Question 1

Arithmetic progression of subtractions — detect the misfit Find the odd one out: 105, 85, 60, 30, 0, -45, -90.

Accepted Answer

Introduction / Context:Here, the numbers are decreasing by successively larger amounts. When such a pattern is regular, any single deviation indicates the odd term. We will reconstruct the intended subtraction pattern and identify which listed number violates it. Given Data / Assumptions: List: 105, 85, 60, 30, 0, -45, -90. We suspect a steadily increasing subtraction (by fixed steps). Concept / Approach:Compute consecutive differences to see if they follow a simple sequence such as −20, −25, −30, −35, −40, −45. If the given list fails one of these expected transitions, the result at that point is the misfit. Step-by-Step Solution:105 → 85: −20.85 → 60: −25.60 → 30: −30.Expect next: 30 − 35 = −5 (if continuing −35), but the list shows 0.Continuing the expected pattern: −5 − 40 = −45; then −45 − 45 = −90.Thus the only inconsistent value is 0; it should have been −5 for a smooth −20, −25, −30, −35, −40, −45 scheme. Verification / Alternative check:Look at the tail end: from −45 to −90 is a −45 step, consistent with the intended increment in subtractions. The discrepancy occurs solely at the 30 → 0 transition where −35 is expected. Why Other Options Are Wrong:85, 60, 30, and −45 each aligns with the expected stepped subtractions around them; only the zero breaks the run. Common Pitfalls:Assuming all differences must be equal; here they grow by 5 each time. Missing that nuance can hide the odd term in plain sight. Final Answer:0

Question 2

Two interleaved progressions (+3 and +5): find the next term Sequence: 8, 7, 11, 12, 14, 17, 17, 22, ( ... ). What comes next?

Accepted Answer

Introduction / Context:Interleaved series contain two independent subsequences occupying alternating positions. Detecting each subsequence and extending the appropriate one yields the next term correctly. Given Data / Assumptions: Main sequence: 8, 7, 11, 12, 14, 17, 17, 22, ... Odd positions: 1st, 3rd, 5th, 7th, ... Even positions: 2nd, 4th, 6th, 8th, ... Concept / Approach:Separate odd-index and even-index terms and examine the pattern of each. The 9th term will be part of the odd-index subsequence, so extend that one by its rule. Step-by-Step Solution:Odd-index subsequence (positions 1,3,5,7,...): 8, 11, 14, 17, ... ⇒ +3 each time ⇒ next odd-index term = 20.Even-index subsequence (positions 2,4,6,8,...): 7, 12, 17, 22, ... ⇒ +5 each time.The 9th term is odd-indexed ⇒ answer = 20. Verification / Alternative check:Continuing: after 20 (9th), the 10th would be 27 (even-index subsequence +5 from 22). This confirms both subsequences are consistent. Why Other Options Are Wrong:27 would be the 10th term, not the 9th; 22 and 24 do not follow the +3 progression for the odd-index track at this step; 26 also belongs to a different continuation. Common Pitfalls:Adding a constant to the entire series without separating the two interwoven patterns. Always split odd and even positions when increments seem to oscillate. Final Answer:20

Question 3

Alternate ×3 and ÷2 pattern Complete the series: 8, 24, 12, 36, 18, 54, ( ... ).

Accepted Answer

Introduction / Context:This series alternates between multiplication and division by simple constants. Recognizing the two-step loop allows a quick computation of the next term from the last known value. Given Data / Assumptions: Series: 8, 24, 12, 36, 18, 54, ... Observed operations: ×3, ÷2, ×3, ÷2, ... Concept / Approach:From any term to the next: if the previous step was ×3, the next is ÷2, and vice versa. Apply the operation appropriate after 54 (which followed a ×3 from 18) — therefore divide by 2. Step-by-Step Solution:8 → 24: ×3.24 → 12: ÷2.12 → 36: ×3.36 → 18: ÷2.18 → 54: ×3.54 → next: ÷2 ⇒ 27. Verification / Alternative check:Continuing further would give 27 → 81 (×3) and then 81 → 40.5 (÷2), maintaining the loop. The identified step is consistent. Why Other Options Are Wrong:108 or 72 correspond to applying ×2 or ×4 rather than ÷2; 68 and 30 do not match the established pattern. Common Pitfalls:Missing the alternation and applying the same operation repeatedly. Always confirm the last two transitions to detect the loop. Final Answer:27

Question 4

Powers of two minus one Find the next term: 15, 31, 63, 127, 255, ( ... ).

