Quantitative Aptitude - Arithmetic Ability Questions

log 27 = 1.431
log33 = 1.431
3 log 3 = 1.431
log 3 = 0.477
log 9 = log(32)= 2 log 3 = (2 x 0.477) = 0.954

The given number series is 3  24  186  1008  5040  20160

Here  the given series follows a pattern that,

3

3 x 8 = 24

24 x 7 = 168 not 186

168 x 6 = 1008

1008 x 5 =  5040

5040 x 4 = 20160

Hence the Odd One in the number series is 186.

Here the given number series is 5  11  21  44  ?  175

Now the given series follows a pattern, that

x2 + 1, x2 - 1, x2 + 2, x2 - 2, x2 + 3, x2 - 3,...

Then the missing number is x2 - 2

= 44 x 2 - 2 = 88 - 2 = 86

Hence, the missing number in the number series is 86.

Next number of the sequence 1, 4, 12, 32,...

1 = 2 x 20

4 = 2 x 21

12 = 3 x 22

32 = 4 x 23

80 = 5 x 24.

Given Number series is 18     37     76     155     314     635

follows a pattern that, 

18

18 x 2 +1 = 37

37 x 2 +2 = 76

76 x 2 +3 = 155

155 x 2 +4 = 314

314 x 2 +5 = 633 not 635

Hence, the odd man is 635.