is 14 - 2 = 12.Step 2: Second triple: C, D, O has positions C=3, D=4, O=15. The jump from D to O is 11.Step 3: Third triple: E, F, P has positions E=5, F=6, P=16. The jump from F to P is 10.Step 4: The jumps from the second to the third letters are 12, 11 and 10, decreasing by 1 each time.Step 5: The next triple should start with G and H as consecutive letters, and the third letter should be 9 positions ahead of H.Step 6: H is letter 8, so 8 + 9 = 17, which corresponds to Q. Therefore the last triple is G, H, Q. Verification / Alternative check: Collecting the pattern, we have triples (A, B, N), (C, D, O), (E, F, P), (G, H, Q). The offsets from the second to the third letters are successively 12, 11, 10 and 9. This clean decreasing sequence confirms that the structure holds across all four triples, so G, H, Q is the only correct completion. Why Other Options Are Wrong: Triples such as J, K, L or G, H, I ignore the decreasing offset pattern and instead try to continue with simple consecutive letters. Sets such as G, H, J do not respect the specific 9 letter jump from H, and therefore break the carefully observed pattern across the triples. Common Pitfalls: A common mistake is to focus only on the consecutiveness of the first two letters and guess any letter after them, overlooking the deliberate pattern in the third letter. Exam series questions frequently encode such gradually changing offsets, so checking differences in positions is essential. Final Answer: The three letters that correctly fill the blanks are G, H, Q.

Question 9

In the pattern b w _ y z a, d s t u v _, _ o p q r e, choose the group of letters that should fill the blanks so that all three groups follow a logical pattern.

Accepted Answer

Introduction / Context: This problem deals with three groups of six letters each, where three positions are missing. The groups are aligned so that comparing letters at the same position across groups reveals a systematic pattern. Our task is to find which triple of letters completes the pattern consistently in all six positions. Given Data / Assumptions: Groups (with blanks): b w _ y z a, d s t u v _, _ o p q r e. There are three blanks: third in the first group, sixth in the second group and first in the third group. We expect an alphabetic relationship when letters from the same column are compared across the three groups. Concept / Approach: We arrange the three groups vertically by columns. For each column, we check whether there is a regular pattern such as constant steps forward or backward in the alphabet. Once we deduce the pattern for columns that are already complete, we apply it to the columns that contain blanks to find the missing letters. Step-by-Step Solution: Step 1: Write the groups in columns:Column 1: b, d, _Column 2: w, s, oColumn 3: _, t, pColumn 4: y, u, qColumn 5: z, v, rColumn 6: a, _, eStep 2: Examine Column 2: w (23), s (19), o (15). Each step is minus 4. Column 4 and Column 5 show the same pattern: y (25), u (21), q (17) and z (26), v (22), r (18) also decrease by 4 each step.Step 3: Apply this to Column 3. We have t (20) and p (16). Working backwards by 4 gives 24, which corresponds to x. So the first blank is x.Step 4: For Column 1, b (2) and d (4) increase by 2, so the third value should be 6, which is f. Thus the third group starts with f.Step 5: For Column 6, a (1) and e (5) suggest an arithmetic pattern with step 2, so the middle element must be 3, which is c.Step 6: The three blanks are therefore x (third in group one), c (sixth in group two) and f (first in group three). Verification / Alternative check: Rewriting all three groups with the filled blanks gives: b w x y z a, d s t u v c, f o p q r e. Checking every column now shows consistent arithmetic progressions in positions in the alphabet. No contradictions appear when we test all six columns together. Why Other Options Are Wrong: Other suggested triples, such as x, e, d or x, c, d, fail to preserve the strict arithmetic sequences within the columns, either breaking the constant difference of minus 4 or the plus 2 and plus 2 relationships. Only x, c, f satisfies all column wise patterns simultaneously. Common Pitfalls: Some learners only check one or two columns and neglect to verify the pattern across all six, leading to choices that satisfy partial constraints but not the full structure. It is important to ensure that a candidate triple works consistently in every relevant column. Final Answer: The letters that correctly fill the blanks are x, c, f in order.

Question 10

In the string prp qrp prr pqr qrp rpr qqr rpr qpr qrr qpr qpr, every third character from the left is replaced by numbers starting from 1. After this replacement, which symbol (letter or number) is 16th from the right?

