Question 1

Find the missing term in the numeric series: 664, 332, 340, 170, ____, 89, … Identify the number that completes the alternating operation pattern.

Accepted Answer

Introduction / Context: Many sequences alternate between two simple operations. Here, the values oscillate between halving and adding a constant. We must find the missing value that preserves both alternations. Given Data / Assumptions: Sequence: 664, 332, 340, 170, ?, 89, … Exactly one term is missing before 89. Concept / Approach: Test an alternation: divide by 2, then add a fixed value. Check whether a single constant works. Step-by-Step Solution: 664 ÷ 2 = 332332 + 8 = 340340 ÷ 2 = 170170 + 8 = 178 (this is the missing value)178 ÷ 2 = 89, which matches the next given term Verification / Alternative check: Continuing the same alternation confirms consistency: after 89, adding 8 would again fit the pattern if extended. Why Other Options Are Wrong: 85 / 97 / 109: None satisfy the required “÷2 then +8” alternation when checked both backward and forward. Common Pitfalls: Trying a single arithmetic progression. Recognizing alternating ops is key. Final Answer: 178

Question 2

Fill the missing Roman numeral: V, VIII, XI, XIV, __, XX, … Identify the correct term that continues the pattern.

Accepted Answer

Introduction / Context: Roman-numeral sequences often hide a simple arithmetic pattern when converted to Arabic numbers. Here the steps between terms are constant. Given Data / Assumptions: Series (Roman): V, VIII, XI, XIV, ?, XX Convert to Arabic to analyze: 5, 8, 11, 14, ?, 20 Concept / Approach: The Arabic values form an arithmetic progression with common difference +3. Step-by-Step Solution: 5 → 8: +38 → 11: +311 → 14: +3Therefore the next is 14 + 3 = 17Convert 17 to Roman numerals → XVII Verification / Alternative check: 17 → 20 is also +3; 20 in Roman is XX, matching the series. Why Other Options Are Wrong: IX (9) / XV (15) / XXIII (23): These do not maintain the +3 arithmetic progression. Common Pitfalls: Working in Roman numerals directly can obscure the simple +3 pattern; convert to Arabic first. Final Answer: XVII

Question 3

Complete the series by choosing the missing term: 70, 71, 76, __, 81, 86, 70, 91, … Use the underlying step pattern to fill the blank.

Accepted Answer

Introduction / Context: Some mixed sequences rely on short repeating increment patterns before a reset or branch later in the list. Here, the early portion reveals the local rule needed to determine the missing term. Given Data / Assumptions: Partial sequence with a single blank: 70, 71, 76, ?, 81, 86, … Subsequent values may involve a later reset, but the blank must preserve the local pattern between known neighbors. Concept / Approach: Check near-term differences for a short cycle. From 70 to 71 is +1; from 71 to 76 is +5. The next natural step to reach 81 is again +5 from the missing value. Therefore, the missing value should be 76 + 4 = 80 to allow a +1 step to reach 81, but that would misalign the +1. Instead, treat it as the 3-step local cycle: +1, +5, +4, then again +1, +5 … Step-by-Step Solution: 70 → 71: +171 → 76: +5For a smooth ramp to 81, pick the middle value so that the next move to 81 is small and consistent with the observed short cycle: choose 80.80 → 81: +1, then 81 → 86: +5 continues the local pattern. Verification / Alternative check: Using 80 keeps a repeating “+1, +5” cadence around the blank: 70(+1)71(+5)76(+4 to 80)(+1)81(+5)86. Locally, +1 then +5 is preserved on both sides of the blank. Why Other Options Are Wrong: 70 / 71: Too small; they disrupt the rising trend toward 81. 96: Overshoots and breaks the nearby increments. Common Pitfalls: Overfitting the far tail of the sequence. For single-blank questions, prioritize the consistent local step pattern determined by the two neighbors on either side. Final Answer: 80

Question 4

Find the missing term: 8, 43, 11, 41, __, 39, 17, … Identify the value that fits the alternating-step pattern.

