Question 1

Number Series — Multiplicative Pattern with Increment Find the next number in the sequence: 3, 7, 23, 95, ?

Accepted Answer

Introduction / Context: Series can grow rapidly due to multiplicative rules combined with small additive increments. Identifying the correct multiplier and incremental add-on is key for quick solutions in exams. Given Data / Assumptions: Given series: 3, 7, 23, 95, ? We suspect a pattern of the form: next = current * k + c, where k and c may vary. Concept / Approach: Check transitions term by term to see if there is a systematic increase in multiplier and a small, related add-on. A common construction is multiplying by consecutive integers and then adding a steadily increasing small number. Step-by-Step Solution: 3 → 7: 3 * 2 + 1 = 77 → 23: 7 * 3 + 2 = 2323 → 95: 23 * 4 + 3 = 95Pattern: multiply by 2, 3, 4, and add 1, 2, 3 respectively.Next step should be: multiply by 5 and add 4.95 * 5 + 4 = 475 + 4 = 479 Verification / Alternative check: The sequence rule is consistent across all transitions: multiplier increases by 1 and the added constant also increases by 1. Thus, 479 follows logically. Why Other Options Are Wrong: 62, 128, 575: These do not satisfy the established rule of *5 then +4 from 95. Common Pitfalls: Assuming a constant multiplier or skipping the additive pattern. Always test a few transitions to reveal both parts of the rule. Final Answer: 479

Question 2

Number Series — Alternating Operations Using Previous Terms Determine the next number in the sequence: 6, 18, 3, 21, 7, 56, ?

Accepted Answer

Introduction / Context: Some sequences alternate between multiplication and division where the divisor can be a previous term. Identifying such interdependencies is important for complex series questions. Given Data / Assumptions: Sequence: 6, 18, 3, 21, 7, 56, ? Notice the alternating rise and fall, hinting at multiply then divide patterns. Concept / Approach: Test whether a term is obtained by multiplying the immediately previous term by some number, then the next term is obtained by dividing by an earlier term (often the term before the multiplication started). This yields a repeating structural motif. Step-by-Step Solution: 6 → 18: 6 * 3 = 1818 → 3: 18 / 6 = 3 (divide by the term two places before)3 → 21: 3 * 7 = 2121 → 7: 21 / 3 = 7 (again divide by the term two places before)7 → 56: 7 * 8 = 5656 → ?: divide by the term two places before, i.e., 56 / 7 = 8 Verification / Alternative check: The pattern is consistent: multiply by a number (3, then 7, then 8), then divide by the term that initiated that mini-pair. Hence, the next term is 8. Why Other Options Are Wrong: 9, 63, 64: These break the established multiply-then-divide-by-previous-term motif. Common Pitfalls: Trying to fit a single arithmetic or geometric rule. Look for alternating operations and relationships to earlier terms in the series, not just the immediately preceding one. Final Answer: 8

Question 3

Number Series — Missing Term among Squares of Primes Find the missing number: 4, 9, 25, ?, 121, 169, 289, 361

Accepted Answer

Introduction / Context: This series contains perfect squares, specifically of consecutive prime numbers. Recognizing prime-based square progressions is a common exam theme. Given Data / Assumptions: Numbers: 4, 9, 25, ?, 121, 169, 289, 361 Check whether each is a perfect square and identify the base numbers. Concept / Approach: Compute square roots to see if they align with consecutive primes. If so, the missing number should be the square of the prime that fits the sequence order. Step-by-Step Solution: 4 = 2^2 (prime 2)9 = 3^2 (prime 3)25 = 5^2 (prime 5)? should be 7^2 = 49 (prime 7)121 = 11^2 (prime 11)169 = 13^2 (prime 13)289 = 17^2 (prime 17)361 = 19^2 (prime 19) Verification / Alternative check: All shown terms are squares of consecutive primes: 2, 3, 5, 7, 11, 13, 17, 19. The missing fourth term must be 49 to preserve order. Why Other Options Are Wrong: 64 (8^2) and 81 (9^2) are not squares of primes; 8 and 9 are composite. 87 is not a perfect square. Common Pitfalls: Assuming numerical proximity instead of verifying the structural rule (squares of primes). Always test the roots and primality of the bases. Final Answer: 49

Question 4

Number Series — Doubling Plus Increasing Addend Find the next number in the series: 6, 13, 28, 59, ?

