MathDB
Number and Remainders

Source:

February 1, 2009
number theoryleast common multiple

Problem Statement

A number which when divided by 10 10 leaves a remainder of 9 9, when divided by 9 9 leaves a remainder of 8 8, by 8 8 leaves a remainder of 7 7, etc., down to where, when divided by 2 2, it leaves a remainder of 1 1, is: <spanclass=latexbold>(A)</span> 59<spanclass=latexbold>(B)</span> 419<spanclass=latexbold>(C)</span> 1259<spanclass=latexbold>(D)</span> 2519<spanclass=latexbold>(E)</span> none of these answers <span class='latex-bold'>(A)</span>\ 59 \qquad<span class='latex-bold'>(B)</span>\ 419 \qquad<span class='latex-bold'>(C)</span>\ 1259 \qquad<span class='latex-bold'>(D)</span>\ 2519 \qquad<span class='latex-bold'>(E)</span>\ \text{none of these answers}