Question 1
Let $$n$$ be a positive integer such that $$1\le n\le1000$$. Let $$M_{n}$$ be the number of integers in the set $$X_{n}=\{\sqrt{4n+1},\sqrt{4n+2},...,\sqrt{4n+1000}\}$$. Let $$a=\max\{M_{n}:1\le n\le1000\}$$, and $$b=\min\{M_{n}:1\le n\le1000\}$$. Find $$a-b$$.
Correct Answer: 22
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