One way that the new SAT tests whether you understand an equation is to ask questions about the relationship between certain variables. For example,
If z triples while x doubles, what happens to y?


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:
If z triples while x doubles, what happens to y?


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 = x3/2z, 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.
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