Some Data Sufficiency questions present you with scenarios: stories that could play out in various complicated ways, depending on the statements. How do you get through these with a minimum of time and fuss?

Try the below problem. (Copyright: me! I was inspired by an OG problem; I’ll tell you which one at the end.)

* “During a week-long sale at a car dealership, the most number of cars sold on  any one day was 12. If at least 2 cars were sold each day, was the average daily number of cars sold during that week more than 6?

“(1) During that week, the second smallest number of cars sold on any one day was 4.

“(2) During that week, the median number of cars sold was 10.”

First, do you see why I described this as a “scenario” problem? All these different days… and some number of cars sold each day… and then they (I!) toss in average and median… and to top it all off, the problem asks for a range (more than 6). Sigh.

Okay, what do we do with this thing?

Because it’s Data Sufficiency, start by establishing the givens. Because it’s a scenario, Draw It Out.

Let’s see. The “highest” day was 12, but it doesn’t say which day of the week that was. So how can you draw this out?

Neither statement provides information about a specific day of the week, either. Rather, they provide information about the least number of sales and the median number of sales.

The use of median is interesting. How do you normally organize numbers when you’re dealing with median?

Bingo! Try organizing the number of sales from smallest to largest. Draw out 7 slots (one for each day) and add the information given in the question stem:

Now, what about that question? It asks not for the average, but whether the average number of daily sales for the week is more than 6. Does that give you any ideas for an approach to take?

Because it’s a yes/no question, you want to try to “prove” both yes and no for each statement. If you can show that a statement will give you both a yes and a no, then you know that statement is not sufficient. Try this out with statement 1

(1) During that week, the least number of cars sold on any one day was 4.

Draw out a version of the scenario that includes statement (1):

Can you find a way to make the average less than 6? Keep the first day at 2 and make the other days as small as possible:

The sum of the numbers is 34. The average is 34 / 7 = a little smaller than 5.

Can you also make the average greater than 6? Try making all the numbers as big as possible:

(Note: if you’re not sure whether the smallest day could be 4—the wording is a little weird—err on the cautious side and make it 3.)

You may be able to eyeball that and tell it will be greater than 6. If not, calculate: the sum is 67, so the average is just under 10.

Statement (1) is not sufficient because the average might be greater than or less than 6. Cross off answers (A) and (D).

Now, move to statement (2):

(2) During that week, the median number of cars sold was 10.

Again, draw out the scenario (using only the second statement this time!).

Can you make the average less than 6? Test the smallest numbers you can. The three lowest days could each be 2. Then, the next three days could each be 10.

The sum is 6 + 30 + 12 = 48. The average is 48 / 7 = just under 7, but bigger than 6. The numbers cannot be made any smaller—you have to have a minimum of 2 a day. Once you hit the median of 10 in the middle slot, you have to have something greater than or equal to the median for the remaining slots to the right.

The smallest possible average is still bigger than 6, so this statement is sufficient to answer the question. The correct answer is (B).

Oh, and the OG question is DS #121 from OG13. If you think you’ve got the concept, test yourself on the OG problem.

Key Takeaway: Draw Out Scenarios

(1) Sometimes, these scenarios are so elaborate that people are paralyzed. Pretend your boss just asked you to figure this out. What would you do? You’d just start drawing out possibilities till you figured it out.

(2) On Yes/No DS questions, try to get a Yes answer and a No answer. As soon as you do that, you can label the statement Not Sufficient and move on.

(3) After a while, you might have to go back to your boss and say, “Sorry, I can’t figure this out.” (Translation: you might have to give up and guess.) There isn’t a fantastic way to guess on this one, though I probably wouldn’t guess (E). The statements don’t look obviously helpful at first glance… which means probably at least one of them is!

So you’ve been told over and over that guessing is an important part of the GMAT. But knowing you’re supposed to guess and knowing when you’re supposed to guess are two very different things. Here are a few guidelines for how to decide when to guess.

