Mazen,
I think a better approach here would have been to eliminate any answer that explicitly matched what the author was talking about in the fourth paragraph. In theory, what you did should have had the same result.
Anything that cannot be true is going to be something that is not necessarily true. You're misunderstanding what it means for something to be "not necessarily true".
Both of the following statements are "not necessarily true":
1. I will eat 2 bagels tomorrow.
2. I will eat 2 million bagels tomorrow.
Is 1 necessarily true? Clearly not - I might have no bagels, or 1 bagel, or 3 bagels, and maybe even a few more than that. So 1 is not necessarily true.
Is 2 necessarily true? Clearly not - I might have no bagels, or 1 bagel, or 2 bagels, or 3 bagels, or maybe even a few more than that. So 2 is not necessarily true.
2 looks different than 1 because 2 is also impossible - I can't physically consume that many bagels. What my discussion of 2 above just demonstrates is that things that are impossible - things that "cannot be true" or "must be false" - are just a part of the things that are "not necessarily true."
There is a distinction between "cannot be true" and "not necessarily true" just like there is a distinction between "beagle" and "dog". No beagle fails to be a dog - nothing that cannot be true fails to be something that is not necessarily true. There is a distinction because the inclusion only works one way - plenty of dogs aren't beagles; plenty of things are not necessarily true without being things that cannot be true.
The situation you're talking about thus cannot happen. If one answer cannot be true and another answer is not necessarily true, that's already TWO answers that aren't necessarily true - and that would make them both correct, for this question or anything like it in form. That's not possible.
The following thread is helpful for more on this topic:
viewtopic.php?t=7011
Robert Carroll