Question 1

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, 4116 Intended 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 2

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

Accepted Answer

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

Question 3

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

Accepted Answer

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

Question 4

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 5

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 = 23^2 841 = 29^2 961 = 31^2 1296 = 36^2 1681 = 41^2 1849 = 43^2 2209 = 47^2 Concept / 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 6

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

Question 7

Wrong Term in the Cubic-Difference Series: 2, 3, 11, 38, 102, 229, 443 — one term breaks the pattern where successive differences should be 1^3, 2^3, 3^3, 4^3, 5^3, 6^3.

Accepted Answer

Introduction / Context: Progressive-difference series often use perfect powers as successive increments. Here the intended differences are consecutive cubes. Given Data / Assumptions: Proposed rule: a(n) = a(n-1) + k^3 for k = 1, 2, 3, 4, 5, 6, … Starting from 2, the correct cumulative path should be +1, +8, +27, +64, +125, +216, … Concept / Approach: Compute actual differences and compare to the target k^3 milestones. Step-by-Step Solution: 2 → 3: +1 = 1^3 ✓3 → 11: +8 = 2^3 ✓11 → 38: +27 = 3^3 ✓38 → 102: +64 = 4^3 ✓102 → 229: +127 (should be +125 = 5^3) ✗If corrected to 102 + 125 = 227, then 227 → 443 would be +216 = 6^3 ✓ Verification / Alternative check: Every step aligns with perfect cubes if 229 is replaced by 227; no other single-term change achieves perfect alignment. Why Other Options Are Wrong: 11, 38, 102, 443: each sits exactly at the cumulative totals expected from the +1, +8, +27, +64, +216 scheme (with the 5th increment corrected to 125). Common Pitfalls: Mistaking 127 for 125 (5^3). This small slip is a classic trap in cube-based difference series. Final Answer: 229

Question 8

Wrong Term at the Tail of a Fibonacci-like Increment Series: 2, 3, 5, 8, 14, 23, 41, 69 — find the lone wrong term by analyzing the intended pattern of cumulative increments.

Accepted Answer

Introduction / Context: Several series use increasing differences that themselves follow a simple additive pattern. A single miscopy at the end often breaks a near-Fibonacci run of differences. Given Data / Assumptions: Series: 2, 3, 5, 8, 14, 23, 41, 69. Observed differences: +1, +2, +3, +6, +9, +18, +28. Concept / Approach: Notice that the differences roughly follow a rule of “add the previous significant jump” (3, then 6 = 3+3, then 9 = 3+6, then 18 = 9+9). By that logic, after +18, the next should be +27 (not +28). Step-by-Step Solution: 2 → 3: +13 → 5: +25 → 8: +38 → 14: +6 (≈ 3 + 3)14 → 23: +9 (≈ 3 + 6)23 → 41: +18 (≈ 9 + 9)Next expected jump: 27 (≈ 9 + 18), hence 41 + 27 = 68; but the series shows 69. Verification / Alternative check: With 68 in place of 69, the increments form a consistent internal pattern without forcing earlier edits. Why Other Options Are Wrong: 8, 14, 23, 41: each fits the derived increment logic; only the final term overshoots by 1. Common Pitfalls: Trying to retrofit a multiplicative rule; the additive increment structure is the minimal-consistency explanation. Final Answer: 69

Question 9

Wrong Term in the Alternating ×2.5 and ×2 Series (with one error): 3, 7.5, 15, 37.5, 75, 167.5, 375 — identify the lone incorrect term.

Accepted Answer

Introduction / Context: Alternating-multiplier series frequently toggle between two simple factors. Here, the intended pattern is ×2.5, then ×2, repeating. Given Data / Assumptions: Given series: 3, 7.5, 15, 37.5, 75, 167.5, 375. Intended pattern: multiply alternately by 2.5 and 2. Concept / Approach: Apply the alternating multipliers and compare expected vs given terms to find the mismatch. Step-by-Step Solution: 3 × 2.5 = 7.5 ✓7.5 × 2 = 15 ✓15 × 2.5 = 37.5 ✓37.5 × 2 = 75 ✓75 × 2.5 = 187.5 (but given 167.5) ✗Continuing the intended rule: 187.5 × 2 = 375 ✓ Verification / Alternative check: All positions agree with the alternating ×2.5 and ×2 pattern except the 6th term, which must be 187.5, not 167.5. Why Other Options Are Wrong: 37.5, 75, 15, 375: each aligns with the intended alternating multipliers. Common Pitfalls: Rounding or copying errors at the 6th term. The multipliers are exact; no rounding is needed. Final Answer: 167.5

Question 10

Wrong Term in a Halving-Difference Series: 36, 20, 12, 8, 6, 5.5, 4.5 — find the single term that breaks the “subtract half the previous difference” rule.