Accepted Answer

Introduction / Context: This problem combines counting and positional reasoning in a long string of letters. After every third letter is replaced by a number, we must identify the symbol that appears at a specific position from the right. The key ideas are careful counting and understanding how the replacement rule affects positions. Given Data / Assumptions: Original sequence of letters: prp qrp prr pqr qrp rpr qqr rpr qpr qrr qpr qpr (twelve groups of three letters each). Spaces are only for readability; the sequence effectively has 36 positions. Every third character from the left (positions 3, 6, 9 and so on) is replaced by numbers starting from 1 in order. Concept / Approach: Each original letter occupies a position in a linear sequence of 36 characters. Replacing the letter at each third position with a number does not change the total number of positions; it only changes what symbol occupies those positions. We can therefore reason entirely with position indices. Once we know which position from the left corresponds to the 16th from the right, we can see whether that position is one of the replaced ones. Step-by-Step Solution: Step 1: There are twelve groups of three letters each, so the total length of the sequence is 12 × 3 = 36 symbols.Step 2: The 16th symbol from the right is the same as the (36 - 16 + 1)th symbol from the left, which is the 21st symbol.Step 3: The replacement rule covers every third position from the left: positions 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 and 36.Step 4: Position 21 is one of these replaced positions, so it contains a number rather than a letter.Step 5: The first replaced position (3rd) is numbered 1, the second (6th) is 2, and so on. Thus the number at the nth replaced position is n.Step 6: Position 21 is the 7th replaced position (since 21 = 3 × 7). Therefore the number written there is 7. Verification / Alternative check: We can list the replaced positions together with their numbers: position 3 = 1, 6 = 2, 9 = 3, 12 = 4, 15 = 5, 18 = 6, 21 = 7, 24 = 8, 27 = 9, 30 = 10, 33 = 11, 36 = 12. This clearly shows that the 21st position from the left has the number 7 and thus corresponds to the 16th position from the right. Why Other Options Are Wrong: Options q and r would only be correct if the 21st position was not one of the replaced positions, which it is. The number 6 belongs at position 18, and any other number or letter does not match the systematic numbering pattern of every third position. Common Pitfalls: A common mistake is to miscount positions from the left or to assume that double digit numbers such as 10 occupy two positions, which is not the case here. Each replacement position holds a single symbol, representing the number for that place. Another error is forgetting to convert 16th from the right into its equivalent from the left before applying the replacement rule. Final Answer: After the described replacement, the symbol that is 16th from the right is the number 7.

Question 11

In the alphabetic series CGE, RNP, FJH, OKM, IMK, __, find the next three letter group that correctly follows the pattern.

Accepted Answer

Introduction / Context: This question features an alphabetic series of three letter groups where the pattern is not immediately obvious from one group to the next. Often such sequences are made by interleaving two simpler subsequences, each with its own rule. Our goal is to uncover these subsequences and then extend them to determine the missing group. Given Data / Assumptions: Series: CGE, RNP, FJH, OKM, IMK, __. Each term is a group of three letters. The pattern may be split into odd and even positioned groups. Concept / Approach: The strategy is to separate groups at odd and even positions. The odd positioned groups (first, third and fifth) may follow one rule, while the even positioned groups (second and fourth, and then sixth) may follow another. After recognising these patterns, we use them to compute the next even positioned group. Step-by-Step Solution: Step 1: List odd position groups: 1st CGE, 3rd FJH, 5th IMK. Convert letters to positions: C=3, G=7, E=5; F=6, J=10, H=8; I=9, M=13, K=11.Step 2: Observe that from CGE to FJH each letter increases by 3 (3 to 6, 7 to 10, 5 to 8). From FJH to IMK, again each letter increases by 3 (6 to 9, 10 to 13, 8 to 11).Step 3: Thus, the odd subsequence advances by adding 3 to each letter. If we extended it further, the next odd group would be LPN, but that is not required for this question.Step 4: Now list even position groups: 2nd RNP and 4th OKM. Positions are R=18, N=14, P=16 and O=15, K=11, M=13.Step 5: From RNP to OKM each letter decreases by 3 (18 to 15, 14 to 11, 16 to 13).Step 6: Continue this rule: subtract 3 from IMK (the 5th group) to find the 6th group. I=9 becomes F=6, M=13 becomes J=10, K=11 becomes H=8, so we get FJH. However FJH is not an option, so we recognise that the even subsequence should be derived from the previous even group OKM, not from IMK.Step 7: Apply the subtraction rule to OKM instead: O=15 minus 3 = L=12, K=11 minus 3 = H=8, M=13 minus 3 = J=10, so the next even group is LHJ. Verification / Alternative check: Now the two subsequences are: odd groups CGE, FJH, IMK (each +3 per letter) and even groups RNP, OKM, LHJ (each -3 per letter). The interleaved full series becomes CGE, RNP, FJH, OKM, IMK, LHJ, which is coherent. Among the options, only LHJ fits this dual pattern. Why Other Options Are Wrong: Groups such as JHL, HJL or JKL do not arise from subtracting 3 from all letters of OKM. At least one letter in each of these alternatives breaks the consistent minus 3 progression of the even subsequence, so they cannot be the correct continuation. Common Pitfalls: One pitfall is to try to find a single rule relating each group to the next in sequence, which is very complicated here. Recognising that two subsequences are interleaved simplifies the task drastically. Another error is to change the direction of movement for some letters but not others, which destroys the regularity of the pattern. Final Answer: The three letter group that correctly continues the series is LHJ.