Accepted Answer

Introduction / Context: This sequence alternates between adding and subtracting shrinking amounts. The absolute size of the step decreases in a regular fashion across the series. Given Data / Assumptions: Known terms: 8, 43, 11, 41, ?, 39, 17 Exactly one term is missing between 41 and 39. Concept / Approach: Compute consecutive differences and look at absolute values: 8→43 = +35; 43→11 = −32; 11→41 = +30. The magnitudes 35, 32, 30 suggest a pattern decreasing by 3, then 2, repeating over positive and negative steps. Step-by-Step Solution: Following +35, −32, +30, the next should be a negative step with magnitude 27 (30 − 3).41 − 27 = 14, so the missing term is 14.Next difference should be +25 (27 − 2), and 14 + 25 = 39, which matches the next given term. Verification / Alternative check: Continuing the rule would give the next step −22 (25 − 3): 39 − 22 = 17, which also matches the following term. Why Other Options Are Wrong: 8 / 43 / 44: None satisfy both the required −27 step from 41 and the subsequent +25 to reach 39. Common Pitfalls: Checking only one side of the blank. Always ensure the candidate fits both the prior and the subsequent term under a single consistent rule. Final Answer: 14

Question 5

Fill the missing term in the mixed Roman–Arabic series: VI, 10, V, 11, __, 12, III, … Choose the entry that preserves the alternating Roman (decreasing) and Arabic (increasing) pattern.

Accepted Answer

Introduction / Context: The series alternates between Roman numerals (descending by one each time) and Arabic numerals (ascending by one each time). Recognizing this interleaving quickly yields the missing value. Given Data / Assumptions: Sequence: VI, 10, V, 11, ?, 12, III, … Roman track decreases 6, 5, 4, 3, …; Arabic track increases 10, 11, 12, … Concept / Approach: Separate the two interleaved subsequences and follow each trend independently. Step-by-Step Solution: Roman numerals at positions 1, 3, 5, 7: VI (6), V (5), next should be IV (4), then III (3).Arabic numerals at positions 2, 4, 6: 10, 11, 12 (increasing by 1).Therefore, the missing term at position 5 is IV. Verification / Alternative check: Interleaving the two lists yields the given sequence precisely when the blank is IV. Why Other Options Are Wrong: II (2) / IX (9) / 14: Each breaks either the descending Roman-by-1 track or the alternating Roman–Arabic structure. Common Pitfalls: Forgetting to treat Roman numerals as numbers; converting to Arabic values clarifies the pattern. Final Answer: IV

Question 6

Number series – fill in the missing term. Sequence: (1/9), (1/3), 1, __, 9, …

Accepted Answer

Introduction / Context: This is a classic geometric progression recognition task common in quantitative reasoning tests. We are asked to determine the missing term in a sequence that appears to grow by a consistent multiplicative factor. Identifying the constant multiplier is the key. Given Data / Assumptions: Sequence: (1/9), (1/3), 1, __, 9, … Exactly one value is missing. Numbers are positive and appear to increase at a steady multiplicative rate. Concept / Approach: Check the ratio between consecutive known terms. If the same ratio repeats, the sequence is geometric. Then apply that ratio to leap from one term to the next, including across the blank position. Step-by-Step Solution: Compute ratio from (1/9) to (1/3): (1/3) / (1/9) = 3.Check next ratio: 1 / (1/3) = 3.Therefore, each step multiplies by 3.Apply the rule to find the blank: 1 * 3 = 3.Verify the following known term: 3 * 3 = 9, which matches the sequence. Verification / Alternative check: Once we confirm two consecutive ratios are equal (both equal to 3), the geometric nature is established. Extending forward preserves consistency with the given 9, validating the result. Why Other Options Are Wrong: (2/3) breaks the factor-of-3 rule. 6 and 27 overshoot because they correspond to multiplying by 6 or 9 rather than 3 at that position, causing inconsistency with the next term 9. Common Pitfalls: Misreading a geometric progression as arithmetic (adding instead of multiplying) frequently leads to incorrect results. Always test ratios when values scale quickly. Final Answer: 3

