Question 1

Number series – find the wrong term (identify the outlier) Series: 8, 13, 21, 32, 47, 63, 83

Accepted Answer

Introduction / Context:You need to identify the single erroneous term in a steadily increasing series. These questions often use simple, steadily growing increments; one term will break the rule. Given Data / Assumptions: Series: 8, 13, 21, 32, 47, 63, 83. Exactly one term is incorrect. Concept / Approach:Examine first differences. For many such sequences, the differences themselves increase with a constant step. If the step is consistent except at one place, that term is the outlier. Step-by-Step Solution: Compute differences: 13−8 = 5; 21−13 = 8; 32−21 = 11; 47−32 = 15; 63−47 = 16; 83−63 = 20.A natural pattern would be to increase the difference by +3 each time: 5, 8, 11, 14, 17, 20.Following this, after 32 the next increment should be 14 (not 15), giving 32 + 14 = 46.Therefore the term 47 is inconsistent; it should have been 46 for a perfect +3-difference ladder. Verification / Alternative check:With the corrected 46, the next differences continue +3: 46→63 is +17 and 63→83 is +20, matching the intended pattern 5, 8, 11, 14, 17, 20. Why Other Options Are Wrong: 13, 21, 32, 83 are compatible with a steadily increasing difference sequence; removing any of them breaks more than one step and cannot restore a clean +3 progression. Common Pitfalls:Assuming Fibonacci-like addition without checking differences; not verifying the entire tail after a suspected correction. Final Answer:47

Question 2

Number series – find the wrong term (identify the outlier) Series: 1, 2, 4, 8, 16, 32, 64, 96

Accepted Answer

Introduction / Context:This is a powers-of-two recognition task. The series should follow a simple doubling pattern; one term does not. Given Data / Assumptions: Series: 1, 2, 4, 8, 16, 32, 64, 96. Exactly one term is wrong. Concept / Approach:Check if each term is double the previous one. Powers of two proceed as 1, 2, 4, 8, 16, 32, 64, 128, … Step-by-Step Solution: From 1 onward: ×2 gives 2 ✔, ×2 gives 4 ✔, ×2 gives 8 ✔, ×2 gives 16 ✔, ×2 gives 32 ✔, ×2 gives 64 ✔.The next should be 64×2 = 128, not 96. Therefore 96 is the outlier. Verification / Alternative check:In a pure doubling progression, any deviation breaks the exact ratio of 2. Only 96 violates this principle. Why Other Options Are Wrong: 4, 16, 32, 64 are all honest powers of two placed correctly. Common Pitfalls:Misreading 96 as 128; overlooking that every consecutive ratio must be exactly 2 for a powers-of-two run. Final Answer:96

Question 3

Number series – find the wrong term (identify the outlier) Series: 3, 4, 10, 32, 136, 685, 4116

Accepted Answer

Introduction / Context:This higher-difficulty series hides a two-part step: multiply by an increasing integer n and then add the same n. If one term breaks this rule, it is the wrong term. Given Data / Assumptions: Series: 3, 4, 10, 32, 136, 685, 4116. Assume exactly one term is incorrect. Concept / Approach:Test the rule: next = current * n + n, with n growing 1, 2, 3, 4, 5, 6, … This pattern is compact and explains rapid growth. Step-by-Step Solution: Start: 3 → 4: 31 + 1 = 4 ✔4 → 10: 42 + 2 = 10 ✔10 → (expected) with n=3: 103 + 3 = 33, but the list has 32 ✖Continuing from the corrected 33: with n=4, 334 + 4 = 132 + 4 = 136 ✔Next with n=5: 1365 + 5 = 680 + 5 = 685 ✔Next with n=6: 6856 + 6 = 4110 + 6 = 4116 ✔ Verification / Alternative check:Only the third transition fails the rule as printed. Replacing 32 by 33 restores perfect adherence to “*n + n”. Thus, 32 is the single wrong term. Why Other Options Are Wrong: 4, 10, 136, 4116 all fit exactly into the multiply-and-add-by-the-same-n rule when the series is corrected at the third place. Common Pitfalls:Trying to fit a different rule to all numbers instead of validating a simple consistent rule; ignoring that one local fix should make the entire list consistent. Final Answer:32

