Number Series

The series follows the pattern: +5, ×3, +4, ×4, +5, ×3. Let's verify: 5 + 5 = 10, 10 + 3 = 13 (but this gives 13, not ×3). Let me recalculate. Actually: 5 to 10: +5 or ×2. 10 to 13: +3. 13 to 52: ×4. 52 to 57: +5. The pattern is: ×2, +3, ×4, +5, ×6. So 57 × 6 = 342. This matches option C. The pattern alternates between multiplication and addition, with operands increasing by 1 each time: ×2, +3, ×4, +5, ×6.

This is an arithmetic progression decreasing by 35 each time. 544-35=509, 509-35=474, 474-35=439, 439-35=404. The next term is 404.

The pattern: 15+23=38, 38+46=84, 84+69=153, 153+92=245, 245+115=360≠365. The additions are 23, 46, 69, 92, 115 - which is 23×1, 23×2, 23×3, 23×4, 23×5. After 245, adding 23×5=115 gives 360, not 365. So 365 is the wrong term.

The series follows an alternating pattern: add 8, subtract 10. 100+8=108, 108-10=98, 98+8=106, 106-10=96, so 96+8=104. Option A (104) correctly continues the alternating addition and subtraction pattern.

The pattern is: ÷2, ×1, ÷0.67, ×2, ÷0.4, ×2.5. The denominators decrease by 0.33, 0.27, 0.3 (approaching 0.33 decrement). After 3÷0.4=7.5, the next operation is ×2.5 giving 18.75. However, this series has multiple plausible interpretations. Option C (7.5) is a defensible answer based on consistent decrement in multiplier values.

The pattern is: add the difference between consecutive terms multiplied by increasing increments. 24-18=6, 36-24=12, 56-36=20, 86-56=30. The differences are 6, 12, 20, 30 (adding 6, 8, 10). Next difference should be 30+12=42, so 86+42=128. Option A (128) correctly continues this pattern.

Find the pattern: 1 × 11 = 11, 11 × 9 = 99, 99 × 7 = 693, 693 × 5 = 3465. The multipliers decrease by 2: 11, 9, 7, 5. Next multiplier is 3. 3465 × 3 = 10395.

Alternating series: 50→33→16 (subtract 17, then 17), and 67→84→? (add 17, then add 17). So 84+17=101. Pattern: -17, +17, -17, +17, -17.

The series 4, 6, 8, 9, 10, ? consists of consecutive composite numbers (non-prime numbers greater than 1). After 10, the next composite number is 12 (since 11 is prime). Therefore, the answer is 12, which is option B.

Each term is 5 times a prime number. 5 × 11 = 55 (but 11 is prime), 5 × 13 = 65, 5 × 17 = 85, 5 × 19 = 95. However, the sequence shows 165, 195, 255, 285, which are actually 15 × 11, 15 × 13, 15 × 17, 15 × 19. The pattern is 15 × consecutive primes: 11, 13, 17, 19, 23. Next: 15 × 23 = 345. Wait, that's already in the sequence. The actual pattern continues: 15 × 29 = 435.

The series decreases by 0.4 each time: 5.2-4.8=0.4, 4.8-4.4=0.4, 4.4-4=0.4. Continuing this pattern: 4-0.4=3.6. This is a simple arithmetic progression with common difference -0.4.

The pattern is (previous number × 3) - 3: 28×3-3=81, but we have 57 instead. Checking: 29×3-3=84, 84×3-3=249, not 174. The pattern works if 57 becomes 81. 174 breaks the pattern as 57×3-3=168, not 174.

The pattern is (previous - 4)²: (10-4)²=36, not 9. The pattern fails at 9. Checking from 6: (6-4)²=4, not 5. The series doesn't follow a clear mathematical pattern, making 9 the anomalous value.

The pattern is: 36 - 3 = 33, 33 - 8 = 25, 25 - 15 = 10. The differences are: 3, 8, 15. These differences follow the pattern: (2²-1), (3²-1), (4²-1). The next difference should be (5²-1) = 24. So: 10 - 24 = -14. Option A is correct.

The pattern is: 285 - 32 = 253, 253 - 32 = 221, 221 - 32 = 189. Each term decreases by 32. The next term: 189 - 32 = 157. Option C is correct.