MathDB
1998 Gauss (7) #24

Source:

February 26, 2017
Gauss

Problem Statement

On a large piece of paper, Dana creates a “rectangular spiral” by drawing line segments of lengths, in cm, of 1, 1, 2, 2, 3, 3, 4, 4, ... as shown. Dana’s pen runs out of ink after the total of all the lengths he has drawn is 3000 cm. What is the length of the longest line segment that Dana draws?
<spanclass=latexbold>(A)</span> 38<spanclass=latexbold>(B)</span> 39<spanclass=latexbold>(C)</span> 54<spanclass=latexbold>(D)</span> 55<spanclass=latexbold>(E)</span> 30<span class='latex-bold'>(A)</span>\ 38 \qquad <span class='latex-bold'>(B)</span>\ 39 \qquad <span class='latex-bold'>(C)</span>\ 54 \qquad <span class='latex-bold'>(D)</span>\ 55 \qquad <span class='latex-bold'>(E)</span>\ 30