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Source: AHSME 1986 problem 7

September 30, 2011
floor functionceiling functionAMC

Problem Statement

The sum of the greatest integer less than or equal to xx and the least integer greater than or equal to xx is 55. The solution set for xx is
<spanclass=latexbold>(A)</span> {52}<spanclass=latexbold>(B)</span> {x  2x3}<spanclass=latexbold>(C)</span> {x  2x<3}<spanclass=latexbold>(D)</span> {x  2<x3}<spanclass=latexbold>(E)</span> {x  2<x<3} <span class='latex-bold'>(A)</span>\ \Big\{\frac{5}{2}\Big\}\qquad<span class='latex-bold'>(B)</span>\ \big\{x\ |\ 2 \le x \le 3\big\}\qquad<span class='latex-bold'>(C)</span>\ \big\{x\ |\ 2\le x < 3\big\}\qquad \\ <span class='latex-bold'>(D)</span>\ \Big\{x\ |\ 2 < x \le 3\Big\}\qquad<span class='latex-bold'>(E)</span>\ \Big\{x\ |\ 2 < x < 3\Big\}