MathDB
2022 AMC 12B Problem 6

Source: 2022 AMC 10B # 8 / 2022 AMC 12B #6

November 17, 2022
AMCAMC 122022 AMC2022 AMC 12BAMC 102022 AMC 10B

Problem Statement

Consider the following 100100 sets of 1010 elements each: \begin{align*} &\{1,2,3,\cdots,10\}, \\ &\{11,12,13,\cdots,20\},\\ &\{21,22,23,\cdots,30\},\\ &\vdots\\ &\{991,992,993,\cdots,1000\}. \end{align*} How many of these sets contain exactly two multiples of 77?
<spanclass=latexbold>(A)</span>40<spanclass=latexbold>(B)</span>42<spanclass=latexbold>(C)</span>43<spanclass=latexbold>(D)</span>49<spanclass=latexbold>(E)</span>50<span class='latex-bold'>(A)</span> 40\qquad<span class='latex-bold'>(B)</span> 42\qquad<span class='latex-bold'>(C)</span> 43\qquad<span class='latex-bold'>(D)</span> 49\qquad<span class='latex-bold'>(E)</span> 50