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GMAT Prep 1 number line data sufficiency question

Expert replies
by mike9950 » Thu Jan 07, 2010 8:11 pm
There have been other posts about this question but I am still quite unclear as to why C is the correct answer.

On the number line shown, is zero half-way 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.

I chose B.

Here is my logic. We can rephrase the question as: is r = - s?

From statement 2:

t-r = t - (-s) ==> r = - s

If they didn't have the number line shown, I could understand how you would need statement 1 in order to be sure that s is positive. However, if s were to be negative, then from statement 2, r would be positive. But in the picture, r is to the left of s! This would contradict the number line they provide! Or Is this a situation where you can't assume that the numbers are increasing from left to right on the number line?

Could someone clear this up...

Thanks!
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Source: — Data Sufficiency |

by Stuart@KaplanGMAT » Fri Jan 08, 2010 6:03 am
mike9950 wrote:T

Here is my logic. We can rephrase the question as: is r = - s?

From statement 2:

t-r = t - (-s) ==> r = - s
The problem is that you've mistranslated statement (2). It should be translated as:

|t - r| = |t - -(s)|

or

|t - r| = |t + s|

which has multiple solutions.

To answer your final question, we have to be careful about making assumptions in DS, but we can trust the order of points when they're clearly shown in a diagram.

If s were negative, then r could still be negative and to the left of s. For example, if we choose:

s = -2
r = -4
t = -1

then we get:

|-1 - (-4)| = |-1 + (-2)|

|3| = |-3|

3 = 3

so we've satisfied statement (2) and get a "no" answer to the original question.

We could also, of course, choose:

s = 3
r = -3
t = 6

giving us:

|6 - (-3)| = |6 + 3|
|9| = |9|

fulfilling statement (2), and giving us a "yes" answer to the original question.
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