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

[rburkett]

DS Problem from the online lab:

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

I am not so concerned about the actual answer as I am about the question as it is written. As a qualifying statement - I may be getting tripped up over sematics.

My understanding of the use of the word "Can" in this instance implies possibility, regardless of degree.

When the writers create this type of question, do we need to take it to mean:

*IS* the positive integer n written as the sum of two different positive prime numbers?

(1) n is greater than 3
(2) n is odd

Thank you.

[RonPurewal]

DS Problem from the online lab:

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

I am not so concerned about the actual answer as I am about the question as it is written. As a qualifying statement - I may be getting tripped up over sematics.

My understanding of the use of the word "Can" in this instance implies possibility, regardless of degree.

When the writers create this type of question, do we need to take it to mean:

*IS* the positive integer n written as the sum of two different positive prime numbers?

(1) n is greater than 3
(2) n is odd

Thank you.

no, you mean "can". ironically, this is the case for precisely the reason you have articulated here: it's a question of possibility.
for instance, 8 can be written as the sum of 2 different primes: 8 = 3 + 5.
on the other hand, 11 cannot be written as the sum of 2 different primes. try it; it's not possible.
the question of whether 8 "is" written as the sum of 2 primes isn't even a meaningful question.

[gmat11]

Ron-what would be the answer to the question above?

According to me its D. Is it right?

[JPG]

Sorry to harp on this but now I am confused ... for both statements (1) and (2) there are numbers which can be written as the sum of two primes and numbers which cannot. Wouldn't the answer be E then?

[RonPurewal]

Sorry to harp on this but now I am confused ... for both statements (1) and (2) there are numbers which can be written as the sum of two primes and numbers which cannot. Wouldn't the answer be E then?

correct, answer is (e).

all you need is one example that's a "yes" and one example that's a "no".
9 is a "yes", because it can be written as 2 + 7.
11 is a "no", because it can't be written as the sum of two positive primes at all. (because one of the primes would have to be even, that prime must be 2. that leaves the only possibility as 2 + 9, which doesn't work because 9 isn't prime.)

therefore, both statements together are still insufficient.

(e)