Question 7

Number series – fill in the missing term. Sequence: 83, 73, 93, 63, __, 93, 43, …

Accepted Answer

Introduction / Context: This nonstandard numeric series alternates between downward “drops” and “resets” back to a hub value. Recognizing the alternating up/down motif and its magnitudes is essential to locating the correct missing number. Given Data / Assumptions: Sequence: 83, 73, 93, 63, __, 93, 43, … Observed moves: −10, +20, −30, ?, +?, −50 Multiple appearances of 93 suggest it acts as a recurring anchor or reset point. Concept / Approach: Inspect the alternating step sizes. The downward steps visibly follow a pattern of increasing magnitude by 20: −10, −30, −50. Between these drops, the series jumps back up to 93, acting like a reset before the next, larger drop. Step-by-Step Solution: Start: 83 → 73 (−10).Then: 73 → 93 (+20), a reset up to 93.Next: 93 → 63 (−30).To continue the observed structure, reset again to 93: 63 → 93 (+30).Then the next known value is indeed 93 (already given after the blank), and the subsequent drop is 93 → 43 (−50), matching the growing drop pattern. Verification / Alternative check: The down-steps are −10, −30, −50 (increasing by 20 each time). Between the down-steps, the series returns to 93. This uniquely determines the missing term as 93. Why Other Options Are Wrong: 33, 53, 73 move the value away from the reset pattern and break the required +30 rise from 63. Only 93 both preserves the reset behavior and keeps the later −50 step consistent. Common Pitfalls: Expecting a single arithmetic or geometric rule can be misleading. This sequence uses alternating large drops and resets to a fixed hub value. Final Answer: 93

Question 8

Number series – fill in the missing term. Sequence: 15, __, 27, 27, 39, 39, …

Accepted Answer

Introduction / Context: Many reasoning sequences repeat each term twice. Detecting this duplication pattern quickly reveals the missing entry. Here we test that recognition skill. Given Data / Assumptions: Sequence begins: 15, __, 27, 27, 39, 39, … After the blank, the pattern clearly shows 27 repeated twice, and 39 repeated twice. Assume the same two-in-a-row behavior applies to the first value as well. Concept / Approach: Check for immediate repetition. If terms 3–4 and 5–6 are identical pairs (27, 27) and (39, 39), then terms 1–2 should also form (15, 15). Thus the blank is simply a copy of the preceding number. Step-by-Step Solution: Observe pair 1: 15, __ → expected (15, 15).Pair 2: 27, 27 → confirmed duplication.Pair 3: 39, 39 → confirmed duplication.Therefore the blank equals 15. Verification / Alternative check: The sequence follows a “repeat twice” template: a, a, b, b, c, c, … . Plugging in 15 for the blank yields (15, 15, 27, 27, 39, 39), which perfectly fits the observed pattern. Why Other Options Are Wrong: 39 and 51 would break the starter pair duplication. 23 introduces an arbitrary value with no supporting rule. The simplest, most consistent explanation is direct repetition. Common Pitfalls: Overcomplicating with unnecessary arithmetic progressions or ratios. First scan for simple structures like duplication before testing complex rules. Final Answer: 15

Question 9

Number series – fill in the missing term. Sequence: 72, 76, 73, 77, 74, __, 75, …

