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.

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.

Let the average after 7th inning = x

Then average after 16th inning = x - 3

16(x-3)+87 = 17x 

 x = 87 - 48 = 39

The terms of the series are products of two consecutive prime numbers i.e.

(2 x 3), (3 x 5), (5 x 7), (7 x 11),.....

So, 165 is wrong and must be replaced by (11 x 13) i.e. 143.

Here given 

2, 3, 6, 15, ? , 157.5

2 x 1.5 = 3

3 x 2  = 6

6 x 2.5 = 15

15 x 3 = 45

45 x 3.5 = 157.5

Therefore, the missing number is 45

a+b=5   ...(1)    and    3a+2b=20 ...(2)

Multiplying (1) by 2 and subtracting from (2), we get : a=10.

Putting a=10 in (1), we get : b=-5

Therefore,   (3a+b) = 3 x 10+(-5)=30-5=25.

28 May, 2006 = (2005 years + Period from 1.1.2006 to 28.5.2006)

Odd days in 1600 years = 0

Odd days in 400 years = 0

5 years = (4 ordinary years + 1 leap year) = (4 x 1 + 1 x 2) = 6 odd days

(31[jan] + 28 [Feb]+ 31[Mar] + 30[April] + 28[May] ) = 148 dayss = (21 weeks + 1 day) = 1 odd day.

Total number of odd days = (0 + 0 + 6 + 1) = 7 = 0 odd days.

Given day is Sunday

The given number series is 125,   138,   164,   ?,   255

125

125 + 13x1 = 138

138 + 13x2 = 164

164 + 13x3 = 203

203 + 13x4 = 255

Hence, the missing number in the series is 203.