What to Do When You Find a Weighted Average Question In the Verbal Section of the GMAT

No MathWeighted averages show up everywhere on the GMAT. Most test-takers are prepared to see them on the Quantitative Section, but they’ll show up on the Integrated Reasoning and Verbal Sections, as well.  Because it is such an exam staple, we want to make sure that we have a thorough, intuitive understanding of the concept.

In class, I’ll typically start with a simple example. Say you have two solutions, A and B. A is 10% salt and B is 20% salt. If we combine these two solutions to get a composite solution that is 14% salt, do we have more A or B in this composite solution? Most students eventually see that we’ll have more of solution A, but it doesn’t always feel instinctive. If we had had equal quantities of both solutions, the combined solution would have been 15% salt – equidistant from 10% and 20%. So, if there is 14% salt, the average skews closer to A than B, and thus, there must be more of solution A.

I’ll then give another example. Say that there is an intergalactic party in which both humans and aliens are present. The humans, on average, are 6 feet tall. The aliens, on average, are 100 feet tall. If the average height at the party is 99 feet, who is dominating the party? It isn’t so hard to see that this party is packed with aliens and that the few humans present would likely spend the evening cowering in some distant corner of the room. The upshot is that it’s easier to feel the intuition behind a weighted average question when the numbers are extreme.

Take this tough Critical Reasoning argument for example:

To be considered for inclusion in the Barbizon Film Festival, a film must belong either to the category of drama or of comedy. Dramas always receive more submissions but have a lower acceptance rate than comedy. All of the films are either foreign or domestic. This year, the overall acceptance rate for domestic films was significantly higher than that for foreign films. Within each category, drama and comedy, however, the acceptance rate for domestic films was the same as that for foreign films.

From the cited facts it can be properly concluded that

(A) significantly fewer foreign films than domestic films were accepted.
(B) a higher proportion of the foreign than of the domestic films submitted were submitted as dramas.
(C) the rate of acceptance of foreign films submitted was the same for drama as it was for comedies.
(D) the majority of the domestic films submitted were submitted as comedies.
(E) the majority of the foreign films submitted were submitted as dramas.

Okay. We know that dramas had a lower acceptance rate than comedies, and we know that the overall acceptance rate for domestic films was significantly higher than the acceptance rate for foreign films. So, let’s assign some easy numbers to try and get a handle on this information:

Say that the acceptance rate for dramas was 1% and the acceptance rate for comedies was 99%.

We’ll also say that the acceptance rate for domestic films was 98% and the acceptance rate for foreign films was 2%.

The acceptance rate within both domestic and foreign films is a weighted average of comedies and dramas. If only dramas were submitted, clearly the acceptance rate would be 1%. If only comedies were submitted, the acceptance rate would be 99%. If equal amounts of both were submitted, the acceptance rate would be 50%.

What do our numbers tell us? Well, if the acceptance rate for domestic films was 98%, then almost all of these films must have been comedies, and if the acceptance rate for foreign films was 2%, then nearly all of these films must have been dramas. So, domestic films were weighted towards comedies and foreign films were weighted towards drama. (An unfair stereotype, perhaps, but this is GMAC’s question, not mine.)

We can see that answer choice A is out, as we only have information regarding rates of acceptance, not absolute numbers. C is also out, as it violates a crucial premise of the question stem – we know that the acceptance rate for dramas is lower than for comedies, irrespective of whether we’re talking about foreign or domestic films.

That leaves us with answer choices B, D and E. So now what?

Let’s pick another round of values, but see if we can invalidate two of the three remaining options.

What if the acceptance rate for domestic films was 3% and the acceptance rate for foreign films was still 2%? (We’ll keep the acceptance rate for dramas at 1% and the acceptance rate for comedies at 99%.) Now domestic films would be mostly dramas, so option D is out – the majority of domestic films would not be comedies, as this  answer choice states.

