http://i.imgur.com/asvwBMQ.png
The answer to 1 is かねます. But how do I decide between this and 得ません?

I'm under the impression that 得ない is used when something is objectively impossible to do whereas かねる is more subjective. So going back to the question, if the boss is away, the speaker can't give an answer regarding that case because of reasons (he doesn't know anything about the case, he doesn't have the permission to speak about it, etc). Well, if he doesn't know anything, he objectively can't say anything about it can he? (so can 得ない be used?). If he doesn't have permission, then I suppose he could break the rule and give an answer so 得ない can't be used?

The answer to 2 is っこない.
っこない seems to be used subjectively when asserting something is impossible so I'm fine with the answer. But can かねる also be used? If not, what's the difference between the two?

かねる has a nuance of "would like to but can't", making it perfect for the polite apology in 1.

Are those J-Test questions? Sure hope they're not N1 or I'm gonna have to study

Thanks Vempele.

anotherjohn Wrote:Are those J-Test questions?(

They're from the old Kanzen Master N2 Grammar book (page 100)

The only one that matches the politeness level for 2 is っこない. っこない is informal, as is なんか, and they're often used together to emphasise something. I think that なんか is the biggest hint, since using it together with かねない, which is very formal, sounds very strange. It'd approach joke level if you said it to a friend.