2024 AMC 12A Problem 5A data set containing 202020 numbers, some of which are 666, has mean 454545. When all the 666s are removed, the data set has mean 666666. How many 666s were in the original data set?(A) 4\text{(A)}\;4(A)4(B) 5\text{(B)}\;5(B)5(C) 6\text{(C)}\;6(C)6(D) 7\text{(D)}\;7(D)7(E) 8\text{(E)}\;8(E)8Related TopicsCoreMean, Median, Mode, and RangeCheck AnswerYour answer:ABCDECheckHints (3)Hint 1a1+⋯+a20−n+6+6+⋯+6⏟n=20×45a_1+\cdots+a_{20-n}+\underbrace{6+6+\cdots+6}_{n}=20\times45a1+⋯+a20−n+n6+6+⋯+6=20×45Hint 2a1+⋯+a20−n=(20−n)66a_1+\cdots+a_{20-n}=(20-n)66a1+⋯+a20−n=(20−n)66Hint 3By subtracting the equation in Hint 2 from Hint 16n=20×45−(20−n)666n=20\times45-(20-n)666n=20×45−(20−n)6660n=20(66−45)=20(21)60n=20(66-45)=20(21)60n=20(66−45)=20(21)n=7n=7n=7Related Problems (3)AMC 10A/12A 2025 (Problem 4/3)AMC 10B/12B 2025 (Problem 17/14)2024 AMC 10A Problem 12Final Answer(D) 7