But first, know that there are two kinds of guesses: random guesses and educated guesses. Both have their place on the GMAT. Random guesses are best for the questions that are so tough, that you don’t even know where to get started. Educated guesses, on the other hand, are useful when you’ve made at least some progress, but aren’t going to get all the way to an answer in time.

Here are a few different scenarios that should end in a guess.

Scenario 1: I’ve read the question twice, and I have no idea what it’s asking.

This one is pretty straightforward. Don’t worry about whether the question is objectively easy or difficult. If it’s too hard for you, it’s not worth doing. In fact, it’s so not worth doing that it’s not even worth your time narrowing down answer choices to make an educated guess. In fact, if it’s that difficult, it may even be better for you to get it wrong!

To make the most of your random guesses, you should use the same answer choice every time. The difference is slight, but it does up your odds of getting some of these random guess right.

Scenario 2: I had a plan, but I hit a wall.

Often, when this happens, you haven’t yet spent 2 minutes on the problem. So why guess? Maybe now you have a better plan for how to get to the answer. I know this is hard to hear, but don’t do it! To stay on pace for the entire section, you have to stay disciplined and that means that you only have one chance to get each question right.

The good news is that no 1 question you get wrong will kill your score. But, 1 question can really hurt your score if you spend too long on it! Once you realize that your plan didn’t work, it’s time to make an educated guess. You’ve already spent more than a minute on this question (hopefully not more than 2!), and you probably have some sense of which answers are more likely to be right. Take another 15 seconds (no more!) and make your best educated guess.

Scenario 3: I got an answer, but it doesn’t match any of the answer choices.

This is another painful one, but it’s an almost identical situation to Scenario 2. It means you either made a calculation error somewhere along the way, or you set the problem up incorrectly to begin with. In an untimed setting, both of these problems would have the same solution: go back over your work and find the mistake. On the GMAT, however, that process is too time-consuming. Plus, even once you find your mistake, you still have to redo all the work!

Once again, though it might hurt, it’s still in your best interest to let the question go. If you can narrow down the answer choices, great (though don’t spend longer than 15 or 20 seconds doing so). If not, don’t worry about it. Just make a random guess and vow to be more careful on the next one (and all the rest after that!).

Scenario 4: I checked my pacing chart and I’m more than 2 minutes behind.

Pacing problems are best dealt with early. If you’re more than 2 minutes behind, don’t wait until another 5 questions have passed and you realize you’re 5 minutes behind. At this point, you want to find a question in the next 5 that you can guess randomly on. The quicker you can identify a good candidate to skip, the more time you can make up.

This is another scenario where random guessing is best. Educated guessing takes time, and we’re trying to save as much time as possible. Look for questions that take a long time to read, or that deal with topics you’re not as strong in, but most importantly, just make the decision and pick up the time.

Wrap Up

Remember, this test is not like high school exams; it’s not designed to have every question answered. This test is about consistency on questions you know how to do. Knowing when to get out of a question is one of the most fundamental parts of a good score. The better you are at limiting time spent on really difficult questions, the more time you have to answer questions you know how to do.

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You’ve heard a million times that you’re supposed to create Official Guide (OG) problem sets in order to practice for the test. But how do you actually do so in a way that will help you get the most out of your study?

Fear not! This article is coming to your rescue.

Initially, when you’re studying a new topic or problem type, you won’t do sets of problems; instead, you’ll just try one problem at a time. As you gain experience, though, you’re going to want to do 3 problems in a row, or 5, or 10.

Why?

Because the real test will never give you just one problem!

The GMAT will give you many questions in a row and they’ll be all jumbled up—an SC, then a couple of CRs, then back to another SC (that tests different grammar rules than the first one), and so on.

You want to practice two things:

(1) Jumping around among question types and topics

(2) Managing your timing and mental energy among a group of questions

When do I start doing problem sets?

