The SAT Prep Black Book(97)
So 8 of the tables will need to have an extra seat, which makes (E) the right answer.
Notice that this isn’t really the kind of question you would probably ever be asked in a math class, and the solution I just gave isn’t the kind of solution your math teacher would ever accept. This is normal for the SAT, and we need to get used to it.
Also notice that the answer choices form a series in this question, and the correct answer happens to be the largest number in the series, which is something that I said doesn’t happen often. I was right—it doesn’t happen often—but that doesn’t mean it never happens. In this case, when I see that the answer I like is the last number in a series, I’d just double-check my work and make sure I hadn’t made a mistake, and move on.
One more thing—you might ask how I knew to start out by multiplying 4 and 19. But I didn’t “know” that would lead to the answer right away until I tried it. On the SAT Math section, we have to be willing to play with questions like this, and we have to get away from the idea of following established formulas.
Page 414, Question 4
This question often overwhelms test-takers who think in terms of school math, because it has two variables in it, and one of those variables (m) is actually impossible to solve for. In school math, it might be a problem if we couldn’t solve for a variable, but this is SAT Math. The SAT often gives us questions in which it’s impossible to work out the value of a particular variable.
Since the question asks which answer choice would be equal to the original expression when a equals 4, and since every answer choice has 4’s in it instead of a, I would start out by plugging 4 in for a, and determining that the original given expression equals 4m2 + 4m + 4. Then we can go through each answer choice and distribute the 4 in each one, until we end up with a choice that also results in 4m2 + 4m + 4 as an answer.
The answer choice that fits the bill is (D).
Notice that the choices here fit a pattern we discussed earlier in this book: the elements of the right answer appear very frequently in the wrong answers.
In other words, in this case, the correct answer has the parenthetical expression with m2 , m, and 1. Notice that 3 out of the 5 choices have m2 somewhere in them, 4 out of 5 have m, and 4 out of 5 have 1 in them. Also notice that 4 out of 5 don’t have a 4 in the parentheses, and 4 out of 5 don’t involve squaring the expression in parentheses (like choice (B) does).
So if we were going to try to predict the right answer, based purely on the answer choices, we’d probably want the choice with these attributes:
oincludes m2
oincludes m
oincludes 1
odoesn’t have a 4 in the parentheses
odoesn’t square the expression in parentheses
We’d want that answer choice because those are the most popular features in the field of answer choices. The choice that satisfies all of those conditions is (D), which is the right answer in this case.
Just to be completely clear, let me point out that I would never, ever recommend that you answer a question based only on figuring out which choice has the most popular features. That will work a whole lot of times, but it doesn’t work every time, and my goal is for us to be correct on every single question. So this idea is a pattern to be considered, not a rule to be followed unfailingly.
In this particular question, if we accidentally misread (E) and thought it was correct, being aware of the imitation pattern might let us realize that none of the other answer choices have a 4 inside the parentheses, which is probably a bad sign. If we liked (A) for some reason, then noticing that the other choices were all highly similar to one another and that none of them had m3 might help us realize we needed to re-evaluate our conclusion.
Notice that we answered the question without ever finding out what m represents. This kind of thing is normal for the SAT. On the SAT, we need to get away from the idea that we have to solve for every variable we see in a question.
Page 414, Question 5
This question frustrates a lot of students because they’ve never seen a diagram like this in their math classes. But we have to remember that this kind of thing is standard on the SAT: no matter how much you practice, you’re going to encounter things on test day that don’t look like anything else you’ve ever seen, at least on the surface. We have to learn how to attack these kinds of situations systematically, and confidently.
In this case, they’re asking us for the area of the shaded portion. As trained test-takers we know two things:
They have to give us all the geometry formulas we need.
They didn’t give us a formula for the area of a portion of a square.
That means there must be a way to figure out the area of this shaded region without having a formula uniquely for that purpose.