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AMC 8 2004 Problem 19

Source:

November 28, 2010
number theoryleast common multiple

Problem Statement

A whole number larger than 22 leaves a remainder of 22 when divided by each of the numbers 3,4,53, 4, 5 and 66. The smallest such number lies between which two numbers?
<spanclass=′latex−bold′>(A)</span> 40 and 49<spanclass=′latex−bold′>(B)</span> 60 and 79<spanclass=′latex−bold′>(C)</span> 100 and 129<spanclass=′latex−bold′>(D)</span> 210 and 249<spanclass=′latex−bold′>(E)</span> 320 and 369<span class='latex-bold'>(A)</span>\ 40\text{ and }49\qquad <span class='latex-bold'>(B)</span>\ 60\text{ and }79\qquad <span class='latex-bold'>(C)</span>\ 100\text{ and }129\qquad <span class='latex-bold'>(D)</span>\ 210\text{ and }249\qquad <span class='latex-bold'>(E)</span>\ 320\text{ and }369
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