Question 1

Find the next term in the letter series: YEB, WFD, UHG, SKI, ( ? ). Use column-wise shifts: first letters −2 each step, seconds +1, +2, +3, +4…, thirds alternate +2, +3, +2, +3…

Accepted Answer

Introduction / Context:Three-letter series often encode separate arithmetic progressions in each letter position, including alternating increments.Given Data / Assumptions:Terms: Y E B; W F D; U H G; S K I; next = ?Indices: A=1 … Z=26; wrap-around permitted conceptually.Concept / Approach:Analyze each column: 1st letters step backward by 2; 2nd letters increase with growing increments; 3rd letters alternate +2, +3.Step-by-Step Solution:1st letters: Y(25) → W(23) → U(21) → S(19) → Q(17).2nd letters: E(5) → F(6) (+1) → H(8) (+2) → K(11) (+3) → O(15) (+4).3rd letters: B(2) → D(4) (+2) → G(7) (+3) → I(9) (+2) → L(12) (+3).Hence next term is Q O L.Verification / Alternative check:Reconstructing backwards from QOL recovers the same increments, confirming consistency.Why Other Options Are Wrong:TOL breaks the −2 pattern in the first column; QGL/QNL do not satisfy the +4 or alternating +3 requirement.Common Pitfalls:Assuming constant steps in the second/third columns; here, one column has growing steps, another alternates.Final Answer:QOL.

Question 2

Find the next term in the series: BEH, KNQ, TWZ, ( ? ). Each position advances by +9 in the alphabet with wrap-around.

Accepted Answer

Introduction / Context:Here, each of the three letter positions undergoes the same forward shift by a fixed value across terms.Given Data / Assumptions:Series: B E H; K N Q; T W Z; next = ?Alphabet indices with wrap-around (A=1 … Z=26).Concept / Approach:Compute letter-to-letter jumps across terms for each position; a constant +9 emerges.Step-by-Step Solution:First letters: B(2) → K(11) (+9) → T(20) (+9) → C(3) (+9 wrap).Second letters: E(5) → N(14) (+9) → W(23) (+9) → F(6) (+9 wrap).Third letters: H(8) → Q(17) (+9) → Z(26) (+9) → I(9) (+9 wrap).Verification / Alternative check:Reversing from CFI by −9 retrieves TWZ, confirming the fixed-shift pattern.Why Other Options Are Wrong:IJL, BDF, ADG use different step sizes and do not preserve the +9 rule in all three positions.Common Pitfalls:Missing wrap-around arithmetic when passing Z to A.Final Answer:CFI.

Question 3

Fill the missing group: A, CD, GHI, ( ? ), UVWXY. Group lengths grow 1, 2, 3, 4, 5; starting letters advance by +2, +4, +6, +8: A → C → G → M → U.

Accepted Answer

Introduction / Context:The pattern involves two controls: the number of letters per group and the starting letter progression.Given Data / Assumptions:Groups: 1, 2, 3, 4, 5 letters respectively.Starting letters: A, C, G, M, U with jumps +2, +4, +6, +8.Concept / Approach:Determine the correct starting letter for the 4-letter group and then list 4 consecutive letters.Step-by-Step Solution:A(1) → C(3) +2; C(3) → G(7) +4; G(7) → M(13) +6; M(13) → U(21) +8.Hence the 4-letter group must start at M: M N O P.Verification / Alternative check:Counting letters per group (1→2→3→4→5) matches A / CD / GHI / MNOP / UVWXY.Why Other Options Are Wrong:LMNO starts at L, not M; MNO has only 3 letters; NOPQ starts at N, not M.Common Pitfalls:Focusing only on group length and missing the non-linear jumps in starting letters.Final Answer:MNOP.

Question 4

Find the next triple in the series: ABD, DGK, HMS, MTB, SBL, ( ? ). Per-position jumps increase by +1 each time (wrapping at Z).

