Quantitative Aptitude - Arithmetic Ability Questions

The given number series 22, 26, 42, 78, 142, 244 follows a pattern that,

$$\begin{gathered} 22 \\ 22 + 22 = 22 + 4 = 26 \\ 26 + 42 = 26 + 16 = 42 \\ 42 + 62 = 42 + 36 = 78 \\ 78 + 82 = 78 + 64 = 142 \\ 142 + 102 = 142 + 100 = 242 \end{gathered}$$ 

Hence, the odd one in the given number series is 244.

The given series follows a pattern that,

$$\begin{gathered} 4 + 32 = 4 + 9 = 13 \\ 13 + 52 = 13 + 25 = 38 \\ 38 + 72 = 38 + 49 = 87 \\ 87 + 92 = 87 + 81 = 198 \end{gathered}$$ 

Hence, the odd man in the given number series is 12.

Let the required numbers be 33a and 33b. 

Then 33a +33b= 528   =>   a+b = 16.

Now, co-primes with sum 16 are (1,15) , (3,13) , (5,11) and (7,9).

Therefore, Required numbers are  ( 33 x 1, 33 x 15), (33 x 3, 33 x 13), (33 x 5, 33 x 11), (33 x 7, 33 x 9)

The number of such pairs is 4