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## Help - GMATPrep DS Number Line Question

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queenisabella Rising GMAT Star
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Help - GMATPrep DS Number Line Question Sun Mar 11, 2012 2:20 pm
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this is the 2nd time i've seen this question and i'm still struggling with it. can someone please help explain to me the rationale, and the fastest way to solve this?

DATA SUFFICIENCY:

On the number line shown, is zero halfway between r and s?
(1) s is to the right of zero.
(2) The distance between t and r is the same as the distance between t and -s.

OA is C
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Mike@Magoosh GMAT Instructor
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Sun Mar 11, 2012 4:52 pm
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.

Does this make sense? Please let me know if you have any questions on what I've said here.

Mike

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Last edited by Mike@Magoosh on Mon Mar 12, 2012 8:42 am; edited 1 time in total

amitkoul777@gmail.com Just gettin' started!
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Sun Mar 11, 2012 5:44 pm
Hi Mike,

Can you please explain the below ?

b) t > 0, s < 0, r < 0 ---> t = 1, s = -2, r = -4, answer to prompt = NO

As per statement 2, distance between t & r is same as distance between t & -s.
In b) distance between t & r is 5 units but distance between t & -s is 1 unit.

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Mike@Magoosh GMAT Instructor
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Mon Mar 12, 2012 8:45 am
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

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GMATGuruNY GMAT Instructor
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Fri Mar 23, 2012 12:00 pm
For an alternate approach, check my solution to a very similar problem here:

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

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