Question 12

In the series GMQ, JOT, MQW, ?, determine the next three letter group that continues the pattern.

Accepted Answer

Introduction / Context: This is an alphabetic series composed of three letter groups. The pattern appears to be regular, but we must carefully track how each letter in one group transforms into the corresponding letter in the next group. Once the shift pattern is identified, we can calculate the next group. Given Data / Assumptions: Series: GMQ, JOT, MQW, ? Each group consists of three letters. The transformation from one group to the next is consistent. Concept / Approach: The approach is to convert letters in each position to their numerical positions in the alphabet and then calculate the differences between corresponding letters from term to term. If we see constant shifts such as plus a fixed number, we can extend those shifts to find the missing group. Step-by-Step Solution: Step 1: Write positions: G=7, M=13, Q=17; J=10, O=15, T=20; M=13, Q=17, W=23.Step 2: From GMQ to JOT the differences are: 7 to 10 is +3, 13 to 15 is +2, 17 to 20 is +3.Step 3: From JOT to MQW the differences are: 10 to 13 is +3, 15 to 17 is +2, 20 to 23 is +3.Step 4: The pattern is therefore a repeated positional shift of +3, +2, +3 for the first, second and third letters respectively.Step 5: Apply this rule to MQW. Positions are M=13, Q=17, W=23.Step 6: Add the shifts: 13 + 3 = 16 (P), 17 + 2 = 19 (S), 23 + 3 = 26 (Z). The next group is PSZ. Verification / Alternative check: Check each group transition: GMQ → JOT → MQW → PSZ. Every step uses the same shift (3, 2, 3) in the three letter positions. Among the options, only PSZ uses letters P, S and Z, which correspond to these final positions. No other option is compatible with this exact positional shift. Why Other Options Are Wrong: Groups such as PTZ, ORY or VXY involve different shifts in at least one letter position. For instance, PTZ would require different increments from MQW that do not match the established +3, +2, +3 pattern. Hence these cannot be the correct continuation. Common Pitfalls: Some test takers may focus only on the first letters and believe the pattern is simple, then guess without verifying the other positions. It is crucial to confirm that all three letter positions follow a consistent rule across every transition in the sequence. Final Answer: The three letter group that correctly continues the given series is PSZ.

Question 13

In the series 625, 625, 600, ?, 475, 875, find the missing number that makes the sequence follow a consistent rule.

