Question 1

Identify the odd term in the near-square sequence: 1, 4, 9, 16, 20, 36, 49.

Accepted Answer

Introduction / Context: Most numbers listed are perfect squares. The task is to pick the single non-square. Knowledge of low squares (1^2 to 10^2) is sufficient to resolve such items quickly and reliably. Given Data / Assumptions: 1 = 1^2 4 = 2^2 9 = 3^2 16 = 4^2 36 = 6^2 49 = 7^2 20 is not a perfect square Concept / Approach: Check each entry against the set of perfect squares. Since the surrounding values are exact squares, the non-square becomes evident. Step-by-Step Solution: Confirm squares: 1, 4, 9, 16, 36, 4920 lies between 16 (4^2) and 25 (5^2) and is not a squareTherefore, 20 is the odd term Verification / Alternative check: Square roots: √20 ≈ 4.472 (not integer), whereas √36 = 6 and √49 = 7. Why Other Options Are Wrong: 1/9/49 are perfect squares and fit the pattern; removing them would break the natural square progression. Common Pitfalls: Misclassifying 49 (sometimes mistaken as non-square) or overlooking that 20 is not between any consecutive integer squares. Final Answer: 20

Question 2

Choose the odd number out: 10, 25, 45, 54, 60, 75, 80.

Accepted Answer

Introduction / Context: In many odd-one-out sets, divisibility by a common factor distinguishes most elements from a single exception. Here, observe multiples of 5 versus a number that is not a multiple of 5. Given Data / Assumptions: Multiples of 5 among the terms: 10, 25, 45, 60, 75, 80 54 is not a multiple of 5 Concept / Approach: Apply the divisibility rule for 5: numbers ending with 0 or 5 are multiples of 5. Scan each term’s last digit to classify quickly. Step-by-Step Solution: 10 → ends with 0 ⇒ multiple of 525/45/60/75/80 → end with 5 or 0 ⇒ multiples of 554 → ends with 4 ⇒ not a multiple of 5 ⇒ odd element Verification / Alternative check: Compute remainders modulo 5: 54 mod 5 = 4, while the others give remainder 0. Why Other Options Are Wrong: 10/45/75 are clear multiples of 5, hence part of the majority set. Common Pitfalls: Overthinking with primes or digit sums; the simplest divisibility cue (last digit) is sufficient here. Final Answer: 54

Question 3

Identify the odd term: 16, 25, 36, 72, 144, 196, 225.

Accepted Answer

Introduction / Context: This list contains mostly perfect squares; the aim is to pick the solitary non-square. Recognizing squares up to at least 15^2 is enough to answer confidently. Given Data / Assumptions: 16 = 4^2, 25 = 5^2, 36 = 6^2 144 = 12^2, 196 = 14^2, 225 = 15^2 72 is not a perfect square Concept / Approach: Check each number for being an exact square. One term will not match any n^2 with integer n; that is the odd one out. Step-by-Step Solution: Confirm squares: 16, 25, 36, 144, 196, 22572 falls between 8^2 = 64 and 9^2 = 81 → not a squareHence 72 is the odd term Verification / Alternative check: Prime factorization: 72 = 2^3 * 3^2 — an odd exponent remains, so it cannot be a perfect square. Why Other Options Are Wrong: 36/196/225 are perfect squares and conform to the theme. Common Pitfalls: Confusing 144 as non-square; it is 12^2. Rapid recognition of common squares prevents such slips. Final Answer: 72

Question 4

Find the odd number out: 6, 9, 15, 21, 24, 28, 30.

Accepted Answer

Introduction / Context: Many odd-one-out puzzles can be solved via quick divisibility tests. Here, note that most numbers are divisible by 3 while one is not, making it stand out as the odd term. Given Data / Assumptions: Sequence: 6, 9, 15, 21, 24, 28, 30 Divisibility by 3 test: digit sum divisible by 3 ⇒ number divisible by 3 Concept / Approach: Apply the digit-sum test to each term. All but one will pass; the failing number is the outlier. Step-by-Step Solution: 6 → 6 divisible by 3 ✔9 → 9 divisible by 3 ✔15 → 1+5=6 divisible by 3 ✔21 → 2+1=3 divisible by 3 ✔24 → 2+4=6 divisible by 3 ✔28 → 2+8=10 not divisible by 3 ✖30 → 3+0=3 divisible by 3 ✔ Verification / Alternative check: Direct division: 28/3 leaves remainder 1; each of the others divides evenly by 3. Why Other Options Are Wrong: 24/30/21/15 are all multiples of 3 and thus fit the majority pattern. Common Pitfalls: Assuming “evenness” is the rule; here 24 and 30 are even yet multiples of 3, so parity alone is not the key classifier. Final Answer: 28

Question 5

Identify the odd term in the list: 1, 4, 9, 16, 23, 25, 36.