Accepted Answer

Introduction / Context:This sequence consists of numbers of the form 2^n − 1. Recognizing these Mersenne-type values enables immediate continuation by increasing n by one and computing the next term. Given Data / Assumptions: Terms: 15, 31, 63, 127, 255. Forms: 2^4 − 1 = 15, 2^5 − 1 = 31, 2^6 − 1 = 63, 2^7 − 1 = 127, 2^8 − 1 = 255. Concept / Approach:Continue the pattern with n = 9 to get 2^9 − 1. Compute 2^9 = 512, then subtract 1 to obtain the next value. Step-by-Step Solution:Identify n values: 4, 5, 6, 7, 8.Next exponent n = 9.Compute 2^9 = 512; subtract 1 ⇒ 511. Verification / Alternative check:The ratio between successive terms approaches 2 as n grows, and differences roughly double, consistent with powers of two minus one. The exact continuation 511 is standard. Why Other Options Are Wrong:513, 517, and 523 are not equal to 2^9 − 1; 383 corresponds to 2^8 − 1 + 128, not part of this pattern. Common Pitfalls:Using addition or multiplication tables instead of identifying the exponential structure. Always test whether terms align with a simple power-based form. Final Answer:511

Question 5

Two interleaved arithmetic sequences (+3, −2) Complete: 3, 7, 6, 5, 9, 3, 12, 1, 15, ( ... ).

Accepted Answer

Introduction / Context:In interleaved series, odd and even positions follow different linear rules. Recognizing each subsequence allows you to extend the correct one to find the next term in the main sequence. Given Data / Assumptions: Main sequence: 3, 7, 6, 5, 9, 3, 12, 1, 15, ... Odd-index positions: 1st, 3rd, 5th, 7th, 9th (values 3, 6, 9, 12, 15). Even-index positions: 2nd, 4th, 6th, 8th (values 7, 5, 3, 1). Concept / Approach:Observe that odd-index terms increase by +3, while even-index terms decrease by −2. The 10th term is even-indexed, so apply the even rule (−2 from the previous even term). Step-by-Step Solution:Odd-index subsequence: 3 → 6 → 9 → 12 → 15 (add 3 each time).Even-index subsequence: 7 → 5 → 3 → 1 (subtract 2 each time).Next (10th) term = previous even term (1) − 2 = −1. Verification / Alternative check:If continued, the 11th term (odd-index) would be 18 (15 + 3), confirming both patterns remain consistent beyond the provided segment. Why Other Options Are Wrong:18 is the 11th term, not the 10th; 13 and 3 belong to the odd-index progression; 0 breaks the −2 pattern from 1. Common Pitfalls:Failing to separate the sequence into two tracks and trying to force a single constant difference across all terms. Final Answer:-1

Question 6

Double then ±1 alternating rule Find the next term: 16, 33, 65, 131, 261, ( ... ).