Question 4

Number series – find the wrong term (identify the outlier) Series: 105, 85, 60, 30, 0, -45, -90

Accepted Answer

Introduction / Context:Descending sequences frequently subtract steadily increasing steps. Your task is to detect the single number that breaks an otherwise clean pattern of subtractions. Given Data / Assumptions: Series: 105, 85, 60, 30, 0, -45, -90. Exactly one term is wrong. Concept / Approach:Check the consecutive differences; if they should grow by a fixed amount (such as +5), you can spot the misfit where a different jump occurs. Step-by-Step Solution: 105 → 85: −2085 → 60: −25 (difference magnitude grew by 5)60 → 30: −30 (grew by 5 again)Following this pattern, the next should be −35, so 30 − 35 = −5, not 0.From −5 continuing the +5 growth: −5 − 40 = −45; then −45 − 45 = −90.Therefore “0” is the incorrect term; the correct value at that position should be −5. Verification / Alternative check:Rewritten series with the corrected term: 105, 85, 60, 30, −5, −45, −90 has differences −20, −25, −30, −35, −40, −45, a perfect arithmetic progression of differences. Why Other Options Are Wrong: 105, 60, −45, −90 can all be retained when the single faulty “0” is fixed; the difference ladder becomes consistently stepwise by 5. Common Pitfalls:Stopping after noticing two identical steps (−30, −30) and calling an earlier term wrong; always project the rule forward to confirm. Final Answer:0

Question 5

Number series – find the wrong term (identify the outlier) Series: 2, 5, 10, 17, 26, 37, 50, 64

Accepted Answer

Introduction / Context:This series is built from a simple formula pattern. Spotting a single wrong value requires recognizing that each term follows the same rule relating its position to a basic function. Given Data / Assumptions: Series: 2, 5, 10, 17, 26, 37, 50, 64. Exactly one term is wrong. Concept / Approach:Test the hypothesis a(n) = n^2 + 1, a very common construct in such sequences, where n starts at 1. Step-by-Step Solution: n = 1: 1^2 + 1 = 2 ✔n = 2: 2^2 + 1 = 5 ✔n = 3: 3^2 + 1 = 10 ✔n = 4: 4^2 + 1 = 17 ✔n = 5: 5^2 + 1 = 26 ✔n = 6: 6^2 + 1 = 37 ✔n = 7: 7^2 + 1 = 50 ✔n = 8: 8^2 + 1 = 65, not 64 ✖ Verification / Alternative check:Replacing the final 64 with 65 gives a perfect match for a(n) = n^2 + 1 across all positions. No other term breaks the pattern. Why Other Options Are Wrong: 17, 26, 37, 50 all exactly equal n^2 + 1 for n = 4, 5, 6, 7 respectively; removing them would destroy the clean quadratic rule. Common Pitfalls:Assuming a difference-based rule and missing the simpler square-plus-one formula; ignoring that only the last item fails the test. Final Answer:64

Question 6

Number series – find the wrong term (identify the outlier) Series: 125, 126, 124, 127, 123, 129

Accepted Answer

Introduction / Context:This is a classic alternating-increment/decrement pattern. The rule adds and subtracts consecutive integers in turn; one number breaks the rhythm. Given Data / Assumptions: Series: 125, 126, 124, 127, 123, 129. Exactly one wrong term. Concept / Approach:Check if the series alternates between “+k” and “−(k+1)” for k = 1, 2, 3, … A standard form is: +1, −2, +3, −4, +5, −6, … Step-by-Step Solution: 125 → 126: +1 ✔126 → 124: −2 ✔124 → 127: +3 ✔127 → 123: −4 ✔Next should be +5: 123 + 5 = 128, but the list has 129 ✖ Verification / Alternative check:Continuing the pattern after the correction would require the next step to be −6. Since only one term must be wrong, 129 is the outlier (should have been 128). Why Other Options Are Wrong: 126, 124, 123 all fit the alternating +1, −2, +3, −4 pattern exactly; removing any of them ruins the clean alternation. Common Pitfalls:Trying a fixed-difference rule; ignoring that alternating increase/decrease with step sizes 1, 2, 3, 4, … is a well-used pattern in reasoning tests. Final Answer:129

