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AMC 12 2022b Problem 6

  • Paper

Consider the following 100100 sets of 1010 elements each: {1,2,3,…,10},{11,12,13,…,20},{21,22,23,…,30},⋮{991,992,993,…,1000}.\begin{align*} &\{1,2,3,\ldots,10\}, \\ &\{11,12,13,\ldots,20\},\\ &\{21,22,23,\ldots,30\},\\ &\vdots\\ &\{991,992,993,\ldots,1000\}. \end{align*} How many of these sets contain exactly two multiples of 77?

\textbf{(A)}\ 40 \textbf{(B)}\ 42 \textbf{(C)}\ 43 \textbf{(D)}\ 49 \textbf{(E)}\ 50

Dataset text AMC 12 2000 to 2025. Quoted with source.

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B

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