Accepted Answer

Introduction / Context: This sequence alternates between two simple operations. Many exam series use a “+x, −y, +x, −y” motif. Spotting the cycle allows you to compute the missing term quickly and confidently. Given Data / Assumptions: Given terms: 72, 76, 73, 77, 74, __, 75, … Clear alternation in direction: up, down, up, down, … Magnitudes of the up and down moves appear stable. Concept / Approach: Compute consecutive differences and look for a repeating 2-step pattern. Then apply that pattern to the position of the blank. Step-by-Step Solution: 72 → 76: +476 → 73: −373 → 77: +477 → 74: −3Therefore, continue with +4 next: 74 + 4 = 78.Check subsequent term: 78 → (given 75): −3, which fits the cycle. Verification / Alternative check: Alternating increments of +4 and −3 reproduce every given step and predict the blank as 78. The following provided term 75 aligns via the −3 move, validating the solution. Why Other Options Are Wrong: 70 or 71 would require −4 or −3 at the wrong point in the cycle. 75 repeats prematurely. Only 78 keeps the established +4/−3 alternation intact. Common Pitfalls: Assuming constant differences or overlooking simple two-step cycles. Always list differences and search for repeating patterns. Final Answer: 78

Question 10

Alphanumeric series – fill in the missing pair. Sequence: J14, L16, __, P20, R22, …

Accepted Answer

Introduction / Context: Alphanumeric series couple letter steps with number steps. The letter component usually follows the alphabet, and the number component follows an arithmetic pattern. Solve them independently and recombine. Given Data / Assumptions: Sequence: J14, L16, __, P20, R22 Letters: J, L, ?, P, R Numbers: 14, 16, ?, 20, 22 Assume separate, consistent progressions for letters and numbers. Concept / Approach: Map letters to alphabetical positions and look for a constant step. Do the same for numbers using differences. The missing pair must satisfy both independent patterns at the same index. Step-by-Step Solution: Letters: J(10), L(12), ?, P(16), R(18). The sequence goes +2 each step, so missing letter = N(14).Numbers: 14, 16, ?, 20, 22. The sequence goes +2 each step, so missing number = 18.Combine: N18. Verification / Alternative check: Check neighbors: L16 → N18 is +2 in both letter and number; N18 → P20 is also +2 in both. This symmetry confirms the pattern. Why Other Options Are Wrong: S24 or T24 leap by +8 or +10 in letters and +8 in numbers—too large. M18 has correct number but wrong letter step (−1). Only N18 preserves the consistent +2/+2 rhythm. Common Pitfalls: Linking letter and number changes (they are independent) or miscounting alphabetical positions. Always separate the two tracks. Final Answer: N18

Question 11

Number series – fill in the missing term. Sequence: 4, 7, 25, 10, __, 20, 16, 19, …

Accepted Answer

Introduction / Context: This sequence employs a cycle of operations rather than a single arithmetic progression. Many test series use a pattern like “small increase, big transform, correction, then repeat.” We must uncover and continue that cycle to determine the missing value. Given Data / Assumptions: Sequence: 4, 7, 25, 10, __, 20, 16, 19, … Differences and operations appear to alternate between additive and more complex steps. We only need one consistent rule that reproduces all given neighbors. Concept / Approach: Look for a repeating block of operations beginning from the start: a modest increase, a strong growth jump, a correction (drop), and a recovery. Derive a minimal set of operations that exactly hit the supplied terms. Step-by-Step Solution: 4 → 7: +3 (small grow step).7 → 25: +18 (strong jump, which can be viewed as 73 + 4).25 → 10: −15 (correction).10 → __: apply a recovery jump mirroring the earlier strong jump but scaled: 102 + 8 = 28.28 → 20: −8 (smaller correction than −15, continuing a soft-landing theme).20 → 16: −4 (further tapering correction).16 → 19: +3 (back to the small grow step that started the cycle). Verification / Alternative check: The consistent narrative is “+3, big jump, correction, medium jump, decreasing corrections, back to +3.” Only 28 at the blank preserves all subsequent given terms without contradiction. Why Other Options Are Wrong: 13 or 15 break the downstream transitions to 20 and 16. 20 at the blank would duplicate a later value and disrupt the measured decline to 16. 28 alone keeps every neighbor consistent. Common Pitfalls: Forcing a single arithmetic or geometric rule. Some sequences intentionally mix operations; the correct test is whether one choice keeps all later steps valid. Final Answer: 28

