What will be the best approach to finding all the prime numbers less than 75 that leave an odd reminder when we divide them with 5?

An infinite number of mathematicians are standing behind a bar. The first asks the barman for half a pint of beer, the second for a quarter pint, the third an eighth, and so on. How many pints of beer will the barman need to fulfill all mathematicians' wishes?

In a certain country ½ of 5 = 3. If the same proportion holds, what is the value of 1/3 of 10?

John enters a small room. The Door Closes.
When the door opens, John is in a larger room.

Explain?

A man is found dead in his bathroom naked with blood scattered all around him. The bathroom was locked from the inside and there is no trace of any struggle. There is nothing in the bathroom except his pant with the belt still around and his shirt. Also, the medic team can't find any incision in his body that may have been the reason behind so much blood loss.

The Police department is clueless regarding this murder mystery.
Can you?

There are a hundred statements.

First person says: At least one of the statements is false.

Second person says: At least two of the statements is false.

Third person says: At least three of the statements are false.

Fourth person says: At least four of the statements are false.

..

..

..

Hundredth person says: At least a hundred of the statements are false.

Analysing it, how many statements do you think are false and how many are true?

I am a five-letter word and comprises two different vowels and three same consonants. I am so strong that I can spoil your entire work.

Can you find out who am I?

I know a number which is spelt in alphabetical order.
Do you?

Replace the letters of words with a number so that the below equation holds true

BASE +
BALL
---------
GAMES
----------

Two friends Smith and Andrew were talking about the bravery of their families. Smith told great stories about his courageous grandfather who fought for Britain in "World War I". Andrew told that his grandfather was so brave that in 1919 just after the war he was honoured with a bravery medal with the words "For our Courageous Soldiers In World War I" embedded into it. Smith knows that his friend is lying. How?