Accepted Answer

Introduction / Context:Three synchronous letter streams evolve with steadily increasing forward jumps; wrap-around arithmetic applies at Z→A.Given Data / Assumptions:Series: A B D; D G K; H M S; M T B; S B L; next = ?Alphabet indices A=1 … Z=26; after 26, continue from 1.Concept / Approach:Observe jump sizes in each column: they grow by +1 each step (e.g., +3, +4, +5, +6, +7 … for 1st column), with similar patterns in other columns but starting at different offsets.Step-by-Step Solution:1st letters: A(1) → D(4) +3 → H(8) +4 → M(13) +5 → S(19) +6 → Z(26) +7.2nd letters: B(2) → G(7) +5 → M(13) +6 → T(20) +7 → B(2) +8 wrap → K(11) +9.3rd letters: D(4) → K(11) +7 → S(19) +8 → B(2) +9 wrap → L(12) +10 → W(23) +11.Thus the next triple is Z K W.Verification / Alternative check:Subtracting the same jumps in reverse retrieves SBL, confirming pattern integrity.Why Other Options Are Wrong:XKW breaks the +7 requirement for the first column; ZKU/ZAB fail other column jumps.Common Pitfalls:Not accounting for wrap-around when sums exceed 26.Final Answer:ZKW.

Question 5

Number series – Find the wrong number 1, 2, 4.5, 11, 30, 92.5, 329 Exactly one term is incorrect. Identify the wrong number.

Accepted Answer

Introduction / Context:“Find the wrong number” tasks typically conceal a consistent growth scaffold (e.g., multiply by a gradually increasing factor and adjust by a small constant). The goal is to locate the lone term that breaks the otherwise smooth progression.Given Data / Assumptions:Series shown: 1, 2, 4.5, 11, 30, 92.5, 329Exactly one number is wrong.Concept / Approach:Check adjacent ratios and required adjustments. From the start we see a consistent “multiply by about 2.x then small correction” ladder: 1 → 2 (×2), 2 → 4.5 (×2.25, a modest step-up), 4.5 → 11 (≈ ×2.44 with a tiny subtraction), and 11 → 30 (≈ ×2.73 with a tiny subtraction). A sudden jump to 92.5 would imply an oversized factor and breaks the otherwise steady acceleration.Step-by-Step Solution:From 1 to 2: ×2 (clean start).From 2 to 4.5: ×2.25 (smooth increase).From 4.5 to 11: ≈ ×2.444… (still a gentle step-up).From 11 to 30: ≈ ×2.727… (steady acceleration).Next expected factor should be near ~3.0, which would give ≈ 90 from 30; the displayed 92.5 is off-pattern and also causes the final term 329 to be inconsistent with a clean next step.Verification / Alternative check:Replacing 92.5 with a near-3× value (≈ 90–94) produces a smooth monotone acceleration; 92.5 specifically disrupts later consistency and is the unique standout among the given answer choices.Why Other Options Are Wrong:2, 4.5, 11 → these early anchor points form a credible, gradually accelerating base.None of these → exactly one implausible spike exists (92.5).Common Pitfalls:Judging only by absolute differences; ratio smoothness is the more reliable cue in multiplicative ladders.Final Answer:92.5

Question 6

Number series – Find the wrong number (Fibonacci-style sum of two previous) 2, 5, 7, 12, 19, 32, 50 Exactly one term is incorrect. Identify the wrong number, given the intended rule “each term = sum of previous two terms”.

Accepted Answer

Introduction / Context:Many series are built like the Fibonacci sequence: a(n) = a(n−1) + a(n−2). One rogue term will break the recurrence while all others fit perfectly.Given Data / Assumptions:Series: 2, 5, 7, 12, 19, 32, 50Target rule: each term equals the sum of its two immediate predecessors.Concept / Approach:Verify the sum-of-previous-two rule at every step and find the single violation.Step-by-Step Solution:2 + 5 = 7 → OK.5 + 7 = 12 → OK.7 + 12 = 19 → OK.12 + 19 = 31 → should be 31, but the series shows 32 → violation.19 + 31 = 50 → the last term 50 is consistent if “32” is corrected to 31.Verification / Alternative check:Replacing 32 with 31 restores the recurrence across the whole tail, proving 32 is the lone error.Why Other Options Are Wrong:7, 12, 19 → all satisfy the rule with the corrected middle term.None of these → incorrect; 32 is uniquely inconsistent.Common Pitfalls:Mistaking the last number (50) as wrong because it is large; it actually validates once the prior term is fixed.Final Answer:32

