Notice that choice (A) reflects a mistake that would be pretty easy to make here: if we assumed that each house icon represented one house, then we’d think (A) was right. But each icon represents 2,000 houses, so the right answer is 28,000. That makes (E) right.
As always, I’d also try to think about where some of the other wrong answers might have come from. In this case, (B) is what we’d get if we counted all the icons in the entire chart (including 1991 – 2000) and also made the mistake of thinking each icon only represented one house. (C) is what we’d get if we correctly realized that each icon represented 2,000 houses but accidentally only counted the third row. Finally, (D) is what we’d get if we didn’t count the second row for some reason.
I always try to figure out where some of the wrong answers are coming from because it helps me be sure I’ve understood the question. It’s not necessary to figure out every wrong answer, even though we were able to do that in this question. But if you can’t figure out where any of them are coming from at all, then there’s a very good chance you made a mistake, and you should re-check your work.
Also note that, in this case, 3 out of the 5 choices are numbers in the tens of thousands. This strongly suggests (BUT DOES NOT GUARANTEE) that the right answer should be one of those 3. If we had accidentally overlooked the information about each icon counting for 2,000 houses, then noticing that most of the answer choices are huge numbers should have helped us realize we might have missed something.
This is a perfect example of the kind of question that you should absolutely lock down, double-check, and be done with in well under a minute, possibly in as little as 10 seconds. It’s important to work quickly and efficiently through questions like this in order to save time for questions where you might have more difficulty gaining a foothold.
One last thing: note that this question, like many SAT Math questions, is primarily a critical reading question at heart. The major way people will make mistakes here is by misreading the question or the chart, not by failing to multiply the numbers 14 and 2,000.
Page 413, Question 2
This question presents us with a type of drawing that we might not ever have encountered before. But that’s fine: remember that this question, like all SAT Math questions, can only be made out of the same basic math ideas that were in the Math Toolbox earlier in this book. So let’s see what we can figure out.
We know the diagram is drawn to scale, because it doesn’t say that it’s not. But the answer choices are so close to one another that it would probably be hard to answer this question by eyeballing the drawing and using the scale.
So let’s think in terms of geometry. We know that we can fill in the measurements of the angles opposite the labeled angles, because opposite angles are identical. So the angle opposite the 35-degree angle is also 35 degrees, and the one opposite the 45-degree angle is also 45 degrees.
Now it looks like we’re getting somewhere: once we label those opposite angles, we can see that w is the third angle in a triangle, and that the other two angles are 35 degrees and 45 degrees.
That means w + 35 + 45 = 180. So w + 80 = 180, which means w is 100 degrees. So (B) is right.
Notice that (B) is in the middle of a 3-term series in the answer choices, with the other two terms differing by 10. This should alert you to the fact that it would be very easy to be off by 10 in this question if we forgot to carry a digit during the addition or the subtraction. So we should go back and check to make sure we didn’t mess that up.
Still, it’s very reassuring that we like the answer choice in the middle of this range, because typically the College Board likes to make the number in the middle of the range be correct. (As we discussed in the section on patterns, they do this because it gives us the option to be off in either direction and still find an answer choice reflecting our mistake.)
This is another question that probably should take less than 30 seconds to do. We want to answer it quickly, check to make sure we’re right, and move on.
Page 414, Question 3
A lot of students ask me about this question because they can’t figure out how to set it up algebraically.
But this is the SAT—we don’t have to do it algebraically! In fact, in most cases I prefer not to use algebra on the SAT, because it often takes longer and it increases the chance that we’ll make a mistake.
So let’s just think about this. (There’s no magical way to “just think about” a question—all we do is dive in somewhere and then see what adjustments, if any, we need to make.)
If each of the 19 tables had 4 people, then there would be seats for 76 people, because 4*19 = 76. We need to find seats for 84 people, though, which is 8 more than 76.