samratpahwa
The teacher asked a student to write forst few natural numbers on the board.
By mistake, the student wrote a number twice. If the average of all numberson the board is 28 (2/7). Whatis the number which is written twice?
(A)12
(B)16
(C)28
(D)44
(E)none
Tia
Dear Tia,
I'm happy to respond.

My friend, I am not sure what the source of this question is, but it is definitely not a GMAT practice question. It is loaded with typos, the wording is unclear, and so far as I can tell, there's nothing particularly elegant about the solution.
First of all, here is what the prompt is trying to say:
The teacher asked a student to write all the natural numbers from 1 to n on the board. By mistake, the student wrote a number twice, so that there was a total of (n +1) numbers on the board. If the average of all numbers on the board is \(28\frac{2}{7}\), what is the number that was written twice?That's a grammatically correct and unambiguous statement of the question itself. This question seems to rely on guess-and-check strategies, and it would have been quite laborious without a calculator. This is way out-of-scope of anything the GMAT would ask.
If you found this in a book that claims to be preparing you for the GMAT, burn that book.
If this is a question you created, I would say it's very important to understand the subtle constraints of a good GMAT Quant question. A poorly conceived question involves a laborious calculation. A well conceived question may look as if it requires a long calculation, but it can be solve quickly with an elegant shortcut. Keep this in mind as you think about GMAT Quant questions.
Does all this make sense?
Mike