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SMO 2011 Junior Round 1 Question 4

SMO · SMO 2011 Junior Round 1

Question 4

Let $$x=1\underbrace{00\cdots0}_{2011}\,1\underbrace{00\cdots0}_{2012}\,50.$$
The two indicated blocks contain $2011$ and $2012$ zeros, respectively. Which of the following is a perfect square?
  1. $x-75$
  2. $x-25$
  3. $x$
  4. $x+25$
  5. $x+75$