Don’t worry if this sounds a little vague right now. We’ll see several examples of it when we go through real SAT questions from the College Board in a few pages.
Hidden Pattern 4: Try To Avoid Firsts And Lasts In A Series
Sometimes some or all of the answer choices in a math question will form a series. These series might be pretty easy to recognize in some cases, like if the answer choices are 7, 8, 9, 10, and 11. In other cases, the series might be less obvious, and it might be related to a concept in the question: if the question is talking about dividing some quantity by 4, then the answer choices might contain the series 3, 12, 48, because each number in the series is one fourth of the next number in the series.
The College Board seems to include series in the answer choices when it hopes that you’ll make a mistake and repeat a step in the solution one time too many or too few, ending up with one of the wrong answers in the series. In other words, if a question involves finding the perimeter of a triangle with sides of 5 units each, the answer choices might include the series 10, 15, 20, because the College Board is hoping you’ll either add 5 one time too few (ending up with 10) or one time too many (ending up with 20).
For this reason, when a series is involved in the answer choices, we’ll typically find that the correct answer isn’t the first or last number in the series. The College Board seems to like to put the correct answer near the middle of the series in order to allow you to make a mistake in either direction and still find a wrong answer that reflects your mistake.
Remember, as with the other patterns in this section, that this isn’t an unbreakable rule. So I’m not saying that we’ll never, ever find the right answer at the beginning or the end of a series; sometimes we will. I’m just saying that it’s more common to find it in one of the middle positions of a series, and that it helps to be aware of that.
Hidden Pattern 5: Wrong Answers Try To Imitate Right Answers
The College Board likes to create wrong answers that incorporate elements of correct answers, probably in an attempt to make it harder for you to eliminate answer choices on the basis of a partial solution. In other words, if you’re working on a question where the answer choices are all algebraic expressions and you figure out that the correct answer should include the expression 2r along with some other stuff, then you’ll often find that a majority of the answer choices include 2r. This way, the College Board can try to force you to figure out the rest of the question in order to identify the correct answer.
While this can be an annoying thing for the College Board to do, you’ll find that you can actually use it to your advantage in many cases: after you think you’ve solved a question, if you see that the wrong answers seem to include a lot of the elements in common with the choice that you like, you can often take that as a good sign that you’ve thought about the question correctly.
In other words, if the wrong answers seem to be imitating parts of the right answer, that’s typically a sign that you’ve understood the question correctly. (Notice I said, “typically,” and not “always.”)
We’ll see several examples of this, and of the other SAT Math patterns, when we go through some questions from the Blue Book in a few pages.
Special Math Technique: Learning From Diagrams
Many math questions on the SAT will involve diagrams. You probably already knew that. But you might not know that SAT diagrams can actually give away a lot of information about the best ways to attack a particular question.
When an SAT diagram is drawn to scale, you can often extract important information from it just by looking at it. For example, you can eyeball the relative sizes of angles and the relative lengths of line segments.
But when a diagram isn’t drawn to scale—or simply isn’t provided at all—you can often learn even more.
When the College Board decides to leave out a diagram or to include a diagram that isn’t drawn to scale, they make this decision because including an accurate diagram would give away the answer to the question you’re being asked. In these situations, it’s often helpful to try to draw your own scaled diagram in the test booklet if you can.
Similarly, the College Board will sometimes show you a diagram and then provide a further explanation of that diagram in the written portion of the question. Again, the reason for this is simple: If the written information had been labeled directly on the diagram in the first place, the answer to the question would have been a lot easier to figure out.
So if you want to maximize your score on the SAT Math section, you’re going to need to practice using diagrams. Whenever you see a diagram on the test, be very alert to the things that are left out of it. Always be prepared to augment the given diagram (or provide a substitute diagram of your own). You may be surprised at how many questions become much, much easier once you catch on to this.