Accepted Answer

Introduction / Context: This problem presents a relatively short but non obvious number series. The pattern is not a simple arithmetic progression. Instead, it emerges when the numbers are grouped into pairs and the relationship between the pair sums is studied. Our goal is to use this structure to find the missing term. Given Data / Assumptions: Series: 625, 625, 600, ?, 475, 875. There are six numbers, which can naturally be thought of as three pairs. We assume a regular relationship among these pairs rather than individual successive differences. Concept / Approach: When a series has an even number of terms, especially six, it can be useful to group them into pairs: (first, second), (third, fourth) and (fifth, sixth). Then we examine how the sums or differences of these pairs behave. If the sums follow a simple pattern, we can deduce the missing value that restores this pattern. Step-by-Step Solution: Step 1: Form pairs from the series: (625, 625), (600, ?), (475, 875).Step 2: Compute the sums of the first and third pairs: 625 + 625 = 1250 and 475 + 875 = 1350.Step 3: Observe that these sums differ by 100: 1350 - 1250 = 100.Step 4: A natural progression for three pair sums is an arithmetic sequence: 1250, 1300, 1350, with a common difference of 50.Step 5: Therefore the middle pair should sum to 1300.Step 6: Since the third term in the original series is 600, we require 600 + ? = 1300. Thus, ? = 1300 - 600 = 700. Verification / Alternative check: With the missing term set to 700, the complete pairs become (625, 625), (600, 700) and (475, 875). Their sums are 1250, 1300 and 1350, which form a clean arithmetic progression with common difference 50. No other option yields such a simple and elegant pattern for the pair sums. Why Other Options Are Wrong: Values like 545, 675, 725 or 650 would give middle pair sums of 1145, 1275, 1325 or 1250 respectively, none of which produce an evenly spaced sequence between 1250 and 1350. Therefore these alternatives break the emerging structure and cannot be correct. Common Pitfalls: A common mistake is to search only for patterns in the single step differences between adjacent terms, which seem irregular here. Recognising that the sequence might be organised into meaningful pairs and looking at pair sums reveals the hidden regularity in this series. Final Answer: The missing number that makes the series follow a consistent pair sum pattern is 700.

Question 14

In the series 999, 990, 998, 991, 997, 992, ?, find the next number that continues the pattern.

Accepted Answer

Introduction / Context: This series alternates between decreasing and increasing values. Frequently, such patterns are created by interleaving two simple sequences, one on the odd positions and one on the even positions. Identifying these two subsequences is the key to finding the next term. Given Data / Assumptions: Series: 999, 990, 998, 991, 997, 992, ? We assume that odd and even positions follow different but simple rules. The next term is in the 7th position. Concept / Approach: We extract the numbers in odd positions and even positions separately. If each subsequence has its own constant difference pattern, then we can extend the appropriate subsequence to find the missing term in the combined series. Step-by-Step Solution: Step 1: Write the odd position terms: 1st 999, 3rd 998, 5th 997, 7th ?.Step 2: This odd subsequence clearly decreases by 1 each time: 999, 998, 997, 996.Step 3: Therefore the 7th term in the series, belonging to the odd subsequence, must be 996.Step 4: For completeness, list even position terms: 2nd 990, 4th 991, 6th 992. This subsequence increases by 1 each time, confirming a neat opposing pattern. Verification / Alternative check: Recombine the two subsequences: 999 (odd), 990 (even), 998 (odd), 991 (even), 997 (odd), 992 (even), 996 (odd). The odd positions form a strictly decreasing sequence and the even positions form a strictly increasing sequence, both by steps of 1. This confirms that 996 is the only correct continuation for the series. Why Other Options Are Wrong: Numbers like 1000 or 1001 would break the decreasing pattern in the odd positions. A value like 999 would repeat a previous odd term, and 993 belongs more naturally to the even subsequence pattern and not to the odd one at this position. Common Pitfalls: Some test takers try to see a single pattern through the entire list without separating odd and even positions, which can be confusing. Recognising that the series may be interleaving two simpler progressions simplifies the reasoning dramatically. Final Answer: The number that correctly continues the pattern is 996.

Question 15

In the series 8, 14, 26, 44, 68, (?), determine the next term that maintains the numeric pattern.

