E should be the right answer.
Since x> -2 and x<7, x can be any number between these two values but x cannot be more than 7 or less than -2.
a) x>2 includes values that are more than 7, so it is not correct
b) x> -7 incudes values that are less than -2, so it is not correct
c) x< 2 includes values that can be less -2, so it is not always correct
d)x > -7 is inconsistent with the statement that x> -2
e) using poe E is the correct answer
This is a classical question and classical mistake in answering this kind of questions.
When it says x<7 then it MUST be true that x is less than 8, or 9, etc. But x>-2, so it must be true that it is greater than -3, -4 etc. X may or may not be less than 6 if all we know is that it is less then 7. It may or may not be less than -1 if all we know is that it is greater than -2.
If the question is asked differently, then answer would be different. For example if the question is like this:
Which of the following statement will ensure x is less than 7 and greater than -2?
Then you would need to look at it from another perspective. If x is less than 7, 6 or 5 etc., then we would be able to ensure x is less than 7. If x is greater than -2, -1 or 0 etc., then we would be able to ensure x is less than -2.
Basically all we are deriving at is if one (A) is true, then the other (B) is always true. But we just need to know which one is A and which one is B.
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