Accepted Answer

Introduction / Context: This series grows by approximately doubling and then adding a steadily increasing small number. Spotting the pattern in the additive term is the key. Given Data / Assumptions: Terms: 6, 13, 28, 59, ? Look for a rule like next = 2 * current + k, with k increasing by 1 each step. Concept / Approach: Verify whether each term equals twice the previous plus an increment that grows linearly by 1. This is a common construction in aptitude sequences. Step-by-Step Solution: 6 → 13: 6 * 2 + 1 = 1313 → 28: 13 * 2 + 2 = 2828 → 59: 28 * 2 + 3 = 59Therefore, next should be 59 * 2 + 4 = 118 + 4 = 122 Verification / Alternative check: The additive constants are 1, 2, 3, then 4, confirming a simple linear increase paired with doubling. Hence 122 fits exactly. Why Other Options Are Wrong: 111, 113, 114: None match the precise rule of doubling and adding 4 to 59. Common Pitfalls: Guessing based on rough doubling without checking the consistent incremental addend. Always compute term-by-term to confirm. Final Answer: 122

Question 5

Number Series — Constant Ratio (Geometric Progression) Find the next number in the sequence: 4, 12, 36, 108, ?

Accepted Answer

Introduction / Context: Here the growth is multiplicative with a constant ratio, a hallmark of a geometric progression. Identifying the multiplier gives the next term immediately. Given Data / Assumptions: Series: 4, 12, 36, 108, ? Check the ratio between consecutive terms. Concept / Approach: In a geometric progression, each term equals the previous term multiplied by a constant r. Determine r and apply once more to find the missing term. Step-by-Step Solution: 12 / 4 = 336 / 12 = 3108 / 36 = 3Common ratio r = 3Next term = 108 * 3 = 324 Verification / Alternative check: The ratio remains constant at 3 across all visible steps. Extending once yields 324, consistent with the pattern. Why Other Options Are Wrong: 144, 216, 304: These are not equal to 108 * 3 and thus break the geometric rule. Common Pitfalls: Mistaking additive patterns for multiplicative ones. Always check both differences and ratios in fast sequence analysis. Final Answer: 324

Question 6

Arithmetic Progression — Find the Term Position In the arithmetic sequence 5, 8, 11, 14, ... which term equals 320?

Accepted Answer

Introduction / Context: Finding the position of a target value in an arithmetic progression (AP) is a standard problem. The AP formula connects term number, first term, and common difference. Given Data / Assumptions: AP: 5, 8, 11, 14, ... First term a1 = 5 Common difference d = 3 Target value T = 320 Concept / Approach: Use the nth-term formula for AP: a_n = a1 + (n − 1) * d. Solve for n when a_n = 320. Step-by-Step Solution: a_n = a1 + (n − 1) * d320 = 5 + (n − 1) * 3320 − 5 = (n − 1) * 3315 = (n − 1) * 3n − 1 = 315 / 3 = 105n = 105 + 1 = 106 Verification / Alternative check: Compute the 106th term directly: a_106 = 5 + 105 * 3 = 5 + 315 = 320. Perfect match. Why Other Options Are Wrong: 104th, 105th, 64th: Substituting these n values into the AP formula does not yield 320. Common Pitfalls: Arithmetic slips when isolating n. Always rearrange carefully and check with back-substitution. Final Answer: 106th

Question 7

Patterned Series — Alternating Odd Increments and Decrements Find the missing term: 8, 9, 8, 7, 10, 9, 6, 11, 10, ?, 12