Accepted Answer

Introduction / Context:Some sequences double the current value and then alternately add or subtract 1. Recognizing the alternation (+1, −1, +1, −1, ...) is key to predicting the next figure after a given term. Given Data / Assumptions: Sequence: 16, 33, 65, 131, 261, ... Rule suspected: next = (current * 2) ± 1, with signs alternating. Concept / Approach:Verify the rule across steps, then apply it once more. The pattern appears to be: ×2 + 1, ×2 − 1, ×2 + 1, ×2 − 1, ... Step-by-Step Solution:16 → 33: 16*2 + 1 = 33.33 → 65: 33*2 − 1 = 65.65 → 131: 65*2 + 1 = 131.131 → 261: 131*2 − 1 = 261.261 → next: 261*2 + 1 = 523. Verification / Alternative check:Checking sign alternation confirms consistency across all transitions. Therefore, 523 must be the continuation. Why Other Options Are Wrong:521 would require −1 (not the correct sign at this step); 613 and 721 do not follow ×2 ± 1; 511 corresponds to a different pattern entirely. Common Pitfalls:Missing the ± alternation and applying +1 (or −1) repeatedly, which quickly derails the sequence. Final Answer:523

Question 7

Difference-halving expectation — identify the odd term Sequence: 445, 221, 109, 46, 25, 11, 4. Which entry is the misfit?

Accepted Answer

Introduction / Context:Odd-man-out puzzles often hide a pattern in successive differences. If you expect roughly halving gaps or a smooth decline, any break in that rhythm reveals the odd term. We will analyze the differences to spot the inconsistency. Given Data / Assumptions: Series: 445, 221, 109, 46, 25, 11, 4. Goal: detect a regular reduction pattern and find where it is violated. Concept / Approach:Compute consecutive differences and compare them. A consistent halving/near-halving or steadily tightening decrease should appear; if one step is disproportionately off the expected size, the endpoint of that step is likely the misfit. Step-by-Step Solution:445 → 221: −224.221 → 109: −112 (exactly half of −224).109 → 46: −63 (not close to half of −112 which would be −56; this is a notable break).46 → 25: −21 (now much smaller; if previous had been −56, a plausible follow might be −28 or −27).25 → 11: −14; 11 → 4: −7 (these two restore a halving feel: −14 then −7).Thus, the jump to 46 (with −63) disrupts the otherwise near-halving cadence; 46 is the odd term. Verification / Alternative check:Had the third difference been −56, the next could have been around −28, then −14, then −7, creating a smooth halving sequence from −224 onwards. The value 46 forces a −63 difference and derails this pattern. Why Other Options Are Wrong:221 and 109 fit the clean −224 then −112 halving; 25, 11, and 4 fit the smaller tail reductions (−21, −14, −7) more naturally than 46 does. Common Pitfalls:Looking only at raw values rather than differences, or accepting any decrease as fine without checking the regularity of the step-size progression. Final Answer:46

Question 8

Identify the odd number by structural property List: 19, 26, 33, 46, 59, 74, 91. Which one is the odd one out?

Accepted Answer

Introduction / Context:When a numeric set lacks a clear arithmetic pattern, examine number-theory features like parity, divisibility, and primality. If exactly one term is prime while the rest are composite, the prime is the natural odd-man-out. Given Data / Assumptions: Candidates: 19, 26, 33, 46, 59, 74, 91. Goal: choose the single value that differs in basic factorization status (prime vs. composite). Concept / Approach:Test primality: a prime has no factors other than 1 and itself. Composite numbers factor into smaller integers. We look for a unique prime amidst composites, considering that 19 at the start might tempt but is not among the provided options to select (we must choose from the listed answer choices). Step-by-Step Solution:26 = 2 * 13 ⇒ composite.33 = 3 * 11 ⇒ composite.46 = 2 * 23 ⇒ composite.74 = 2 * 37 ⇒ composite.91 = 7 * 13 ⇒ composite.59 is prime (not divisible by 2, 3, 5, 7; √59 ≈ 7.68, so only small primes need testing). Verification / Alternative check:Among the provided options (26, 33, 46, 59, 74), only 59 cannot be factored. Therefore 59 stands apart. Why Other Options Are Wrong:26, 33, 46, and 74 are all composite; each shares the majority property and thus cannot be the odd one out. Common Pitfalls:Overlooking that the selectable answers differ from the full list and misidentifying a different prime not present among the options. Always select from the given choices. Final Answer:59

Question 9

Single perfect square amidst non-squares — pick the odd one out Sequence: 190, 166, 145, 128, 112, 100, 91. Which number is different?

