Question

A boy with a collection of marbles realizes that if he makes a group of 5 or 6 marbles at a time there are always 2 marbles left. can you explain why the boy cannot have prime number of marbles?

Answer 1

Solution:-
Suppose 'x' be any number.
Then, according to the question,
Number of marbles are 5x + 2 or it is 6y + 2 because the remainder is always 2 when it is divided by 5 or 6.
⇒ Marbles are a multiple of 5 or 6 plus 2.
that is 30n + 2 = 2(15n +1)
From the above situation we can say that the number of marbles must be a multiple of 5 × 6 = 30 + 2 
So we can say that it cannot be a prime number.