2016 AMC 8 Problems/Problem 19

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19. The sum of $25$ consecutive even integers is $10,000$. What is the largest of these $25$ consecutive integers?

$(A)\mbox{ }360\mbox{           }(B)\mbox{ }388\mbox{           }(C)\mbox{ }412\mbox{           }(D)\mbox{ }416\mbox{           }(E)\mbox{ }424\mbox{           }$