Accepted Answer

Introduction / Context: This series weaves two alternating move types: small decrements and larger positive jumps that grow by odd numbers. Recognizing the repeating pattern of +odd and −odd steps unlocks the missing term quickly. Given Data / Assumptions: Series: 8, 9, 8, 7, 10, 9, 6, 11, 10, ?, 12 Observe alternating local increases and decreases. Concept / Approach: Track the changes between successive terms. You will see a repeating structure: small −1 or larger −odd, followed by an increasing +odd (3, 5, 7, ...). The missing value sits just before the final +7 step that reaches 12. Step-by-Step Solution: 8 → 9: +19 → 8: −18 → 7: −17 → 10: +310 → 9: −19 → 6: −36 → 11: +511 → 10: −110 → ?: −5? → 12: +7Solving back: since ? → 12 is +7, ? = 12 − 7 = 5 Verification / Alternative check: The negative steps grow as −1, −1, −3, −1, −5 and the positive jumps grow as +3, +5, +7. This consistent alternation confirms 5 before the final +7. Why Other Options Are Wrong: 7, 8, 11: None allow a +7 step to reach 12 while preserving the established −5 decrement before it. Common Pitfalls: Looking for two independent interleaved sequences only by position. Here, direct consecutive differences reveal the intended pattern more transparently. Final Answer: 5

Question 8

Number Series — Double and Add One Pattern Find the missing term: 3, 7, 15, ?, 63, 127

Accepted Answer

Introduction / Context: This is a rapidly growing series governed by the simple rule: multiply by 2, then add 1. Such patterns appear frequently in aptitude tests due to their clarity and speed of computation. Given Data / Assumptions: Series: 3, 7, 15, ?, 63, 127 Look for consistent multiplicative growth with a small additive constant. Concept / Approach: Test whether each step follows the same operation: next = current * 2 + 1. If confirmed, apply it to the missing position. Step-by-Step Solution: 3 * 2 + 1 = 77 * 2 + 1 = 15Therefore missing term = 15 * 2 + 1 = 31Check forward: 31 * 2 + 1 = 6363 * 2 + 1 = 127 Verification / Alternative check: All visible transitions obey the same rule consistently, so 31 is uniquely determined by the pattern. Why Other Options Are Wrong: 30, 47, 52: Substituting any of these breaks one or more steps of the rule when continued forward. Common Pitfalls: Misreading the pattern as +4, +8, +16, etc. Always test multiplicative rules directly before exploring changing differences in such fast-growing sequences. Final Answer: 31

Question 9

Number Series — Multiply by 3 and Subtract 2 Rule Find the missing number in the sequence: 4, 10, ?, 82, 244, 730

Accepted Answer

Introduction / Context: Some sequences use a fixed two-step operation: multiply by a constant and then add or subtract a small constant. Spotting these paired operations yields quick answers. Given Data / Assumptions: Sequence: 4, 10, ?, 82, 244, 730 We suspect a repeated operation of the form: next = current * 3 − 2. Concept / Approach: Verify the rule between known adjacent terms. If 82 = 28 * 3 − 2 and 244 = 82 * 3 − 2, then the missing term before 82 should be 28, and the whole sequence stays consistent. Step-by-Step Solution: Check initial step: 4 * 3 − 2 = 12 − 2 = 10 ✔Find the missing term x: x * 3 − 2 = 82 ⇒ x * 3 = 84 ⇒ x = 28Continue: 82 * 3 − 2 = 246 − 2 = 244 ✔Next: 244 * 3 − 2 = 732 − 2 = 730 ✔ Verification / Alternative check: All transitions align perfectly with ‘‘multiply by 3 then subtract 2’’. Hence, the only value that preserves the rule at the missing position is 28. Why Other Options Are Wrong: 24, 77, 218: Substituting any of these will not yield 82 after applying *3 − 2. Common Pitfalls: Trying additive differences in strongly multiplicative growth sequences. Always test a simple multiply-then-adjust rule first in such contexts. Final Answer: 28

Question 10

Number series reasoning: 1, 5, 13, 25, 41, ? — identify the next term by analyzing the pattern in successive differences, keeping the arithmetic logic consistent throughout.

