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Megapolis Hotel Babies

Source: Problem #13 2016 AMC 10B

February 21, 2016
AMCAMC 102016 AMC 10BAMC 10 B

Problem Statement

At Megapolis Hospital one year, multiple-birth statistics were as follows: Sets of twins, triplets, and quadruplets accounted for 10001000 of the babies born. There were four times as many sets of triplets as sets of quadruplets, and there was three times as many sets of twins as sets of triplets. How many of these 10001000 babies were in sets of quadruplets?
<spanclass=latexbold>(A)</span> 25<spanclass=latexbold>(B)</span> 40<spanclass=latexbold>(C)</span> 64<spanclass=latexbold>(D)</span> 100<spanclass=latexbold>(E)</span> 160<span class='latex-bold'>(A)</span>\ 25\qquad<span class='latex-bold'>(B)</span>\ 40\qquad<span class='latex-bold'>(C)</span>\ 64\qquad<span class='latex-bold'>(D)</span>\ 100\qquad<span class='latex-bold'>(E)</span>\ 160