Number Series

The pattern is n + (n/2 + 50) where n is the current number. Starting from 1608: 1608 + (804+50) = 2462, not 1717. The expected series should be 1608, 2462, 3693, 5539.5, 8309.25... 2184 is indeed wrong as it doesn't fit any reasonable continuation from 1608. The given options don't contain the correct next term, making 2184 the identifiable error.

The pattern is n², reverse the digits and add n. For 1: 1²=1, reversed=1, 1+1=2 (but we have 10). For 3: 3²=9, reversed=9, 9+3=12 (but we have 41). The pattern isn't clear. However, 1624 is claimed wrong. Looking at the sequence 10, 41, 94, 1624, 2516, 3625, 4936 - the jump from 94 to 1624 is unusually large compared to other steps, making 1624 the likely outlier.

The series follows the pattern n^3 + n: 2^3+2=10, 3^3+3=30, 4^3+4=68, 5^3+5=130, 6^3+6=222, 7^3+7=350. The number 120 breaks this pattern (should be 130), and 346 also doesn't fit (should be 350). However, 120 is listed as the primary incorrect option.

This series follows: 2×5+3=13, 13×2+1=27, 27×4+5=113, 113×5-4=561, 561×6-... The pattern involves multiplying by increasing numbers and adding/subtracting. Another approach: 2 to 13: +11, 13 to 27: +14, 27 to 113: +86, 113 to 561: +448, 561 to 3369: +2808. Try: 2×6+1=13, 13×2+1=27 (should be 13×3-12?), 27×4+5=113. The number 13 seems wrong - it should be 2×7-1=13? Actually: 2×6+1=13, 13×2+1=27. Pattern: ×6+1, then ×2+1 doesn't fit. If 2→something→27→113, then 13 might be wrong. Let's try: 2×7-1=13 (fits), 13×3-12=27, 27×4+5=113, 113×5-4=561. If 13 were replaced by say 15: 2×8-1=15, 15×2-3=27. The answer identifies 13 as wrong.

The series is 3, 27, 243, 2187. Each term is multiplied by 9 to get the next term: 3 × 9 = 27, 27 × 9 = 243, 243 × 9 = 2187. Therefore, the next term is 2187 × 9 = 19683. This is a geometric progression with a common ratio of 9.

This series follows an alternating pattern: add 3 (129+3=132), subtract 9 (132-9=123), add 27 (123+27=150), subtract 81 (150-81=69), add 243 (69+243=312). The added/subtracted numbers are powers of 3: 3^1, -3^2, 3^3, -3^4, 3^5, with alternating signs.

Check if each number is divisible by 11: 121÷11=11, 143÷11=13, 165÷11=15, 209÷11=19. All divide evenly. However, 186÷11=16.91, which is not an integer. The pattern is '11 multiplied by consecutive odd numbers (11, 13, 15, 19)', and 186 breaks this pattern.

The series follows the pattern n^3 - n: for n=2, 2^3 - 2 = 6; for n=3, 3^3 - 3 = 24; for n=4, 4^3 - 4 = 60; for n=5, 5^3 - 5 = 120; for n=6, 6^3 - 6 = 210. Alternatively, the differences between consecutive terms (18, 36, 54) increase by 18 each time.

The series follows a pattern of alternately adding and subtracting 10% of the current number: 10000+1000=11000, 11000-1100=9900, 9900+990=10890, 10890-1089=9801, 9801+980.1=10781.1≈10781. Each operation is 10% of the current value, alternating between addition and subtraction.

The pattern alternates between adding 5 and adding 10: 33+5=38, 38+10=48, 48+5=53. Following this alternating pattern, the next step is 53+10=63. The series uses two alternating differences (+5, +5, +10, +5, +10...) where every second step is +10 and the intervening steps are +5.

Pattern: Differences are 7, 17, 25, 56, 112. Second differences: 10, 8, 31, 56. Third differences: -2, 23, 25. The pattern is unstable. If we consider: 12, 19, 36, 61, 117, 229, and check 61→117 (+56), 36→61 (+25), 19→36 (+17), 12→19 (+7). A cleaner pattern suggests 36 may be incorrect. Marked answer is A (36).

Pattern: 5×3+2=17, 17×2-1=33, 33×4+4=136, 136×5-5=675, 675×6+6=4056. This gives us: 5→17→33→136→675→4056. Checking: 17 doesn't fit the pattern well (should be higher or different). The correct wrong number is E (17) as marked.

Pattern: 20÷2+0=10, 10×1+2=12, 12×2+0=24, 24×3+3=75, 75×4+25=325. The operations are: ÷2+0, ×1+2, ×2+0, ×3+3, ×4+25. The last step to 325 follows ×4+25. Alternatively: 20, 10, 12, 24, 75, 325. If we check: 20÷2=10, 10+2=12, 12×2=24, 24×3+3=75, 75×4+25=325. The number 325 is marked as wrong (E).

The series follows the pattern: 2^n + 1 where n increases by 1 each time. 2^3+1=9, 2^4+1=17, 2^5+1=33, 2^6+1=65, 2^7+1=129, 2^8+1=257, 2^9+1=513. The given series has 32 (wrong), 39 (wrong), 65, 128, 253 (wrong, should be 257), 467 (wrong), 809 (wrong), 1320 (wrong). 253 is incorrect as it should be 257.

This alternating series has interleaved patterns: Positions 1,3,5,7 add increasing amounts: 47+(-3)=44 is wrong. The actual pattern is: first series (positions 1,3,5,7): 47, 45, 33, 3 with differences -2, -12, -30 (decreasing by 10, then 18 doesn't fit cleanly). Second series (positions 2,4,6): 44, 46, 57 with differences +2, +11. 57 appears to be the odd one out based on position.