The SAT Prep Black Book(100)
The question asks what percent of the votes were cast for Candidate 1 given that Candidate 1 received 28,000 more votes. Most people will try to solve this by figuring out that 28,000 is 1% of 2.8 million. So far, so good. Then they’ll assume that this must mean Candidate 1 got 51% of the vote. They’ll choose (D), and they’ll move on to the next question without giving this a second thought.
And they’ll be wrong.
Here’s the mistake: if Candidate 1 pulls 51% of the vote, than Candidate 2 must pull 49%, and 51% is 2 percentage points more than 49%, not 1 percentage point more. So in order for Candidate 1 to have a 1 percentage-point margin over Candidate 2, the correct split isn’t 51 – 49.
It’s 50.5 to 49.5.
That’s why (C) is correct.
Notice that there are 3 answer choices that end in a 5, and only 2 that end in a 1. This goes along with the imitation pattern, and it strongly suggests that the correct answer should end in a 5. Also, notice that 3 out of the 5 choices involve decimals, which also suggests that 51% isn’t correct. We could even say that 50.5% is the middle entry in a series of sorts, where the other numbers are 50.05 and 55—it’s not a traditional series in the mathematical sense, but there’s a clear progression with reference to the decimal places, and (C), the right answer, is in the middle of that progression.
This is yet another great example, then, of the tremendous importance of thinking about the answer choices as part of the question. They’re not just there to take up space—the College Board uses them deliberately, in ways that we can exploit.
Page 416, Question 9
Sometimes people make this question a lot harder than it needs to be, by coming up with a decimal approximation for √18 or by converting it to 3√2. But it’s much easier just to start by squaring both sides, so we get 2p = 18. That means p = 9.
Remember that SAT Math gets a lot easier if we look for ways to keep it simple.
Page 416, Question 10
This question, like many SAT Math questions, is really just a matter of knowing definitions and doing basic arithmetic.
When we round the given number to the nearest whole number, we get 2. When we round it to the nearest tenth, we get 1.8. Since 2 – 1.8 is 0.2, the answer is just 0.2.
Notice that this question is pretty impossible to answer if we don’t understand the concept of rounding, or if we don’t know which decimal place represents tenths. Also notice that the math is incredibly basic, but people will still miss this question because of its strange presentation.
Page 417, Question 11
As is often the case, there are many ways to answer this question. We could do it with pure algebra, letting x be the number of towels and writing 6 = 2x/5. But that would be a little more formal than I like to be on the SAT Math section.
So let’s just think through it instead. If 6 towels represents 2/5 of all the towels, than 3 towels must represent 1/5 (because 3 is half of 6 and 1/5 is half of 2/5). So if 3 towels are 1/5 of the towels, then there must be 15 towels, because 3*5 is 15. So the answer is 15.
Just to be clear, there’s nothing inherently wrong with doing it algebraically, as long as you feel comfortable with that and you set it up correctly and don’t make any mistakes. I’m just more comfortable with mental math, and I find that it tends to work a lot better on the SAT, so I encourage it in my students as much as possible.
Page 417, Question 12
This question is very difficult for a lot of test-takers. But if we just remember to read carefully and pay attention to details, we can figure this out.
The question describes 5 points on a line, like this: A B C D E.
We know that AD is 4.5, and BE is 3.5. Why not try to plot that out?
When we do try to plot it, we realize that we don’t have enough information yet. If AD is 4.5 and BE is 3.5, there’s an infinite number of ways we could draw that. For instance, it might look like this:
Or it might look like this:
Or anything in between.
At first, this uncertainty might seem troubling, but we have to remember that this is an SAT Math question, and that SAT Math questions often deal in uncertainty. So there’s no need to panic—we just need to figure out how it can be possible that the test is allowing there to be multiple arrangements here.
One clue is the phrasing of the question: it asks for “one possible value” of the BC length. As trained test-takers, we know that the College Board only uses that phrase in a question when there are multiple possible values involved. So it’s clearly okay for us not to be sure exactly where A, B, D, and E are relative to one another in every case. We only need to work out one single possible arrangement. So let’s pick the one where D and E are very close together, like this: