Hi, there. I'm happy to help with this.
So, from the diagram, we know r < s < t. That's it.
Prompt:
On the number line shown, is zero halfway between r and s?
In other words, |r| = |s|, or r = -s. That is the question.
Statement #1:
s is to the right of zero.
From this, we know only that s is positive, but nothing else. This gives us almost no information, so by itself, it's
not sufficient.
Statement #2:
The distance between t and r is the same as the distance between t and -s.
This one is tricky, because it opens a several possibilities.
a) t > 0, s > 0, r < 0 ----> t = 3, s = 2, r = -2, answer to prompt = YES
b) t < 0, s < 0, r < 0 ---> t = -1, s = -3, r = -5, answer to prompt = NO
Two different configurations consistent with this statement lead to two different answers. Therefore, Statement #1, by itself, is
not sufficient.
Combined Statements #1 & #2:
Now, we know we must have t > 0 and s > 0. Therefore, -s will be a negative number. We also know now that -s and r are both to the left of t, so if they are both the same distance from t, they must be in the same place ---- i.e. -s = r. This leads to a definitive YES answer to the prompt. Combined, the statements are
sufficient.
Answer =
E
Does this make sense? Please let me know if you have any questions on what I've said here.
Mike