Question 7

Number series (find the wrong term): 8, 14, 26, 48, 98, 194, 386

Accepted Answer

Introduction / Context:This is a number-series error-detection question. You are given a sequence and must spot the single term that breaks an otherwise consistent rule. Such questions test your ability to see hidden patterns like fixed increments, geometric growth, or patterned differences. Given Data / Assumptions: Series: 8, 14, 26, 48, 98, 194, 386. Exactly one term is incorrect. Look for a consistent pattern across all valid transitions. Concept / Approach:First check simple recurrences. The consecutive differences are key: compute each difference and see if those differences follow a rule (for instance, doubling). If a single step violates the discovered rule, that term is the outlier. Step-by-Step Solution:Compute differences: 14−8=6, 26−14=12, 48−26=22, 98−48=50, 194−98=96, 386−194=192.Notice a near-doubling pattern for the increments: starting from 6, doubling gives 6, 12, 24, 48, 96, 192.Compare with actual: 6, 12, 22, 50, 96, 192. The third and fourth increments should be 24 and 48, not 22 and 50.If the third increment were 24, the third term would be 26+? No, apply from the second term: 14 + 12 = 26 (correct), then +24 = 50 (so the next term should be 50, not 48). Thereafter +48 = 98 (which matches), +96 = 194, +192 = 386.Therefore, the lone inconsistent term is 48 (it should be 50 under the doubling-difference rule). Verification / Alternative check:Repaired series: 8, 14, 26, 50, 98, 194, 386 with differences 6, 12, 24, 48, 96, 192 (perfect doubling). Only the third term 48 → 50 correction fixes all later terms without further edits. Why Other Options Are Wrong: 14, 98, 194, 386 all fit the repaired doubling-difference structure. Common Pitfalls: Looking for a multiply-by rule and missing the clear pattern in the differences. Changing multiple terms; the task is to identify a single wrong value. Final Answer:48

Question 8

Number series (find the wrong term): 3, 10, 27, 4, 16, 64, 5, 25, 125

Accepted Answer

Introduction / Context:Error-spotting in series often uses mini-patterns that repeat. Here, numbers are grouped in triplets with a clear base–square–cube relationship. One value in the first triplet does not match the rule. Given Data / Assumptions: Series: 3, 10, 27, 4, 16, 64, 5, 25, 125. Exactly one term is wrong. Triplet idea: (n, n^2, n^3) for successive bases n. Concept / Approach:Group the terms: (3, 10, 27), (4, 16, 64), (5, 25, 125). In a correct pattern, each triplet should be base, base^2, base^3. Step-by-Step Solution:Triplet 1 expected: 3, 9, 27 (since 3^2=9 and 3^3=27).Given: 3, 10, 27 → the middle term should be 9, not 10.Triplet 2: 4, 16, 64 is correct (4^2=16, 4^3=64).Triplet 3: 5, 25, 125 is correct (5^2=25, 5^3=125). Verification / Alternative check:Replacing 10 by 9 makes each triplet perfect base–square–cube blocks, removing the sole inconsistency. Why Other Options Are Wrong: 3, 4, 27, 25 all fit their respective base, square, and cube roles in the observed pattern. Common Pitfalls: Not noticing the 3-term repeating motif and instead searching for a single-step recurrence across all nine terms. Final Answer:10