Similarly, what if the acceptance rate for domestic films was 98% and the rate for foreign films was 97%? Now the foreign films would be mostly comedies, so option E is also out – the majority of foreign films would not be dramas, as this answer choice states.

Because the acceptance rate is lower for dramas than it is for comedies, and foreign films have a lower acceptance rate than do domestic films, the foreign films must be weighted more heavily towards dramas than domestic films are. This analysis is perfectly captured in option B, which is, in fact, the correct answer.

Takeaway: certain concepts, such as weighted averages, are such exam staples that will appear in both Quant and Verbal questions. If you see one of these examples in the Verbal Section, assigning extreme values to the information you are given can help you get a handle on the underlying logic being tested.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And be sure to follow us on FacebookYouTubeGoogle+ and Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles written by him here.

Are There Set Rules for Answering GMAT Sentence Correction Questions?

SAT WorryThe other day I was working with a tutoring student on Sentence Correction when she expressed some understandable frustration: when we did Quantitative questions together, she said, she felt like she could rely on ironclad rules that never varied (the rules for exponents don’t change depending on the context of the problem, for example), but when we did Sentence Correction, the relevant rules at play in a given question seemed less obvious.

Was there a way, she wondered, to view Sentence Correction with the same unwavering consistency with which we view Quantitative questions? While I understand her frustration, the answer is, alas, an unqualified “no.” English is far too complex for us to boil down Sentence Correction to a series of stimulus-response reflexes. Context and logic always matter.

To see why we can’t go on autopilot during Sentence Correction questions, consider the following problem:

Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also caused erosion and very quickly deforested whole regions. 

A) Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also

B) Not only did the systematic clearing of forests in the United States create farmland (especially in the Northeast), which gave consumers relatively inexpensive houses and furniture, but also

C) The systematic clearing of forests in the United States, creating farmland (especially in the Northeast) and giving consumers relatively inexpensive houses and furniture, but also

D) The systematic clearing of forests in the United States created farmland (especially in the Northeast) and gave consumers relatively inexpensive houses and furniture, but it also

E) The systematic clearing of forests in the United States not only created farmland (especially in the Northeast), giving consumers relatively inexpensive houses and furniture, but it

If you fully absorbed the class discussion about the importance of parallel construction, you probably noticed an indelible parallel marker here: “not only.” Okay, you think. Any time I see not only x, I know but also y should show up later in the sentence.

This isn’t wrong, per se, but the construction “not only/but also” is only applicable in certain circumstances. So before we jump to the erroneous conclusion that this is the construction that is called for in this sentence, let’s examine its underlying logic in more detail.

Take the simple example, “On the way to work, I not only got stuck in traffic, but also….” Think about your expectations for what should come next in this sentence – getting stuck in traffic was the first unfortunate thing to happen to this hapless subject, and we’re expecting a second unfortunate event in the latter part of the sentence. Not only/but also is appropriate when we’re talking about similar things.

Now consider the construction. “On the way to work, I got stuck in traffic, but…” Now our expectations are markedly different – the second half of the sentence is going to contrast with the first. We’re expecting something different.

Let’s go back to our GMAT sentence. We’re comparing the consequences of the clearing of forests. First, the clearing “created farmland and gave consumers inexpensive houses” (good things). However, it also “caused erosion and deforested the region” (bad things). Because we’re comparing two very different consequences, the construction “not only/but also” – which is used to compare similar things – is inappropriate. Now we can safely eliminate answers A, B and E.

That leaves us with C and D. First, let’s examine C. Notice there’s a participial modifier in the middle of the sentence set off by commas, and a sentence should still be logical if we remove these modifiers. We would then be left with, “The systematic clearing of forests in the United States, but also caused erosion and very quickly deforested whole regions.” This clearly doesn’t work – the initial subject (the systematic clearing) has no verb, so C is wrong. This leaves us with answer choice D, which is the correct answer.