Accepted Answer

Introduction / Context: This question involves a number series where the differences between terms are not constant but show a regular progression. Recognising how these differences grow from term to term is the key to predicting the next number in the sequence. Given Data / Assumptions: Series: 8, 14, 26, 44, 68, ? All terms are positive integers. The changes between terms are expected to follow a simple increasing pattern. Concept / Approach: We first calculate the differences between consecutive terms. If these differences grow or shrink in a regular way, such as adding a constant amount, we can extrapolate that pattern to determine the next difference and hence the next term. Step-by-Step Solution: Step 1: Compute first differences: 14 - 8 = 6, 26 - 14 = 12, 44 - 26 = 18, 68 - 44 = 24.Step 2: The differences are 6, 12, 18 and 24.Step 3: Each difference increases by 6: 12 - 6 = 6, 18 - 12 = 6 and 24 - 18 = 6.Step 4: Therefore the next difference should be 24 + 6 = 30.Step 5: Add this to the last term in the series: 68 + 30 = 98. Verification / Alternative check: We can see the difference sequence explicitly as multiples of 6: 6 × 1, 6 × 2, 6 × 3 and 6 × 4. The next difference should naturally be 6 × 5 = 30. Using any other value for the difference would break this neat multiplication pattern. Thus 98 fits perfectly as the next term. Why Other Options Are Wrong: Values such as 94, 96, 102 or 112 correspond to differences of 26, 28, 34 and 44 from 68, none of which continues the multiples of 6 pattern. They therefore disrupt the observed second level structure and must be discarded. Common Pitfalls: Some learners may guess the next number based on approximate growth without explicitly computing differences, which can easily lead to wrong answers. Always computing the difference pattern is a reliable way to decode such series questions. Final Answer: The next term that maintains the pattern of increasing differences is 98.

Question 16

In the alphanumeric series B2, K12, T72, ...., find the next term that correctly follows the pattern.

Accepted Answer

Introduction / Context: This is an alphanumeric series where both the letter part and the number part follow their own patterns. To find the next term, we must treat the letters and numbers separately, identify the rule in each component and then combine the results. Given Data / Assumptions: Series: B2, K12, T72, ? Each term consists of one letter followed by a positive integer. We assume the rules for the letters and the numbers are consistent throughout the series. Concept / Approach: The approach is to first map the letters to their positions in the alphabet and inspect the jumps between them. Separately, we examine how the numeric part changes from one term to the next. After identifying these two rules, we extend both patterns simultaneously to obtain the missing term. Step-by-Step Solution: Step 1: Consider the letters: B, K and T. Positions are B=2, K=11, T=20.Step 2: Compute differences: 11 - 2 = 9 and 20 - 11 = 9. The letters move forward by 9 positions each time.Step 3: The next letter is therefore 20 + 9 = 29. Modulo 26, 29 corresponds to 3, which is the letter C.Step 4: Now consider the numbers: 2, 12 and 72.Step 5: Each number is multiplied by 6 to produce the next one: 2 × 6 = 12 and 12 × 6 = 72.Step 6: Continue this rule: 72 × 6 = 432.Step 7: Combine the letter and number parts. The next term is C432. Verification / Alternative check: Summarising the pattern, the letter advances by a constant shift of +9 (B → K → T → C), and the number is repeatedly multiplied by 6 (2 → 12 → 72 → 432). This produces a very clean and consistent structure. No other combination of letter and number among the options matches both rules at the same time. Why Other Options Are Wrong: Options such as A434, A432, C434 or D432 either have the wrong letter, breaking the +9 letter shift, or have an incorrect number that does not equal 72 × 6. Only C432 respects both the alphabetic and numeric rules simultaneously. Common Pitfalls: One common mistake is to search only for patterns in the numeric part and ignore that the letters must also follow a regular progression. Another is to assume the numbers grow by repeated addition rather than multiplication, which does not hold here. Exam questions often combine a simple alphabetic shift with a multiplicative numeric pattern. Final Answer: The next term in the alphanumeric series is C432.

Question 17

What should come in place of the question mark in the following number series: 1, 3, 24, 360, 8640, 302400, ?

