We do know (when trying to decide between C and E) that statement 2 says the number of women on the sightseeing tour is less than 30. This lets us know what the maximum number is.

If the ratio of Women:Children is 5:2, and the number of women is less than 30, then we also know that the number of women must be a multiple of 5, or it wouldn't reduce down to a 5:2 ratio.

As for why the LCM of 2 and 5 gives us the least number of children on the tour, here is my reasoning.

We know that whatever the number of children on the tour is, with relation to the men, that number must reduce to 5, and that same number with relation to the women, must reduce to 2. We have to find the lowest number that can do both. That's 10.

10 is divisible by 5 so if the # of children was 10, in order for Children:Men to be 5:11, the number of men on the tour must be 22.

In order for the women:children ratio to be 5:2, with the number of children being 10, that's 5*2, so 5 (on the women's side) * 5 = 25.

We know the number of children cannot be greater than 10 because the next number that reduces to 5 and 2 is 20. If you reduce 20 to 2, that's by 10, so if women:children = 5:2 and children = 20, then Women = 50, and Statement 2 says "the number of women on the tour is less than 30"

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J Allen Morris

**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.