MathDB
Five-digit divisibility

Source: 2016 AMC 8 #24

November 23, 2016
AMC 82016 AMC 8

Problem Statement

The digits 11, 22, 33, 44, and 55 are each used once to write a five-digit number PQRSTPQRST. The three-digit number PQRPQR is divisible by 44, the three-digit number QRSQRS is divisible by 55, and the three-digit number RSTRST is divisible by 33. What is PP?
<spanclass=latexbold>(A)</span>1<spanclass=latexbold>(B)</span>2<spanclass=latexbold>(C)</span>3<spanclass=latexbold>(D)</span>4<spanclass=latexbold>(E)</span>5<span class='latex-bold'>(A) </span>1\qquad<span class='latex-bold'>(B) </span>2\qquad<span class='latex-bold'>(C) </span>3\qquad<span class='latex-bold'>(D) </span>4\qquad <span class='latex-bold'>(E) </span>5