Discussion
If x ≠ 0, −1, then is 
greater than 
?
(1) x < 1
(2) x > 1
| (A) | if statement (1) ALONE is sufficient to answer the question but statement (2) alone is not sufficient; |
| (B) | ... |
| (C) | ... |
| (D) | ... |
| (E) | ... |
| (F) | ... |
The solution is
Posted: 12/12/2011 21:11
Not totally clear on why (2) alone is sufficient in this case.
Posted: 12/13/2011 22:45
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.
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.