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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
Posts: 233
Location: United States
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Can the positive integer n be written as the sum of two [#permalink]  07 Nov 2003, 12:43
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0% (00:00) correct 0% (00:00) wrong based on 0 sessions
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
Posts: 656
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Where did you get this question?!
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
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Kudos [?]: 10 [0], given: 0

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
Joined: 15 Sep 2003
Posts: 74
Location: california
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Kudos [?]: 6 [0], given: 0

1 is not prime....but you are correct the answer is E
Director
Joined: 28 Oct 2003
Posts: 503
Location: 55405
Followers: 1

Kudos [?]: 10 [0], given: 0

"1 is not prime"

I never stated or implied that it was.
Manager
Joined: 26 Aug 2003
Posts: 233
Location: United States
Followers: 1

Kudos [?]: 2 [0], given: 0

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
Joined: 03 Feb 2003
Posts: 1609
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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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