Number Series

The series follows a pattern of dividing each term by 2: 240÷2=120, 120÷2=60, 60÷2=30, 30÷2=15. The missing term is 30. Option A (90) would require multiplying by 1.5, which doesn't fit the pattern. Option C (60) repeats the previous term, and Option D (75) doesn't follow the halving rule.

Series: 4, 6, 17, 54, 219, 1098. Pattern: 4×1+2=6, 6×2+5=17, 17×3+3=54, 54×4+3=219, 219×5+3=1098. Wait, let's check: 4×1+2=6, 6×3-1=17, 17×3+3=54, 54×4+3=219, 219×5+3=1098. Actually: 4, (4×1+2)=6, (6×3-1)=17, (17×3+3)=54, (54×4+3)=219, (219×5+3)=1098. The multipliers are 1, 3, 3, 4, 5 - not consistent. Better: 4, 4+2=6, 6+11=17, 17+37=54, 54+165=219... Differences: 2, 11, 37, 165, 879. Second differences: 9, 26, 128, 714. Not clear. Actually: 4×1.5=6, 6×2.83≈17, 17×3.18≈54. Let me try: 4, (4+2)=6, (6×3-1)=17, (17×3+3)=54, (54×4+3)=219. The 6 doesn't fit the pattern. Starting from 17: ×3+3, ×4+3, ×5+3 works. So 6 is the odd one out.

Series: 12, 11, 19, 45, 164, 795. Pattern: 12×1-1=11, 11×2-3=19, 19×3-12=45, 45×4-16=164, 164×5-25=795. Subtractions: 1, 3, 12, 16, 25 = 1², (3), (12 not square), 4², 5². The third subtraction should be 9 (3²) not 12. If subtraction was 9: 19×3-9=48, not 45. So 19 breaks pattern. Alternative: 12-1=11, 11+8=19, 19+26=45, 45+119=164... differences follow pattern. But better: Differences are 1, 8, 26, 119, 631. These multiply by ~3. The issue is 19 - it should make the pattern 12×1-1, then ×2-2, ×3-3, ×4-4, ×5-5. Checking: 12×1-1=11, 11×2-2=20 (not 19), 20×3-3=57 (not 45). Actually 19 is wrong because it breaks ×n-1 pattern: 12×1-1=11, 11×2-1=21 (not 19).

Series: 5, 65, 715, 6435, 45046, 225225. Pattern: 5×13=65, 65×11=715, 715×9=6435, 6435×7=45045 (but 45046 given), 45045×5=225225. The multipliers decrease by 2: 13, 11, 9, 7, 5. The fifth term should be 6435×7=45045, not 45046. So 45046 is wrong.

The pattern alternates between division by 2 and subtraction by 2. The first pair 100, 50 follows 100÷2=50. The second pair 52, 26 follows 52÷2=26. The third pair starts with 28, so applying division: 28÷2=14. The fourth pair 16, 8 confirms the pattern with 16÷2=8. Each number is either halved or reduced by 2 in an alternating sequence.

The correct series should be 72, 74, 80, 92, 112 where the differences between consecutive terms are 2, 6, 12, 20. These differences follow the pattern n(n+1): 1×2=2, 2×3=6, 3×4=12, 4×5=20. The number 73 breaks this elegant pattern, making it the wrong number. If 73 is removed, the series follows a consistent mathematical rule.

The series follows the pattern: multiply by 2, then multiply by 3/4, alternating. 2 × 2 = 4, 4 × 3/4 = 3, 3 × 2 = 6, 6 × 3/4 = 4.5, 4.5 × 2 = 9. The number 10 breaks the pattern as it should be 9. Options A, B, C, D are all correct numbers in the series. Therefore option E (None of these) is correct as none of the listed numbers (2, 4, 3, 6, 4.5) are wrong.

The pattern involves subtracting consecutive odd squares: 895 - 5² = 870, 870 - 7² = 821, 821 - 9² = 740, 740 - 11² = 619. Following this pattern, 619 - 13² should equal 450, not 445. The next term would be 450 - 15² = 225.

Testing the pattern: Each term ×2+2 should give next term (×1.5, ×2.5 alternating or mixed). Pattern varies but 15, 32, 66, 141, 298, 621 suggests no single term is definitively 'wrong'. The pattern could be ×2+2, ×2.5+1, ×2+9, etc. No clear single wrong number. E (None of these) is appropriate as the series is ambiguous.

Pattern analysis: 20÷2=10, 10+1=11 should be 10+2=12, 12÷2=6 but we have 15, 15×2=30, 30+15=45 should be 30×2.5=75. The pattern is ÷2, +2, ÷2, +2... But 11 breaks it (should be 12). Also 15 breaks alternate pattern. Option B (11) is the clearest wrong number.

The series follows an alternating pattern of multiply by 1/2, then multiply by 4, 6, 8, and so on. Starting from 4: 4×1/2=2, 2×4=8, 8×1/2=4, 4×6=24, 24×1/2=12, 12×8=96, 96×1/2=48. The missing term is 48.

The pattern is: add 4, then 9, then 16, then 25 (squares of consecutive integers: 2², 3², 4², 5²). 198+4=202, 202+9=211, 211+16=227, 227+25=252. The next term is 252, matching option B.

Each term is the square of consecutive prime numbers: 5²=25, 7²=49, 11²=121, 17²=289. The next prime is 23, and 23²=529. The primes used are 5, 7, 11, 17, 23 - check that each is prime and consecutive.

The correct answer is 81. The series shows perfect squares in descending order: 169 = 13², 144 = 12², 121 = 11², 100 = 10². Following this pattern, the next term is 9² = 81. The sequence is decreasing by one in the base number: 13, 12, 11, 10, 9.

The pattern is multiply by decreasing multipliers: ×6.5, ×5.5, ×4.5, ×3.5. Checking: 236×6.5=1534 ✓, 1534×5.5=8437 (but given 8437.5), 8437×4.5=37966.5 ✓, 37966.5×3.5=132882.75 ✓. The term 8437.5 breaks the pattern—it should be 8437.