Question 9

Number series (find the wrong term): 1, 5, 9, 15, 25, 37, 49

Accepted Answer

Introduction / Context:Some series hide two interleaved patterns. Recognizing the separation into odd-position and even-position terms is critical. Here, odd positions are perfect squares of odd integers, and even positions should be even squares plus one. Given Data / Assumptions: Series: 1, 5, 9, 15, 25, 37, 49. Exactly one term is wrong. Consider splitting into two subsequences by position. Concept / Approach:Extract odd-index terms (1st, 3rd, 5th, 7th) and even-index terms (2nd, 4th, 6th). Check for recognizable patterns like perfect squares or small adjustments (+1 or −1) to squares. Step-by-Step Solution:Odd positions: 1, 9, 25, 49 → these are 1^2, 3^2, 5^2, 7^2 (perfect squares of consecutive odd numbers). Pattern is correct.Even positions: 5, 15, 37 → compare with even squares + 1: 2^2+1=5 (matches), 4^2+1=17 (expected), 6^2+1=37 (matches).Thus the fourth term 15 should be 17; it is the only mismatch. Verification / Alternative check:Corrected series: 1, 5, 9, 17, 25, 37, 49. Now both subsequences satisfy their respective rules perfectly (odd squares; even squares + 1). Why Other Options Are Wrong: 9, 25, 37, 49 all align with the detected structure; replacing any of them breaks a consistent rule that the rest obey. Common Pitfalls: Treating all steps uniformly and missing the interleaving of two simple, elegant patterns. Assuming differences must be constant or regularly increasing without considering positional rules. Final Answer:15

Question 10

Number series (find the wrong term): 4, 10, 22, 46, 96, 190, 382

Accepted Answer

Introduction / Context:This series is designed around a pattern in the differences rather than the terms themselves. Spotting a doubling rule in the increments allows us to identify the single erroneous value quickly and confidently. Given Data / Assumptions: Series: 4, 10, 22, 46, 96, 190, 382. Exactly one number is incorrect. Concept / Approach:Compute consecutive differences and check if those differences follow a clean pattern such as doubling. A single misfit in differences points to the adjacent incorrect term in the original sequence. Step-by-Step Solution:Differences: 10−4=6, 22−10=12, 46−22=24, 96−46=50, 190−96=94, 382−190=192.Expected doubling chain from 6 would be 6, 12, 24, 48, 96, 192.Compare: actual has 50 (should be 48) and 94 (should be 96). Adjusting the term that causes both errors resolves them together: if the fourth difference were 48, then the next term after 46 would be 46+48=94, not 96.Hence, 96 is the incorrect term; it should be 94 for a perfectly doubling set of increments. Verification / Alternative check:Repaired series: 4, 10, 22, 46, 94, 190, 382 with differences 6, 12, 24, 48, 96, 192 — flawless doubling. Why Other Options Are Wrong: 4, 10, 46, 382 do not break the doubling-difference rule once 96 is corrected to 94; removing them would damage an otherwise perfect pattern. Common Pitfalls: Changing a difference directly instead of identifying which term must be corrected to restore a global rule. Final Answer:96

Question 11

Number series (find the wrong term): 2, 6, 24, 96, 285, 568, 567

Accepted Answer

Introduction / Context:Many series use repeated multiplication by small integers. Here the early terms suggest a clean multiplier pattern that one middle term violates. Identifying the intended rule lets us single out the erroneous value. Given Data / Assumptions: Series: 2, 6, 24, 96, 285, 568, 567. Exactly one term is wrong. First three jumps look multiplicative. Concept / Approach:Check ratios between successive terms: 6/2=3, 24/6=4, 96/24=4. This indicates the multipliers 3, then 4, then 4 again. A natural continuation would be another simple integer multiplier next (e.g., *3 or *2). The most immediate consistency check is 96 * 3 = 288; compare with the given 285 to detect the likely misprint/error. Step-by-Step Solution:From 2 → 6 (×3), 6 → 24 (×4), 24 → 96 (×4).Continuing with a reasonable small-integer multiplier (×3), the next should be 96 × 3 = 288, but the series shows 285.Therefore 285 is the outlier; correcting it to 288 restores a smooth multiplicative pattern.Subsequent terms can then sensibly proceed (for example ×2 = 576, then −9 = 567 if a terminal tweak is intended), but the only clearly inconsistent value relative to the immediate prior step is 285. Verification / Alternative check:Local consistency check: all earlier steps are exact integer multipliers; only 96 → 285 fails that property (it is not a neat multiplication by any small integer). Replacing 285 with 288 fixes the break. Why Other Options Are Wrong: 6, 24, 96, 567 each can be reconciled with reasonable subsequent steps once 285 is corrected; none is as clearly inconsistent as 285. Common Pitfalls: Overfitting late terms; for error-spotting, prioritize the first clear violation of an emerging rule. Final Answer:285