Accepted Answer

Introduction / Context: Some decreasing series are produced by repeatedly halving the previous step’s subtraction. We look for one term that violates that precise halving cadence. Given Data / Assumptions: Given terms: 36, 20, 12, 8, 6, 5.5, 4.5. Expected differences should follow: −16, −8, −4, −2, −1, −0.5, … Concept / Approach: Compute actual step differences and compare to the “each difference halves” template. Step-by-Step Solution: 36 → 20: −16 (OK)20 → 12: −8 (OK)12 → 8: −4 (OK)8 → 6: −2 (OK)6 → 5.5: −0.5 (should be −1) → mismatchIf corrected to 6 → 5: −1, then 5 → 4.5: −0.5 fits the halving rule. Verification / Alternative check: The only inconsistent step is at 6 → 5.5; replacing 5.5 with 5 restores perfect halving. Why Other Options Are Wrong: 20, 12, 6, 4.5: each sits exactly on the halving path once 5.5 is corrected to 5.0. Common Pitfalls: Assuming the last two steps are both flexible; the halving rule fixes them uniquely. Final Answer: 5.5

Question 11

Find the Missing Code in the 5-Letter Pattern: BYCXW, CXDWV, EVFUT, GTHSR, ? — determine the next 5-letter block.

Accepted Answer

Introduction / Context: Letter-series questions often operate column-wise (position by position). Each position can advance forward or backward with regular steps, producing a structured 5-column evolution. Given Data / Assumptions: Blocks: BYCXW, CXDWV, EVFUT, GTHSR, ? Work column-wise across the five positions. Concept / Approach: Extract each column and look for arithmetic progressions on alphabet indices (A=1 … Z=26), noting some move forward (+) while others move backward (−). Step-by-Step Solution: Col1: B(2) → C(3) → E(5) → G(7): +1, +2, +2 → next +2 → I(9)Col2: Y(25) → X(24) → V(22) → T(20): −1, −2, −2 → next −2 → R(18)Col3: C(3) → D(4) → F(6) → H(8): +1, +2, +2 → next +2 → J(10)Col4: X(24) → W(23) → U(21) → S(19): −1, −2, −2 → next −2 → Q(17)Col5: W(23) → V(22) → T(20) → R(18): −1, −2, −2 → next −2 → P(16)Thus the next block is I R J Q P. Verification / Alternative check: The 1/2/2 stepping pattern repeats across symmetric forward/backward columns, reinforcing IRJQP as the only consistent continuation. Why Other Options Are Wrong: KPOLN, KPLON, JOKPO: they do not satisfy all five column progressions simultaneously. Common Pitfalls: Reading left-to-right as a single word transformation; the safe method is column-wise progression tracking. Final Answer: IRJQP

Question 12

Find the Next Triple: QPO, SRQ, UTS, WVU, (?) — choose the correct continuation.

Accepted Answer

Introduction / Context: This is a descending triplet pattern with the starting letter increasing by 2 each step while letters inside each triplet descend by 1. Given Data / Assumptions: Triplets: QPO, SRQ, UTS, WVU, ? Within each triplet, letters decrease left→right by 1 (e.g., Q, P, O). Concept / Approach: Track the first letters: Q, S, U, W → each +2 steps → next is Y. Then build a descending triple starting from Y. Step-by-Step Solution: First letters: Q → S (+2) → U (+2) → W (+2) → Y (+2).Triplet for Y: Y, X, W (each −1). Verification / Alternative check: All previous triplets obey the same structure; continuing yields YXW uniquely. Why Other Options Are Wrong: XVZ, ZYA, VWX: they break either the +2 jump for the first letter or the strict descending-by-1 internal order. Common Pitfalls: Forgetting that the inner order is always descending by 1 from the first letter. Final Answer: YXW

Question 13

Find the Next Pair: AZ, CX, FU, (?) — determine the next two-letter code using consistent forward/backward jumps.

Accepted Answer

Introduction / Context: Two-letter codes frequently move forward on the first letter and backward on the second, with step sizes themselves increasing in a simple progression. Given Data / Assumptions: Pairs: AZ, CX, FU, ? First letters: A → C → F → ? (forward) Second letters: Z → X → U → ? (backward) Concept / Approach: Identify the step pattern: first letters go +2, then +3, then +4; second letters go −2, then −3, then −4. Step-by-Step Solution: First letter: A(+2)=C, C(+3)=F, F(+4)=J → next first letter J.Second letter: Z(−2)=X, X(−3)=U, U(−4)=Q → next second letter Q.Hence the next pair is JQ. Verification / Alternative check: Both directions’ step sizes increase by 1 each time, so JQ is uniquely determined. Why Other Options Are Wrong: IR, IV, KP: they violate the +2/+3/+4 and −2/−3/−4 stepping scheme. Common Pitfalls: Keeping step sizes constant rather than increasing them by 1 at each move. Final Answer: JQ

Question 14

Find the Next Triple: OTE, PUF, QVG, RWH, (?) — extend the 3-column forward progression.

