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# Can the positive integer n be written as the sum of two

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Manager
Joined: 26 Aug 2003
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Can the positive integer n be written as the sum of two [#permalink]

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07 Nov 2003, 13:43
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Can the positive integer n be written as the sum of two different positive prime numbers?
(1) n is greater than 3.
(2) n is odd.
Director
Joined: 03 Jul 2003
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07 Nov 2003, 13:48
Where did you get this question?!
Director
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07 Nov 2003, 14:44
1)insufficient-- 5 can be written as the sum of two different positive primes, 6 can not.
2)insufficient-- 5 can be written as the sum of two different positive primes, 1 can not.

together: 5 can be written as the sum of two different positive primes, 11 can not.

E?
Manager
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07 Nov 2003, 18:15
1 is not prime....but you are correct the answer is E
Director
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08 Nov 2003, 21:55
"1 is not prime"

I never stated or implied that it was.
Manager
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09 Nov 2003, 17:16

I find this to be an ambiguous problem. The question asks if you can write an n from summing two prime numbers. But does give any more specifics, this leaves room two answer, E or C.

If anyone has solid explanation, it's certainly welcome!
SVP
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11 Nov 2003, 01:28
initially n is a positive integer

(1) n>3
consider 4 -- cannot be written as a sum of different primes
consider 7=2+5 -- can be; NOT SUFF

(2) n is odd
consider n=1 -- cannot be written as a sum of different primes
consider n=7=2+5 can be; NOT SUFF

combine and consider
n=5, 7, 9, 11, ...
5=2+3; BUT
11 cannot be written as a sum; NOT SUFF

E.
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