MathDB
Rodblocked (my 1000th post)

Source: 2017 AMC 10A #10/12A #6

February 8, 2017
2017 AMC 10A2017 AMC 12AAMC 10AMC 12countingAMC

Problem Statement

Joy has 3030 thin rods, one each of every integer length from 11 cm through 3030 cm. She places the rods with lengths 33 cm, 77 cm, and 1515 cm on a table. She then wants to choose a fourth rod that she can put with these three to form a quadrilateral with positive area. How many of the remaining rods can she choose as the fourth rod?
<spanclass=latexbold>(A)</span>16<spanclass=latexbold>(B)</span>17<spanclass=latexbold>(C)</span>18<spanclass=latexbold>(D)</span>19<spanclass=latexbold>(E)</span>20<span class='latex-bold'>(A) </span>16\qquad<span class='latex-bold'>(B) </span>17\qquad<span class='latex-bold'>(C) </span>18\qquad<span class='latex-bold'>(D) </span>19\qquad<span class='latex-bold'>(E) </span>20