Question 1

Find the wrong term in the number series: 0, 1, 9, 36, 99, 225, 441. The intended rule is “square of triangular numbers”: Tn^2 where Tn = 0,1,3,6,10,15,21… Identify the incorrect term.

Accepted Answer

Introduction / Context: Many classic series use triangular numbers Tn = n*(n+1)/2 and then apply a transformation such as squaring. Here, terms visibly align with Tn^2—except one. Given Data / Assumptions: Series: 0, 1, 9, 36, 99, 225, 441. Triangular numbers: 0, 1, 3, 6, 10, 15, 21… Squares: 0^2=0, 1^2=1, 3^2=9, 6^2=36, 10^2=100, 15^2=225, 21^2=441. Concept / Approach: Map each series term to Tn^2. All match perfectly except the 5th term. Step-by-Step Solution: 0 → 0^2 = 0 ✔1 → 1^2 = 1 ✔9 → 3^2 = 9 ✔36 → 6^2 = 36 ✔99 → should be 10^2 = 100 ✖225 → 15^2 = 225 ✔441 → 21^2 = 441 ✔ Verification / Alternative check: Once 99 is corrected to 100, the entire sequence becomes a clean Tn^2 progression without exception. Why Other Options Are Wrong: 9, 36, and 225 correctly correspond to 3^2, 6^2, and 15^2. Common Pitfalls: Overlooking the triangular-index pattern and testing random square bases; always check Tn = 0,1,3,6,10… Final Answer: 99 is the wrong term (should be 100).

Question 2

Find the wrong term in the number series: 2, 3, 6, 15, 45, 156.5, 630. The intended pattern multiplies by 1.5, 2, 2.5, 3, 3.5, 4 … Identify the incorrect term.

Accepted Answer

Introduction / Context: This wrong-term hunt features steadily increasing multipliers by 0.5 each step. We check every transition to isolate the single incorrect value. Given Data / Assumptions: Series: 2, 3, 6, 15, 45, 156.5, 630. Hypothesized rule: multiply by 1.5, then 2.0, then 2.5, then 3.0, then 3.5, then 4.0… Concept / Approach: Verify each step against the progressive-multiplier rule and see which term breaks it. Step-by-Step Solution: 2 × 1.5 = 3 ✔3 × 2 = 6 ✔6 × 2.5 = 15 ✔15 × 3 = 45 ✔45 × 3.5 = 157.5 → but series shows 156.5 ✖If corrected to 157.5, then 157.5 × 4 = 630 ✔ Verification / Alternative check: All early steps are exact; the only inconsistency is the penultimate multiplier result (156.5 vs 157.5). Fixing this restores a perfect ×1.5, ×2, ×2.5, ×3, ×3.5, ×4 pattern. Why Other Options Are Wrong: 3, 6, 15, and 45 all correctly satisfy their respective multipliers. Common Pitfalls: Assuming a different additive rule; the multiplicative ladder is standard in such progressions. Final Answer: None of the listed earlier terms are wrong; the incorrect value is 156.5, which should be 157.5.

Question 3

Find the wrong term in the number series: 5, 8, 16, 26, 50, 98, 194. A consistent rule from the beginning should be “next = 2 × previous − 2”. Identify the incorrect entry.

Accepted Answer

Introduction / Context: We test a simple affine recurrence that fits almost all steps: multiply by 2 and subtract 2. Given Data / Assumptions: Series: 5, 8, 16, 26, 50, 98, 194. Candidate rule: a(n+1) = 2*a(n) − 2. Concept / Approach: Check each transition under the rule and locate the earliest violation. Step-by-Step Solution: 5 → 8: 2*5 − 2 = 8 ✔8 → 16: 2*8 − 2 = 14 ✖ (given 16)If we correct to 14, then 14 → 26: 2*14 − 2 = 26 ✔26 → 50: 2*26 − 2 = 50 ✔50 → 98: 2*50 − 2 = 98 ✔98 → 194: 2*98 − 2 = 194 ✔ Verification / Alternative check: Only the second step fails; fixing 16 to 14 repairs the entire tail perfectly. Why Other Options Are Wrong: 26, 50, and 98 all satisfy the rule when the earlier misprint is corrected. Common Pitfalls: Mistaking downstream consistency for independent correctness; the first inconsistency typically identifies the wrong term. Final Answer: 16 is the wrong term (should be 14).

Question 4

Complete the series and evaluate A ÷ 36: 36, 216, 64.8, 388.8, A, 699.84, 209.952. Rule alternates ×6 and ×0.3 (i.e., ×3/10). Find A and then compute A ÷ 36.