Accepted Answer

Introduction / Context: Each position in the triplet advances by +1 through the alphabet. Treat the sequence column-wise to find the next term. Given Data / Assumptions: Triplets: O T E, P U F, Q V G, R W H, ? Column advances: O→P→Q→R→S; T→U→V→W→X; E→F→G→H→I. Concept / Approach: Apply +1 to each column simultaneously. Step-by-Step Solution: First column: O,P,Q,R → next S.Second column: T,U,V,W → next X.Third column: E,F,G,H → next I.Thus the next triple is S X I. Verification / Alternative check: Uniform +1 shifts across columns ensure a unique continuation. Why Other Options Are Wrong: SYJ, TXI, SXJ: each breaks at least one column’s +1 rule. Common Pitfalls: Attempting to read diagonally; the structure is strictly column-wise. Final Answer: SXI

Question 15

Find the Next Code: MHZ, NIW, OKT, PNQ, (?) — determine the 3-letter continuation by analyzing per-column shifts.

Accepted Answer

Introduction / Context: Three-letter codes can evolve via independent arithmetic progressions on each column. Identify those step sizes and extend them. Given Data / Assumptions: Codes: M H Z, N I W, O K T, P N Q, ? Column shifts appear regular but asymmetric. Concept / Approach: Compute column-wise movements (A=1 … Z=26): Step-by-Step Solution: Col1: M→N→O→P: +1 each → next Q.Col2: H→I (+1), I→K (+2), K→N (+3): step sizes +1, +2, +3 → next +4 → R.Col3: Z→W (−3), W→T (−3), T→Q (−3): constant −3 → next −3 → N.Hence the next code is Q R N. Verification / Alternative check: The strictly increasing +1/+2/+3 pattern in column 2, paired with constant −3 in column 3, uniquely yields QRN. Why Other Options Are Wrong: RRN, QRM, QQN: each violates at least one of the column progressions. Common Pitfalls: Assuming equal steps in all columns; only column 1 is constant +1, column 2 accelerates, column 3 stays −3. Final Answer: QRN

Question 16

Number series – find the missing term: 156, 506, ( ? ), 1806. Identify the value that correctly completes the pattern and replaces the question mark.

Accepted Answer

Introduction / Context: Number-series questions often rely on consistent growth rules such as fixed differences, second-order differences, or alternating operations. The task is to infer the governing pattern and apply it to find the missing term between 506 and 1806. Given Data / Assumptions: Series: 156, 506, ?, 1806. Exactly one standard monotone pattern is intended (no alternating sub-series are indicated). We must choose from the provided options. Concept / Approach: The cleanest hypothesis is an arithmetic pattern with increasing differences. Compute first differences and check if they themselves grow by a constant amount. This “second-order constant difference” model is common in test-series design and leads to linear growth in the increments across consecutive terms. Step-by-Step Solution: Let the missing term be x. Then differences are: 506 − 156 = 350, x − 506, and 1806 − x.Assume a constant step-up of +200 in the differences: 350, 550, 750.Solve x − 506 = 550 → x = 1056.Check final difference: 1806 − 1056 = 750, which matches the expected +200 step-up from 550. Verification / Alternative check: Differences become 350 → 550 → 750, which rise by a constant 200. This second-order consistency verifies x = 1056 and rules out other options (856, 1456, 1506), which would break the constant 200 increase. Why Other Options Are Wrong: 856: Would give differences 350, 350, 950 (no constant step in the increments). 1456: Would give 350, 950, 350 (pattern breaks and is non-monotone). 1506: Would give 350, 1000, 300 (again inconsistent growth of differences). Common Pitfalls: Jumping to a multiplicative pattern due to large numbers; however, steady second-order differences are simpler and fit all four terms exactly. Final Answer: 1056

Question 17

Number series – compute the next term: 2, 5, 10, 19, 36, ?

Accepted Answer

Introduction / Context: Some series grow by adding a changing difference that follows its own recurrence. Here, the term-to-term increments themselves follow a simple relation, allowing the next term to be predicted cleanly. Given Data / Assumptions: Series: 2, 5, 10, 19, 36, ? We examine first differences and look for a recurrence on the differences. Concept / Approach: Compute consecutive differences, then see if those differences follow a compact rule (e.g., doubling and subtracting a constant). This “recurrence on differences” is a common pattern in competitive exams. Step-by-Step Solution: Differences: 5−2 = 3, 10−5 = 5, 19−10 = 9, 36−19 = 17.Observe the meta-pattern on differences: 3 → 5 → 9 → 17. Each new difference = 2 * (previous difference) − 1.Check: 3*2−1 = 5; 5*2−1 = 9; 9*2−1 = 17. Next difference = 17*2−1 = 33.Next term = 36 + 33 = 69. Verification / Alternative check: Attempting multiplicative rules on the original terms leads to inconsistency; the difference-based recurrence fits all transitions exactly and predicts a unique next value of 69. Why Other Options Are Wrong: 70/71/68 would require next differences of 34/35/32, which break the 2*d − 1 recurrence produced by the established run of differences. Common Pitfalls: Mistaking the differences as primes or squares; while 3,5 are prime, the governing rule is the 2*d − 1 recurrence, not primality. Final Answer: 69

Question 18

Number series – alternating +1 and ×2 pattern: 2, 3, 6, 7, 14, 15, ?