Accepted Answer

Introduction / Context: The sequence is dominated by perfect squares with a single intrusion. Recognizing squares at a glance is the fastest approach to identifying the non-matching term. Given Data / Assumptions: Squares present: 1(=1^2), 4(=2^2), 9(=3^2), 16(=4^2), 25(=5^2), 36(=6^2) 23 is not a perfect square Concept / Approach: Confirm each as a square or not, and pick the sole non-square as the odd item. Step-by-Step Solution: Check 23: it lies between 16 and 25; √23 ≈ 4.796, not integerAll others equal n^2 for integer nHence, 23 is the odd term Verification / Alternative check: Prime factorization also shows 23 is prime and not a square of any integer. Why Other Options Are Wrong: 9/25/36 are perfect squares and belong in the square set. Common Pitfalls: Confusing 25 with 5^3 (it is 5^2); mixing cube recognition with square recognition. Final Answer: 23

Question 6

Pick the odd number out: 3, 5, 9, 11, 14, 17, 21.

Accepted Answer

Introduction / Context: One simple way to spot an odd one out is to look for parity differences (even vs odd), especially in a set dominated by odd numbers. The given list predominantly contains odd integers, with a single even intruder. Given Data / Assumptions: Odd numbers present: 3, 5, 9, 11, 17, 21 Even number present: 14 Concept / Approach: The parity rule is decisive: only one term is even while all others are odd. Therefore that term is the odd one out in the broader sense of pattern matching. Step-by-Step Solution: Check parity: 3(O), 5(O), 9(O), 11(O), 14(E), 17(O), 21(O)Only 14 is even ⇒ odd-man-out Verification / Alternative check: Other properties (primality, divisibility) produce more than one mismatch. Parity uniquely isolates 14 here. Why Other Options Are Wrong: 21/17/9 are odd numbers and conform to the majority pattern. Common Pitfalls: Overcomplicating with prime checks (e.g., 9 and 21 are composite); parity offers the cleanest single exception. Final Answer: 14

Question 7

Choose the odd term: 10, 14, 16, 18, 21, 24, 26.

Accepted Answer

Introduction / Context: Another parity-based odd-one-out: scan the list for a single odd among evens or vice versa. Rapid parity checks are often the fastest way to resolve such items in competitive exams. Given Data / Assumptions: Evens: 10, 14, 16, 18, 24, 26 Odd: 21 Concept / Approach: Since only 21 does not share even parity with the rest, it is the outlier by parity classification. Step-by-Step Solution: Check parity: 10(E), 14(E), 16(E), 18(E), 21(O), 24(E), 26(E)Hence, 21 is the odd term Verification / Alternative check: Other simple rules (like divisibility by 3) would exclude multiple terms; parity yields a unique odd entry here. Why Other Options Are Wrong: 26/24/18 are even and thus align with the dominant pattern. Common Pitfalls: Looking for arithmetic sequences or factor patterns when an obvious parity cue suffices. Final Answer: 21

Question 8

Find the odd number out: 3, 5, 7, 12, 13, 17, 19.

Accepted Answer

Introduction / Context: This set is dominated by primes; a single composite number appears among them. Recognizing small primes (up to about 20) quickly isolates the outlier. Given Data / Assumptions: Primes present: 3, 5, 7, 13, 17, 19 Composite present: 12 (divisible by 2, 3, 4, 6) Concept / Approach: Classify each as prime or composite. The composite entry among mostly primes is the odd one out. Step-by-Step Solution: Check: 12 is composite; all the others listed are prime numbersTherefore, 12 is the odd term Verification / Alternative check: Trial division confirms primality of 13, 17, 19 and composite nature of 12; 12 = 3*4 = 2*6. Why Other Options Are Wrong: 19/17/13 are prime and belong with the majority of the set. Common Pitfalls: Mislabeling 1 as prime (not applicable here) or overlooking small composite checks. Final Answer: 12

Question 9

Spot the odd entry in the alternating pattern: 5, 16, 6, 16, 7, 16, 7, 16, 9.

