Number Series

Analyze the differences: 675-627=48, 627-580=47, 580-542=38, 542-509=33, 509-485=24, 485-472=13. The pattern should be subtracting decreasing numbers (48, 47, 46, 45...). The difference 580-542=38 breaks this pattern - it should be 580-534=46. If 580 were 534, the pattern would work. Thus 580 is the wrong number.

Check the pattern of differences: 20-13=7, 48-20=28, 112-48=64, 237-112=125, 453-237=216, 796-453=343. These should follow the pattern 1³=1, 2³=8, 3³=27, 4³=64, 5³=125, 6³=216. The first difference 7 doesn't fit - it should be 1 (or 20 should be 14 to make difference 1). Since 20 doesn't fit the cubic pattern, it's the wrong number.

Calculate differences: 96-89=7, 108-96=12, 120-108=12, 139-120=19, 154-139=15, 166-154=12. The pattern alternates between adding 7 and 12: 89+7=96, 96+12=108, 108+7=115, 115+12=127, etc. However, 120 breaks this pattern - it should be 115 to maintain the +7, +12 alternation. Thus 120 is the wrong number.

Analyze the multipliers: 7×4=28, 28×3.5=98, 98×3=294, 294×2.5=735, 735×2=1470, 1470×1.5=2205, 2205×1=2205. The pattern multiplies by decreasing values: 4, 3.5, 3, 2.5, 2, 1.5, 1. However, 2200 doesn't fit - after 2205×1.5=2205, the next should be 2205×1=2205, not 2200. The number 2200 is wrong because it doesn't follow this pattern.

Check the division pattern: 10080÷6=1680, 1680÷10=168 (not 335), 335÷5=67 (not 84). The pattern should be dividing by 6, 10, 5, 4, 3... However, 1680÷10=168, not 335. The number 335 breaks the divisibility pattern. If we had 1680÷5=336, then 336÷4=84, which would fit better. Thus 335 is the wrong number.

The differences between consecutive numbers are: 28-23=5, 34-28=6, 41-34=7, 49-41=8. The differences increase by 1 each time. Following this pattern, the next difference should be 9, so 49+9=58, which is option D.

The pattern is n² - n for n = 10, 12, 15, 19, 23, 28: 100 (10²-10), 140 (12²-4), 216 (15²-15), 340 (19²-21), 525, 780 (28²-4). The pattern breaks at 525. For n=23, the correct term should be 23² - 23 = 529 - 23 = 506, not 525. Alternatively, looking at the pattern of subtracting n, the sequence 10, 4, 15, 21, ?, 4 is inconsistent. Another valid pattern: differences between consecutive terms increase by consecutive odd numbers starting from 9: 140-100=40, 216-140=76 (40+36), 340-216=124 (76+48), next should be 124+61=185, giving 525, then 185+70=255, giving 780. However, checking 460 from another series suggests the odd number increments should be 36, 48, 60, 72, 84, making 525 incorrect.

The pattern is: next term = (previous term) / (position number), then add a constant 8. So: 48/1 + 0 = 48, 48/2 + 0 = 24, 24/3 + 0 = 8? That doesn't work. Another approach: multiply the term by its position to get a constant: 48×1=48, 24×2=48, 16×3=48, 12×4=48. The pattern is term × position = 48. So: 9×5 = 45 ≠ 48, and 8×6 = 48. Therefore, 9 is the wrong number; it should be 8 to maintain the pattern.

The pattern is: subtract consecutive odd numbers (starting from 7) from the next perfect square. 361 - 17 = 344, 400 - 19 = 381, 441 - 21 = 420, 484 - 23 = 461, 529 - 25 = 504, 576 - 27 = 549. The term 460 is incorrect; it should be 461 (22² - 23).

Check pattern: 200 + 1×10 = 210, 210 + 2×7 = 224, 224 + 3×12 = 260. For 260: should add 4×(difference pattern). The pattern of additions is 10, 14, 36, 62, 182. These don't form a consistent sequence. Alternative: 200×1.05=210, 210×1.067≈224, 224×1.161≈260, 260×1.238≈322. 322×1.565≈504. The growth pattern accelerates; 260 doesn't fit the squared difference pattern that should give 262.

Pattern: multiply by increasing integers and add consecutive numbers. 9×1+5=14, 14×2+12=40, 40×3+21=141, but given is 129. Checking further: 129×4+32=548 (given 536), 536×5+45=2705 (matches), 2705×6+60=16290 (given 16260). The pattern appears inconsistent or 40 is the error.

The pattern follows a doubling difference: 3(+7)=10, 10(+14)=24, 24(+28)=52, 52(+56)=108. The added number doubles each time (7, 14, 28, 56). The next addition should be 56×2=112, so 108+112=220.

This is an arithmetic progression where each term increases by 7: 6+7=13, 13+7=20, 20+7=27. To find the missing term, add 7 to the last given number: 27+7=34. The common difference is consistently 7 throughout the series.

The series pattern is: multiply by 2 and add 2, then multiply by 3 and add 2, then multiply by 4 and add 2, etc. Checking: 31×2+2=64 (correct), 64×3+2=194 (should be 194), 194×4+2=778 (but given 784 - WRONG), 778×5+2=3892 (but given 3925), 3892×6+2=23374 (but given 23556). The error starts at 194. If we replace 194 with the correct value following the pattern, we can verify 194 is indeed the wrong term.

The pattern is adding consecutive multiples of 123: 123×1=123, 123×2=246, 123×3=369, 123×4=492, 123×5=615, 123×6=738. Checking: 499+123=622, 622+246=868, 868+369=1237, 1237+492=1729, 1729+615=2344, 2344+738=3082. Option C (3082) is correct.