Question 1

Find the odd number out in the sequence: 3, 5, 11, 14, 17, 21.

Accepted Answer

Problem restatementIdentify the single term that does not follow the same basic property as the others in the list 3, 5, 11, 14, 17, 21. Given data Sequence: 3, 5, 11, 14, 17, 21 Task: Find the one number that differs in a simple, common property. Concept / ApproachStart with the simplest structural checks: parity (odd/even), perfect squares/cubes, small prime/composite patterns, and quick divisibility. The simplest clear separator here is parity. Step-by-step check 3 → odd 5 → odd 11 → odd 14 → even 17 → odd 21 → odd Exactly one term (14) is even; all others are odd. Verification / AlternativePrime/composite is not decisive here (21 and 14 are composite, others are prime), but parity produces a unique outlier: only 14 is even. Common pitfalls Overfitting: trying to impose a complex pattern when a basic property (odd/even) already yields a unique answer. Mixing prime vs composite leads to two composites (14 and 21), not a single outlier. Final Answer14

Question 2

Find the odd number out in the sequence: 8, 27, 64, 100, 125, 216, 343.

Accepted Answer

Problem restatementAmong 8, 27, 64, 100, 125, 216, 343, pick the single term that does not share the same core property. Given data Sequence: 8, 27, 64, 100, 125, 216, 343 Task: Find the unique outlier. Concept / ApproachCheck for perfect powers. These look like cubes around small integers. Step-by-step validation 8 = 23 (cube) 27 = 33 (cube) 64 = 43 (cube) 100 ≠ n3 for integer n (not a cube) 125 = 53 (cube) 216 = 63 (cube) 343 = 73 (cube) Every term is a perfect cube except 100. Verification / AlternativeNearest cubes around 100 are 43 = 64 and 53 = 125; 100 lies between them and is not a cube. Common pitfalls Seeing 100 as a perfect square (102) and assuming all are squares—several terms are not squares but are cubes. Final Answer100

Question 3

Find the odd number out in the sequence: 10, 25, 45, 54, 60, 75, 80.

Accepted Answer

Problem restatementFrom 10, 25, 45, 54, 60, 75, 80, identify the single outlier. Given data Sequence: 10, 25, 45, 54, 60, 75, 80 Concept / ApproachCheck divisibility patterns (by 2, 3, 5). The presence of many multiples of 5 suggests a quick screen. Step-by-step validation 10 → divisible by 5 25 → divisible by 5 45 → divisible by 5 54 → not divisible by 5 60 → divisible by 5 75 → divisible by 5 80 → divisible by 5 All except 54 are multiples of 5; hence 54 is the outlier. Verification / AlternativeDivisibility by 5 requires the last digit 0 or 5. Only 54 ends with neither. Common pitfalls Checking only evenness—several terms are even, but that does not isolate a unique outlier. Final Answer54

Question 4

Find the odd number out in the sequence: 396, 462, 572, 427, 671, 264.

Accepted Answer

Problem restatementAmong 396, 462, 572, 427, 671, 264, select the number that does not share the principal divisibility property of the rest. Given data Sequence: 396, 462, 572, 427, 671, 264 Concept / ApproachTest for a strong common factor. A quick check shows many are divisible by 11. Use the 11-divisibility rule or direct division. Step-by-step validation 396 ÷ 11 = 36 exactly (divisible by 11) 462 ÷ 11 = 42 exactly (divisible by 11) 572 ÷ 11 = 52 exactly (divisible by 11) 427 ÷ 11 = 38 remainder 9 (not divisible by 11) 671 ÷ 11 = 61 exactly (divisible by 11) 264 ÷ 11 = 24 exactly (divisible by 11) All listed numbers are multiples of 11 except 427. Verification / Alternative11-rule: Alternating sum of digits is a multiple of 11. 396: (3 − 9 + 6) = 0 → divisible 462: (4 − 6 + 2) = 0 → divisible 572: (5 − 7 + 2) = 0 → divisible 427: (4 − 2 + 7) = 9 → not divisible 671: (6 − 7 + 1) = 0 → divisible 264: (2 − 6 + 4) = 0 → divisible Common pitfalls Using only divisibility by 3: that splits the set but does not produce a unique outlier. Final Answer427

Question 5

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

Accepted Answer

Problem restatementFrom 6, 9, 15, 21, 24, 28, 30, determine the single term that does not share the common divisibility property. Given data Sequence: 6, 9, 15, 21, 24, 28, 30 Concept / ApproachMost terms look like multiples of 3. Use the sum-of-digits test for divisibility by 3. Step-by-step validation 6 → 6 (sum 6) → divisible by 3 9 → 9 (sum 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 Exactly one term (28) is not divisible by 3. Verification / AlternativeDirect division confirms: 28 ÷ 3 = 9 remainder 1 (not a multiple of 3). Common pitfalls Relying on evenness: several terms are even, so parity does not isolate a unique outlier. Final Answer28

Question 6

Find the odd number out in the sequence: 1, 4, 9, 16, 23, 25, 36.

Accepted Answer

Problem restatementAmong 1, 4, 9, 16, 23, 25, 36, identify the unique term that does not share the core property of the others. Given data Sequence: 1, 4, 9, 16, 23, 25, 36 Concept / ApproachThese are mostly perfect squares of consecutive integers. Step-by-step validation 1 = 12 4 = 22 9 = 32 16 = 42 23 ≠ n2 for integer n 25 = 52 36 = 62 All are perfect squares except 23. Verification / AlternativeNote that 23 lies strictly between 42=16 and 52=25, so it cannot be a perfect square. Common pitfalls Misreading 23 as 62 (which is 36), or assuming it fits the square pattern. Final Answer23

Question 7

Find the odd number out in the sequence: 1, 4, 9, 16, 20, 36, 49.

Accepted Answer

Problem restatementFrom 1, 4, 9, 16, 20, 36, 49, choose the number that does not share the main property with the rest. Given data Sequence: 1, 4, 9, 16, 20, 36, 49 Concept / ApproachThe terms are largely perfect squares of small integers; check each. Step-by-step validation 1 = 12 4 = 22 9 = 32 16 = 42 20 ≠ n2 for integer n 36 = 62 49 = 72 All are perfect squares except 20. Verification / Alternative20 lies between 42=16 and 52=25, confirming it is not a perfect square. Common pitfalls Assuming every term is a square by pattern recognition without checking 20 individually. Final Answer20

Question 8

Sequence given without instruction: '2, 5, 10, 17, 26, 37, 50, 64' (task not specified).

Accepted Answer