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AMC (AIMO validation set) / https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_6 / Consider the following 100 sets of 10 elements each:

Problem

Answer published by the source. Consult the official source to check your work against its answer.

problem

Consider the following

100

sets of

10

elements each: \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

7

Plain-text mathematical notation (without MathML)

Consider the following 100 sets of 10 elements each:
\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 7?

Original LaTeX notation

Consider the following $100$ sets of $10$ elements each:
\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 $7$?

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Source and history

upstream_id / Original problem ID: https://artofproblemsolving.com/wiki/index.php/2022_AMC_12B_Problems/Problem_6
task_id: a30d9527-13b3-50b1-a4cf-6c7e36b668f3
task_key: default--train--https~3a~2f~2fartofproblemsolving~2ecom~2fwiki~2findex~2ephp~2f2022~5fAMC~5f12B~5fProblems~2fProblem~5f6
task_revision_id: 2
config / split: default / train

Official source

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