Question

The sum of 3 non zero prime numbers is 100 .One of them exceeds the other by 36 . Find the largest number ?

Answer 1

Let x , x + 36 and y are the three prime numbers.

According to the given condition,

x + x +36 + y = 100

⇒ 2x + y = 64 ..................(1)

Since x is a prime number, then 2x will be an even number.

Also addition of two even numbers results in an even number,

∴ from equation (1),we can conclude that y must be an even prime number.

⇒ y = 2 , as " 2 " is the only even prime number.

Put y = 2 in equation (1), we get

2x + 2 = 64 ⇒ x = 31

So the required prime numbers are 31, 31+36, 2 or 31, 67 and 2