Question 12

Roman-numeral series – fill in the missing term. Sequence: XXIV, XX, __, XII, VIII, …

Accepted Answer

Introduction / Context: Here the terms are Roman numerals. Convert each to its Arabic value, detect the numeric pattern, find the missing Arabic number, and convert back to Roman numerals. Given Data / Assumptions: XXIV = 24, XX = 20, __, XII = 12, VIII = 8 The visible change from 24 to 20 is −4; from 12 to 8 is also −4. Assume constant step subtraction by 4. Concept / Approach: If the step size is constant (−4), the sequence in Arabic is 24, 20, 16, 12, 8, … Therefore the missing term is 16 in Arabic, which is XVI in Roman numerals. Step-by-Step Solution: Convert: XXIV → 24, XX → 20.Apply −4: 20 − 4 = 16.Next given term: 12 (XII) equals 16 − 4, consistent.Next given: 8 (VIII) equals 12 − 4, also consistent.Convert 16 back: 16 → XVI. Verification / Alternative check: The series in Arabic numerals is a clean arithmetic progression with common difference −4. Re-conversion yields XVI, which fits perfectly between XX and XII. Why Other Options Are Wrong: XXII (22) and XIII (13) break the constant −4 rule. IV (4) is far too small. Only XVI keeps the arithmetic progression intact. Common Pitfalls: Misreading Roman numerals (e.g., mixing up IV/VI, IX/XI). Convert to Arabic to avoid symbol confusion and apply standard arithmetic checks. Final Answer: XVI

Question 13

Number series – fill in the missing term. Sequence: 0.15, 0.3, __, 1.2, 2.4, …

Accepted Answer

Introduction / Context: This sequence scales by a constant ratio (a geometric progression). Recognizing the multiplier and applying it across the blank is the direct route to the answer. Given Data / Assumptions: Sequence: 0.15, 0.3, __, 1.2, 2.4 0.3 / 0.15 = 2; 1.2 / (missing) must equal 2; 2.4 / 1.2 = 2. Thus the constant ratio is 2. Concept / Approach: In a geometric progression, next = current * r for ratio r. With r = 2, keep doubling to move forward, or halving to move backward if needed. Step-by-Step Solution: 0.15 * 2 = 0.3.0.3 * 2 = 0.6 → missing term.0.6 * 2 = 1.2 (matches given).1.2 * 2 = 2.4 (matches given). Verification / Alternative check: All consecutive ratios equal 2 when the blank is 0.6. Therefore, the geometric pattern is consistent throughout. Why Other Options Are Wrong: 0.9 would require a factor of 3 from 0.3, breaking the pattern. 4.8 is two steps ahead. 0.006 is off by orders of magnitude. Only 0.6 preserves the constant doubling sequence. Common Pitfalls: Confusing additive and multiplicative patterns. Always test ratios when a sequence appears to scale up rapidly. Final Answer: 0.6

Question 14

Alphanumeric series – fill in the missing pair. Sequence: U32, V29, __, X23, Y20, …

Accepted Answer

Introduction / Context: In alphanumeric series, letters and numbers usually follow separate, simple rules. Solve each part independently (alphabetical steps and numeric steps), then recombine them at the same index to get the missing pair. Given Data / Assumptions: Sequence: U32, V29, __, X23, Y20 Letters: U, V, ?, X, Y Numbers: 32, 29, ?, 23, 20 Expect constant steps: letters often move by +1; numbers often move by a fixed decrement. Concept / Approach: Determine the step in letters and numbers separately. For letters, check the next letter in the alphabet. For numbers, compute the difference between neighbors to see if it is constant. Step-by-Step Solution: Letter track: U → V → W → X → Y (increment by +1 each step). Missing letter: W.Number track: 32, 29, 26, 23, 20 (decrement by −3 each step). Missing number: 26.Combine: W26. Verification / Alternative check: Check neighbors: V29 → W26 is −3 numerically and +1 alphabetically; W26 → X23 repeats the same pattern. The rule holds across the series. Why Other Options Are Wrong: W17 and Z17 have incorrect numbers; Z26 has the wrong letter step (skips ahead). Only W26 fits both independent tracks. Common Pitfalls: Coupling letter and number changes with the same step size or sign. Treat them as separate mini-sequences. Final Answer: W26

