On the number line shown, is zero halfway between r and s?

<--r------s--t-->

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

THE ANSWER IS C/ GMAT-PREP

I assumed statement 2 alone was sufficient, however I was wrong. My question is what is the best approach or method, in short amount of time, in going about solving this problem? Your input is appreciated....

Additional question: When taken together statement 1 and 2, is it ok to create an equation out of statement 2?

That is, t-r=t-(-s) the two t's cancel out and you are left with -r=s/ s=+ve t=+ve r=-ve
Then I plugged in numbers to determine whether the two statements together is sufficient to answer the question.

Furthermore, I assumed statement 2 alone was sufficient using the equation -r=s, however I was wrong. Perhaps, I missed something. Could please clarify this for me. Your input and assistance is greatly appreciated.

i would always think about these things SPATIALLY / VISUALLY at first, and set up algebraic equations only as a "plan b". the problem with algebraic equations is that it's too easy to fall into traps.

the particular trap you've fallen into in your interpretation of (2) is that of assuming "-s" is to the LEFT of "t". there is no good reason whatsoever to make this assumption, and, what's more, at least one good reason (viz., "the gmat loves to test exactly these sorts of assumptions) not to make it.
of course, you don't need reasons to be very careful about your assumptions; that should be your default state.

if "-s" is to the right of "t", then you have
<--r-------s---t-----------(-s)-->
in which case 0 is in no-man's-land between "t" and "-s".
in this case, note that "s" is negative. also note that (-s) is positive in this case, a situation that is difficult to digest for most students.

taking statements (1) and (2) together eliminates the above possibility, leaving only the case that you have outlined.

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incidentally, the fault in your algebraic approach lies in writing the distance between t and (-s) as t - (-s). this writing is correct only if t is greater than (-s), an assumption that, as we've seen, is unjustified.
the correct way to write the distance is |t - (-s)| = |t + s|, an expression that is thoroughly unhelpful in solving this problem.

How do you approach such problems ? The strategy guides does not focus too much on these types of questions ?

the best way to approach these problems, in my opinion, is encapsulated by what i've posted above:



there you go. you should try to develop your spatial understanding of the problem, and should reserve algebraic solutions for problems that have no ready spatial interpretation.

you should also make sure that you consider number properties, heavily, when you approach these problems.
many of these number-line problems hinge fundamentally on whether certain numbers are positive or negative, or, similarly, whether unknowns are placed to the left or right of each other on the number line.

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incidentally, pretty much exactly the same things are true for COORDINATE problems (i.e., problems in the x-y plane):
* again, you should be able to interpret most problem statements SPATIALLY
* you should reserve algebraic solutions for problems that are clearly intended as algebraic, such as statement 1 of this problem. in that statement, not only is the comparison illogical from a spatial standpoint (you can't intuitively compare a slope to an intercept), but the two quantities in the statement, slope and y-intercept, are EXACTLY the quantities that appear in the standard form of the equation of a line (y = mx + b).
unless a problem is that obviously intended to be algebraic, don't solve it with algebra except as a last resort.