## SAT Math Tutorial

*Direct Variation vs. Inverse Variation*

#### Intro

The SAT often asks questions about direct variation and inverse variation. These questions use wording like “…varies directly with…”, “…varies inversely with…”, “…is directly proportional to…” and “…is inversely proportional to…”

The formulas for direct and inverse variation are as follows.

**Direct Variation**

As one variable increases, the other variable increases proportionately.

**Inverse Variation**

As one variable increases, the other variable decreases proportionately.

Here is a typical SAT variation problem.

#### Sample Problem

If varies directly with , and when , then what is the value of when ?

#### Solution

The first step for this problem is to determine whether to use the direct variation formula or the inverse variation formula.

In this case, the problem states that “ varies directly with .” Thus, the relationship between and is a **direct** one, requiring the direct variation formula, .

Next, find the value for by substituting the appropriate values for and into the direct variation formula.

Once the value of is determined, substitute it into to see the true relationship between and .

Finally, the question asks for “the value of when .” So substitute 48 for in the equation above and solve for .

Thus, the answer is .

**Challenge Questions**

How would the answer change if the question stated that “ varies inversely with ?” What if it stated that “ varies inversely as the square of ?”

# About The Author

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Math Expert And SAT Instructor |

Jared, founder of The Knowledge Roundtable, is passionate about the advancement of knowledge. He has a B.S. in astronomy and physics from UMass and an MBA in Advanced Financial Analytics, also from UMass. He has a day job as a Data Scientist in Boston. He has over 500 hours of tutoring experience... |