# Number Theory Inequality

Level pending

Given the set $$\{2, 3, 4, \ldots, n \}$$ , we choose a subset $$7$$ distinct integers. Given that, no matter what $$n$$ is, we can find two integers $$X, Y$$ in our subset such that $$1< \frac{Y}{X} <2$$, what is the greatest possible value of $$n$$?

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