Question 7

Number series – Find the wrong number (descending multipliers by 0.5) 2, 14, 91, 546, 3002, 15015 Exactly one term is incorrect. Multipliers descend by 0.5 each time (×7, ×6.5, ×6, ×5.5, ×5). Identify the wrong number.

Accepted Answer

Introduction / Context:This classic pattern multiplies by factors that decrease by 0.5 each step: ×7, ×6.5, ×6, ×5.5, ×5. A single incorrect value will break the exact products.Given Data / Assumptions:Series: 2, 14, 91, 546, 3002, 15015Intended multipliers: 7, 6.5, 6, 5.5, 5Concept / Approach:Compute each product exactly and compare with the displayed term.Step-by-Step Solution:2 × 7 = 14 → OK.14 × 6.5 = 91 → OK.91 × 6 = 546 → OK.546 × 5.5 = 3003 → series shows 3002 → wrong here.3003 × 5 = 15015 → final term consistent with the intended rule.Verification / Alternative check:Only one-off error (3002 vs 3003) occurs; all other multiplications are exact.Why Other Options Are Wrong:14, 91, 15015 → each matches the exact descending-multiplier rule.None of these → incorrect because 3002 is the sole mismatch.Common Pitfalls:Assuming rounding; here the products are exact integers and leave no rounding ambiguity.Final Answer:3002

Question 8

0, 7, 26, 63,?

Accepted Answer

The given series is in the below pattern,we can see thatNext term ( Tn ) = n3 - 1 { where , putting n = 1 , 2 , 3 , 4 , 5 respectively }First term = T1 = 13 - 1 = 0Second term = T2 = 23 - 1 = 7Similarly we can find the all others termsThird term = 26Fourth term = 63Fifth term( ? )= 124 Hence we get the value of ? = 124

Question 9

–1, 0,?, 8, 15, 24

Accepted Answer

The number pattern is described in the below image. As per figure we can see the number series is in specific pattern which will help us to find the next number. It is clear that we are getting the next terms on adding + 1 , + 3 , + 5 , + 7 , + 9 in previous term respectively.First term = - 1Second term = First term + 1 ⇒ Second term = -1 + 1 = 0 Third term = Second term + 3 ⇒ Third term = 0 + 3 = ( ? ) ∴ ( ? ) = 3Similarly we can calculate the all others terms ⇒ Fourth term = 8 ⇒ Fifth term= 15

Question 10

1, 2, 6, 24,? ,720

Accepted Answer

As per given series , we can see thatFirst term = 1Second term = First term × 2 ⇒ Second term = 1 × 2 = 2Similarly we can find the all others termsThird term = Second term × 3 ⇒ Third term = 2 × 3 = 6Fourth term = Third term × 4 ⇒ Fourth term = 6 × 4 = 24Fifth term = Fourth term × 5 ⇒ Fifth term = 24 × 5 = ? ∴ ? = 120 Sixth term = Fifth term × 6 ⇒ Sixth term = 120 × 6 = 720

Question 11

3120,?, 122, 23, 4

Accepted Answer

As per above given series , we can see that Descending order of given series - Next term = ( 5 x previous term ) + odd number ( which starts 3 ) Here , 5th term = 44th term = 5 × 5th term + 3 ⇒ 4th term = 5 × 4 + 3 = 233rd term= 5 × 4th term + 7 ⇒ 3rd term= 5 × 23 + 7 = 122Similarly , we can find all others terms also. 2nd term = 5 × 3rd term + 11 ⇒ 2nd term = 5 × 122 + 11 = ? ⇒ ? = 6211st term = 5 × 2nd term + 15 ⇒ 1st term = 5 × 621 + 15 =3120

Question 12

18, 20, 23, 32, 48, 73, 109

Accepted Answer

The series is 18 +12 = 19; 19 + 22 = 23; 23 + 32 = 32; 32 + 42 = 48; 48 + 52 = 73 + 62 = 109

Question 13

Number series – Find the wrong number (double then add n) 3, 7, 16, 35, 72, 153, 312 Exactly one term is incorrect. Identify the term that breaks the rule “a(n) = 2*a(n−1) + n”.