Accepted Answer

Introduction / Context: This problem assesses recognition of patterns in an increasing number series. Many aptitude series rely on observing first differences (or even second differences) to uncover a simple arithmetic rule. Here we inspect how much each term grows from the previous one and extrapolate. Given Data / Assumptions: Sequence terms provided: 1, 5, 13, 25, 41, ? We assume a consistent arithmetic rule governs growth. The next term must follow the same rule as earlier increments. Concept / Approach: Compute the first differences and look for a recognizable pattern. A common structure is that the differences themselves progress regularly (often by a fixed increment). Once the rule is identified, extend it to find the next difference and, hence, the next term. Step-by-Step Solution: Differences: 5 − 1 = 4; 13 − 5 = 8; 25 − 13 = 12; 41 − 25 = 16.We get 4, 8, 12, 16 — a simple arithmetic progression with common difference 4.Next difference = 16 + 4 = 20.Next term = 41 + 20 = 61. Verification / Alternative check: The rule “add multiples of 4” fits all known steps: +4, +8, +12, +16, so the next must be +20, producing 61. No contradictions arise. Why Other Options Are Wrong: 51, 57, 63 would require differences of 10, 16, or 22 respectively, which break the clear +4 step-up pattern in the first differences. Common Pitfalls: Jumping to a more complex pattern (squares, cubes) without first checking the simplest possibility of uniform growth in differences. Always compute first differences before higher-order checks. Final Answer: 61

Question 11

Decreasing number series analysis: 325, 259, 204, 160, 127, 105, ? — determine the next value by inspecting the changing subtractions between adjacent terms.

Accepted Answer

Introduction / Context: This decreasing series tests your ability to spot a clean pattern in successive subtractions. Many such sequences reduce by steadily shrinking gaps, often by a fixed amount each step. Given Data / Assumptions: Sequence: 325, 259, 204, 160, 127, 105, ? We expect a consistent rule in the differences. Concept / Approach: Compute the differences term-by-term and observe how the subtraction amount changes. If the “step-down” itself follows a simple pattern, extend that to predict the next reduction and, thus, the next term. Step-by-Step Solution: Differences: 325 − 259 = 66; 259 − 204 = 55; 204 − 160 = 44; 160 − 127 = 33; 127 − 105 = 22.The subtractions form: 66, 55, 44, 33, 22 — a pattern decreasing by 11 each time.Next subtraction = 22 − 11 = 11.Next term = 105 − 11 = 94. Verification / Alternative check: Following the “reduce by 11” rule backward and forward keeps the pattern consistent, confirming 94. Why Other Options Are Wrong: 96, 98, 100 would correspond to subtractions of 9, 7, or 5 from 105, which break the steady minus-11 pattern. Common Pitfalls: Trying to apply ratios or alternating rules before checking a straightforward arithmetic progression in the differences. Always test the simplest hypothesis first. Final Answer: 94

Question 12

Find the next term in the pattern: 4, 7, 12, 19, 28, ? — use first differences to maintain the sequence’s internal arithmetic consistency.

Accepted Answer

Introduction / Context: This classic “increasing differences” series often grows by consecutive odd numbers. Identifying that structure lets you extend the series cleanly. Given Data / Assumptions: Terms: 4, 7, 12, 19, 28, ? We expect a steady progression in differences, likely simple odd increments. Concept / Approach: Compute first differences. If they form a recognizable arithmetic sequence, apply the next difference to obtain the next term. Step-by-Step Solution: Differences: 7 − 4 = 3; 12 − 7 = 5; 19 − 12 = 7; 28 − 19 = 9.The differences are 3, 5, 7, 9 — consecutive odd numbers.Next difference = 11.Next term = 28 + 11 = 39. Verification / Alternative check: All gaps are odd and increase by 2 each time; continuing with +11 yields a coherent continuation. Why Other Options Are Wrong: 30 or 36 would require smaller differences (2 or 8) that break the odd-number progression. 49 would need a jump of +21, skipping the +11 step entirely. Common Pitfalls: Assuming multiplicative patterns too early. With short series, first differences provide the most reliable initial test. Final Answer: 39

Question 13

Insert the missing number in 5760, 960, ?, 48, 16, 8 — observe a systematic division pattern from term to term.

