"Must be true" and "Can be true" maths questions

[mohit.wrangler]

I want to concretise my understanding about "Must be true" and "Can be true" questions in Maths. So, I concluded their definition as follows:

If the question demands value of x to be in the range [2,5] inclusive.

if any option in answer choices includes all value demanded by the question, such as x>0, x>-5, x<6, x<10 will be correct answer for "Must be true". An another way to approach is: if any value in demanded range does not fall within the range defined by the option, it will be wrong for "Must be true".

If at least one value in option's range satisfies any one value in demanded range, [2,5], then it qualifies for "Can be true".

Let me if there any fault in the above two understandings.

Here is one question:


here, the range of values of x which will come out is: [-infinity, 2) OR (3, infinity], where brackets have their respective mathematical meaning.

The official answer choices are B and C which are fine to me.
The question asks for "May be true." which is similar to "Can be true". So as per my understanding option A, which is x>2, should also be a correct answer because any value from this option x =3.5>2 also satisfies demanded range [-infinity, 2) OR (3, infinity].

Similarly, answer choice D should also be correct.

Please rectify If I am wrong.

[tommywallach]

The question you posted is from a flawed source that you should stop using. The language itself is wrong (an official GRE question would say "COULD" not "MAY"), and the answers are wrong. I believe the question MEANT to say "Which of the following could NOT be true. There cannot be multiple answers in a question like this, so then the answer would be E (because the ONLY range x cannot be in is between 2 and 3). All other answer choices are possible, actually, including A.

As for your logic, it's fine, but I do think you're OVERthinking things. These words "could" and "must" don't have a distinct mathematical meaning. They mean exactly what they mean in real life. If something MUST be true, there can be no exceptions. If something CAN be true, there will be exceptions.

-t