Accepted Answer

Introduction / Context:A common construction is a(n) = 2*a(n−1) + n, where n starts at 1 for the first transition and increases by 1 each step. One erroneous term typically disrupts the clean recurrence.Given Data / Assumptions:Series: 3, 7, 16, 35, 72, 153, 312Hypothesized rule: a(n) = 2*a(n−1) + n with n = 1, 2, 3, …Concept / Approach:Apply the recurrence term-by-term and locate the violation.Step-by-Step Solution:From 3: 2*3 + 1 = 7 → OK.From 7: 2*7 + 2 = 16 → OK.From 16: 2*16 + 3 = 35 → OK.From 35: 2*35 + 4 = 74 → the series shows 72 → wrong here.Continuing with corrected 74: 2*74 + 5 = 153 → OK; 2*153 + 6 = 312 → OK.Verification / Alternative check:With “74” in place of “72,” the recurrence holds across the whole sequence, so “72” is the only error.Why Other Options Are Wrong:7, 35, 153 → all consistent once the single error is fixed.None of these → incorrect because “72” uniquely breaks the rule.Common Pitfalls:Using n = 0 at the first step; this series clearly starts with n = 1 (giving +1 at the first transition).Final Answer:72

Question 14

6, 10, 14, 34, 66, 130, 258

Accepted Answer

The series is x 2 - 2, x 2 - 2, x 2 - 2, x 2 - 2, ......

Question 15

Number series – Find the wrong number (multiply by n then add n) 3, 4, 10, 32, 136, 685, 4116 Exactly one term is incorrect. The intended rule is a(n) = a(n−1)*n + n (with n = 1, 2, 3, …). Identify the wrong number.

Accepted Answer

Introduction / Context:Some sequences use a tidy recurrence a(n) = a(n−1)*n + n. One bad insertion breaks two adjacent gaps; fixing that single value restores the pattern across the run.Given Data / Assumptions:Series: 3, 4, 10, 32, 136, 685, 4116Intended rule: a(n) = a(n−1)*n + n (n = 1, 2, 3, …)Concept / Approach:Validate each transition against the recurrence and find the outlier.Step-by-Step Solution:3 → 4: 3*1 + 1 = 4 → OK.4 → 10: 4*2 + 2 = 10 → OK.10 → 32: expected 10*3 + 3 = 33 → series shows 32 → wrong here.With 33 in place, 33 → 136: 33*4 + 4 = 136 → OK.136 → 685: 136*5 + 5 = 685 → OK.685 → 4116: 685*6 + 6 = 4116 → OK.Verification / Alternative check:The single correction 32 → 33 yields a perfect recurrence throughout, proving “32” is the unique wrong number.Why Other Options Are Wrong:10, 136, 4116 → all comply once the third term is corrected.None of these → incorrect because “32” is the only mismatch.Common Pitfalls:Assuming multiple errors; well-posed exam items almost always contain exactly one erroneous insertion.Final Answer:32

Question 16

380, 188, 92, 48, 20, 8, 2

Accepted Answer

Pattern is : - 192, - 96, - 48, - 24, -12, - 6

Question 17

4, 10, 22, 46, 96, 190, 382

Accepted Answer

Pattern is : + 6, + 12, + 24, + 48, +96, + 192

Question 18

Wrong Term in the Fibonacci-Sum Style Series: 13, 14, 27, 45, 68, 109, 177 — exactly one term is incorrect. Identify the wrong term and justify your choice by revealing the intended rule (each term should be the sum of the previous two).

