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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

_________________
Magoosh GMAT Instructor
http://gmat.magoosh.com/

Dear amitkoul777@gmail.com

Very sorry about that --- apparently, I made some arithmetic mistake when I first typed that. I correct it in the original post, and here's the corrected line:

b) t < 0, s < 0, r < 0 ---> t = -1, s = -3, r = -5, answer to prompt = NO

Distance from t = -1 and r = -5 is 4.
Distance from t = -1 and -s = 3 is 4.

Thank you for pointing that out, and please let me know if you have any other questions.

Mike

_________________
Magoosh GMAT Instructor
http://gmat.magoosh.com/

For an alternate approach, check my solution to a very similar problem here:

http://www.beatthegmat.com/best-approach-plz-t67985.html

_________________
Mitch Hunt
GMAT Private Tutor and Instructor
GMATGuruNY@gmail.com
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