Accepted Answer

Introduction / Context:Sometimes the quickest way to isolate an odd term is to check for well-known special classes of numbers (like perfect squares). If only one number belongs to such a class, it is the outlier regardless of the surrounding differences pattern. Given Data / Assumptions: Candidates: 190, 166, 145, 128, 112, 100, 91. Check: is any one a perfect square? Concept / Approach:Test each term: a perfect square is of the form n^2 for some integer n. Among two-digit or three-digit values, 100 (= 10^2) is an immediate standout. The rest are not perfect squares (no integer √n). Step-by-Step Solution:100 = 10^2 ⇒ perfect square.190, 166, 145, 128, 112, 91: none equals m^2 for an integer m. √190 ≈ 13.78, √166 ≈ 12.88, √145 ≈ 12.04, √128 ≈ 11.31, √112 ≈ 10.58, √91 ≈ 9.54, all non-integers.Therefore, 100 uniquely belongs to the “perfect square” category. Verification / Alternative check:Even if you attempt to fit a decreasing-difference rule, you will not find a compelling uniform pattern that singles out any term other than 100 by a fundamental property. The square-status criterion is decisive. Why Other Options Are Wrong:166, 145, 128, and 112 are not perfect squares and thus share the majority status with 190 and 91; they are not the odd ones out. Common Pitfalls:Overcomplicating the pattern hunt and missing simple number classes. Always scan for perfect squares, cubes, or triangular numbers as a first pass. Final Answer:100

Question 10

n^3 − 1 pattern (consecutive cubes minus one) Find the next term: 7, 26, 63, 124, 215, 342, ( ... ).

Accepted Answer

Introduction / Context:The series matches the form n^3 − 1 for consecutive integers n. Recognizing this lets you continue by moving to the next integer and applying the same formula. Given Data / Assumptions: 7 = 2^3 − 1 26 = 3^3 − 1 63 = 4^3 − 1 124 = 5^3 − 1 215 = 6^3 − 1 342 = 7^3 − 1 Concept / Approach:Next n = 8 ⇒ next term = 8^3 − 1 = 512 − 1 = 511. Step-by-Step Solution:Identify formula: term(n) = n^3 − 1.Compute for n = 8: 8^3 = 512.Subtract 1 ⇒ 511. Verification / Alternative check:Differences between terms grow roughly as 3n^2 − 3, consistent with cubic behavior. The explicit computations confirm the pattern exactly. Why Other Options Are Wrong:481, 391, 421, and 450 are not equal to 8^3 − 1 and do not continue the exact n^3 − 1 rule. Common Pitfalls:Misreading 124 as 125 (a perfect cube) and assuming cubes themselves, not “cubes minus one.” Always check each term. Final Answer:511

Question 11

Multiples of 11 property — pick the odd one out Numbers: 385, 462, 572, 396, 427, 671, 264. Which one is different?

Accepted Answer

Introduction / Context:One efficient technique for odd-man-out sets is to check divisibility by a common factor that most numbers share. If all but one are multiples of a particular integer (here 11), the non-multiple is the outlier. Given Data / Assumptions: Candidates: 385, 462, 572, 396, 427, 671, 264. Hypothesis: Most of these might be divisible by 11. Concept / Approach:Use the 11-divisibility test or quick division to confirm whether each number is a multiple of 11. The one failing the test is the odd term. Step-by-Step Solution:385 = 35 * 11 ⇒ multiple of 11.462 = 42 * 11 ⇒ multiple of 11.572 = 52 * 11 ⇒ multiple of 11.396 = 36 * 11 ⇒ multiple of 11.671 = 61 * 11 ⇒ multiple of 11.264 = 24 * 11 ⇒ multiple of 11.427 ÷ 11 = 38 remainder 9 ⇒ not a multiple of 11. Verification / Alternative check:The alternating digit sum test for 11 confirms the same: for 427, (4 − 2 + 7) = 9, not a multiple of 11. All others pass cleanly by direct factorization shown. Why Other Options Are Wrong:385, 462, 572, 396, 671, and 264 are all multiples of 11 and hence share the majority property. Common Pitfalls:Overlooking easy divisibility patterns and instead trying complex relationships. A quick 11-check saves time here. Final Answer:427

Question 12

Perfect cubes with one impostor — choose the odd one out Set: 1, 8, 27, 64, 124, 216, 343. Which number does not belong?

