Solution:

1726

A) 1345 sum of digits(13, prime)
B) 1754 sum of digits(17, prime)
C) 1726 sum of digits(16, not prime)
D) 1235 sum of digits(11, prime)

Solution:

First fill the 8 liters jug complete - 4, 8, 0
Fill the 5 liters jug with 8 liters jug - 4, 3, 5
Pour back the beer from 5 liters jug to 12 liters jug - 9, 3, 0
Pour the 3 liters from 8 liters jug to 5 liters jug - 9, 0, 3
Fill the 8 liters jug completely from 12 liters jug - 1, 8, 3
Fill the 5 liters jug from the 8 liters jug - 1, 6, 5
Pour the entire 5 liters jug back in 12 liters jug - 6, 6, 0

You have successfully split the beer into two equal parts.

Solution:

Yes it is possible in Roman Numerals. In Roman Numerals,
9 = IX
10 = X
11 = XI

Thus by removing one from 9, you are getting 10 and by removing one from 11, you are getting 10 again.

Solution:

There is a simple logic to solve this question.
The size of the chocolate is 2 x 8. Thus, you need to have 2 x 8 = 16 pieces.
Every time you break the chocolate, you will get one extra piece.
Thus, to get 16 pieces, you must break it (16 - 1) = 15 times.

Solution:

It was only a trick

I borrowed my parents (Pound 50 + Pound 50 = Pound 100).
I bought the book for Pound 97 and i had Pound 3 change.
So, the money that i borrowed and bought the book are Pound 100 (borrowing money)
and the change Pound 3 also the borrowing money the book is Pound 97
Total: Pound 97 + Pound 3(the change) = Pound 100
The money that i used to buy the book all i borrowed.
Pound 97 is the borrowing money, change: Pound 3 also the borrowing money. Pound 97 + Pound 3 = Pound 100

Solution:

Flyball should pay Lavy $11 instead of accepting his counter offer as in that case the club will end up paying almost double the amount.

Solution:

Solution is shown in image below

Solution:

31

Explanation:
Ramanujan lighting the candles in binary.
11110 =30
11111 =31

Solution:

There is no reason whatever why the customer's original deposit of Rs.100 should equal the total of the balances left after each withdrawal.
The total of withdrawals in the left-hand colum may equal Rs.100, but is is purely coincidence that the total of the right-hand column is close to Rs.100.
Let us show another example, but starting with Rs.200 in the bank:
Withdrawals Balance left
Rs.50 Rs.150
Rs.25 Rs.125
Rs.10 Rs.115
Rs.8 Rs.107
Rs.5 Rs.102
Rs.2 Rs.100
Rs.100 Rs.699
Moral of this story? Don't Total Balances

Solution:

There are six unique answers

Ans1:
7 x 4 = 28
36 / 4 = 9
1 + 4 = 5

Ans2:
9 x 4 = 36
28 / 4 = 7
1 + 4 = 5

Ans3:
3 x 8 = 24
56 / 8 = 7
1 + 8 = 9

Ans4:
7 x 8 = 56
24 / 8 = 3
1 + 8 = 9

Ans5:
4 x 8 = 32
56 / 8 = 7
1 + 8 = 9

Ans6:
7 x 8 = 56
32 / 8 = 4
1 + 8 = 9

Solution:

He should shoot at the ground.

If Kangwa shoots the ground, it is Rafael's turn. Rafael would rather shoot at Ferdinand than Kangwa, because he is better.
If Rafael kills Ferdinand, it is just Kangwa and Rafael left, giving Kangwa a fair chance of winning.
If Rafael does not kill Ferdinand, it is Ferdinand's turn. He would rather shoot at Rafael and will definitely kill him. Even though it is now Kangwa against Ferdinand, Kangwa has a better chance of winning than before.