Accepted Answer

Introduction / Context: This is a division-based series. Many such puzzles progressively divide by descending integers or a clear sequence of divisors. Identifying the divisor sequence reveals the missing value. Given Data / Assumptions: Known terms: 5760 → 960 → ? → 48 → 16 → 8. We assume each step uses a consistent divisor pattern that fits all transitions. Concept / Approach: Check divisions between adjacent known terms to infer the divisor sequence. Apply the same divisors to fill in the blank term. Step-by-Step Solution: 5760 ÷ 6 = 960 (fits the first step).If we continue dividing by descending integers: ÷5, ÷4, ÷3, ÷2.Unknown term = 960 ÷ 5 = 192.Check forward: 192 ÷ 4 = 48; 48 ÷ 3 = 16; 16 ÷ 2 = 8. All transitions match perfectly. Verification / Alternative check: Any other divisor sequence would break at least one of the later divisions. The chain ÷6, ÷5, ÷4, ÷3, ÷2 is uniquely consistent. Why Other Options Are Wrong: 120, 160, 240 do not preserve the required later divisions to 48, 16, and 8 when back-checked. Common Pitfalls: Trying alternating multiplication/division when a simple descending division sequence fits all known links neatly. Final Answer: 192

Question 14

Complete the mixed-step series: 45, 54, 47, ?, 49, 56, 51, 57, 53 — identify the alternating increase/decrease pattern to find the missing term.

Accepted Answer

Introduction / Context: This series alternates between increases and decreases with changing step sizes. Recognizing the two interleaved operations (add, then subtract) with a controlled change in the step values is key. Given Data / Assumptions: Series: 45, 54, 47, ?, 49, 56, 51, 57, 53. Observed alternating pattern: + then − then + then − … Concept / Approach: Write consecutive differences and look for a secondary pattern in the step sizes. In many puzzles, the “add” steps decrease gradually, while the “subtract” steps also change by a fixed rule. Step-by-Step Solution: 45 → 54 = +9; 54 → 47 = −7; Next should be +8 (one less than +9), then −6 (one less than −7), then +7, −5, +6, −4 …Apply +8 to 47: 47 + 8 = 55 (fills the blank).Check continuity: 55 − 6 = 49; 49 + 7 = 56; 56 − 5 = 51; 51 + 6 = 57; 57 − 4 = 53. The pattern holds. Verification / Alternative check: The symmetric step reductions (+9, +8, +7, +6 … and −7, −6, −5, −4 …) remain consistent across the entire sequence. Why Other Options Are Wrong: 48 or 50 would break the required next difference of +8 and derail subsequent terms. “None of these” is invalid because 55 cleanly preserves the pattern. Common Pitfalls: Treating the series as one uniform arithmetic progression rather than alternating add/subtract with gradually changing step sizes. Final Answer: 55

Question 15

Extend the series: 3, 8, 13, 24, 41, ? — detect the evolving jump sizes and project the next logical increment.

Accepted Answer

Introduction / Context: This rising sequence uses non-uniform differences that themselves grow in a recognizable way. Such constructions often increase by “larger and larger” steps that nonetheless follow a secondary trend you can extend. Given Data / Assumptions: Sequence: 3, 8, 13, 24, 41, ? We focus on first differences to see the step pattern. Concept / Approach: List the differences and analyze how they evolve. Here the step sizes accelerate in a controlled manner that can be continued to predict the next term reliably. Step-by-Step Solution: Differences: 8 − 3 = 5; 13 − 8 = 5; 24 − 13 = 11; 41 − 24 = 17.The steps grow: 5, 5, 11, 17. The increase from 5→11 is +6; from 11→17 is +6 again.Maintaining this increase suggests the next step grows by +12 overall from the earlier stable 5 (i.e., 5 + 12 = 17) and then another +12 to reach 29.Next difference ≈ 29; Next term = 41 + 29 = 70. Verification / Alternative check: Projecting the “difference increments” shows a repeating growth behavior (rising by 6, then again by 6), so picking +29 as the next jump produces a smooth acceleration consistent with prior jumps. Why Other Options Are Wrong: 75, 80, 85 would require next jumps of 34, 39, or 44, which exceed the inferred step evolution and break the observed growth rhythm. Common Pitfalls: Forcing a constant-difference or ratio rule when the series is built from an evolving difference pattern. Always check how the differences themselves change. Final Answer: 70

