The SAT Prep Black Book(94)
This doesn’t mean that questions with multiple variables are impossible to figure out on the SAT. It’s just that sometimes it’s possible to know the value of an expression that involves several variables even if you can’t know the values of the variables themselves.
For instance, if I tell you that ab2 - 7 = 53, and then ask you for the value of ab2, you can still figure out that ab2 is 60, even if it’s impossible to know the values of a or b individually.
One of the test’s main signals that it might not be possible to solve for every variable in an expression is when they ask you for the value of an expression that contains multiple variables, rather than asking for the value of an individual variable within that expression. In the ab2 example I just gave, I couldn’t ask for a or b individually because there wasn’t enough information about them; that’s why I had to ask for the entire expression ab2.
So if you see a question that asks for the value of x + y or some other expression with more than one variable, don’t make the mistake of assuming that you have to find x and y individually. It may be more expedient to try to solve for the entire x + y expression all at once.
One example of a question that involves multiple variables that can’t be approached individually is question 16 from page 919 in the second edition of the College Board’s Blue Book. My explanation for that question appears later in this book, when I go through a selection of challenging SAT Math questions.
It’s Not School Math—Your Work Doesn’t Matter
Lots of test-takers experience significant difficulty on the SAT Math section for a reason that might seem strange to a lot of people: they try to approach each question in a formalized way that would satisfy a math teacher.
But by now we know that the SAT doesn’t reward the same things that school rewards. And the SAT Math section is no different.
The bottom line is that the SAT doesn’t care what kind of work you do to arrive at the answer that you choose. The SAT only cares if the answer that you choose is correct. That’s it.
This fact has two very important implications for us as test-takers. First, it means that we can, and should, get in the habit of looking for the fastest, most direct route to the answer, even if that route doesn’t involve solving a formal equation (or even writing anything down at all). Second, it means that we have to make sure we don’t make any small mistakes in our solution that might lead us to mark the wrong answer even if our overall approach is formally sound, because the College Board will never know what our approach was. For the College Board, a wrong answer is a wrong answer no matter how solid the approach to the question was, and a right answer is a right answer no matter what you did to arrive there.
So remember that the SAT Math section often features questions where formulaic solutions are literally impossible to use.
In the parts of this book where I provide solutions to real SAT Math questions from the College Board’s Blue Book, you’ll often see that the approach I recommend wouldn’t be acceptable to most math teachers, because it’s not formal. This isn’t because I’m not good at math; it’s because I’m very, very good at SAT Math, and in SAT Math there’s no value in approaching things formulaically. In fact, there’s usually a lot more value in abandoning formulaic math whenever possible.
So try to get in the habit of finding the most direct approach to a question that you possibly can, and remember that the only thing that matters to the College Board is that you mark the correct answer!
Avoid Decimal Expressions Unless A Question Uses Them
In high school and college math classes, we’re often encouraged to use decimal values rather than fractions. For instance, we might write “0.8” instead of “4/5.”
On the SAT, it’s usually a bad idea to express things in terms of decimals, unless the answer choices are also in decimal form. When we work with decimals, we often miss opportunities to simplify and reduce expressions that are much easier to see when we keep everything in fraction form.
For instance, if a question involves multiplying 4/5 by 5/6, then using fractions might help me see right away that the 5’s cancel out and I’m left with 4/6, which is the same thing as 2/3. If I had to enter that into a calculator, I’d probably lose time, and I’d also run the risk of hitting the wrong key or something. In general, we’ll have a much better chance of finding the shortest possible solution if we get in the habit of avoiding decimal expressions on the SAT.
The only real exception to this comes when a question involves decimal expressions in its answer choices. When the College Board sets a question up like that, they’re usually trying to get us to realize that we can simply approximate the answer, often by using the scale of a diagram or some other clue in the question, and that the correct answer choice will be the only one that’s close to our approximation. In these situations, it can be very helpful to use the decimal approximation to solve the question—but in just about every other situation, it’ll be smarter to stick with fractions.