The SAT Prep Black Book(89)

To keep that from happening, the College Board does its best to include 4 wrong answers to each question that try to anticipate the mistakes that you’re likely to make.

This might seem pretty mean-spirited on the part of the College Board, but we can actually use it to our advantage as test-takers. Since the College Board tries to come up with wrong answers to tempt us into making mistakes—and since it has to do this in standardized, repetitive ways, just like everything else it does—then we can learn to use the concepts and relationships that appear in the answer choices to get an idea of what the question is actually asking about.

This will make a lot more sense after we talk about common patterns that we’ll encounter in the answer choices, and after we go through some solutions from the Blue Book together. We’ll cover some of those common patterns starting on the next page, and then we’ll do the Blue Book solutions a few pages after that.





Hidden Test Design Patterns of SAT Math Questions


Most of the hidden patterns on the SAT math section have to do with using the answer choices to help you check your answers, where that’s possible. Looking at the answer choices can reassure you that you have the right answer (or help show you your mistakes so you can correct them).

Many students are surprised to find out that these patterns appear reliably and consistently in real SAT Math questions from the College Board, because they really have very little to do with actual math rules—they’re purely related to the test-design principles required by the standardization of the test. So before we get into these patterns, I’d like to take a moment to remind you why they’re a part of the SAT.

As we discussed at the beginning of this book, it’s important to remember that the SAT is not a normal test. It has a very specific purpose and must, therefore, follow very specific rules to make sure that questions are designed to test the same skills in the same underlying ways, without actually repeating the questions. It’s also important to remember that the SAT is predominantly a multiple-choice test, and that the multiple-choice format only requires a test-taker to separate right answers from wrong answers, rather than requiring you to provide correct answers on your own. This means that the relationships among right answers and wrong answers must remain constant for all real tests, because changing those relationships would involve changing the nature of the multiple-choice questions and breaking the standardization rules of the test.

Keep these things in mind as we discuss the patterns in the SAT Math section, and as you encounter real SAT Math questions in the future.





Hidden Pattern 1: Halves and Doubles


Very often, one of the wrong answer choices will be twice as much as the right answer choice, or half as much as it. This is especially true when the problem involves multiplying or dividing an amount by 2. If you solve a problem and get an answer like 18, a wrong answer choice like 36 might reassure you that you’re right.

Remember that this pattern is an indication that you’re probably right, not a confirmation that you’re definitely right. Also, it’s important not to get it backwards—in the same hypothetical example, the right answer might be 36, and the wrong answer might be 18! Be very aware of this useful pattern, but don’t rely on it exclusively.





Hidden Pattern 2: Right Answer, Wrong Time


One of the ways that the SAT will try to confuse you is by giving you a problem that involves two or three steps. When it does that, one of the wrong answers will often be the number that you would get if you stopped after one of the earlier steps. For example, a problem might ask you to find the price for pens by giving you the prices for different combinations of pencils and erasers. The problem might require you to figure out the price of pencils in order to figure out the price for erasers, and one of the wrong answer choices would be the price of pencils. Because this wrong answer is actually a number that you found in the process of solving the problem, seeing it in as a wrong answer can reassure you that you’re on the right track.





Hidden Pattern 3: Substitution


As I said before, the SAT likes to give you problems that look complicated but have very simple solutions. The test often does this by showing you a rather complicated expression that you can simplify by substituting one thing for another. If you start looking for substitution opportunities, you’ll find them all over the test, and they’ll make your life easier. For example, the SAT will often reward you for substituting a difference of squares like x2 – y2 with the expression (x – y)(x + y). On the other hand, it might also reward you for going in the other direction, and realizing that (x – y)(x + y) can be restated as x2 – y2.