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MATH / Let S be the set of all integers k such that, if k is in S, then (17k)/(66) and (13k)/(105) are terminating decimals. What is the smallest integer in S that is greater than 2010?

Problem

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problem

Let SS be the set of all integers kk such that, if kk is in SS, then 17k66\frac{17k}{66} and 13k105\frac{13k}{105} are terminating decimals. What is the smallest integer in SS that is greater than 2010?
Plain-text mathematical notation (without MathML)
Let S be the set of all integers k such that, if k is in S, then (17k)/(66) and (13k)/(105) are terminating decimals. What is the smallest integer in S that is greater than 2010?
Original LaTeX notation
Let $S$ be the set of all integers $k$ such that, if $k$ is in $S$, then $\frac{17k}{66}$ and $\frac{13k}{105}$ are terminating decimals. What is the smallest integer in $S$ that is greater than 2010?

level

Level 5

type

Number Theory

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Source and history

task_id
345cc11a-008c-5a3a-b0ef-1a005b92def7
task_key
number~5ftheory--test--345cc11a-008c-5a3a-b0ef-1a005b92def7
task_revision_id
1
config / split
number_theory / test

Official source

initial import