MathDB
Literally Longer Than #12-15 Combined

Source: 2017 AMC10A #16

February 8, 2017
AMCAMC 10AMC 10 A2017 AMC 10AAMC 122017 AMC 12A

Problem Statement

There are 1010 horses, named Horse 1, Horse 2, …\ldots, Horse 10. They get their names from how many minutes it takes them to run one lap around a circular race track: Horse kk runs one lap in exactly kk minutes. At time 0 all the horses are together at the starting point on the track. The horses start running in the same direction, and they keep running around the circular track at their constant speeds. The least time S>0S > 0, in minutes, at which all 1010 horses will again simultaneously be at the starting point is S=2520S = 2520. Let T>0T>0 be the least time, in minutes, such that at least 55 of the horses are again at the starting point. What is the sum of the digits of TT?
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> 6<span class='latex-bold'>(A)</span>\ 2\qquad<span class='latex-bold'>(B)</span>\ 3\qquad<span class='latex-bold'>(C)</span>\ 4\qquad<span class='latex-bold'>(D)</span>\ 5\qquad<span class='latex-bold'>(E)</span>\ 6
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