Accepted Answer

Introduction / Context: This sequence alternates between a changing value and a fixed value (16). The non-16 terms should form a simple increasing run, but there is a discrepancy. Identifying the intended pattern reveals which non-16 entry is incorrect. Given Data / Assumptions: Positions 1,3,5,7,9 (odd positions) are: 5, 6, 7, 7, 9 Positions 2,4,6,8 (even positions) are constant: 16, 16, 16, 16 Natural intended pattern for odd positions is a steady increase: 5, 6, 7, 8, 9 Concept / Approach: Check the odd-position subsequence independently. If the design is to increment by 1 at each odd position, the fourth odd position should be 8, not 7. Hence, the duplicate 7 violates the pattern and is the odd term. Step-by-Step Solution: Extract odd positions: [5, 6, 7, 7, 9]Expected: [5, 6, 7, 8, 9]Mismatch at the fourth odd position ⇒ value should be 8 but is 7Therefore, the erroneous entry is “7” (the repeated one) Verification / Alternative check: Replacing the repeated 7 with 8 yields a clean alternating pattern: 5,16,6,16,7,16,8,16,9 — a neat, consistent design. Why Other Options Are Wrong: 9 and 6 fit the expected progression; “None of these” is unnecessary since a single mismatch exists. Common Pitfalls: Judging the whole sequence without isolating the alternating streams; missing that 16 is a deliberate constant on even positions. Final Answer: 7

Question 10

Find the odd number out in the pattern: 582, 605, 588, 611, 634, 617, 600.

Accepted Answer

Introduction / Context: Many numeric sequences alternate between two fixed increments. Testing a simple +a, −b pattern often resolves such sets. Here, adding 23 and subtracting 17 alternately fits all but one term. Given Data / Assumptions: Start at 582 Hypothesis: +23, −17, +23, −17, … Concept / Approach: Apply the alternating operations consecutively and compare the expected list with the given list. The mismatch pinpoints the odd term. Step-by-Step Solution: 582 + 23 = 605 ✔605 − 17 = 588 ✔588 + 23 = 611 ✔611 − 17 = 594 (but the list shows 634) ✖Continuing the pattern from the correct 594: +23 ⇒ 617 ✔; −17 ⇒ 600 ✔ Verification / Alternative check: Reconstructing the intended sequence yields: 582, 605, 588, 611, 594, 617, 600. Only 634 breaks the pattern, while all other terms align neatly when 594 is used in its place. Why Other Options Are Wrong: 611/605/600 conform to the alternating +23/−17 rule; 634 does not and is therefore the odd entry. Common Pitfalls: Trying non-alternating progressions or varying step sizes, which complicates rather than clarifies the structure; overlooking that two neighbors can validate the intended steps. Final Answer: 634

Question 11

Choose the odd number out: 22, 33, 66, 99, 121, 279, 594.

Accepted Answer

Introduction / Context: Multiples of a particular integer (here 11) often dominate such sets. Identifying the one number that is not a multiple isolates the odd term cleanly. Given Data / Assumptions: Multiples of 11: 22 (=11*2), 33 (=11*3), 66 (=11*6), 99 (=11*9), 121 (=11*11), 594 (=11*54) 279 / 11 = 25.363… (not an integer) Concept / Approach: Check divisibility by 11 for each entry. Basic factoring or quick division confirms membership in the set of multiples of 11. Step-by-Step Solution: Compute 279 ÷ 11 = 25.363… ⇒ not divisibleAll others divide evenly by 11Therefore, 279 is the odd number out Verification / Alternative check: Use the 11-divisibility test (alternating sum of digits): for 279, (2 − 7 + 9) = 4 ≠ 0 mod 11; for 594, (5 − 9 + 4) = 0 ⇒ divisible by 11. Why Other Options Are Wrong: 33/121/594 are multiples of 11 and thus belong to the main group. Common Pitfalls: Assuming 121 is special (it is 11^2 yet still a multiple of 11 and fits the rule). Final Answer: 279

Question 12

Find the odd term in 2, 5, 10, 50, 500, 5000 (consider divisibility and scaling patterns).

