CAT Questions

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The given number series is 6, 6, 9, 18, 45, ?

Here the series follows a pattern that,

6 

6 x 1 = 6

6 x 1.5 = 9

9 x 2 = 18

18 x 2.5 = 45

45 x 3 = 135

Hence, the next number in the given number series is 135.

17th June, 1998 = (1997 years + Period from 1.1.1998 to 17.6.1998)
Odd days in 1600 years = 0
Odd days in 300 years = 1
97 years has 24 leap years + 73 ordinary years.
Number of odd days in 97 years ( 24 x 2 + 73) = 121 = 2 odd days.
Jan. Feb. March. April. May. June.
(31 + 28 + 31 + 30 + 31 + 17) = 168 days
168 days = 24 weeks = 0 odd day.
Total number of odd days = (0 + 1 + 2 + 0) = 3.
Given day is Wednesday.

The given series 

12   24   26.5   79.5   ?   330 follows a pattern that,

12 x 2 = 24

24 + 2.5 = 26.5

26.5 x 3 = 79.5

79.5 + 3 = 82.5

82.5 x 4 = 330

Hence, the missing number is 82.5

Clearly, the numerators of the fractions in the given sequence follow the series of 2, 3, 5, 7,... and the denominator follows 3, 9, 27, 81, 243, ...
Then, the next term in the given sequence is  935 = 9243 = 127 .