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 a,b,c be our prime numbers
a+b+c = 100
Since prime numbers are odd (except 2), the sum of three odd numbers has to be 'odd'. Hence the sum to be even 1 of the number has to be even. Hence one of the prime number has to be '2'
2+ b + c = 100
b + c = 98
b - c = 36...(given one exceeds the other by 36)
2b = 134
b = 67
c = 31
Hence the prime numbers are 2, 31, 67 && the sum = 100.
Hope this helps.