In this case, I’m noticing that the answer choices are kind of falling into 3 different groups, in a sense. We have negative numbers, then we have 2 and 3, and then we have 5. Hmmmm.
Let’s try actually plotting line l and see what it looks like. Here’s a rough approximation of the situation described in the question:
If we plot the points (0,0) and (2,1), and then think about the options offered by each of the answer choices, we might start to notice something. (A) and (B) clearly don't work if you're trying to draw line that would go through either value and (2,1), and be perpendicular to the existing line:
The values for (C) and (D) don’t work, either:
Only (E) is in anywhere near the proper place to create a line that passes through (2,1) and is perpendicular to the original line l. So (E) must be right:
(I realize that none of the diagrams I supplied is exactly to scale, but the diagrams you would draw for yourself in your test booklet would also be out-of-scale. During the test, the point isn’t to create a perfectly scaled drawing, but to get a solid idea of where the different elements of the question would be relative to one another.)
So, as we’ve just seen, it’s possible to solve this question, which is the last one in the section and which was missed by a lot of people, without ever using any kind of formula or consulting a calculator or even adding two single-digit numbers. All we had to do was remember to notice the answer choices, plot a few points (or even just think about plotting some of them), and then realize that only one answer choice was close to working.
Notice that the College Board could have made this question much harder by including wrong answers that were closer to the right answer, or by changing the overall scale of the question. But they didn’t. They left a shortcut for alert test-takers to seize. Remember that, and look for these kinds of things on other questions.
Page 464, Question 6
People mess this question up all the time, but it’s really just a pretty straightforward application of the concept of slope. We know that for two reasons: the first one is that the diagram shows a diagonal line with its horizontal and vertical changes marked off, and the second reason (perhaps a bit more obvious) is that the question includes the word “slope.”
Remember that slope, by definition, is the ratio of the vertical change to horizontal change. That means that, in this case, for every 7 units of vertical change there are 16 units of horizontal change. If we only have 3.5 units of vertical change, then we need 8 units of horizontal change to maintain the ratio, because 3.5 is half of 7 and 8 is half of 16. So the correct answer is (A).
Notice that one of the wrong answers is 32, which is what we get if we accidentally double 16 instead of cutting it in half.
Page 468, Question 15
I often talk about how the College Board likes to mislead you by making questions seem to be something they’re not. This question might be one of the all-time best examples of that technique. It starts out looking like a classic probability question, one of those situations where somebody has a certain number of things in a bag and you have to calculate the chance that they’ll pull a certain kind of thing out of the bag at random.
But that’s not what it is at all. Instead, it’s much simpler than that, but it’s unlike anything that any test-taker has probably ever seen before.
This is one more example of why you can’t take anything for granted on the SAT. Everything needs to be read carefully.
Ari starts out with 3 red things and 4 green things. If he takes 13 more pieces and we need to end up with more reds than greens, we might imagine that the 13 is made up of 7 reds and 6 greens, just as a place to start; if that's the case, then there would be 10 red and 10 green, which doesn't satisfy the requirements of the question. So in order to end up with more reds than greens, Ari would need to pull out at least 8 reds, so the answer is 8.
Again, there's absolutely no formula for this, and it has nothing to do with probability. It's just reading and thinking. Most SAT Math questions are just reading and thinking.
Page 468, Question 16
A lot of people who see this question immediately start worrying about the word “tri-factorable,” as though it were a real math term instead of something that the College Board made up specifically for this question.
There are two ways that we can figure out that the word “tri-factorable” was just made up for this question. The first way is that the question tells us what the word means: a tri-factorable number is one that is the product of 3 consecutive numbers. (If this were a real math term, the College Board wouldn’t bother to define it. For slope questions, they don’t say, “What is the slope of this line, if slope is defined as blahblahblah,” because you’re supposed to know what slope is, because slope is a real math concept.)