Number Systems

sukhman wrote:there is no diagram , but answer given is C, mine was obviously E

Dear Sukman,
I searched the web, and found some versions with simple diagrams. Apparently, this question is originally from GMAT Prep, and the diagram looks something like this

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On the number line shown , is zero halfway between r and s?
In other words, do r & s have the same absolute value but opposite signs? Does r = -s?

Statement #1: s is to the right of zero
By itself, this tells us nothing. Point r could be anywhere, to right or left of zero. This statement, alone and by itself, is insufficient.

Statement #2: the distance between t and r is the same distance between t ans -s
Well, this certainly would be true if r = -s, so that they were at one and the same place. That would give a "yes" answer to the prompt.
BUT, imagine if, say, r = -4, s = -2, and t = -1. Then -s = +2, and both r = -4 and -s = +2 are a distance of 3 from t = -1. This would be consistent with the statement, and would produce a "no" response to the prompt.
Because we can find either a "yes" or "no" answer to the prompt consistent with this statement, this statement does not allow us to isolate a single definitive answer. Therefore, this statement, alone and by itself, is insufficient.

Now, the very tricky part of the problem: the combined statements:
Combined:
s is to the right of zero
the distance between t and r is the same distance between t ans -s
Well, let's think about this. Both s and t must be positive numbers, so -s will be a negative number. Well, if r is positive, there is no way the distance from positive number t to positive number r would be the same as the the distance from positive number t to negative number -s. Therefore, from the second statement, we know r must be negative. Therefore, r and -s are both negative numbers. so is positive number t is the same distance from both of them, this means r and -s must be at the exact same place on the number line. In other words, r = -s, an answer of "yes" to our prompt question. Combined, the statements are sufficient.
OA = [spoiler](C)[/spoiler]

It may be that you found an answer of (E) because you didn't have a diagram. If the problem says "in the diagram" and wherever you found the problem doesn't have a diagram, chances are very very good that you will be operating with inadequate information, and may well get the question incorrect precisely because you have inadequate information. If you do a Google search by the text of the problem, you can often find other places on the web where that problem is posted, and chances are good that you find any relevant diagram.

Does all this make sense?
Mike