Accepted Answer

Introduction / Context:Most terms here are perfect cubes, making the single non-cube the odd one out. Identifying cubes is straightforward by remembering small n^3 values or quickly testing cube roots for integers. Given Data / Assumptions: Numbers: 1, 8, 27, 64, 124, 216, 343. Known cubes: 1^3=1, 2^3=8, 3^3=27, 4^3=64, 6^3=216, 7^3=343. Concept / Approach:Check each term for being an exact cube. The non-cube in the set is the outlier. Step-by-Step Solution:1 = 1^3 ⇒ cube.8 = 2^3 ⇒ cube.27 = 3^3 ⇒ cube.64 = 4^3 ⇒ cube.124 is not a perfect cube (5^3 = 125; 124 is one less).216 = 6^3 ⇒ cube.343 = 7^3 ⇒ cube. Verification / Alternative check:Since 124 falls directly between 5^3 − 1 and 5^3, it cannot be a cube. All other numbers are exact cubes of small integers. Why Other Options Are Wrong:8, 27, 64, and 216 are perfect cubes. They belong to the dominant category and thus are not the odd ones out. Common Pitfalls:Confusing 124 with 125 (which is 5^3). Carefully verify the exact value before concluding. Final Answer:124

Question 13

Quadratic odd-difference growth with one mismatch — pick the odd term Sequence: 19, 28, 39, 52, 67, 84, 102. Which number is the odd one out?

Accepted Answer

Introduction / Context:Sequences that grow by successive odd numbers are common. If the odd increments are expected to increase by 2 each time (e.g., +9, +11, +13, +15, +17, +19, ...), a single term violating the next required jump will be the odd one out. Given Data / Assumptions: Series: 19, 28, 39, 52, 67, 84, 102. Differences: 28−19=9, 39−28=11, 52−39=13, 67−52=15, 84−67=17, 102−84=18. Concept / Approach:The pattern of differences is intended to be consecutive odd numbers: 9, 11, 13, 15, 17, 19, ... Therefore after 84, the next value should be 84 + 19 = 103. A value of 102 indicates a break in that rule and is thus the misfit. Step-by-Step Solution:Compute differences: 9, 11, 13, 15, 17 (all odd, increasing by 2).Expected next difference = 19.Expected next term = 84 + 19 = 103.Given next term = 102 (short by 1) ⇒ mismatch. Verification / Alternative check:If we replace 102 with 103, the differences become 9, 11, 13, 15, 17, 19 — a perfect consecutive odd-number pattern. Hence 102 is the sole inconsistency. Why Other Options Are Wrong:52, 84, 67, and 39 fit the consecutive odd-difference growth; removing any of them breaks earlier correct steps. Common Pitfalls:Assuming constant differences, or missing that the gap sequence is itself structured (odd integers increasing by 2). Always analyze the first few differences to detect intent. Final Answer:102

Question 14

Odd Man Out – Identify the inconsistent term in the pattern: Sequence: 4, 9, 19, 39, 79, 160, 319