Accepted Answer

Introduction / Context:In many number-series questions, the guiding rule is that each term equals the sum of the two preceding terms (a Fibonacci-like construction). Detecting one violation pinpoints the wrong term.Given Data / Assumptions:Series as given: 13, 14, 27, 45, 68, 109, 177.Exactly one term is erroneous; the rest must follow a single consistent rule.Concept / Approach:Test the Fibonacci-sum rule a(n) = a(n-1) + a(n-2). If the rule holds everywhere except at one index, that index is the wrong term.Step-by-Step Solution:Check 3rd term: 13 + 14 = 27 ✓Check 4th term: 14 + 27 = 41 ≠ 45 → mismatchAssuming the rule is correct, the 4th term should be 41, not 45.Continue with corrected term (41): 27 + 41 = 68 ✓41 + 68 = 109 ✓68 + 109 = 177 ✓Verification / Alternative check:With only the 4th term corrected to 41, the remainder of the sequence fits the rule perfectly. No other single change yields full consistency.Why Other Options Are Wrong:27: equals 13 + 14, hence correct.68: equals 27 + 41 (with repaired 4th term), hence consistent.109: equals 41 + 68, hence consistent.177: equals 68 + 109, hence consistent.Common Pitfalls:Stopping at the first mismatch and changing the preceding term. The minimal-change strategy is to change the mismatching term itself (45 → 41).Final Answer:45

Question 19

Wrong Term in the Prime-Square Series: 529, 841, 961, 1296, 1681, 1849, 2209 — identify the term that breaks the pattern (squares of consecutive odd primes).

Accepted Answer

Introduction / Context:Square-number series often use squares of consecutive integers or, more specifically, consecutive primes. Here, most terms are squares of consecutive odd primes.Given Data / Assumptions:529 = 23^2841 = 29^2961 = 31^21296 = 36^21681 = 41^21849 = 43^22209 = 47^2Concept / Approach:Identify whether each term is the square of a consecutive odd prime: 23, 29, 31, 37, 41, 43, 47.Step-by-Step Solution:529 → 23^2 ✓841 → 29^2 ✓961 → 31^2 ✓1296 → 36^2 (not prime) ✗1681 → 41^2 ✓1849 → 43^2 ✓2209 → 47^2 ✓Verification / Alternative check:If the intended missing prime were 37, its square would be 1369, not 1296. Hence 1296 is the unique misfit.Why Other Options Are Wrong:529, 841, 961, 1681: each is p^2 for odd primes (23, 29, 31, 41).Common Pitfalls:Assuming “consecutive squares” instead of “squares of consecutive odd primes.” 36 is composite, so 36^2 breaks the prime-square motif.Final Answer:1296

Question 20

Wrong Term in the Fibonacci-Sum Style Series: 1, 3, 4, 7, 11, 18, 27, 47 — exactly one term is incorrect. Identify it and explain the intended rule (sum of previous two).

Accepted Answer

Introduction / Context:A common construction in series questions is a(n) = a(n-1) + a(n-2). We check each position to find the unique violation.Given Data / Assumptions:Given sequence: 1, 3, 4, 7, 11, 18, 27, 47.We expect each term from the 3rd onward to equal the sum of the two previous terms.Concept / Approach:Systematically verify the sum-of-previous-two property; the first mismatch highlights the wrong term.Step-by-Step Solution:4 = 1 + 3 ✓7 = 3 + 4 ✓11 = 4 + 7 ✓18 = 7 + 11 ✓Next should be 11 + 18 = 29, but the series shows 27 → mismatch.With 29 in place of 27, the next term is 18 + 29 = 47, which matches the last term.Verification / Alternative check:Only by changing 27 to 29 does the entire series align to the rule without further edits.Why Other Options Are Wrong:18, 11, 7, 47: each satisfies the rule relative to its neighbors when 27 is corrected to 29.Common Pitfalls:Changing two terms to “force-fit” a different rule. The minimal edit principle points to 27 as the lone error.Final Answer:27

Number Series Questions

Questions

Practice smarter