Quantitative Aptitude - Arithmetic Ability Questions

4 o'clock, the hands of the watch are 20 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 50 min. spaces.
55 min. spaces are gained in 60 min 

50 min. spaces are gained in 6055×50 min. or 54611 

Required time = 54611 min. past 4.

$$\begin{gathered} [(K-L)2-K+L2]4K = ab \\ K2+L2-2KL-K2+L2+2KL4K= ab \end{gathered}$$

=> - 4KL/4K = a/b

=> L = - a/b

=> bL = -a

Let the average after 7th inning = x

Then average after 16th inning = x - 3

16(x-3)+87 = 17x 

 x = 87 - 48 = 39

Here in the given series, it follows a pattern that

77 + 2 = 79

79  - 3 = 76

76 + 5 = 81

81 -  7 = 74

74 + 11 = 85

Consecutive adding and subtracting of prime numbers.

So the wrong number in the given series is 75.

The given number series is 

3, 5, 8, 15, 28, 51, ?

Here the pattern it follows is

3

3 + 2 = 5 ( add prime number less than 3 i.e, 2)

5 + 3 = 8 (3 is prime number less than 5)

8 + 7 = 15 (7 is prime number less than 8)

15 + 13 = 28 (13 is prime number less than 15)

28 + 23 = 51 (23 is prime number less than 28)

51 + 47 = 98 (47 is prime number less than 51)

Hence, the next number in the given number series is 98.