Accepted Answer

Introduction / Context: When a set primarily comprises even numbers formed through scaling by 10 or by even factors, the lone odd number typically stands out. Here, quick parity and divisibility checks help isolate the odd term without over-engineering a complicated progression rule. Given Data / Assumptions: Numbers: 2, 5, 10, 50, 500, 5000 Parity: 2, 10, 50, 500, 5000 are even; 5 is odd Several terms form a scale-by-10 chain: 50 → 500 → 5000 Concept / Approach: Use parity as the primary discriminator. Evenness is shared by all but one term; that exception is the odd number 5. Although various multiplicative links exist among the evens (notably powers of 10), 5 does not participate in those “even” continuations, making it the cleanest odd-man-out. Step-by-Step Solution: Check parity: 2(E), 5(O), 10(E), 50(E), 500(E), 5000(E)Thus 5 uniquely differs in parityAdditionally, from 50 onward each term is 10 times the previous; 5 does not lie on this scaling chain Verification / Alternative check: Modulo checks: 5 mod 2 = 1 (odd), while the others are 0 (even). Any alternative “multiply by 10” chain also excludes 5 as a member. Why Other Options Are Wrong: 2/10/5000 are even and compatible with the evident scaling/ten-based pattern; they are not unique outliers. Common Pitfalls: Forcing a single ratio across the entire list; recognizing parity plus partial ten-scaling is sufficient to identify the anomaly. Final Answer: 5

Question 13

Complete the sequence of consecutive cubes: 1, 8, 27, 64, 125, 216, (…)? Select the correct next term.

Accepted Answer

Introduction / Context: The sequence lists perfect cubes of consecutive natural numbers. Identifying which n^3 comes after 216 resolves the item. Cube recognition up to 7^3 is widely used in aptitude questions. Given Data / Assumptions: 1 = 1^3 8 = 2^3 27 = 3^3 64 = 4^3 125 = 5^3 216 = 6^3 Concept / Approach: Since 216 is 6^3, the next cube is 7^3. Compute 7^3 by multiplying 7 * 7 * 7 to obtain 343. Step-by-Step Solution: 6^3 = 216Next n = 7 ⇒ 7^3 = 7 * 7 * 7 = 343 Verification / Alternative check: Sequence thus continues: 1, 8, 27, 64, 125, 216, 343 — consecutive cubes from 1 to 7. Why Other Options Are Wrong: 354/392/245 are not perfect cubes and do not match the consecutive-cube pattern. Common Pitfalls: Confusing cubes with squares; for example, 256 is 4^4, not in this list. Accurate recall of small cubes helps avoid mistakes. Final Answer: 343

Question 14

Complete the pair-doubling series: 4 → 8, 16 → 32, 64 → ( … ) Find the missing term that continues the same rule.

Accepted Answer

Introduction / Context: This number-series question checks recognition of a simple deterministic rule applied consistently to each pair. Spotting the operation between numbers inside each pair allows us to extend the pattern and fill the blank correctly. Given Data / Assumptions: Three ordered pairs are shown: (4, 8), (16, 32), (64, ?). Within each pair, the second number is derived from the first by the same rule. All numbers are integers and the sequence is monotonic within each pair. Concept / Approach: Look at the mapping inside each pair. If the second element is consistently a multiple of the first, the multiplier should be the same across pairs. Confirm that multiplier by testing the first two pairs, then apply it to the third pair to get the missing value. Step-by-Step Solution: Check pair 1: 4 → 8. This is 4 * 2 = 8.Check pair 2: 16 → 32. This is 16 * 2 = 32.Therefore, the rule inside each pair is “multiply by 2.”Apply the rule to pair 3: 64 → 64 * 2 = 128. Verification / Alternative check: The constant multiplier 2 preserves exact proportional growth. No other consistent single-step operation (addition, subtraction, division) fits both earlier pairs. Hence doubling is uniquely validated here. Why Other Options Are Wrong: -128 / -192: introduce a sign change not used in earlier pairs. 192: would require multiplying 64 by 3, which contradicts the confirmed factor of 2. Common Pitfalls: Mistaking a pair-wise rule for a cross-pair progression. Here each pair is independent but follows the same mapping. Final Answer: 128

Question 15

Odd term in a decreasing pattern: 125, 123, 120, 115, 108, 100, 84, … Identify the wrong number that breaks the intended rule.