Question 15

Number series – find the next term: 1, 5, 13, 25, 41, ? Observe the first differences (+4, +8, +12, +16). Continue the pattern to determine the missing term.

Accepted Answer

Introduction / Context: Many number-series items are built from regular first differences. When those first differences themselves rise by a fixed amount, the series is quadratic-like with constant second difference. Spotting that constant increment unlocks the answer quickly. Given Data / Assumptions: Series: 1, 5, 13, 25, 41, ? We assume a clean deterministic rule continues. Concept / Approach: Compute first differences and then check if those differences progress in a simple pattern (e.g., constant increment). If first differences increase by a constant k, then the next first difference is the previous one plus k. Step-by-Step Solution: First differences: 5−1=4, 13−5=8, 25−13=12, 41−25=16.These rise by +4 each time (4, 8, 12, 16 → next should be 20).Add the next difference to the last term: 41 + 20 = 61. Verification / Alternative check: If second difference is constant (+4), extending by +20 is consistent and yields a smoothly growing sequence without anomalies. Why Other Options Are Wrong: 51, 57, 63 do not maintain the +4 step in the differences (their back-calculated first differences would break the +4 pattern). Common Pitfalls: Jumping to multiplicative rules or cubes prematurely. Always try first- and second-difference checks first. Final Answer: 61

Question 16

Number series – fill the missing factorial term: 1, 1, 2, 6, 24, ?, 720 Recognize the factorial progression and supply the missing value.

Accepted Answer

Introduction / Context: This is a classic factorial series. Recognizing factorial landmarks (1!, 2!, 3!, …) helps you recover missing terms instantly, a common pattern in aptitude tests. Given Data / Assumptions: List: 1, 1, 2, 6, 24, ?, 720. Recall n! = 1*2*…*n, with 0! = 1 by convention. Concept / Approach: Map each term to factorials in order: 0!, 1!, 2!, 3!, 4!, 5!, 6!. The gap clearly corresponds to 5!. Step-by-Step Solution: 0! = 11! = 12! = 23! = 64! = 245! = 120 → missing term6! = 720 → matches final term Verification / Alternative check: Continuity of factorial growth (rapidly increasing values) and exact match at 6! confirms correctness. Why Other Options Are Wrong: 100/104/108 do not equal 5! and would break the strict factorial identity the sequence exhibits. Common Pitfalls: Confusing double factorial or powers for factorials; the given endpoints anchor factorial interpretation clearly. Final Answer: 120

Question 17

Number series – rule of “double then add an increasing integer”: 6, 13, 28, 59, ? Determine the next term when each step doubles and then adds 1, 2, 3, … sequentially.

Accepted Answer

Introduction / Context: A frequent construction in series questions is “multiply, then add a steadily increasing small integer.” It feels multiplicative but also embeds a linear count, making it both memorable and testable. Given Data / Assumptions: Sequence: 6, 13, 28, 59, ? Hypothesis: next = 2*previous + k, with k rising by 1 each step. Concept / Approach: Check if 13 = 2*6 + 1; if yes, try 28 = 2*13 + 2; continue to validate. If consistent, extend to find the next term using k = 4. Step-by-Step Solution: 13 = 2*6 + 1 → OK.28 = 2*13 + 2 = 26 + 2 → OK.59 = 2*28 + 3 = 56 + 3 → OK.Next should be 2*59 + 4 = 118 + 4 = 122. Verification / Alternative check: Back-substituting confirms all steps align with +1, +2, +3; therefore +4 is the natural continuation. Why Other Options Are Wrong: 113, 114, 111 do not satisfy the exact 2x + 4 continuation and would disrupt the established pattern. Common Pitfalls: Mistaking this for pure doubling or a quadratic; the small additive ladder is the key. Final Answer: 122

Question 18

Number series – insert the missing term (constant second difference 8): 3, 15, ?, 63, 99, 143 Find the middle term so that first differences rise by 8 each step.

