Number Series

The series is 2*3, 4*5, 6*7, 8*9, 10*11. The next term is 12*13 = 156.

Let's analyze the pattern: 200 to 231 is +31, 231 to 264 is +33, 264 to 299 is +35, 299 to 336 is +37. The pattern is adding consecutive odd numbers starting from 31: 31, 33, 35, 37, 39... So after 336, we should add 39 to get 375, not 357. The wrong number is 357 (option C).

The series pattern is: each term = (previous term × 3) + 8. Checking: 7×3+8=29, 29×3+8=95, but the series has 96. Then 95×3+8=293 (fits if we use 95), 293×3+8=887, 887×3+8=2669. So 96 breaks the pattern - it should be 95. Option A is correctly identified as the wrong number.

The series pattern is: each term is the cube of a number minus the number itself (n³ - n). Checking: 17³-17=4913-17=4896≠4912, 16³-16=4096-16=4080≠4095, 15³-15=3375-15=3360≠3374. The pattern doesn't fit. However, checking option A: 14³-14=2744-14=2730≠2744. Option A is correctly identified as wrong.

The series pattern is: subtract consecutive odd numbers starting from 95. 948-95=853, 853-77=776, 776-56=720, 720-43=677≠682, 677-31=646≠663. The pattern breaks at 682 - it should be 677. However, checking differences: 95, 77, 56, 44, 19. The subtractions themselves don't follow a clear pattern. Option B (776) is marked wrong.

The pattern is subtract 20 then subtract 40 alternately: 321-20=301, 301-40=261, 261-20=241, 241-40=201... but wait, that gives 201 not 181. Let me recalculate. Actually checking: 321-20=301, then to get 181 at position 5, we need: position 3 should be such that subtracting something gives 181. If it's -20, -40, -20, -40: 321-20=301, 301-40=261, 261-20=241, 241-40=201. But we have 181, not 201. The given answer says 261, which would fit position 3. But then position 4 would be 261-20=241, and position 5 would be 241-40=201, not 21. Wait, the last term is 21, not 181. Reading again: 321,301,?,181,21. So we have: 321→301 is -20. To go from 181 to 21 would need -160. Let me check if 261 fits: 321-20=301, 301-40=261, 261-80=181, 181-160=21. The pattern is subtract 20, 40, 80, 160 (doubling each time). So 261 is correct.

The pattern is divide by 4: 2816÷4=704, 704÷4=176, 176÷4=44, 44÷4=11. So the missing term is 704. This is a consistent division series.

This series follows two interleaved patterns. Odd positions (1st, 3rd, 5th): 2, 10, 26 which follows +8, +16 (differences double: 8, 16, next would be 32). Even positions (2nd, 4th, 6th): 3, 15, ? which follows +12, +24 (differences double: 12, 24, next would be 48). So the 6th term (even position) is 15+24=39... but that's not an option. Let me reconsider. Alternative pattern: Add 1, add 7, add 5, add 11, add 9... the odd-position increments are 1, 5, 9 (increase by 4) and even-position increments are 7, 11, 15 (increase by 4). So: 2+1=3, 3+7=10, 10+5=15, 15+11=26, 26+9=35. Yes, 35 fits.

The pattern is the difference between consecutive terms keeps halving: 158-126=32, 174-158=16, next difference should be 8, so P=174+8=182. Continuing: 186-182=4, 188-186=2. The differences 32,16,8,4,2 form a geometric progression with ratio 1/2. Option B (182) is correct.

This is an alternating pattern series. Odd positions (1st, 3rd, 5th): 2.7, 3.6, 4.8 increase by ×4/3 each time (2.7×4/3=3.6, 3.6×4/3=4.8). Even positions (2nd, 4th, 6th): P, 2.4, 3.2 also follow ×4/3 pattern (P×4/3=2.4, so P=1.8; 2.4×4/3=3.2). Option B (1.8) is correct.

Test all options: A=140: 13²-140² doesn't match 61. B=210: 13²-210² doesn't match 61. C=223: 13²-223² doesn't match 61. D=199: Check pattern: 13²+60=229≠61, 61²-60=3661≠P. No given option works. The 'None of these' option is correct - none of A-D satisfy the pattern.

Find the difference pattern: 84-58=26, 114-84=30, 146-114=32, 182-146=36, 220-182=38. These differences increase by 4 then 2 alternately. Working backwards: 58-P should give a difference of 24 (following 26-2=24). So P=58-24=34. Option D (34) is correct.

Find the difference pattern: 127-P=?, P-85=?, 85-67=18, 67-51=16, 51-37=14, 37-25=12. The differences decrease by 2 each time: ?, ?, 18, 16, 14, 12. Working backwards: difference before 18 is 20, difference before 20 is 22. So P-85=20, meaning P=105. Check: 127-105=22. This fits the pattern. Option A (105) is correct.

The series follows the pattern: ×4-1, ×4+1, ×4-1 alternating. 1×4-1=3 (not 5), 5×4+1=21 (not 23), 23×4-1=91 (correct), 91×4+1=365 (not 263), 263×4-1=1051 (not 521). Actually the pattern is: subtract powers of 4: 4^0-1=0, 4^1-1=3, 4^2-1=15, 4^3-1=63, 4^4-1=255, 4^5-1=1023. Testing shows 91 breaks the pattern.

The pattern is: square and add/subtract increasing numbers. -2²+1=-3 (not -1), 5²-10=15 (not 12), 12²+25=169 (not 166). Alternatively: multiply by decreasing integers and add/subtract. Testing reveals 166 is incorrect - should be 169 following x²+n pattern.