Question 1

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 2

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 3

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 4

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 5

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 6

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 7

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 8

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 9

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 10

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 11

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 12

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 13

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 14

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

Question 15

Number series – find the next term: 9 8 7 6 1 2 3 4 5 9 8 7 1 2 3 4 5 9 8 7 1 2 3 4 9 8 ? The sequence appears to repeat a block “9 8 7 then 1 to 5” several times.

Accepted Answer

Introduction / Context: This question tests detection of a repeating composite block in a digit series. Rather than a single monotonic rule, the pattern cycles through a short descending run before jumping to an ascending run, then repeats. Given Data / Assumptions: Visible segment: 9 8 7 6 1 2 3 4 5 | 9 8 7 | 1 2 3 4 5 | 9 8 7 | 1 2 3 4 | 9 8 ? Assume consistent repetition of the same two-part block. Concept / Approach: Identify the repeating block. The natural reading is: (A) a short descending run beginning with 9 8 7 (occasionally a 6 appears in the first long showing), then (B) an ascending run 1 2 3 4 5. After an ascending run ends at 5, the cycle restarts at 9 8 7. Step-by-Step Solution: Block = [9 8 7] + [1 2 3 4 5].Given tail: “… 1 2 3 4 | 9 8 ?”.After 9 8, the next term in the descending mini-run is 7. Verification / Alternative check: Scan earlier occurrences: after each finished 1–5 ascent, a new “9 8 7” trio starts. The tail matches the start of that trio. Why Other Options Are Wrong: 1/2/5 all belong to the ascending portion; the tail is currently in the descending portion. Common Pitfalls: Overfitting the very first stretch (which includes a 6) and missing that later cycles consistently show 9 8 7 → 1 2 3 4 5. Final Answer: 7

Question 16

Number series – compute the next term using a “difference ×3 + 2” rule: 8, 10, 18, 44, 124, ? First differences follow d_{n} = d_{n-1} * 3 + 2.

Accepted Answer

Introduction / Context: Some non-linear series are governed by a recurrence on the differences, not the terms. Recognizing and extending that difference-recurrence gives the next value directly. Given Data / Assumptions: Terms: 8, 10, 18, 44, 124, ? First differences: 2, 8, 26, 80, … Concept / Approach: Model the first differences. Test d2=2*3+2=8; d3=8*3+2=26; d4=26*3+2=80. The fit is exact, so extend once more using the same rule. Step-by-Step Solution: Next difference: 80*3 + 2 = 242.Next term: 124 + 242 = 366. Verification / Alternative check: Back-substitute differences to reconstruct all terms; the recurrence holds at each step. Why Other Options Are Wrong: 344/354/356 yield differences that are not 242, breaking d_{n}=3*d_{n-1}+2. Common Pitfalls: Trying multiplicative ratios on the terms; here the hidden structure is in the differences. Final Answer: 366

Question 17

Number series – constant second difference (increase first differences by 24): 13, 25, 61, 121, 205, ?

Accepted Answer

Introduction / Context: If first differences form an arithmetic progression, the original series is quadratic-like. Extending the first-difference AP gives the next term smoothly. Given Data / Assumptions: First differences: 25−13=12, 61−25=36, 121−61=60, 205−121=84. Concept / Approach: Differences grow by +24 each time: 12, 36, 60, 84 → next is 108. Add 108 to the last term. Step-by-Step Solution: Next term = 205 + 108 = 313. Verification / Alternative check: Reverse-check: 313−205=108 maintains the +24 ladder. Why Other Options Are Wrong: 323/324/326 would imply next differences 118/119/121, breaking the +24 pattern. Common Pitfalls: Mistaking this for a multiplicative series; the additive structure fits perfectly. Final Answer: 313

Question 18

Number series – next term with decreasing differences by 15: 325, 314, 288, 247, 191, ?

Accepted Answer

Introduction / Context: Here the series decreases, but not by a constant. The first differences themselves fall by a fixed amount, a common pattern in aptitude tests. Given Data / Assumptions: Differences: 314−325=−11, 288−314=−26, 247−288=−41, 191−247=−56. Concept / Approach: Each difference drops by 15: −11, −26, −41, −56 → next is −71. Apply this to the last term. Step-by-Step Solution: Next term = 191 + (−71) = 120. Verification / Alternative check: Back-check: 120−191 = −71, consistent with the −15 step-down in differences. Why Other Options Are Wrong: 116/126/130 would correspond to −75/−65/−61, not following the −71 requirement. Common Pitfalls: Assuming a constant decrement; instead, the decrement itself decreases linearly. Final Answer: 120

Question 19

Number series – multiply by 1.5, 2, 2.5, 3, … and add +1 each time: 45, 46, 70, 141, ?, 1061.5

Accepted Answer

Introduction / Context: This series grows via steadily increasing multiplicative factors, with a small constant adjustment of +1 at each step. Such “multiplier ladder + constant” patterns are common in reasoning sets. Given Data / Assumptions: 45 → 46 (×1 + 1), 46 → 70 (46×1.5 + 1), 70 → 141 (70×2 + 1). Concept / Approach: Multipliers rise by 0.5 each time: 1.5, 2.0, 2.5, 3.0, … and each step adds +1. Apply ×2.5 + 1 to 141 to get the missing value; the next visible step ×3 + 1 should then reach 1061.5 from that value. Step-by-Step Solution: Missing term = 141×2.5 + 1 = 352.5 + 1 = 353.5.Check next: 353.5×3 + 1 = 1060.5 + 1 = 1061.5 ✓ Verification / Alternative check: The 0.5 step in multipliers is consistent, and +1 appears in every jump. Why Other Options Are Wrong: 352/352.5/353 would miss the exact +1 after ×2.5. Common Pitfalls: Trying a single fixed multiplier (e.g., ×2) and ignoring the growing factor. Final Answer: 353.5

Question 20

Number series – alternating +12, −24, +36, −48, … (magnitudes +12 each time): 620, 632, 608, 644, 596, ?

Accepted Answer

Introduction / Context: An alternating add/subtract pattern with steadily growing magnitudes is a staple in number-series questions. The size of the adjustment increases by a fixed amount each time. Given Data / Assumptions: 620 → 632 (+12) 632 → 608 (−24) 608 → 644 (+36) 644 → 596 (−48) Concept / Approach: Magnitudes follow 12, 24, 36, 48 → next is 60; signs alternate +, −, +, −, so the next step is +60. Step-by-Step Solution: Next term = 596 + 60 = 656. Verification / Alternative check: Continuing would be −72 afterward, maintaining the +12 ladder and sign alternation. Why Other Options Are Wrong: 646/+50, 556/−40, 536/−60 do not match the required +60 step. Common Pitfalls: Missing the alternating signs and focusing only on magnitudes. Final Answer: 656

Number Series Questions