Accepted Answer

Introduction / Context: This question tests your understanding of multiplicative number series where each term is obtained by multiplying the previous term with a changing factor. To solve it correctly, we must carefully identify the exact pattern in the multipliers and then extend that pattern to find the missing term. Given Data / Assumptions: - The given series is: 1, 3, 24, 360, 8640, 302400, ?- All terms are positive integers that grow rapidly.- The pattern is expected to be systematic and consistent for every step in the series. Concept / Approach: The natural way to approach this series is to look for a relation between consecutive terms using multiplication. Once we compute the ratios of consecutive terms, we can try to recognise a secondary pattern in those multipliers, such as squares, products, or a simple sequence. After identifying the pattern of multipliers, we use it to compute the next multiplier and hence the missing term. Step-by-Step Solution: - From 1 to 3: multiplier = 3 / 1 = 3.- From 3 to 24: multiplier = 24 / 3 = 8.- From 24 to 360: multiplier = 360 / 24 = 15.- From 360 to 8640: multiplier = 8640 / 360 = 24.- From 8640 to 302400: multiplier = 302400 / 8640 = 35.- So the sequence of multipliers is: 3, 8, 15, 24, 35.- Now find the pattern in multipliers: differences are 5, 7, 9, 11 which increase by 2 each time.- Thus the next difference should be 13, so the next multiplier = 35 + 13 = 48.- Therefore the missing term = 302400 * 48 = 14515200. Verification / Alternative check: - Recreate the multipliers: 3, 8, 15, 24, 35, 48.- Check the differences again: 5, 7, 9, 11, 13 which form an arithmetic progression with common difference 2.- This confirms the internal consistency of the pattern and validates the computed term 14515200. Why Other Options Are Wrong: - 14525100: Very close numerically but does not match 302400 * 48 exactly, so it breaks the exact multiplicative rule.- 154152000: This is far larger than 302400 * 48 and would require a different, unjustified multiplier.- 15425100: Again, this number cannot be expressed as 302400 multiplied by an integer that fits the multiplier pattern.- Only 14515200 is consistent with both the term-to-term multiplication and the pattern in the multipliers. Common Pitfalls: Candidates often try to guess the answer by approximate growth or rough mental multiplication, which leads to close but incorrect values. Another common error is to look only at the original terms and ignore the simpler structure hidden in the sequence of multipliers. It is also easy to miscalculate one of the products and then carry that error forward. Always compute the ratios carefully and double-check the multiplication for the final step. Final Answer: The next term in the series is 14515200, so the correct option is 14515200.

Question 18

In the number series 1, 3, 6, 10, 15, ?, which number should correctly replace the question mark to continue the pattern?

Accepted Answer

Introduction / Context: This problem checks your ability to recognise a classic increasing pattern known as triangular numbers. Such series appear frequently in aptitude tests and competitive examinations, so recognising the underlying idea quickly can save valuable time during the exam. Given Data / Assumptions: - The given series is: 1, 3, 6, 10, 15, ?- All terms are positive integers increasing steadily.- The pattern is expected to be simple and based on addition. Concept / Approach: For increasing series like this, we first examine the differences between consecutive terms. If those differences themselves follow a simple pattern, we can extend that pattern to find the missing term. In many reasoning exams, sequences like 1, 3, 6, 10, 15 represent the sums of the first few natural numbers and are called triangular numbers. Step-by-Step Solution: - Compute the differences: 3 - 1 = 2, 6 - 3 = 3, 10 - 6 = 4, 15 - 10 = 5.- The difference sequence is 2, 3, 4, 5, which clearly increases by 1 each time.- The next difference should therefore be 6.- Add this to the last known term: 15 + 6 = 21.- Hence, the missing term in the series must be 21. Verification / Alternative check: - You can view each term as the sum of the first n natural numbers.- 1 = 1, 3 = 1 + 2, 6 = 1 + 2 + 3, 10 = 1 + 2 + 3 + 4, 15 = 1 + 2 + 3 + 4 + 5.- The next term should be 1 + 2 + 3 + 4 + 5 + 6 = 21, confirming our answer. Why Other Options Are Wrong: - 20: This would break the pattern of consecutive differences and cannot be expressed as the sum of the first six natural numbers.- 22: Does not follow the difference pattern of +2, +3, +4, +5, +6.- 24: Also inconsistent with both the difference pattern and the triangular number interpretation. Common Pitfalls: A common mistake is to assume a constant difference or to miscalculate one of the intermediate sums. Some students also try to use complex formulas where a simple difference pattern is sufficient. Always check the difference sequence first, because many exam series are built directly from it. Final Answer: The missing term is 21, so the correct option is 21.

Question 19

Which number should complete the series 0, 1, 4, 15, ?, 325, 1956 so that the same pattern continues throughout?