Accepted Answer

Introduction / Context: This is a completion-and-evaluation series problem with a clear alternating multiplier pattern. Given Data / Assumptions: Series: 36, 216, 64.8, 388.8, A, 699.84, 209.952. Rule: ×6, then ×0.3, repeating. Concept / Approach: Apply the two-step alternation across the entire sequence, fill A, and finally compute the requested ratio. Step-by-Step Solution: 36 × 6 = 216 ✔216 × 0.3 = 64.8 ✔64.8 × 6 = 388.8 ✔388.8 × 0.3 = A = 116.64 ✔116.64 × 6 = 699.84 ✔699.84 × 0.3 = 209.952 ✔Finally, A ÷ 36 = 116.64 ÷ 36 = 3.24. Verification / Alternative check: Every adjacent ratio alternates between 6 and 0.3, confirming the correctness of A and the final division. Why Other Options Are Wrong: 0.324 and 6.139 are scale/rounding distractors; the exact arithmetic yields 3.24. Common Pitfalls: Confusing ×0.3 with ÷3; note ×0.3 equals ÷(10/3), not ÷3. Final Answer: 3.24.

Question 5

The sequence is: 4, 7, 12, 19, 28, A, 52. Differences increase by successive odd numbers (+3, +5, +7, +9, +11, +13). Compute A^2 − 4^2.

Accepted Answer

Introduction / Context: We are given an increasing sequence and an expression to evaluate after finding the missing term. The intended operation sign is exponentiation: A^2 minus 4^2. Given Data / Assumptions: Sequence: 4, 7, 12, 19, 28, A, 52. Successive differences: +3, +5, +7, +9, +11, +13 (odd numbers in order). Interpret “A 2 – 4 = ?” as A^2 − 4^2 under standard formatting recovery. Concept / Approach: Compute A using the difference pattern, then evaluate the requested expression with perfect squares. Step-by-Step Solution: 4 → 7: +3; 7 → 12: +5; 12 → 19: +7; 19 → 28: +9.Next two differences should be +11 and +13.Therefore A = 28 + 11 = 39, and 39 + 13 = 52 (fits).Compute A^2 − 4^2 = 39^2 − 16 = 1521 − 16 = 1505. Verification / Alternative check: Using odd-number differences produces exact matches at each step, confirming A = 39. Why Other Options Are Wrong: They result from misreading the exponent or using A*2 − 4; the recovered exponent form is consistent with the options. Common Pitfalls: Missing the exponent indicator and interpreting as multiplication; always check difference patterns and option magnitudes. Final Answer: 1505.

Question 6

Fill the missing letter in the letter-triples: FOX, GP?, HQZ. Observe the position-wise sequences to determine the middle missing letter.

Accepted Answer

Introduction / Context: In position-wise letter series, each column (1st, 2nd, 3rd letters) typically follows its own alphabetic progression. Given Data / Assumptions: Triples: F O X, G P ?, H Q Z. Alphabet index: A=1 … Z=26. Concept / Approach: Track each position independently to see consistent +1 or +2 progressions. Step-by-Step Solution: 1st letters: F(6) → G(7) → H(8): +1 each step.2nd letters: O(15) → P(16) → Q(17): +1 each step.3rd letters: X(24) → ? → Z(26): +1 each step implies Y(25). Verification / Alternative check: Rewriting as three parallel sequences (FGH), (OPQ), (XYZ) makes the pattern obvious. Why Other Options Are Wrong: Z would overshoot; T and W do not fit the +1 trajectory. Common Pitfalls: Looking for constant shifts across whole triples rather than column-wise shifts. Final Answer: Y.

Question 7

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 8

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 9

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 10

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 11

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, 329 Exactly 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 12

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, 50 Target 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 13

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, 15015 Intended multipliers: 7, 6.5, 6, 5.5, 5 Concept / 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 14

0, 7, 26, 63,?

Accepted Answer

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

Question 15

–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 = - 1 Second term = First term + 1 ⇒ Second term = -1 + 1 = 0 Third term = Second term + 3 ⇒ Third term = 0 + 3 = ( ? ) ∴ ( ? ) = 3 Similarly we can calculate the all others terms ⇒ Fourth term = 8 ⇒ Fifth term= 15

Question 16

1, 2, 6, 24,? ,720

Accepted Answer

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

Question 17

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 = 4 4th term = 5 × 5th term + 3 ⇒ 4th term = 5 × 4 + 3 = 23 3rd term= 5 × 4th term + 7 ⇒ 3rd term= 5 × 23 + 7 = 122 Similarly , we can find all others terms also. 2nd term = 5 × 3rd term + 11 ⇒ 2nd term = 5 × 122 + 11 = ? ⇒ ? = 621 1st term = 5 × 2nd term + 15 ⇒ 1st term = 5 × 621 + 15 =3120

Question 18

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 19

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, 312 Hypothesized 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 20

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

Accepted Answer

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

Number Series Questions