ajelias wrote:
I understood "can" to mean "is there a possibility that" when obviously that isn't what GMAC thinks it means.
I understand the explanation now, because I suppose since both scenarios can yield either a yes or no answer (aka maybe) that it is INSUFFICIENT, just as if the question were phrased "is the positive integer the sum of two different positive prime numbers?"
However, dictionary.com writes one definition of the word "can" as "to be able to." Doesn't GMAC like to avoid controversy? If I got this question wrong on the actual GMAT, I would be furious with this wording. Asking if n has the ability to be written as the sum of two prime numbers means, according to that definition, that if there is even one possibility that the answer is "yes" then the scenario is SUFFICIENT.
I hope to not see any of this wording on the exam. At least I know to look out for it now though.
I guess I don't understand what it is about the wording that so many people find ambiguous. The use of language here is entirely standard on the GMAT, and in mathematics in general, and you're quite likely to encounter similarly worded questions in the future, so it would be worth taking some time to be sure you understand it.
From the comments above, it may be that the issue is not with the wording of the problem itself, but with approach to DS questions. When you say this:
ajelias wrote:
Asking if n has the ability to be written as the sum of two prime numbers means, according to that definition, that if there is even one possibility that the answer is "yes" then the scenario is SUFFICIENT.
this not how you answer a DS question, at least if I've understood what you're trying to say. In a yes/no DS question, a statement is *not* sufficient if it means that "there is even one possibility that the answer is 'yes'". You have sufficient information if the *only* possible answer to the question is yes. If the answer might be yes, and might be no, then the information is *not* sufficient.
So when we see this question:
"Can the positive integer n be written as the sum of two positive prime numbers? "
first, as in any DS question with an unknown value, n represents some fixed positive integer. We don't know what n is (though we'll learn some things about n from the statements), but it represents a single numerical value. We want to know if n can be expressed as the sum of two primes. We certainly need more information about n to be able to answer this question. If n=1, say, then certainly there is no way to write n as the sum of two primes. But if n=5, say, then we can write n as 3+2. And even using both of the statements, it remains possible that n=5, and n can be expressed as the sum of two primes and the answer is 'yes', or that n=11 and n cannot be expressed as the sum of two primes, and the answer is 'no'. When you can get both a yes and a no answer using your statements, then they are by definition insufficient.
