This question is more like an LSAT question than a GMAT question, but it is definitely valid. It's an example of a Principle Support question, which is basically an abstract form of Strengthen. Specifically, we've been asked for a principle that would REQUIRE Jack to act as he did. In other words, we're in the unusual situation of looking for a strengthener that actually PROVES the conclusion correct. That's not normally what we want. C or E might seem to be in line with Jack's reasoning, but that doesn't matter for this question, because neither one would force him to act as he did.
A) Both his aunt (to whom he made the promise) and his mother (who would benefit) are family members, so this gives no guidance at all. If anything, this might lean us the other way. We could say he had a duty to his aunt (because of the promise) but not to his mother, whom he simply decided to help out.
B) We want a principle that tells him he MUST violate the promise, not one that says it's impermissible to do so.
C) This principle might look appealing, but it doesn't apply here. The text never said that giving money to Jack would harm anyone. It just wouldn't benefit anyone. Since no harm is involved either way, this principle doesn't tell us what to do.
D) He has two options: 1) benefit no one or 2) benefit his mom and others. If the principle tells him to choose whichever option benefits the most people, then he is REQUIRED to choose option 2. Some people is definitely more than NO people.

So D actually forces Jack's decision to be correct.
E) All this does is tell us that Jack no longer has to keep his promise. That doesn't actually tell him what decision to make. He has freedom to choose, so he's not forced down either path.