Not totally clear on why (2) alone is sufficient in this case.

Lolita,

The solution given in the answer key is a little technical.

Let's try plugging in some numbers for statement (2):

We know X > 1, so let's start with 2.

For [1/x], we get 1/2
For [1/(1 + x)], we get 1/3.

The second expression is smaller.


Now let's try 4.

For [1/x], we get 1/4
For [1/(1 + x)], we get 1/5.

Again, the second expression is smaller.


What about when x get really large? Let's try x = 3450.

For [1/x], we get 1/3450
For [1/(1 + x)], we get 1/3451.

Even with a really large X, the second expression is smaller.


So, as you can see, if x > 1, then [1/x] will ALWAYS be larger than [1/(1 + x)].

Here we've proven statement (2) is sufficient.