You’re going to use problem sets to test your skills, so you’ve got to develop some of those skills first. If you’re using our Strategy Guides to study, then at the end of one chapter, you’ll do only two or three OG problems to make sure that you understood the material in the chapter.

Later, though, when you finish the Guide, do a set of problems that mix topics (and question types) from that entire book. Make sure you can distinguish between the similar-but-not-quite-the-same topics in that book, and also practice your skills on both problem solving and data sufficiency. As you finish subsequent Guides, your sets can include problems from everything you’ve done so far. Keep mixing it up!

How do I make the sets?

You’ll need to balance three things when you create a problem set:

(1) Number of problems. Initially, start out with about 3 to 5 problems. As you gain experience and add topics, you’ll increase the size of the sets—we’ll talk more about this a little later.

(2) Type of problem and content.
(a) For quant, always do a mix of Problem Solving (PS) and Data Sufficiency (DS). For verbal, mix at least two of the three types; you can include all three types in larger sets.
(b) Do not do a set of 3 or more questions all from the same chapter or content area—for example, don’t do 3 exponents questions in a row. You know exactly what you’re about to get and the real test will never be this nice to you.

(3) Difficulty level.
(a) Include a mix of easier, medium, and harder questions in your set. For all types except Reading Comprehension, the OG places problems in roughly increasing order of difficulty. On average, aroblem 3 is easier than a problem 50, which is easier than a problem 102. (This does not mean that problem 5 is necessarily harder than problem 3. In general, higher question numbers represent harder questions, but the increase is not linear from problem to problem.)
(b) Note: your personal strengths and weaknesses will affect how you perceive the problems—you might think a lower-numbered problem is hard or a higher-numbered problem is easy. They are… for you! Expect that kind of outcome sometimes.

Timing!

Next, calculate how much time to give yourself to do the problem set.
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Right now, you might be thinking, “Wait, what? I don’t actively want to get stuff wrong!”

In fact, yes, you do. Let me take you on what might seem like a tangent for a moment.

Would you agree that one of the marks of a strong business person is the ability to tell the difference between good opportunities and bad ones? And the ability to capitalize on those good opportunities while letting the bad ones go?

Yes, of course—that’s a basic definition of business. What does that have to do with the GMAT?

The GMAT is a test of your business skills. They don’t really care how great you are with geometry or whether you know every obscure grammar rule in the book. They care whether you can distinguish between good and bad opportunities and whether you can drop the bad ones without a backward glance.

If you want to maximize your score on the GMAT, then you will have a short-list of topics that you want to get wrong fast on the test. My top three in math are combinatorics, 3-D geometry, and anything with roman numerals.

How do you decide what your categories should be? Let’s talk.

But I don’t really want to get stuff wrong… that’s just a metaphor, right?

No, it’s not a metaphor. I really want you to plan how and what you’re going to get wrong! If you haven’t already, read my post about what the GMAT really tests. (You can go ahead and read it right now; I’ll wait.)

In a nutshell, the GMAT is set up to force us to get some of the questions wrong. No matter what you can do, they’ll just give you something harder.

Ultimately, they want to see whether you have the makings of a good business person. One way to test that is to force you into a situation where your choice is between spending extra time and mental energy on something that’s too hard—likely causing yourself to run out of time and energy before the test is over—and cutting yourself off when appropriate.

How do I cut myself off?

First of all, put yourself in this mindset:

You’re at the office, working on a group project.

A colleague of yours is the project manager.

The manager annoys you because he (or she) keeps assigning too many tasks, some of which are not all that important.

Sometimes, you’re rolling your eyes when your colleague tosses a certain piece of work at you; you’re thinking, “Seriously, the client meeting is in 3 days. This is NOT the best use of our remaining time.”

Got that? Okay, now during the test, put yourself in that mindset. The test itself is your annoying colleague. When he drops a roman numeral question in your lap, or a 4-line sentence correction with every last word underlined, you’re already rolling your eyes and thinking, “Are you serious? Come on.”