Accepted Answer

Introduction / Context:This is an odd-man-out question on number series. The goal is to detect the intended rule driving the sequence and then spot the single term that violates that rule. Such patterns frequently involve simple recurrences like multiply-and-add or consistent differences. Given Data / Assumptions: Sequence shown: 4, 9, 19, 39, 79, 160, 319 Assume a uniform rule is intended for all steps. Concept / Approach:A common pattern is “double the previous number, then add 1.” We test each transition for the rule a(n+1) = 2*a(n) + 1 and see where the sequence breaks. Step-by-Step Solution:From 4: 2*4 + 1 = 9 ✔From 9: 2*9 + 1 = 19 ✔From 19: 2*19 + 1 = 39 ✔From 39: 2*39 + 1 = 79 ✔From 79: expected 2*79 + 1 = 159; given term is 160 ✖From 159 (if correct): 2*159 + 1 = 319, which matches the last term ✔ Verification / Alternative check:If we replace 160 with 159, the entire chain satisfies the single rule without exception. The last term 319 confirms the rule by equaling 2*159 + 1. Why Other Options Are Wrong:39, 79, and 319 each comply with “double + 1.” Only 160 breaks the recurrence; 159 would have fit. Common Pitfalls:Looking for changing offsets (like +1, +1, +2) instead of noticing a consistent recurrence; or assuming a late-series deviation implies multiple rules. Final Answer:160

Question 15

Fill in the missing term to continue the alternating +3, −1 pattern: 9, 12, 11, 14, 13, ( ? ), 15

Accepted Answer

Introduction / Context:This is a completion-type number series. Many aptitude sequences alternate between two simple operations. Here the differences appear to repeat in a short cycle, which allows us to fill in the gap accurately. Given Data / Assumptions: Observed sequence: 9, 12, 11, 14, 13, ( ? ), 15 We assume a short repeating pattern of operations. Concept / Approach:Check consecutive differences and see if they alternate: +3, −1, +3, −1, … If so, apply the next +3 step to the known preceding term to obtain the missing value, then confirm by the subsequent −1 step reaching the final given term. Step-by-Step Solution:9 → 12: +312 → 11: −111 → 14: +314 → 13: −113 → ( ? ): +3 ⇒ 1616 → 15: −1 (matches the last term) Verification / Alternative check:Rewriting the pattern: start at 9, then apply (+3, −1) repeatedly to reconstruct the full sequence, which uniquely yields 16 as the middle term. Why Other Options Are Wrong:12, 10, 17, and 14 do not satisfy the alternating +3 then −1 steps while still landing on 15 afterwards. Common Pitfalls:Trying to force a single arithmetic progression; many test items rely on alternating micro-patterns. Final Answer:16

Question 16

Complete the series using the recurring “double then ±1” pattern: 2, 5, 9, 19, 37, ( ? )

Accepted Answer

Introduction / Context:Many series in aptitude tests toggle a small add/subtract around a doubling or tripling rule. Here the numbers suggest doubling plus or minus a small constant in an alternating fashion. Given Data / Assumptions: Sequence: 2, 5, 9, 19, 37, ( ? ) We suspect a pattern of doubling followed by ±1. Concept / Approach:Check terms pairwise: 2*2 + 1 = 5; 5*2 − 1 = 9; 9*2 + 1 = 19; 19*2 − 1 = 37. The sign flips each time: +1, −1, +1, −1. Hence the next step should again be +1. Step-by-Step Solution:2 → 5: 2*2 + 15 → 9: 5*2 − 19 → 19: 9*2 + 119 → 37: 19*2 − 137 → ( ? ): 37*2 + 1 = 75 Verification / Alternative check:Continuing the alternating signs reproduces the earlier structure exactly, confirming 75 fits uniquely. Why Other Options Are Wrong:76 and 74 are off by ±1 from the correct doubling outcome; “None” is invalid since 75 matches. Common Pitfalls:Forgetting the sign alternation and using +1 repeatedly. Final Answer:75

Question 17

Choose the next term in the alternating +5, −7 pattern: 71, 76, 69, 74, 67, 72, ( ? )

