The GMAT Official Guide 2018 Edition - Part 1
The new Official Guide books have landed and Ive got the scoop for you!
In this multi-part series, Ill start by discussing additions and changes to the new Quant problems in The Official Guide for GMAT Review 2018, a.k.a. the OG. Ill follow that up with a discussion of the new Verbal questions from the big OG. Ill also be providing you with the new question numbers, in case you already have OG 2017 and are looking for a list of just the questions that are new to the 2018 edition.
If you have already bought the 2017 edition, theres no need to rush out and get the 2018 edition now; only 15% of the questions are new. If, later, you feel you want more, you can decide at that point whether you want to get the 2018 OG or whether you want to get some other official-source questions, such as the GMAT Prep Question Pack or GMAT Focus.
Chapters 1 through 4 have not changed. Chapter 3 is a Diagnostic test consisting of the same 100 questions that were in the book last year. The Diagnostic questions are, on the whole, good questions, so I can understand why the makers of the GMAT (GMAC) are not swapping out these questions.
In this installment, well concentrate on chapter 5 (Problem Solving, PS).
I did not spot any major differences in terms of specific content areas: there were no distinct trends in terms of dropping or adding a higher proportion of a certain kind of math. I did spot some other intriguing details that I'll share below. And I saw some really interesting new questions!
Note: I cant reproduce the text of questions for copyright reasons, but Ill cite the problem number of any question I discuss so that you can look it up if you do decide to buy the 2018 edition.
Whats new in Problem Solving for the 2018 edition?
There are 35 new PS problems (and 35 old problems were dropped).
As we saw last year, the lowest-numbered new problems (such as #3 and #6) really do just require you to have the basic computation skills. One problem (#33) does require you to know what the term quotient means and how a quotient is used in a math problem.
I noticed multiple problems on which I could use some amount of estimation to solve, including a lot of fast-math shortcuts, especially benchmarking with percents. For more on benchmarking and other fast-math shortcuts, see our series on Fast Math. Then try out problems #40 and #53.
Then challenge yourself: What you can do with #139 and #224? (Hints below, if you want them. Also: #224 can get pretty ugly. A problem like this one is likely destined to be a guess-fast-and-move-on problem for most test-takers.)
Problem #151 is also a great reminder that if you really understand how the theory of standard deviation (SD) works, then you can likely handle even harder SD problems on the GMAT. And if you dontguess and move on right away. Dont bang your head against the wall on something that is so rarely tested in the first place.
All right, are you ready for your hints? Ive got two for each problembut Ive split them out so that your eye doesnt mistakenly see the second hint unless / until you want it. Solutions are at bottom.
Hint #1
#40: Dont dive right in and start solving. Think about the math steps that need to happen. Think about how to minimize those stepswhat do you really need to do? And in what order would be easiest?
#53: The calculations look annoying. Whats a test-taking approach that might work better here than the traditional textbook approach?
#139: Test out some real values for normal fractions to see how fraction properties work. Lets say that you start with 1/2. Then you add to the top: 2/2. Did you just make the number larger or smaller? Why? Go back to 1/2 and add to the bottom instead: 1/3. How did the number change now? What implications does this have for what you want to do to X and Y to maximize the given fraction?
#224: Are you sure you really want to do this? All right, then re-draw this thing and label the angles that are in the triangles but adjacent to the shaded figure. What can you figure out about them?
Hint #2
#40: Dont find the new sum of salaries for all 5 employees. Rather, use just the difference / increase to solve.
#53: Work Backwards. And look for fast-math shortcuts.
#139: In order to maximize the fraction, maximize X and minimize Y. Then, think about how to estimate the annoying fraction that you receive as a result.
#224: Are you sure you want to continue? Okay then. :) All of the triangle angles that are adjacent to the shaded angles must be the same (because these are isosceles triangles and the longest side is always the side matching the shaded polygonso the largest triangle angle is always the angle opposite the shaded figure). Lets call each of those angles x. And if all of those angles are the same, then the opposite angle (the one labeled a in the top triangle) must always equal a in every triangle, too. Finally, every x can be paired with one interior angle of the shaded thing to make a straight, 180-degree line. Can you do anything with that?
Solutions
#40: First, take 10% of the sumthats your increase. [pmath]3250*10% = 325[/pmath]. Then divide that by 5 (use the fast-math shortcut!) to find the per-employee increase: 325 / 5 = first multiply by 2 to get 650, then move the decimal one to the left to get 65.0. Done!
#53: Start with answer (B). Units = 3,150.
Does Revenue = Costs?
Revenues = [pmath]3150*2 = 6300[/pmath].
Costs = 5040 + 40% of Revenues = [pmath]5040 + (6300)(0.4)[/pmath]
Does [pmath]6300 = 5040 + (6300)(0.4)[/pmath]?
No! 40% is almost 50% (which would be 3150), so the right side is going to be too big. The fixed costs (5040) are really high, so we need that starting Revenue figure to be even higher. Glance at the answers; only answer (A) is larger than (B). Done. :)
#139: Make [pmath]X = 9[/pmath] and [pmath]Y = 1[/pmath]. The fraction is [pmath]0.19/0.021[/pmath]. Multiply by 1000 to get rid of the decimals: [pmath]190/21[/pmath]. Ugh. Estimate? 190 divided by 20 would be 9.5 ugh again. Is the answer 9 or 10?
Use other fractions to help you estimate. Recall that [pmath]190/{20}=9.5[/pmath]. What is [pmath]190/10[/pmath]? And what is [pmath]190/30[/pmath]? The former is 19 and the latter is something smaller than 9.5. So when you increase the denominator, the resulting number gets smaller. The denominator 21 is larger than the denominator 20, so the resulting number is smaller than 9.5. The fraction is closest to the number 9.
#224: This is going to be a little messy. Dont say I didnt warn you!
The polygons angles add up to [pmath](n-2)(180)[/pmath], where [pmath]n[/pmath] is the number of sides of the polygon. So the angles of this polygon are [pmath](9-2)(180)[/pmath]. Dont simplify that yet (fast-math principle: Dont do math till you have to). And you can also write each of the angles of the polygon as [pmath]180-x[/pmath], since each polygon angle makes a straight line with one of the [pmath]x[/pmath] angles of a triangle. So the 9 angles of the polygon = [pmath](9)(180-x)[/pmath]. Dont simplify that yet, either.
You now have two different ways to write the sum of the angles of this polygon, so set them equal to each other:
[pmath](9-2)(180) = (9)(180-x)[/pmath]
Notice the similarities in the two sides? Think about how to use that to solve more efficiently:
[pmath](9)(180) - (2)(180) = (9)(180) -(9)(x)[/pmath]
[pmath]- (2)(180) = - (9)(x)[/pmath]
[pmath](2)(180) = (9)(x)[/pmath]
[pmath](2)(20) = x[/pmath]
[pmath]40 = x[/pmath]
If [pmath]x = 40[/pmath], what is [pmath]a[/pmath]? A triangle has 180 degrees, so [pmath]180 = x + x + a = 40 + 40 + a[/pmath]. Therefore, [pmath]a = 100[/pmath].
That last problem is still pretty horrible, even with fast-math principles. But if you are going to do it, at least save yourself the annoyance of calculating some pretty large numbers there.
Join me next time, when well review the new Data Sufficiency problems in OG 2018. Until then, happy studying!