Quantitative Aptitude - Arithmetic Ability Questions

The series follows the following pattern

5 X 5 – 5 = 20

20 X 4 – 4 = 76

76 X 3 – 3 = 225

225 X 2 – 2 = 448

Hence, the term 225 denoted by (d) completes the series

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.

Let the average after 7th inning = x

Then average after 16th inning = x - 3

16(x-3)+87 = 17x 

 x = 87 - 48 = 39

With close observation, you will note that each number in the list is in the middle of two prime numbers. Thus:

4 is in the middle of 3 and 5, 6 is in the middle of 5 and 7, 12 is in the middle of 11 and 13, 18 is in the middle of 17 and 19, 30 is in the middle of 29 and 31. 42 is in the middle of 41 and 43, 60 is in the middle of 59 and 61.

Therefore, the next number would be the one that is in the middle of the next two prime numbers, which is 72 (which is in the middle of 71 and 73).

 22 = 2 x 11

 54 = 2×33

108 = 22×33

135 = 33×5 

198 = 2×32×11

 ∴ L.C.M = 22×33×5×11=5940

At 2 o'clock, the hour hand is at 2 and the minute hand is at 12, i.e. they are 10 min spaces apart. 

To be together, the minute hand must gain 10 minutes over the hour hand. 

Now, 55 minutes are gained by it in 60 min.

  10 minutes will be gained in 6055×10 min. = 101011 min. 

The hands will coincide at 101011 min. past 2.

Let the numbers be x, x + 1, x + 2,  x + 3, x + 4, x + 5 and x + 6,

Then   (x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) + (x + 6)) / 7 = 20.

or  7x + 21 = 140 or 7x = 119 or x =17.

Latest number = x + 6 = 23.

Here the series follow the rule that

12+22 = 5

32+42 = 25

52+62 = 61

72+82 = 113

SO NEXT IS, 92+102 = 181