1986 AHSME Problem 7

The sum of the greatest integer less than or equal to x and the least integer greater than or equal to x is 5. The solution set for x is

\begin{array}{l} \textbf{(A)}\ \Big\{\frac{5}{2}\Big\}\qquad \textbf{(B)}\ \big\{x\ |\ 2 \le x \le 3\big\}\qquad \textbf{(C)}\ \big\{x\ |\ 2\le x < 3\big\}\qquad\\ \textbf{(D)}\ \Big\{x\ |\ 2 < x\le 3\Big\}\qquad \textbf{(E)}\ \Big\{x\ |\ 2 < x < 3\Big\} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.