Accepted Answer

Introduction / Context: “Odd-man-out” series require reconstructing the intended rule and locating the term that violates it. Many competitive-exam series use prime-based decrements, so checking prime differences is a productive first step here. Given Data / Assumptions: Sequence: 125, 123, 120, 115, 108, 100, 84, … Expectation: a smooth numeric rule (often involving primes or consecutive odds). Only one term is wrong; others are consistent with a single rule. Concept / Approach: Test a “subtract consecutive primes” pattern. The first drops are 2, 3, 5, 7, so the next should be 11, then 13, etc. This is a common motif: 125 − 2 = 123; −3 = 120; −5 = 115; −7 = 108; next should be −11 ⇒ 108 − 11 = 97; then −13 ⇒ 97 − 13 = 84. Step-by-Step Solution: Start: 125125 − 2 = 123123 − 3 = 120120 − 5 = 115115 − 7 = 108Intended next: 108 − 11 = 97 (but the given term is 100)Continuing: 97 − 13 = 84 (matches later term) Verification / Alternative check: Once we correct the middle term to 97, the entire chain becomes perfectly consistent with prime decrements: 2, 3, 5, 7, 11, 13. The presence of 84 later strengthens that reconstruction (since 97 − 13 = 84 exactly). Why Other Options Are Wrong: 125 / 115 / 84: each aligns with the prime-decrement pattern once 100 is replaced by 97. Common Pitfalls: Averaging or forcing a mixed rule; here the elegant consecutive-primes subtraction explains all transitions except the erroneous 100. Final Answer: 100

Question 16

Find the wrong term in an incremental pattern: 125, 127, 130, 135, 142, 153, 165, … Exactly one number violates the intended rule.

Accepted Answer

Introduction / Context: Many incremental series grow by adding consecutive prime numbers. Identifying such a pattern and checking each step quickly reveals an outlier. Here, small increments hint at +2, +3, +5, +7, etc., which are the first primes in order. Given Data / Assumptions: Sequence: 125, 127, 130, 135, 142, 153, 165, … We expect consecutive-prime additions. Only one term should break the rule. Concept / Approach: Compute the differences between successive terms and compare them to the prime list: 2, 3, 5, 7, 11, 13, … If all but one step match, the number at which the mismatch occurs is the odd term. Step-by-Step Solution: 127 − 125 = +2 (prime)130 − 127 = +3 (prime)135 − 130 = +5 (prime)142 − 135 = +7 (prime)153 − 142 = +11 (prime)165 − 153 = +12 (but the next prime should be +13)Therefore, the step to 165 is wrong; the correct next term would be 153 + 13 = 166. Verification / Alternative check: Replacing 165 with 166 restores perfect prime increments: +2, +3, +5, +7, +11, +13, which is a standard, widely used pattern. Why Other Options Are Wrong: 130 / 142 / 153 each fits the prime-increment rule exactly. Common Pitfalls: Assuming a mixed odd-number increment; primes are the clean fit and expose the 165 anomaly. Final Answer: 165

Question 17

Locate the wrong term in a “subtract consecutive odds” pattern: 52, 51, 48, 43, 34, 27, 16, …

Accepted Answer

Introduction / Context: A classic decreasing series subtracts consecutive odd numbers: −1, −3, −5, −7, −9, −11, … Detecting one misstep among these consistent decrements identifies the odd term out. Given Data / Assumptions: Sequence: 52, 51, 48, 43, 34, 27, 16, … Expected rule: subtract consecutive odd numbers. Exactly one number is incorrect. Concept / Approach: Compute differences and compare to the sequence of odd numbers 1, 3, 5, 7, 9, 11. A deviation from this list pinpoints the wrong value. Step-by-Step Solution: 52 − 51 = 1 (odd 1)51 − 48 = 3 (odd 3)48 − 43 = 5 (odd 5)43 − 34 = 9 (should have been 7 if strictly consecutive)Proper step: 43 − 7 = 36 (not 34)Continuing: 36 − 9 = 27, 27 − 11 = 16 Verification / Alternative check: Once 34 is corrected to 36, all decrements line up perfectly with 1, 3, 5, 7, 9, 11. The given 27 and 16 already align with the corrected course, confirming that 34 is the only anomaly. Why Other Options Are Wrong: 48 / 43 / 27: each respects the consecutive-odd subtraction once the earlier correction is made. Common Pitfalls: Mistaking a single out-of-order odd decrement (9 vs 7) as a wholesale pattern change. Final Answer: 34