Question 12

Number series (find the wrong term): 196, 169, 144, 121, 101

Accepted Answer

Introduction / Context:This series plainly uses perfect squares in descending order. One term breaks the sequence by not being a perfect square. Spotting the incorrect value is straightforward if you recall common squares. Given Data / Assumptions: Series: 196, 169, 144, 121, 101. Expect consecutive square numbers in reverse. Concept / Approach:Match each term to a perfect square: 14^2, 13^2, 12^2, 11^2, 10^2. The final term should be 100 (10^2), not 101. Step-by-Step Solution:196 = 14^2.169 = 13^2.144 = 12^2.121 = 11^2.Expected next = 10^2 = 100, but given value is 101 → incorrect. Verification / Alternative check:Replacing 101 with 100 yields a perfect countdown of consecutive integer squares: 14^2, 13^2, 12^2, 11^2, 10^2. Why Other Options Are Wrong: 196, 169, 144, 121 are exact squares and belong to the pattern. Common Pitfalls: Mistaking 101 as prime and overlooking that the rule is about squares, not primality. Final Answer:101

Question 13

Number series (find the wrong term): 56, 58, 62, 70, 84, 118, 182

Accepted Answer

Introduction / Context:This sequence is built from additive jumps that follow a powers-of-two pattern. One term breaks the pattern by using an incorrect increment. Detecting the intended differences is the key here. Given Data / Assumptions: Series: 56, 58, 62, 70, 84, 118, 182. Exactly one term is wrong. Concept / Approach:Compute differences and look for a recognizable sequence. Doubling increments (2, 4, 8, 16, 32, 64, …) are common and fit the early and late parts of this series well. Step-by-Step Solution:Intended differences should be: +2, +4, +8, +16, +32, +64.Apply from 56: 56→58 (+2), 58→62 (+4), 62→70 (+8), 70→86 (+16 expected), 86→118 (+32), 118→182 (+64).But the given fourth term is 84 instead of 86, so the +16 step was mistakenly taken as +14. Verification / Alternative check:After correcting 84 to 86, all later terms align perfectly with +32 and +64, confirming that a single misstep occurred at the +16 stage. Why Other Options Are Wrong: 58, 62, 118, 182 are consistent with the intended powers-of-two increments when the earlier error is fixed. Common Pitfalls: Accepting small arithmetic slips (+14 instead of +16) and then trying to force a different rule for later jumps. Final Answer:84

Question 14

Number series (find the wrong term): 1, 5, 5, 9, 7, 11, 11, 15, 12, 17

Accepted Answer

Introduction / Context:Interleaved (alternating) sequences are common in reasoning tests. Here, the even-positioned terms follow a simple repeating increment pattern, and the odd-positioned terms should mirror it. One odd-position term breaks the expected rule. Given Data / Assumptions: Series: 1, 5, 5, 9, 7, 11, 11, 15, 12, 17. Positions: odd indices = 1, 3, 5, 7, 9; even indices = 2, 4, 6, 8, 10. Exactly one term is incorrect. Concept / Approach:Split into two subsequences: Odd positions and even positions. Check if each is an arithmetic progression with a small repeating step pattern (for example, +4 then +2). Identify the first violation. Step-by-Step Solution:Even positions: 5, 9, 11, 15, 17 → increments +4, +2, +4, +2 (a neat repeat).Odd positions: 1, 5, 7, 11, 12 → intended increments should match +4, +2, +4, +2 to stay parallel: 1→5 (+4), 5→7 (+2), 7→11 (+4), 11→13 (+2 expected). The series shows 12 instead of 13.Thus, 12 is the only term that breaks the clean alternating +4, +2 motif. Verification / Alternative check:Correcting 12 to 13 yields two perfectly matched alternating-progressions across odd and even positions, confirming a single localized error. Why Other Options Are Wrong: 9, 11, 15, 17 all fit the alternating +4, +2 increments in their respective subsequences; removing any would spoil a consistent pattern. Common Pitfalls: Treating the entire list as one progression rather than two interwoven ones. Final Answer:12

