Let \(p\) and \(q\) be real numbers with \(|p|<1\) and \(|q|<1\) such that \[p+pq+pq^2+pq^3+\cdots=2\qquad\text{and}\qquad q+qp+qp^2+qp^3+\cdots=3.\] What is \(100pq\)?

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