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10 Feb 2011, 16:05
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B
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If p and q are prime numbers, where p is no more than q, is sum of p and q a prime number?
(1) p is not equal to q.
(2) p is greater than 2.
(1) p is not equal to q.
(2) p is greater than 2.
10 Feb 2011, 16:26
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banksy
If p and q are prime numbers, where p is no more than q, is sum of p and q a prime number?
The sum of two primes to be a prime number necessary but not sufficient condition is one of the primes to be 2 and another more than 2 (so that the sum to be odd and have a chance to be a prime number), for example: 2+3=5 or 2+5=7 or 2+11=13. If both primes are more than 2 then both will be odd primes and their sum will be even>2, so not a prime number
(1) p is not equal to q --> if p=2 and q=3 then the answer will be YES but if p=2 and q=7 then the answer will be NO. Not sufficient.
(2) p is greater than 2 --> \(2<p\) as also given that \(p\leq{q}\) then \(2<p\leq{q}\) thus both primes are more than 2 --> their sum is even so not a prime number. Sufficient.
Answer: B.
10 Feb 2011, 16:41
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oh, I see...
Two odd prime no will always sum up to be an even no cause O+O=E.And statement two proves that both p and q are Odd primes.Thank you Bunuel for the explanation.
Two odd prime no will always sum up to be an even no cause O+O=E.And statement two proves that both p and q are Odd primes.Thank you Bunuel for the explanation.
