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Question
The positive integers A, B, A - B and A + B are all prime numbers The sum of these four primes is
The positive integers A, B, A - B and A + B are all prime numbers The sum of these four primes is
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Solution
The correct option is D prime
The number A-B and A+B both are either even or odd.However they are also both prime.
So they must be odd.Therefore one of A & B is odd and the other is even.
Because A is Prime between A & B .A must be odd prime .Therefore B = 2, the
only even prime . so A-2, A and A+2 are consecutive odd prime and thus must be
3,5 , 7 .
The sum of four prime = 2+3+5+7 = 17 is the prime number
The number A-B and A+B both are either even or odd.However they are also both prime.
So they must be odd.Therefore one of A & B is odd and the other is even.
Because A is Prime between A & B .A must be odd prime .Therefore B = 2, the
only even prime . so A-2, A and A+2 are consecutive odd prime and thus must be
3,5 , 7 .
The sum of four prime = 2+3+5+7 = 17 is the prime number
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