more generally"”
when it comes to data sufficiency, the optimal approach is usually to
figure out all the relationships in the problem
FIRST -- that is, before you start doing any actual mathematics.
as an illustration, let me walk through the statements in the prompt, considering how they are interrelated.
The coordinate of R is 0. The distance between P and R is 1/3 the distance between P and S.
if PR is one-third of PS, then RS must be the other two-thirds.
One-third and two-thirds. That's a ratio of 1 to 2.
So we know that PR is exactly half of RS, or, alternatively, that the coordinate P is -1/2 of the coordinate S.
MOST IMPORTANTLY,
since this is a DS problem, we can now forget all about the 1:2 and the opposite signs -- because the point isn't to find actual answers, it's only to determine
whether you
can find such answers.
so, at this point, all we have to know is:
If I have P, I also have S.
If I have S, I also have P.next...
M is the midpoint of line segment PS
remember, here, that S = -2P, or that P = -S/2 (whichever version is more intuitive for you).
so, M = the average of P and S
= (P + (-2P))/2, or (S + (-S/2))/2
I don't have to simplify these expressions -- it's enough to realize that M is a constant multiple of P (or S), implying that P (or S) is also a constant multiple of M.
So:
If I have P or S, I also have M.
If I have M, I can find P and S.this is the way you should handle DS prompts. you should not regard them as a giant chunk of random statements thrown on the head of the hapless problem-solver; you should
read them dynamically, and
think about how you can USE each statement AS YOU READ IT.