Question 15

Number series (find the wrong term): 25, 36, 49, 81, 121, 169, 225

Accepted Answer

Introduction / Context:This is a squares-based series. All terms are perfect squares of odd numbers in ascending order — except one even square that slips in erroneously. Identifying it requires recognizing the odd-square pattern. Given Data / Assumptions: Series: 25, 36, 49, 81, 121, 169, 225. Exactly one term is wrong. Concept / Approach:List the square roots: 5, 6, 7, 9, 11, 13, 15. All are odd except 6. The intended pattern is consecutive odd integers squared (5^2, 7^2, 9^2, 11^2, 13^2, 15^2). Step-by-Step Solution:25 = 5^2 (odd).36 = 6^2 (even) → suspicious.49 = 7^2 (odd), 81 = 9^2 (odd), 121 = 11^2 (odd), 169 = 13^2 (odd), 225 = 15^2 (odd).Therefore, 36 is the only even square intruding in a run of odd squares. Verification / Alternative check:Removing 36 gives a clean sequence of squares of consecutive odd numbers: 5, 7, 9, 11, 13, 15. Why Other Options Are Wrong: 49, 121, 169, 225 are all odd squares; each supports the intended structure. Common Pitfalls: Assuming all squares in order, missing that the rule is specifically odd squares. Final Answer:36

Question 16

Find the incorrect term in the following number series. Series: 1, 3, 10, 21, 64, 129, 356, 777

Accepted Answer

Introduction / Context: This numeric reasoning task asks you to detect which term does not fit a hidden rule. Many exam series interleave two simpler subseries (odd and even positions). If each subseries follows a clean rule, any violation reveals the incorrect term. Given Data / Assumptions: Series: 1, 3, 10, 21, 64, 129, 356, 777 We test separation into odd-position and even-position strands. We look for a consistent linear recurrence of the form next = 6current + c. Concept / Approach: Split the list: odd positions → 1, 10, 64, 356; even positions → 3, 21, 129, 777. Check each strand for a simple multiplier-plus-constant rule. If one value breaks the pattern, that value is the wrong term. Step-by-Step Solution: Even-position strand: 3 → 21 → 129 → 777 follows next = 6current + 3 (since 63+3=21; 621+3=129; 6129+3=777). Odd-position strand: 1 → 10 → 64 should follow the analogous rule next = 6current + 4 (61+4=10; 610+4=64). Applying that rule again: 6*64 + 4 = 384 + 4 = 388. The series shows 356 instead of 388. Therefore 356 violates the governing rule. Verification / Alternative check: Replacing 356 with 388 yields two perfectly consistent strands with the same structure constants (+3 for even strand, +4 for odd strand). Why Other Options Are Wrong: 21, 129, 10 all satisfy their respective strand rules; removing any of them would break a consistent recurrence. Common Pitfalls: Trying to fit one global rule to all terms, instead of separating the interleaved subsequences. Final Answer: 356

Question 17

Find the incorrect term in the following number series. Series: 5, 10, 40, 80, 320, 550, 2560

Accepted Answer

Introduction / Context: This problem checks recognition of an alternating multiplication pattern. Detecting a simple repeat like ×2, ×4, ×2, ×4 … allows you to identify the misfit quickly. Given Data / Assumptions: Series: 5, 10, 40, 80, 320, 550, 2560 We suspect alternating multipliers. Exactly one term is wrong (the “odd one out”). Concept / Approach: Test an alternating scheme: multiply by 2, then by 4, repeating. If one term fails this scheme, it is the incorrect entry. Step-by-Step Solution: 5 × 2 = 10 ✓ 10 × 4 = 40 ✓ 40 × 2 = 80 ✓ 80 × 4 = 320 ✓ 320 × 2 = 640 (but the series shows 550 ✗) Continuing the rule would give 640 × 4 = 2560 (which matches the last term). Verification / Alternative check: Replacing 550 by 640 makes the entire sequence consistent with ×2, ×4 repetition. Why Other Options Are Wrong: 80, 320, 2560 all satisfy the alternating multiplication rule with their neighbors. Common Pitfalls: Overlooking the alternating nature and searching for a single fixed multiplier. Final Answer: 550

