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Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

The first step of the VA (Variable Approach) method is to modify the original condition and the question. We then recheck the question.

Since 2< √7< 3, we have 47< x < 53 from the original condition '50-√7<x<50+√7'.

Condition 1)
As x is an odd integer, it could be 49 or 51.
Since we don't have a unique solution, condition 1) is not sufficient.

Condition 2)
If √x is an integer, then x is the square of an integer.
49 is the only perfect square of an integer between 47 and 53.
Thus, x=49 and condition 2) is sufficient.

Therefore, B is the answer.

Answer: B