

Variation
One way that the new SAT tests whether you understand
an equation is to ask questions about the relationship between certain
variables. For example,

The easiest way to solve such problems is to just plug
in:
So the value of y will be
^{2}/_{3} of
what it was.
Essentially, these sorts of problems are testing to see
if you understand how an equation works and how different variables
interact. While in a simple equation like the first example, this
is easy to see, it becomes a little more complicated as the equations
get more complex:

Once again, you can still find the answer by plugging
in 2x for x and 3z for z.
You just have to do some additional math:
The value of y will be
^{8}/_{3} of
what it was. Since the original expression was y = x^{3}/2z, we
must figure out what fraction times ^{1}
/_{2} is equal to
^{4}/_{3} :
It’s also possible that you’ll have to know some variation
jargon for the new SAT. There are two terms you need to know: direct and inverse.
A direct relationship between two variables exists when, if one
variable increases, the other variable increases. In the equation
y and x share
a direct relationship, since if x increases,
so does y.
An inverse relationship is just the opposite. In the same
example, y and z have
an inverse relationship, because if z were
to increase, y would decrease.
