Number Series

Calculate differences: 119 - 80 = 39, 166 - 119 = 47, 221 - 166 = 55, 223 - 221 = 2. The differences 39, 47, 55 increase by 8 each time. The next difference should be 55 + 8 = 63, making the last term 221 + 63 = 284, not 223. Option E (223) is correct as the wrong term. Option D (192) is a distractor not in the series.

Calculate differences: 8.5 - 8 = 0.5, 11.5 - 8.5 = 3, 14 - 11.5 = 2.5, 17 - 14 = 3. The pattern alternates between +3 and +0.5. Starting from 8, the sequence should be: 8 + 3 = 11, 11 + 0.5 = 11.5, 11.5 + 3 = 14.5, 14.5 + 0.5 = 15. The term 8.5 breaks this pattern. Option B (8.5) is correct as the wrong term.

30+4=34, 34+9=43, 43+16=59, 59+15=74. The added amounts are 4, 9, 16, 15. These are 2^2, 3^2, 4^2, then 3×5 (3 and 5 from 34 and 43). Next should be 4^2=16: 74+36=110. Option A is correct.

The pattern is 2n + 1: 3×2+1=7, 7×2+1=15, 15×2+1=31, 31×2+1=63. So the next term is 63×2+1=127. Each term is double the previous term plus one.

The pattern is: divide by 2, then add 1, repeated. Check: 2442 ÷ 2 + 1 = 1222 ✓, 1222 ÷ 2 + 1 = 612 ✗ (given as 614). The claimed wrong number is 90, but 90 fits the pattern: 163 ÷ 2 + 1 = 82.5 (should be 82.5, not 90). Let me verify: 2442 → 1222 (÷2+1) ✓, 1222 → 614 (÷2+3? no), 614 → 312 (÷2+5), 312 → 163 (÷2+7), 163 → 90 (÷2+8.5), 90 → 56.25 (÷2+11.25). The pattern shifts. Let me recalculate: 2442 ÷ 2 = 1221, +1 = 1222 ✓. 1222 ÷ 2 = 611, +3 = 614 ✓. 614 ÷ 2 = 307, +5 = 312 ✓. 312 ÷ 2 = 156, +7 = 163 ✓. 163 ÷ 2 = 81.5, +8.5 = 90 ✓. 90 ÷ 2 = 45, +11.25 = 56.25 ✓. All numbers fit a pattern of ÷2 then add an increasing odd number. Wait—the question asks for the wrong number. Let me check if 90 breaks it: 163 ÷ 2 + 8.5 = 90, but 90 ÷ 2 + 11.25 = 56.25. The addition increments are: +1, +3, +5, +7, +8.5, +11.25. The increment from +7 to +8.5 to +11.25 is inconsistent. 90 should be 81.5 + 9 = 90.5 (if following +9). So 90 is indeed the wrong number.

All numbers in the series are palindromic (read the same forwards and backwards): 232, 343, 454, [should be 565], 676. The number 564 breaks this pattern because it reads as 465 in reverse, not 564. The correct number following the pattern would be 565.

The differences between consecutive terms should double each time: 24-21=3, 30-24=6, [42-30=12], [66-42=24]. The number 41 breaks this pattern because 41-30=11 instead of the expected 12. If 42 were in place of 41, the pattern of doubling differences (3, 6, 12, 24) would hold.

The pattern is: add 1³, add 2³, add 3³, add 4³. Starting from 5: 5 + 1 = 6, 6 + 8 = 14 (not 15), 14 + 27 = 41, 41 + 64 = 105, 105 + 125 = 230. The number 15 is incorrect because 6 + 8 should equal 14, not 15. This makes 15 the wrong number that breaks the cubic addition pattern.

The series follows a pattern of subtracting 111 repeatedly: 975-111=864, 864-111=753, 753-111=642, 642-111=531, 531-111=420. However, the given term is 743 instead of 753. So 743 is the wrong number that breaks the pattern. Checking the actual sequence: 975, 864, 743, 642, 531, 420. Differences: 975-864=111, 864-743=121 (wrong), 743-642=101 (inconsistent), 642-531=111, 531-420=111. The term 743 is incorrect; it should be 753 for a consistent -111 pattern.

The pattern is ×2+1 starting from 8: 8×2+1=17, 17×2+2=36, 36×2+3=75, 75×2+4=154, 154×2+5=313. But the last term given is 308, which should be 313. Let me verify: 8→17 (+9), 17→36 (+19), 36→75 (+39), 75→154 (+79), 154→308 (+154). The differences themselves nearly double. Alternatively, the pattern could be 2^n + n: 2^3=8, 2^4+1=17, 2^5+4=36, 2^6+11=75, 2^7+26=154... this is complex. Checking the ×2+1 pattern with incrementing addend: 8×2+1=17, 17×2+2=36, 36×2+3=75, 75×2+4=154, 154×2+5=313. Given term is 308, so 308 is wrong; should be 313.

The series follows a pattern of adding consecutive multiples of 100: +100, +200, +300, +400, +500. Starting from 1331, this gives 1431, 1631, 1931, 2331, 2831. The number 2231 breaks this pattern since 1931 + 400 = 2331, not 2231.

The pattern is dividing by consecutive integers: 144÷2 = 72, 72÷3 = 24, 24÷4 = 6, 6÷5 = 1.2, 1.2÷6 = 0.2. But the series shows 0.3 instead of 0.2, so 0.3 is the wrong number that breaks this pattern.

Pattern: ×1 +7, ×2 +8, ×3 +9, ×4 +10. Starting from 4: 4×1+7 = 11, 11×2+8 = 30 (should be, but 10 is shown), 30×3+9 = 99 (should be, but 48 is shown), 99×4+10 = 406 (should be, but 173 is shown). The pattern breaks at 10, making it the first wrong number in the sequence.

The series follows the pattern n^3 × 2: 2^3 × 2 = 16, 3^3 × 2 = 54, 4^3 × 2 = 128, 5^3 × 2 = 250, 6^3 × 2 = 432, 7^3 × 2 = 686. The term 252 breaks this pattern as it should be 250.

The series should follow the pattern +2, +4, +6, +8, +10: 15, 17, 21, 27, 35, 45. The term 29 breaks this pattern as it should be 35, making 33 the wrong number.