Question 18

Find the wrong number in the series: 3, 8, 15, 24, 34, 48, 63, …

Accepted Answer

Introduction / Context: Here the sequence grows by adding consecutive odd numbers to the previous term. Such a pattern is very common: +5, +7, +9, +11, +13, +15, … A single mis-addition creates the odd term out. Given Data / Assumptions: Series: 3, 8, 15, 24, 34, 48, 63. Intended increments are consecutive odd numbers starting at 5. Only one term deviates from the rule. Concept / Approach: Compute successive differences and compare them with the intended odd list. Replace the faulty term with the correctly incremented value to confirm the pattern. Step-by-Step Solution: 3 + 5 = 8 (OK)8 + 7 = 15 (OK)15 + 9 = 24 (OK)24 + 11 = 35 (but the series shows 34)Continuing intended: 35 + 13 = 48, 48 + 15 = 63 Verification / Alternative check: With 34 corrected to 35, all steps align perfectly with +5, +7, +9, +11, +13, +15. The later terms 48 and 63 already fit the corrected sequence, proving that 34 is the lone error. Why Other Options Are Wrong: 15 / 24 / 48: all are consistent with the intended consecutive-odd increments. Common Pitfalls: Mistaking arbitrary differences; the clean consecutive-odd rule best explains the progression. Final Answer: 34

Question 19

Fill in the next term: 2, 4, 12, 48, 240, ( … ) Follow the evolving multiplier pattern.

Accepted Answer

Introduction / Context: This is a product-based series where each term is obtained by multiplying the previous term by a steadily increasing integer. Identifying the evolving multiplier lets us extend the series confidently. Given Data / Assumptions: Series: 2, 4, 12, 48, 240, … All terms are positive integers; multipliers appear to grow. Concept / Approach: Compute term-wise ratios to the previous term. If the ratios form 2, 3, 4, 5, … then the next multiplier is 6. Apply that to get the missing term. Step-by-Step Solution: 4 / 2 = 212 / 4 = 348 / 12 = 4240 / 48 = 5Next multiplier = 6 ⇒ Next term = 240 * 6 = 1440 Verification / Alternative check: This pattern is strictly multiplicative with consecutive integers. No additive pattern fits all jumps so precisely (2→4→12→48→240), reinforcing the identified rule. Why Other Options Are Wrong: 960 / 1080 / 1920: correspond to multipliers 4, 4.5, or 8 that break the clear 2, 3, 4, 5, 6 progression. Common Pitfalls: Averaging jump sizes or mixing addition with multiplication; the exact integer ratios settle the matter. Final Answer: 1440

Question 20

Continue the pattern of increasing even increments: 2, 6, 12, 20, 30, 42, 56, ( … )

Accepted Answer

Introduction / Context: This additive series increases by consecutive even numbers. Recognizing the difference pattern is key to projecting the next term correctly. Given Data / Assumptions: Series: 2, 6, 12, 20, 30, 42, 56, … Differences look like +4, +6, +8, +10, +12, +14. Concept / Approach: List successive differences. If they are consecutive even numbers starting from 4, extend with the next even number to get the missing term. Step-by-Step Solution: 6 − 2 = 412 − 6 = 620 − 12 = 830 − 20 = 1042 − 30 = 1256 − 42 = 14Next difference = 16 ⇒ Next term = 56 + 16 = 72 Verification / Alternative check: Even-difference ladders are common: starting at 4 and adding 2 each step reproduces every jump perfectly, confirming 72. Why Other Options Are Wrong: 60 / 64 / 70: imply differences of 4, 8, or 14 again; only +16 continues the rising-even pattern. Common Pitfalls: Guessing the next term from a visual trend without calculating differences, which can be misleading. Final Answer: 72

Odd Man Out and Series Questions