Accepted Answer

Introduction / Context: This question involves a recursive number series where each term is generated from the previous term using multiplication and addition. Such patterns are common in higher level reasoning sections and require you to observe not only the numbers themselves but also how each new term is produced. Given Data / Assumptions: - The given series is: 0, 1, 4, 15, ?, 325, 1956.- The pattern is likely based on operations applied to the immediately preceding term.- We assume a consistent rule is applied at every step of the series. Concept / Approach: When the series grows quickly but not by fixed multiples, a good strategy is to check if each term equals the previous term multiplied by some integer and then adjusted by the same integer. That is, we test patterns like a(n+1) = a(n) * k + k where k changes in a simple way, such as 1, 2, 3, and so on. Once this structure is identified, we can extend it to find the missing value. Step-by-Step Solution: - From 0 to 1: 0 * 1 + 1 = 1.- From 1 to 4: 1 * 2 + 2 = 4.- From 4 to 15: 4 * 3 + 3 = 15.- So we see the pattern a(n+1) = a(n) * (n+1) + (n+1), starting with n = 0.- For the next term after 15, use multiplier 4: 15 * 4 + 4 = 60 + 4 = 64.- Then check the next steps: 64 * 5 + 5 = 320 + 5 = 325.- Next: 325 * 6 + 6 = 1950 + 6 = 1956, which matches the series. Verification / Alternative check: - Verify each applied step to ensure no arithmetic mistake: 0, 1, 4, 15, 64, 325, 1956.- The rule a(n+1) = a(n) * (n+1) + (n+1) holds perfectly for every transition.- This confirms that 64 is the only consistent value for the missing term. Why Other Options Are Wrong: - 60: This is 15 * 4 but without the +4 part, so it breaks the observed pattern.- 75 and 80: Neither of these can be written as 15 * 4 + 4, and they do not allow the next given terms 325 and 1956 to be generated consistently.- Only 64 maintains the series rule and matches all subsequent terms. Common Pitfalls: Students often try to use simple differences or ratios between non-consecutive terms and miss the recursive relationship. Another mistake is to notice only the multiplication and forget the addition part, leading to answers like 60 instead of 64. Always confirm your spotted rule against multiple consecutive steps, not just one or two transitions. Final Answer: The number that correctly completes the series is 64, so the correct option is 64.

Question 20

In the series 3, 5/3, 1/3, ?, -7/3, -11/3, which fraction should replace the question mark to maintain the pattern?

Accepted Answer

Introduction / Context: This problem examines your ability to work with fractions in a number series. Even though the values look complicated at first glance, they actually follow a simple arithmetic pattern when expressed with a common denominator. Recognising that structure is the key to solving the question quickly and accurately. Given Data / Assumptions: - The given series is: 3, 5/3, 1/3, ?, -7/3, -11/3.- All terms can be expressed with the same denominator to make comparison easy.- We assume a constant difference pattern, as is common in such questions. Concept / Approach: Whenever a series involves fractions, a good technique is to rewrite all terms using a common denominator. This converts fractional terms into numerators over that denominator, making it easier to observe any arithmetic progression. After finding the constant difference in this transformed form, we can return to the original fraction representation for the missing term. Step-by-Step Solution: - Express each term with denominator 3: 3 = 9/3, 5/3 = 5/3, 1/3 = 1/3.- So the series becomes: 9/3, 5/3, 1/3, ?, -7/3, -11/3.- Find the differences: (5/3 - 9/3) = -4/3, (1/3 - 5/3) = -4/3.- This suggests a constant difference of -4/3 between consecutive terms.- Apply the same difference from 1/3 to get the missing term: 1/3 - 4/3 = -3/3 = -1.- Continue to check: -1 - 4/3 = -3/3 - 4/3 = -7/3 and then -7/3 - 4/3 = -11/3. Verification / Alternative check: - The transformed series of numerators over 3 is: 9, 5, 1, -3, -7, -11.- This is an arithmetic progression with common difference -4.- Rewriting -3 as -3/3 confirms that the missing term is -1 in standard form. Why Other Options Are Wrong: - -2/3 and -4/3: These values do not maintain a constant difference of -4/3 when placed between 1/3 and -7/3.- -2: This corresponds to -6/3, which would break the arithmetic progression in the numerator sequence.- Only -1 gives a consistent arithmetic progression for all given terms in the series. Common Pitfalls: A typical mistake is to treat each fraction separately without converting to a common denominator, which hides the simple linear pattern. Another error is careless subtraction of negative fractions, leading to wrong intermediate values. Always standardise the denominators and compute differences carefully for fraction series questions. Final Answer: The fraction that correctly completes the series is -1, so the correct option is -1.

Number Series Questions