Most people would be tempted to say that 1 is sufficient, but it's not, actually, if you consider that x and y could not share signs. Take some examples:
If x is 3 and y is 2, then indeed 1/x < 1/y, but x > y.
If x is -2 and y is 3, then again 1/x < 1/y, but this time x < y.

Here's where stmt 2 comes in: by itself, it's not enough, since x could be negative and y positive or the other way around. But if you couple it with stmt 1, you get that the only viable case is the second one.