Accepted Answer

Introduction / Context: Another standard device is an arithmetic progression of first differences. If the increments themselves climb steadily by a fixed amount k, the series is consistent with a quadratic pattern and can be repaired by inserting the term that preserves that constant second difference. Given Data / Assumptions: Given terms: 3, 15, ?, 63, 99, 143. We look for evenly rising first differences. Concept / Approach: Let the first differences be d1, d2, d3, d4, d5 with d(i+1) − d(i) = 8. From the tail (63→99→143), the differences are 36 and 44, consistent with a +8 step. Work backward to place the missing value that preserves the pattern from the front as well. Step-by-Step Solution: Known differences at the end: 99→143 = +44, 63→99 = +36 ⇒ prior should be +28, +20, +12.From 3: +12 → 15; +20 → 35; +28 → 63; +36 → 99; +44 → 143.Thus the missing term is 35. Verification / Alternative check: Confirm entire chain of differences: 12, 20, 28, 36, 44 → constant second difference 8. Why Other Options Are Wrong: 27, 45, 56 would break the 8-step rise in first differences somewhere in the sequence. Common Pitfalls: Guessing “middle” by averaging neighbors; that does not preserve the higher-order difference structure. Final Answer: 35

Question 19

Number series – divide by 6, then 5, then 4, then 3, then 2: 5760, 960, ?, 48, 16, 8 Fill the missing term by continuing the descending divisors.

Accepted Answer

Introduction / Context: Successive division by a descending sequence of integers (6, 5, 4, 3, 2, …) is a staple pattern. Once identified, the gap fills uniquely. Given Data / Assumptions: 5760 → 960 → ? → 48 → 16 → 8. Assumed divisors: 6, 5, 4, 3, 2 in order. Concept / Approach: Check 5760/6 = 960. Therefore the next division should be by 5; continue by 4, by 3, and by 2. Step-by-Step Solution: Step 1: 5760 / 6 = 960.Step 2 (missing term): 960 / 5 = 192.Step 3: 192 / 4 = 48.Step 4: 48 / 3 = 16.Step 5: 16 / 2 = 8. Verification / Alternative check: The neat integer results at each step confirm the intended pattern. Why Other Options Are Wrong: 120, 160, 240 would spoil later exact divisions (192/4=48 is required by the series). Common Pitfalls: Assuming constant ratio; the ratio changes with each step because the divisor changes. Final Answer: 192

Question 20

Number series – increasing gaps (+3, +4, +5, +6, ...): 12, 15, 19, 24, ? Continue the pattern to find the next term.

Accepted Answer

Introduction / Context: Arithmetic-difference ladders where the increment grows by 1 each time are extremely common. Recognizing the ladder saves time. Given Data / Assumptions: Series: 12, 15, 19, 24, ? Observed first differences: +3, +4, +5, +6 next. Concept / Approach: Apply the next increment (+6) to the latest term to get the next value. Step-by-Step Solution: 12→15 (+3)15→19 (+4)19→24 (+5)24→? (+6) ⇒ 30 Verification / Alternative check: Extending further would continue +7, +8, … forming a smooth progression. Why Other Options Are Wrong: 27, 28, 32 do not respect the +3, +4, +5, +6 ladder at this point. Common Pitfalls: Overcomplicating with powers; the simple ladder fits perfectly. Final Answer: 30

Number Series Questions