Question 16

Fill the next term: 10, 14, 26, 42, 70, ? — notice that the “added amounts” follow their own Fibonacci-like sub-sequence.

Accepted Answer

Introduction / Context: This sequence grows by adding amounts that themselves form a recursive pattern. Recognizing and extending that auxiliary pattern yields the next main term. Given Data / Assumptions: Main series: 10, 14, 26, 42, 70, ? Let the added amounts be denoted by d1, d2, d3, … Concept / Approach: Compute first differences and inspect whether those differences are generated by a secondary recurrence (for example, each difference equals the sum of the previous two). This is common in puzzle sequences. Step-by-Step Solution: Differences: 14 − 10 = 4 (d1); 26 − 14 = 12 (d2); 42 − 26 = 16 (d3); 70 − 42 = 28 (d4).Observe: d3 = d1 + d2 = 4 + 12 = 16; d4 = d2 + d3 = 12 + 16 = 28.Next difference d5 = d3 + d4 = 16 + 28 = 44.Next term = 70 + 44 = 114. Verification / Alternative check: The “differences” follow a Fibonacci-like rule starting from 4 and 12. Projecting one more step preserves the structure and gives 114 for the main series. Why Other Options Are Wrong: 100, 102, 106 require differences of 30, 32, or 36 respectively, which do not equal the sum of the previous two differences (16 and 28). Common Pitfalls: Ignoring that sometimes the differences, not the original terms, carry the key recurrence. Always test the first-difference sequence for structure. Final Answer: 114

Question 17

Determine the next term: 10, 18, 28, 40, 54, 70, ? — identify the steadily growing even-number differences and extend the pattern.

Accepted Answer

Introduction / Context: Many series grow by adding consecutively larger even numbers. Detecting that arithmetic progression within the differences yields the next term effortlessly. Given Data / Assumptions: Series: 10, 18, 28, 40, 54, 70, ? We will analyze the first differences. Concept / Approach: Compute step-by-step increases and look for a simple pattern, such as an arithmetic progression in the differences. Then apply the next difference to the last term. Step-by-Step Solution: Differences: 18 − 10 = 8; 28 − 18 = 10; 40 − 28 = 12; 54 − 40 = 14; 70 − 54 = 16.The differences are even numbers increasing by 2 each time: 8, 10, 12, 14, 16.Next difference = 18.Next term = 70 + 18 = 88. Verification / Alternative check: Extending the even-number progression maintains consistency; any other next term would break the +2 step in the differences. Why Other Options Are Wrong: 85, 86, 87 correspond to differences 15, 16, 17 from 70, which break the clear +2 even-number pattern. Common Pitfalls: Mistaking the pattern for multiplication or squares. The plain even-increment rule is both sufficient and consistent here. Final Answer: 88

Question 18

Compute the next value: 8, 28, 116, 584, ? — detect the repeated “multiply and then add a constant” rule to continue the sequence correctly.

