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Curious to see what other people's first reaction to seeing this is.

My first thought was: for (18k)/L to be an integer, then L must be a factor of either 18, or K, or both. I thought stmt 1 was sufficient to determine that L was a factor of K but I guess this is incorrect.

I'm assuming it is always the case that (x^2)/(y^2) will never be sufficient to determine that y is a factor of x.

Stmt 2 tells us that L is a factor of K (because K=2L) therefore we know the L in the denominator will cancel out one factor of L in the numerator. This leaves a 1 in the denominator as well.

Curious to see what other people's first reaction to seeing this is.

My first thought was: for (18k)/L to be an integer, then L must be a factor of either 18, or K, or both. I thought stmt 1 was sufficient to determine that L was a factor of K but I guess this is incorrect.

I'm assuming it is always the case that (x^2)/(y^2) will never be sufficient to determine that y is a factor of x.

Stmt 2 tells us that L is a factor of K (because K=2L) therefore we know the L in the denominator will cancel out one factor of L in the numerator. This leaves a 1 in the denominator as well.

The take-away here is that assuming variables always carry rational numbers is not very becoming of a 700-level tester. Question caught me on that assumption too. That's why I love gmatclub problems; they keep you honest!