Solution:

Since it is a 3x3 grid, the area of the grid = 9
We have to arrange 3 white marbles in 9 places, the possible ways = 9c3 = 84

Now you don't have to arrange the blue marbles and thus the possible ways will be 84 only.

Also if you would have started with the blue marbles, the number of ways would have been the same i.e. 84 (9c6)

Solution:

What we already know is that Sn = n (n+1)/2
What we are provided in the question is that
S2n = 3Sn
=> 2n (2n+1)/2 = 3n (n+1)/2
=> 2 (2n+1) = 3 (n+1)
=> 4n+2 = 3n+3
=> n = 1
Thus, S3n/Sn = [3n (3n+1)/2]/[n (n+1)/2] = 3*4/1*2 = 6

Which means that option c is correct.

Solution:

First time = 20 ft
Second time = 10ft down + 10 ft up
Third time = 5ft up + 5ft down
It will go on like this the object stops

Total distance traveled = 20 + (10 + 10) + (5 + 5) + (2.5 + 2.5) + . . .
= 20 + (10 + 5 + 2.5 + ...) + (10 + 5 + 2.5 + ...)
Assuming the object comes to rest at infinity,

Total distance traveled = 20 + [10/ (1 - 0.5)] + [10/ (1 - 0.5)]
= 20 + 20 + 20 = 60

Thus option d is correct.

Solution:

246
*386
----------
1476
1968
738
----------
94956

Solution:

Let the angles be denoted by
a , (a + d) , (a +2d) , (a + 3d) , (a + 4d) , (a + 5d) , (a + 6d) and (a + 7d)

Now, Sum of all the angles in any octagon = 1080 = 8a + 28d
Average of (a + 7d) and (a + 6d) = 153
2a + 13d = 306

Upon solving both, a = 114, d = 6

Thus the average of the smallest two interior angles = (2a + d)/2 = 117

Solution:

a*47*64*1313 is the number

It can also be written as
a * 47 * 8 * 8 * 13 * 101

Now 88 and 117 are two factors
Or 8*11 and 13*9 are two factors

As you can clearly see that 11 and 9 are the missing in the number given to us
Thus a will be 11*9 = 99

Solution:

Let x be the distance of train from bridge, 2l be the length of the bridge and s be the speed of cow

Then according to the question
(x-2)/4s = ( l-5)/s
4l-a = 18 ----- (1)
Also
(a+2l-2)/4s = (l+5-2)/s
a-2l = 14 ----- (2)

On adding (1) and (2), we get
2l = 32

Thus the length of the bridge is 32 meters.

Solution:

Since she has to distribute the chocolates in a manner that none of her friends receive less than 10 chocolates, it is clear that everyone will get at least 10 chocolates which means that 50 chocolates will be distributes offering 10 to each.

Now only 6 chocolates are remaining which has to be distributed among 5 persons

It can be possible in

6+5-1C5-1 = 10C4 = 10C6

Thus option a is correct.

Solution:

Let the capacity of bucket be X liters

Originally in the bucket
X liters milk and 0 liters water

After first draw,
X-E liters milk and E liters water

After 2nd draw
X- [2E-(E^2/X)] and 2E - (E^2)/X liters water

Now as per the details given in the question,
X - [2E-(E^2/X)] / [2E - (E^2)/x] = 16/9

After solving the equation, we get
X = 5E

Thus the capacity of bucket is 5E liters

Solution:

This is quite a tricky puzzle and quite hard to deduce at first impression.

What you have to do is write the number in English
For the first case, 1 and 2 produce 9
1 = One
2= Two
There are three characters in both one and two
3x3 = 9

Similarly for the second case, 3 and 4 produce 20
3 = Three
4 = Four
Three has 5 characters and four has 4 characters
5x4 = 20

Now for the question, seventeen has 9 characters and twelve has 6 characters, thus the missing number is the product of 9 and 6 which is 54.