Question 18

Find the incorrect term in the following number series. Series: 2, 3, 4, 4, 6, 8, 9, 12, 16

Accepted Answer

Introduction / Context: The series is formed by interweaving three independent doubling chains starting from 2, 3, and 4. Identifying these strands shows which value is inconsistent. Given Data / Assumptions: Overall sequence: 2, 3, 4, 4, 6, 8, 9, 12, 16 We expect three strands: start values 2, 3, 4; each subsequent appearance of a strand doubles its previous value. Concept / Approach: Track positions modulo 3 to separate strands: S1: 2 → 4 → 8 → 16; S2: 3 → 6 → 12; S3: 4 → 8 → 16. Any term not equal to the correct doubling for its strand is wrong. Step-by-Step Solution: Positions 1, 4, 7: S1 should be 2, 4, 8; the sequence shows 2, 4, 9 (incorrect; should be 8). Positions 2, 5, 8: S2 is 3, 6, 12 (correct). Positions 3, 6, 9: S3 is 4, 8, 16 (correct). Verification / Alternative check: Replacing 9 by 8 restores perfect doubling for S1 and yields consistent triplets. Why Other Options Are Wrong: 3, 6, 12 are all correct members of strand S2 and therefore not the misfit. Common Pitfalls: Treating the entire list as one sequence instead of three interleaved doubling sequences. Final Answer: 9

Question 19

Find the incorrect term in the following number series. Series: 5, 27, 61, 122, 213, 340, 509

Accepted Answer

Introduction / Context: Many crafted series follow a cubic template like n^3 − 3. If most terms fit a simple formula and one does not, that outlier is the incorrect term. Given Data / Assumptions: Series: 5, 27, 61, 122, 213, 340, 509 We test terms against the model a(n) = k^3 − 3 for consecutive integers k. Concept / Approach: Check each term against k^3 − 3 starting with k = 4 (since 4^3 − 3 = 64 − 3 = 61, which appears). If all others match, the remaining non-matching term is wrong. Step-by-Step Solution: 61 = 4^3 − 3 122 = 5^3 − 3 213 = 6^3 − 3 340 = 7^3 − 3 509 = 8^3 − 3 But 27 = 3^3, not 3^3 − 3 (which would be 24). Therefore 27 breaks the rule. Verification / Alternative check: Replacing 27 by 24 yields a perfect run of k^3 − 3 for k = 3 to 8: 24, 61, 122, 213, 340, 509. Why Other Options Are Wrong: 61, 122, 509 all exactly equal k^3 − 3 for k = 4, 5, 8 respectively. Common Pitfalls: Assuming a single difference pattern rather than testing a direct closed-form formula. Final Answer: 27

Question 20

Find the incorrect term in the following number series. Series: 3, 7, 15, 39, 63, 127, 255, 511

Accepted Answer

Introduction / Context: A classic series uses Mersenne numbers of the form 2^n − 1. If most terms match 2^n − 1 and one does not, that term is the wrong entry. Given Data / Assumptions: Series: 3, 7, 15, 39, 63, 127, 255, 511 Target pattern: 2^2 − 1 = 3, 2^3 − 1 = 7, 2^4 − 1 = 15, 2^5 − 1 = 31, 2^6 − 1 = 63, … Concept / Approach: Compare each term with 2^n − 1 for consecutive n. Any deviation from this exact form identifies the misfit. Step-by-Step Solution: 3 = 2^2 − 1; 7 = 2^3 − 1; 15 = 2^4 − 1. Expected next is 31 = 2^5 − 1, but the series lists 39 (incorrect). Continuing: 63 = 2^6 − 1; 127 = 2^7 − 1; 255 = 2^8 − 1; 511 = 2^9 − 1. Verification / Alternative check: Replacing 39 with 31 yields a perfect run of Mersenne numbers from n = 2 to 9. Why Other Options Are Wrong: 15, 63, 127 all exactly match 2^n − 1 for n = 4, 6, 7 respectively; they are correct members. Common Pitfalls: Looking for ad-hoc multipliers instead of recognizing the well-known 2^n − 1 pattern. Final Answer: 39

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