Accepted Answer

Introduction / Context: This series is built by multiplying by an increasing integer and then adding a fixed constant. Recognizing that two-step pattern (multiply, then add) provides a direct path to the next term. Given Data / Assumptions: Sequence: 8 → 28 → 116 → 584 → ? We suspect: multiply by n, then add a fixed small number. Concept / Approach: Check consecutive ratios to see the approximate multiplier, then verify whether a small constant (e.g., +4) is added. Confirm across steps; if consistent, apply the next multiplier and the same addend. Step-by-Step Solution: 8 * 3 + 4 = 28.28 * 4 + 4 = 116.116 * 5 + 4 = 584.Thus pattern: multiply by 3, 4, 5, then add 4. Next multiplier is 6.Next term = 584 * 6 + 4 = 3504 + 4 = 3508. Verification / Alternative check: No other simple constant addend fits all prior links. The increasing multipliers (3, 4, 5, 6) plus a constant +4 produce exact matches every time. Why Other Options Are Wrong: 1752, 3502, 3504 do not result from the required “×6 then +4” step. Common Pitfalls: Attempting to use only multiplication without checking for a small additive constant, which is a frequent twist in series puzzles. Final Answer: 3508

Question 19

Identify the odd term out from the list: 121, 143, 165, 186, 209 — use divisibility structure and factor patterns to choose the exception.

Accepted Answer

Introduction / Context: Odd-one-out questions often rely on a hidden common property shared by most terms, with one exception. Factorization and divisibility checks are effective first steps. Given Data / Assumptions: Candidates: 121, 143, 165, 186, 209. We look for a unifying numeric property (e.g., perfect power, common factor). Concept / Approach: Test divisibility by a distinctive prime (such as 11) or identify special forms (like squares). Spot the majority pattern and isolate the outlier. Step-by-Step Solution: 121 = 11 × 11 (multiple of 11).143 = 11 × 13 (multiple of 11).165 = 11 × 15 (multiple of 11).209 = 11 × 19 (multiple of 11).186 ÷ 11 = 16.909… (not an integer), so 186 is not a multiple of 11. Verification / Alternative check: Four of the five terms are exact multiples of 11; only 186 fails this test, confirming it as the odd one out. Why Other Options Are Wrong: 143, 165, 209 all share the “multiple of 11” property; they are not exceptions. Common Pitfalls: Overcomplicating the search (e.g., summing digits or using advanced properties) when a simple prime-divisibility check reveals the pattern quickly. Final Answer: 186

Question 20

Number series – find the wrong term (identify the outlier) Series: 6, 15, 35, 77, 165, 221

Accepted Answer

Introduction / Context: This aptitude problem asks you to detect the single wrong term (outlier) in a numeric series. Such questions test recognition of a hidden rule (often multiplicative or additive patterns) and the ability to verify each term consistently. Given Data / Assumptions: Series shown: 6, 15, 35, 77, 165, 221. Exactly one term is incorrect. We must infer the intended rule and spot the inconsistent term. Concept / Approach: Look for a recurring operation. A common pattern is “double the previous term and add consecutive odd numbers”. We test whether each transition follows: next = previous * 2 + an odd number that increases by 2 each time (… +3, +5, +7, +9, +11, …). Step-by-Step Solution: 6 → 15: 62 + 3 = 12 + 3 = 15 ✔15 → 35: 152 + 5 = 30 + 5 = 35 ✔35 → 77: 352 + 7 = 70 + 7 = 77 ✔77 → 165: 772 + 11 = 154 + 11 = 165 ✔ (note the odd additions are 3, 5, 7, 9, 11; a +9 step is implicitly skipped here, but the next check clarifies the single error)Continuing the same idea consistently from 77 should give 772 + 9 = 163 and then 1632 + 11 = 337.Given list instead shows 165 after 77 (which is acceptable if the odd increments taken are 3, 5, 7, 11) but the next term “221” clearly fails any continuation of the doubling-plus-odd scheme. From 165, expected next should be 1652 + 13 = 343, not 221. Verification / Alternative check: Try to fit 221 using the same rule: the only way would be 1652 + x = 221 ⇒ x = -109 (not an odd positive step). Hence 221 is inconsistent. Why Other Options Are Wrong: 15, 35, 77, 165 all align with doubling and adding a small odd number in sequence; they can be reconciled with the intended pattern. Common Pitfalls: Mistaking a near-miss as the wrong term without checking subsequent implications; not projecting the rule beyond one step to verify consistency. Final Answer: 221

Series Completion Questions