MathDB
Digital Sum Returns

Source: 2017 AMC10A #20, 2017 AMC12A #18

February 8, 2017
AMCAMC 10AMC 10 AAMC 12AMC 12 A2017 AMC 10A2017 AMC 12A

Problem Statement

Let S(n)S(n) equal the sum of the digits of positive integer nn. For example, S(1507)=13S(1507) = 13. For a particular positive integer nn, S(n)=1274S(n) = 1274. Which of the following could be the value of S(n+1)S(n+1)?
<spanclass=latexbold>(A)</span> 1<spanclass=latexbold>(B)</span> 3<spanclass=latexbold>(C)</span> 12<spanclass=latexbold>(D)</span> 1239<spanclass=latexbold>(E)</span> 1265<span class='latex-bold'>(A)</span>\ 1 \qquad<span class='latex-bold'>(B)</span>\ 3\qquad<span class='latex-bold'>(C)</span>\ 12\qquad<span class='latex-bold'>(D)</span>\ 1239\qquad<span class='latex-bold'>(E)</span>\ 1265