Unit 9: Assigning Values

Part of scoring well on the SAT Math section, is making the test easier for yourself.  Assigning values to variables is a fantastic strategy for scoring better and moving faster through the math sections.  Here we will go over some of the types of questions you will encounter that welcome this strategy.

x‘s Everywhere

When you have the same variable in an equation in the question and answer choices, you can use this strategy.

Example:

What is the equivalent form of \(\frac{x^2+3x-8}x\) ?

A) \(\;5x-1\)

B) \(\frac x3\)

C) \(x^2-3\)

D) \(\;x+7\)

Strategy:

When there is one variable in both the question and all of the answer choices, and the question is asking you for the equivalent form, plug in 2 for the variable and see which answer choice produces the same numeric value (plugging in 0 or 1 can occasionally give strange results).

In this example, since the question is asking us for the equivalent form and there is one variable (\(x\)) in the question and the answer choices, you can plug in 2 for all the \(x\)s.

What is the equivalent form of \(\frac{\left(2\right)^2+3\left(2\right)-8}2\) ?

A) \(5\left(2\right)-1\)

B) \(\frac23\)

C) \(\left(2\right)^2-3\)

D) \(\;2+7\)

After simplifying, you would find that the fraction in the question is now equal to 1 and the only answer choice that is equal is C).

Making Abstract Manipulations

Example:  

The area of a rectangle is 80 square inches. What is the area, in square inches, of a rectangle with twice the length and half the width?

A) 40

B) 80

C) 100

D) 120

Strategy:

When a problem asks you to make changes to unknown values, and to interpret the effect of those changes, assign values.  This works when you have 2 or more variables that are undefined.  Use numbers that are easy to add/multiply and won’t leave you with fractions or decimals after you make your manipulations.

The question is asking you to make changes to unknown values, the initial length and width of the rectangle.  Therefore, assign values for the length and width.  Make sure that your values multiply to be 80, because our initial area must be 80 square inches.  Here, we’ll use 8 and 10 but you could as easily use 20 and 4.

$$l=8\;\;\;w=10\;\;\;l\times w=80$$

Now change the length and width to interpret the rectangle asked about in the question.

$$new\;length=16\;\;\;\;\;\;\;\;\;new\;width=5\;\;\;\;\;\;\;\;\;\;new\;l\times w=80$$

The answer would be B) 80.

Traps

Sometimes, your variable will not be x.  It could be ab, or some other letter.  The strategy works the same no matter what they call the variable.

You might see a constraint on the x’s everywhere, like “x is a positive integer” or “where > 3”.  In that case, instead of using 2, we’d just use 4.  It works the same for any number that isn’t 0 or 1.

Sometimes, you will have two undefined variables.  You can still assign values – just make them both 2 or other appropriate numbers.