Random Puzzles 

Workings

Hint
How many rats can one cat catch in 5 minutes?

Answer
5.

  5 cats can catch 5 rats in 5 minutes.

So

  1 cat can catch 1 rat in 5 minutes.

  1 cat can catch 2 rats in 10 minutes.

  1 cat can catch 20 rats in 100 minutes.

Therefore

  5 cats can catch 100 rats in 100 minutes.

Workings

Hint
A very tricky puzzle involving prime numbers.

Answer
101.

These are prime numbers, which, when reversed, are also prime.

Workings

Hint
In the word LOG, why might the L have be replaced with 50?

Answer
FO10.

Reasoning
If there is a Roman numeral, it is replaced by its modern equivalent.
   I = 1
   V = 5
   X = 10
   L = 50
   C = 100
   D = 500
   M = 1000

Double-Checking
CLICK = 100 50 1 100 K MILK  = 1000 1 50 K LOG   = 50 O G LIFE  = 50 1 F E ALIVE = A 50 1 5 E FOX   = F O 10

Workings

Hint
This is a very common sequence.

Answer
A.

August, from initial letters of the months of the year.