Odd Man Out and Series
 5, 16, 6, 16, 7, 16, 7, 16, 9 ?

 9
 7
 6
 None of these

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Terms at odd places are 5, 6, 7, 8 etc. and each term at even place is 16. So, 9 is wrong.
Correct Option: A
Terms at odd places are 5, 6, 7, 8 etc. and each term at even place is 16. So, 9 is wrong.
 582, 605, 588, 611, 634, 617, 600 ?

 634
 611
 605
 600

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Alternately 23 is added and 17 is subtracted from the terms. So, 634 is wrong.
Correct Option: A
Alternately 23 is added and 17 is subtracted from the terms. So, 634 is wrong.
 22, 33, 66, 99, 121, 279, 594 ?

 33
 121
 279
 594

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Each number except 279 is a multiple of 11.
Correct Option: C
Each number except 279 is a multiple of 11.
 2, 5, 10, 50, 500, 5000 ?

 0
 5
 10
 5000

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Pattern is 1st x 2nd = 3rd; 2nd x 3rd = 4th, 3rd x 4th = 5th.
Correct Option: D
Pattern is 1st x 2nd = 3rd; 2nd x 3rd = 4th, 3rd x 4th = 5th. But 4th x 5th = 50 x 500 = 25000 ≠ 5000 = 6th.
 1, 8, 27, 64, 125, 216, (...) :

 354
 343
 392
 245

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Number are 1^{3}, 2^{3}, 3^{3}, 4^{3}, 5^{3}, 6^{3}.
Correct Option: B
Number are 1^{3}, 2^{3}, 3^{3}, 4^{3}, 5^{3}, 6^{3}.
So, the missing number is 7^{3} = 343.