Quantitative Aptitude - Arithmetic Ability Questions

The given number series is 3, 12, 39, 120, 364

$$\begin{gathered} 3 \\ 3 + 32 = 3 + 9 = 12 \\ 12 + 33 = 12 + 27 = 39 \\ 39 + 34 = 39 + 81 = 120 \\ 120 + 35 = 120 + 243 = 363 (Not 364) \end{gathered}$$

15th August, 2010 = (2009 years + Period 1.1.2010 to 15.8.2010)

Odd days in 1600 years = 0

Odd days in 400 years = 0

9 years = (2 leap years + 7 ordinary years) = (2 x 2 + 7 x 1) = 11 = 4 odd days.

Jan. Feb. Mar.  Apr.  May.  Jun.  Jul.  Aug.

(31 + 28 + 31 + 30 + 31 + 30 + 31 + 15) = 227 days = (32 weeks + 3 days) = 3 odd days.

Total number of odd days = (0 + 0 + 4 + 3) = 7 =  0 odd days.

Given day is Sunday

Let the numbers be x, x + 2, x + 4, x + 6 and x + 8.

Then  [x + (x + 2) + (x + 4) + (x + 6) + (x + 8) ] / 5 = 61.

or 5x + 20 = 305 or x = 57.

So, required difference = (57 + 8) - 57  = 8