Problem Solving

If 0<r<1<s<2, which of the following must be less than 1?

I. r/s
II. rs
III. s-r

I only
II only
III only
I and II
I and III

I would use a combination of logic and plugin to do this in about 45 seconds.

I. r/s is (smaller positive)/(bigger positive). The result will always be a positive proper fraction (a value between 0 and 1). I must be less than 1.

II. (0.0001)*(1.01) is less than 1 (almost zero), but (0.9999)*(1.9999) is bigger than 1 (almost 2), so rs does not have to be less than 1.

III. 1.0001-0.9999 is less than 1 (almost zero), but 1.9999-0.0001 is bigger than 1 (almost 2), so s-r does not have to be less than 1.

Answer: I only