Accepted Answer

Introduction / Context:This completion problem uses alternating fixed differences: add a constant, then subtract a (different) constant, repeatedly. Recognizing the two-step cycle is the key to predicting the next value. Given Data / Assumptions: Sequence: 71, 76, 69, 74, 67, 72, ( ? ) We suspect alternating +5 and −7. Concept / Approach:Compute successive differences: 71→76 (+5), 76→69 (−7), 69→74 (+5), 74→67 (−7), 67→72 (+5). The pattern dictates the next step must be −7. Step-by-Step Solution:After 67, +5 gives 72 (shown)Next move is −7 ⇒ 72 − 7 = 65 Verification / Alternative check:Replaying the pair (+5, −7) repeatedly rebuilds all terms and uniquely implies 65 next. Why Other Options Are Wrong:77 and 76 correspond to +5 moves; 80 and 69 do not continue the established cycle. Common Pitfalls:Assuming a single arithmetic progression; the two-step cycle is essential here. Final Answer:65

Question 18

Fill in the power-of-two between 64 and 256: 1, 2, 4, 8, 16, 32, 64, ( ? ), 256

Accepted Answer

Introduction / Context:This is a classic power-of-two sequence. Each term doubles the previous one. Recognizing that exponent pattern lets us insert the missing value instantly. Given Data / Assumptions: Known terms: 1, 2, 4, 8, 16, 32, 64, ( ? ), 256 Doubling rule holds throughout. Concept / Approach:Powers of two are 2^0, 2^1, 2^2, … The terms shown run 1, 2, 4, …, 64 (= 2^6), next is 2^7 = 128, then 2^8 = 256. Step-by-Step Solution:64 * 2 = 128128 * 2 = 256 Verification / Alternative check:Listing exponents: 0,1,2,3,4,5,6,(7),8 confirms the placement. Why Other Options Are Wrong:148, 154, 164, and 96 are not powers of two and break the doubling pattern. Common Pitfalls:Mistaking the sequence for an arithmetic progression; here it is geometric (ratio 2). Final Answer:128

Question 19

Complete the two-interleaved sequences (odd and even positions): 10, 5, 13, 10, 16, 20, 19, ( ? )

Accepted Answer

Introduction / Context:Many series are built from two simpler interleaved sequences: one governing the odd-indexed terms and another governing the even-indexed terms. Separating these streams makes the pattern clear and the missing value easy to compute. Given Data / Assumptions: Total sequence: 10, 5, 13, 10, 16, 20, 19, ( ? ) Odd positions (1,3,5,7): 10, 13, 16, 19 Even positions (2,4,6,8): 5, 10, 20, ( ? ) Concept / Approach:Odd-position rule: +3 each step. Even-position rule: ×2 each step. Apply the even-position rule to the last even term to find the 8th term. Step-by-Step Solution:Odd: 10 → 13 → 16 → 19 (add 3 repeatedly)Even: 5 → 10 → 20 → ( ? ) (double each time)Thus, ( ? ) = 20 * 2 = 40 Verification / Alternative check:Re-merging the two subsequences gives 10,5,13,10,16,20,19,40, which respects both rules. Why Other Options Are Wrong:22, 38, 23, 35 do not satisfy the ×2 progression on the even-indexed terms. Common Pitfalls:Trying to force a single-step difference across the whole series instead of splitting into odd/even strands. Final Answer:40

Question 20

Find the next term from alternating +30 and +60 jumps: 165, 195, 255, 285, 345, ( ? )

Accepted Answer

Introduction / Context:This is a difference-pattern series using a repeating two-step increment. Identifying the increment cycle enables direct computation of the next term. Given Data / Assumptions: Sequence: 165, 195, 255, 285, 345, ( ? ) Differences observed: +30, +60, +30, +60, … Concept / Approach:Apply the same two-step cycle to extend the series: after +60 from 285 to 345, the next jump should revert to +30. Step-by-Step Solution:165 + 30 = 195195 + 60 = 255255 + 30 = 285285 + 60 = 345345 + 30 = 375 Verification / Alternative check:The strict repetition (+30, +60) leaves no ambiguity; 375 uniquely fits. Why Other Options Are Wrong:420 and 435 would require +75 or +90; 390 implies +45; 360 is − or +15 shift; none match the cycle. Common Pitfalls:Assuming a single arithmetic progression; the alternating increments are essential. Final Answer:375

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