The GMAT Official Guide 2018 Edition – Part 2:
The new Official Guide (OG) books have landed and I’ve got the scoop for you! (If you’d like, you can start with the first installment of this article series.) Today’s post focuses on Data Sufficiency.
What’s new in Data Sufficiency for the 2018 editions?
There are 26 new Data Sufficiency (DS) problems (and 26 were dropped).
8 new algebra questions were added and only 2 were dropped, but I don’t think that signals anything of major importance. The numbers here are ultimately small—and algebra has always been common on the test. In general, there weren’t any major differences in terms of the content mix showing up in the new vs. dropped questions.
I did notice that quite a few of the new DS problems can be solved via Testing Cases (see #273, #276 through #278, #292, #293, and #334!). If you don’t already feel comfortable Testing Cases, start practicing.
Also, a couple of hard ones really require us to delve into math-logic to solve—more on these below.
Finally, I just have to say that I really like #326. It’s tricky but in a legitimate way: Think the full scenario through! (I’m not going to tell you right now how it’s tricky—I don’t want to give it away. Try it on your own first.)
Let’s talk about the two new math-logic problems, #339 and #382. Try them, then come on back here.
The Logic Games (#339 and #382)
#339 makes us marry information from a table with the problem itself—I think just to see whether we’re really paying close attention. So make sure you write this all down carefully.
= $1 per
= $0.5 per
Now, here’s where the logic comes in. The roses cost more. Keep that in the back of your mind.
Kim and Sue bought the same total number of flowers (and they each bought both and ). The question asks whether Kim spent more.
Look at the prices. If Kim bought more than Sue did, then Kim will have spent more money. If they bought equal numbers, then the spend will be the same. And if Kim had fewer , then she will have spent less.
That knowledge allows you to rephrase this question: Did Kim buy more roses than Sue? If you can get to that question, the problem really opens up. Statement (2) obviously works. And you can test a couple of quick cases to prove that Statement (1) does not.
#382 covers coordinate plane geometry. Fun. (/sarcasm) They ask for the slope of line l, so let’s just start with this: What are the possible kinds of slopes that a line can have?
It can be positive—meaning it’s tilting “up” from left to right. Or negative, if it’s tilting down. It can also equal 0, if the line is totally horizontal. Or it can be undefined—that’s for perfectly vertical lines.
Now, here’s the trap. They want to know the actual slope, not just the type of slope. So it seems like we need to know really specific information to be able to answer. And neither statement appears to provide any “real” information.
It’s true that statement (2) is not sufficient by itself—but don’t be so quick to dismiss statement (1). The -intercept of a line is where that line crosses the -axis—and that always happens where , so that point can be written . And the -intercept is where the line crosses the -axis and can be written .
Statement (1) says that is twice as big as , so you can do a couple of things here.
First, neither nor can be 0, because that would mean the point is on the line … and the question stem said that the line does not pass through the origin—which is .
Next, and have to have the same sign. If , then . But if , then . What would the slopes be if those were the values? Sketch out a number line, add the points, and use “rise over run” to find the slope.
For and , the slope is . And for and , the slope is … hey, it’s again! (Note: The OG solution here says that the slope is ; that’s a typo.)
Is it just a coincidence that we got the same slope? Would it be different if we tried different numbers?
Think the logic through. Slope is always rise over run. The rise is the difference between the two values and the run is always the difference between the two values. In other words, rise over run really means (difference in ) / (difference in ).
The two points we’re using are and so the difference for each is going to be calculated from 0 to whatever the or value is.
Since is always twice as big as , is always going to be twice as far from 0 as . In other words, not only is twice as big as , but the difference in the two values will always be twice as big as the difference in the two values. And that means we have a consistent ratio going on: that ratio is always going to be 1/2. And since the x value is always further from 0 than is the y value (sketch out some examples if you’re not sure), the line is always going to angle downwards—that is, the slope will always be negative. Put those two pieces of information together: The slope will always be . Statement (1) is actually sufficient.
That’s a pretty hard question, so if you’re thinking, “Whaaa … ?” right now, that’s okay. That just means that your task is to figure out how to recognize that this is just too hard so that you can guess quickly on something like this on the real test.
If you find yourself thinking anything along the lines of, “Well, this statement doesn’t seem like it could be enough … because it seems like they haven’t told me much of anything … but I also don’t really understand the significance of saying that the -intercept is twice the -intercept … what does that really mean??”—then that’s a great signal to back away from the problem and move on.
And more traps (#326)
Are you ready to hear about #326? The trap is in statement (1). I think a lot of people are going to dismiss this one as not sufficient without laying out the work—but it actually is sufficient! The key is in the last part of the statement: “and received enough money from the city to cover this cost.” Well, if that cost is over the $15k minimum that the library is guaranteed … then the library must have gotten the bonus last year.
If they averaged 50 new books a month, that’s new books for the year. The average book cost was $28, so that’s . (Note: use fast math principles to calculate: . Then subtract —because 600 was supposed to be multiplied by only 28, not 30. .) (Note #2: You don’t actually have to find that exact number. It’s enough to know whether the number is over $15k. How would you guesstimate that?)
Anyway, it is over the $15k minimum, so the library did get the bonus last year. Sufficient!
Are you mathed-out now? Then let’s move on to Verbal—join me next time for a run-down of the verbal sections of the new OG.