Takeaway: though noticing common constructions on Sentence Correction problems can be helpful, we can never go on autopilot. Ultimately, context, logic, and meaning will always come into play. Before you select any answer, always ask yourself if the sentence is logically coherent before you select it. If you want to ace the GMAT, turning off your brain is not an option.

*GMATPrep question courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And be sure to follow us on FacebookYouTubeGoogle+ and Twitter!

By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can read more articles by him here.

GMAT Mythbuster #3

Myth: The verbal section is more important than the quant section, because more people do well on the quant section, so a high verbal score will have greater impact on your score.

Fact: Schools look at your individual section scores as well as your overall score, and ideal candidate will have a balanced, high score; in some cases, schools are particularly concerned with a candidate’s quantitative abilities, as business school curriculum often requires strong math skills.

An admirable quality of business school aspirants is their desire to study as efficiently as possible (putting it nicely) or to beat the system (telling it like it is). Perhaps inspired by the efficiency models of Amazon, Ikea, and other leading business, GMAT students often look for an edge by attempting to determine which sections or quesitons count more than others. Some recent comments in the blogosphere and on GMAT message boards have led to a belief that the verbal section is such an edge. In this event, the logic goes that, because quantitative scores are higher on average than verbal scores, a high verbal score and an above-average quant score will give you a higher overall score than will the reverse (high quant, average verbal). While this can actually be supported, in a way, by evidence (99th verbal and 70th quant will produce a higher score than 99th quant and 70th verbal), the impact toward your applications may not follow this logic as directly as many believe it will.

Consider the following:

Everything here is hidden until the reader clicks on “read more”

1) Business school curriculum is often heavily rooted in math. Most schools will have you take required coursework in finance, statistics, and accounting, and every discipline involves the use and analysis of numbers. A GMAT score, even if high overall, that betrays a potential quantitative deficiency isn’t one that will likely put your best foot forward. At quantitatively-intensive schools, such a score may indicate that you’ll struggle to keep up with your classmates; at schools that are reputed as being a bit lighter on math skills, we have also found that the admissions committees are concerned about such a reputation as being “technically soft”, and will often require higher quant scores as a credible commitment to employers that their students are just as quantitatively capable as their competition.

2) People have a tendency to emphasize the things that they do well. An unbalanced score may dictate to schools that you took the “path of least resistance” to a higher overall score, by focusing heavily on your stronger suit and just hoping to get by on your weaker subject. Schools make no secret of the fact that they prefer balanced excellence, and such a performance also demonstrates a willingness to address weaknesses in order to get there.

3) Practically speaking, the GMAT is going to give you 37 math questions and 41 verbal questions, with 75 minutes for each section, and your job is to answer them to the best of your ability in order to post a high score. You won’t get a progress report on your scoring as you go, and any time that you save on one section will not carry over to the next. Effectively, you don’t really have the opportunity to sacrifice performance on one section in favor of greater success on the other…there’s just no mechanism for it. In an athletic endeavor, it may be possible to save energy during one part of a game in order to excel at the other, but there you’re conscious of the score the entire time in case you need to “pick it up”. Say that, in a triathlon, I decided to cruise through the swim to save energy for the bike and run, I’d be able to look ahead at my competition partway through the swim to determine if I were letting them get away and recalculate whether I could afford to stay on my strategy. On the GMAT, you won’t know your score partway through the quant section (and, although it’s a grueling test day, “saving your energy” by sluffing off the quant isn’t all that likely to improve your verbal, anyway), so you can’t rely on such a strategy without a fairly high risk of failure. Furthermore, if your quant score were to slip from “above average” (maybe 75th percentile) to “not really tolerable by a top program” (say, 55th), your study strategy to focus on verbal would have backfired. Again, there’s not a reliable-enough benchmark for how you’re tracking to try and cheat the system with such a strategy. Your goal should be to maximize your score by doing the best you can. If there’s any way to “save your energy” effectively, it’s probably to spend less time trying to game the system, and more time taking practice tests, analyzing your results, and making targeted improvements.