Accepted Answer

Introduction / Context: Alternating-operation series are a staple in reasoning tests. The sequence switches between two simple rules in turns, and identifying the alternation is the key to forecasting the next item. Given Data / Assumptions: Series: 2, 3, 6, 7, 14, 15, ? Likely two-rule alternation due to the saw-tooth rise pattern. Concept / Approach: Check consecutive transitions to test a repeating pair of operations. Here, the transitions suggest adding 1 and then doubling, in strict alternation. Step-by-Step Solution: 2 → 3: +13 → 6: ×26 → 7: +17 → 14: ×214 → 15: +1Therefore, the next step must be ×2: 15 × 2 = 30. Verification / Alternative check: Any proposal other than 30 would break the observed strict alternation of +1, ×2, +1, ×2, … across every step. Why Other Options Are Wrong: 16/31/32: These correspond to +1 or ×2 applied in the wrong position (or an extra +1). Only 30 preserves the alternating structure. Common Pitfalls: Forgetting that the very last move was +1 (14 → 15), so the next must be ×2 rather than another +1. Final Answer: 30

Question 19

Alphabet series – identify the next 4-letter block: BCFG, JKNO, RSVW, ?

Accepted Answer

Introduction / Context: Letter-block sequences typically apply fixed step sizes through the alphabet. Once the step pattern inside each 4-letter block is known, predicting the next block is straightforward. Given Data / Assumptions: Blocks: B C F G | J K N O | R S V W | ? Alphabet positions use A=1, B=2, …, Z=26, with wrap-around past Z back to A if needed. Concept / Approach: Within each block, the steps are consistent: +1, then +3, then +1. We also observe that each new block starts several letters ahead of the previous, keeping the same internal stepping. Step-by-Step Solution: Check block 1 (B→C = +1, C→F = +3, F→G = +1).Block 2 (J→K = +1, K→N = +3, N→O = +1).Block 3 (R→S = +1, S→V = +3, V→W = +1).Therefore, block 4 must apply the same +1, +3, +1 stepping starting from the next appropriate letter. After W, continue the pattern to the next block start: take Z as the starting letter (wrap-around). Then Z→A = +1 (wrap), A→D = +3, D→E = +1, producing Z A D E. Verification / Alternative check: Among the options, only ZADE matches the internal +1, +3, +1 rule exactly from its first to last letter with proper wrap-around. Why Other Options Are Wrong: HIKL / STUX / MNPQ do not realize the +1, +3, +1 increments starting from their first letters consistently (or would repeat earlier blocks rather than follow-on progression with wrap-around). Common Pitfalls: Forgetting alphabet wrap-around beyond Z; Z→A is a valid +1 move in cyclic letter series. Final Answer: ZADE

Question 20

Number series – determine the next term: 0, 5, 60, 615, ?

Accepted Answer

Introduction / Context: Some series grow by a “concatenate-like” arithmetic: multiply by a base and then add a steadily increasing addend. Spotting the stable multiplier and the linear growth in the addend reveals the next term quickly. Given Data / Assumptions: Series: 0, 5, 60, 615, ? Values suggest repeated multiplication by 10, followed by adding a multiple of 5. Concept / Approach: Test the hypothesis: each term = previous term * 10 + k, with k increasing by a constant step. Check the successive k values to confirm a linear pattern. Step-by-Step Solution: 0 → 5: 0*10 + 5 = 5 (k = 5)5 → 60: 5*10 + 10 = 60 (k = 10)60 → 615: 60*10 + 15 = 615 (k = 15)k values are 5, 10, 15 → arithmetic progression +5. Next k = 20.Next term = 615*10 + 20 = 6170. Verification / Alternative check: The stable ×10 multiplier is the simplest consistent base; any other option that does not equal 6150 + 20 breaks the linear +5 addend growth. Why Other Options Are Wrong: 6030/6130/6000 do not follow the +5 progression in the additive part (they would correspond to k = −120, −20, or −150 respectively, none of which match the established arithmetic). Common Pitfalls: Interpreting “615” as a concatenation artifact rather than 60*10+15; the arithmetic model explains all transitions precisely. Final Answer: 6170

Number Series Questions