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Remainder r when divided by d

Source: 1976 AHSME Problem 15

May 17, 2014
modular arithmeticAMC

Problem Statement

If rr is the remainder when each of the numbers 1059, 1417,1059,~1417, and 23122312 is divided by dd, where dd is an integer greater than 11, then drd-r equals
<spanclass=latexbold>(A)</span>1<spanclass=latexbold>(B)</span>15<spanclass=latexbold>(C)</span>179<spanclass=latexbold>(D)</span>d15<spanclass=latexbold>(E)</span>d1<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>15\qquad<span class='latex-bold'>(C) </span>179\qquad<span class='latex-bold'>(D) </span>d-15\qquad <span class='latex-bold'>(E) </span>d-1