LevelOne wrote:
From (2) I derived:
s+20 = 400/t-1
s = 400/t
am I moving in the right direction? is (2) sufficient because there are two variables and two equations? thanks
Great question!
The "# of equations vs # of unknowns" rule is an extremely powerful tool in DS; the better you understand it, the less math you'll have to do to score points (which should make you very happy!).
Here's the full wording of the rule:
To solve a system of n variables, one requires n distinct, linear, equations.
If the question you posted had been an algebra problem, (2) would not have been sufficient, because your equations aren't linear.
A simple definition (certainly sufficient for the GMAT) of a "non-linear" equation is one with an exponent other than one. When we have multiple variables, we often have hard to recognize non-linear equations.
Let's look at your second equation:
s = 400/t.
We can rearrange this to:
st = 400.
This is a non-linear equation since when we isolate t or s in the first equation and then substitute into this one, we'll get an s^2 or t^2 term. When we solve this quadratic, we'll get two solutions, one positive and one negative.
However, it's always important to focus on the content of a particular question; as ssmiles points out, time cannot be negative. In distance/rate/time questions, we can always ignore negative solutions, since they just don't make sense in the real world. Another common area of math in which we can ignore negative solutions is geometry (which is why, for example, when you have r^2 = 36 we don't worry that the radius could be +/-6).
So, since this question is about time, we can ignore the non-linear issue and be confident that our two distinct equations are sufficient to solve for the unknowns.
