https://gmat.gregmat.com/practice/custom-practice/?problem=gmat-let-2n-2x2-16x-8
In the solution, it is clearly stated that n>3, then how come n>2 is the correct solution?
As per n>2, this statement fails when 2<n<=3 and the question asks “must be true”. This range does not fall in the must category.
You’re conflating two things. You’re assuming the question is asking if the regions n > 2 and n > 3 are identical. Clearly, they overlap for every real number past 3, but they differ in the (2, 3] interval. As such, your logic about the “solution space” of n > 2 and n > 3 not being identical is correct, but that isn’t what the question is asking.
This is what the question is asking:
If you already know n > 3, then is the statement n > 2 true?
In other words, imagine I wrote you a bank cheque but hid the exact amount. The only thing I tell you is that it’s for more than 5 million dollars. Now, if your uncle asked you whether the gift I gave you was over 1 million, you would say yes, right? That’s essentially the crux of the question.
Perfectly explained and an apt analogy. Thank you.