Here’s the key step: let yourself get just a little annoyed—but with the test, not yourself. You’re not feeling badly that you don’t like the problem; you don’t feel as though you’re falling short. No way! Instead, your colleague is trying to get you to do something that is clearly a waste of time. Roll your eyes. To appease your colleague, figure out whether there’s enough here for you to make an educated guess. Then pick something and move on to more important tasks.

How do I know when to cut myself off?

Quick: name your top three annoyances in quant. Now do the same in verbal. Here’s another one of mine: an RC detail EXCEPT question on a really technical topic with very long answer choices. (In other words, I have to find the four wrong answers in order to find the one right answer… and the topic area is very long and annoying.)

That’s your starting point: you already know you dread these areas. Back this up with data: make sure that these really are the worst ones for you. “Worst” is defined as “I rarely get these right and even when I do, I still use too much time and brain energy.”

Next, check to see how commonly tested the particular topic or question type is. You can’t afford to blow off algebra—that’s too broad a topic. You can, though, blow off sequences.

For some topics, you do want to try to be able to answer lower-level questions. For instance, if one of my students just hates polygons (triangles, squares, rectangles), he has my blessing to blow off harder questions—the ones that combine shapes, for example, or that move into the 3-D arena. He does need to learn the more basic formulas, though, so that he isn’t missing too many lower-level questions.

Your particular mix of pet peeves will almost certainly change over time. Initially, I had some other things at the top of my list, such as weighted averages. Then, I discovered a much better way to do those problems, so 3-D geometry took its place.

Some topics, though, will always be weaknesses. I’ve never liked combinatorics and doubt I ever will. That’s perfectly fine, particularly when the topic is not that commonly tested anyway!

Sound off in the comments below: what areas do you hate the most? Your new strategy is to get those wrong fast and redirect that time and mental energy elsewhere!

Did you know that you can attend the first session of any of our online or in-person GMAT courses absolutely free? We’re not kidding! Check out our upcoming courses here.

Last week, we talked about the first two elements of getting the most out of your CATs.

#1: How NOT to use your practice CATs

#2: How to analyze your strengths and weaknesses with respect to timing

This week, we’re going to dive even further into strengths and weaknesses using the Assessment Reports.

#3: Run the reports.

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My last two articles (part 1 and part 2) gave you some advanced tools to analyze deductive reasoning. Now it’s time to dive into the wonderful world of inductive reasoning, which appears much more often, especially in the following GMAT question types:

• Assumption
• Strengthen
• Weaken
• Evaluate
• Fill in the blank
• Identify the role
• Identify the overall reasoning
• Identify the conclusion
• Mimic the reasoning (sometimes)

According to Wikipedia:

“Inductive reasoning (as opposed to deductive reasoning) is reasoning in which the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion. While the conclusion of a deductive argument is supposed to be certain, the truth of an inductive argument is supposed to be probable, based upon the evidence given.”

Therefore, in inductive arguments, conclusions are a matter of opinion, some more strongly supported than others.

Beyond the basics: P.O.S.E.

First, from class and your own study, you should be able to DECONSTRUCT arguments–in other words, identify the background, conclusion, premises, counterpoint, and counter premises of all inductive arguments. Our books cover that skill thoroughly if you need more work.

Next, you should learn to categorize each conclusion by type.

Fortunately, the GMAT uses only a few basic argument patterns, with similar assumptions and a limited number of ways to strengthen or weaken those assumptions. If you can spot and name those patterns, you’re well on your way to drastically improving your CR score.
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A couple of months ago, we talked about what to do when a geometry problem pops up on the screen. Do you remember the basic steps? Try to implement them on the below GMATPrep® problem from the free tests.

* ”In the xy-plane, what is the y-intercept of line L?

“(1) The slope of line L is 3 times its y-intercept
“(2) The x-intercept of line L is – 1/3”

My title (3 Steps to Better Geometry) is doing double-duty. First, here’s the general 3-step process for any quant problem, geometry included:

All geometry problems also have three standard strategies that fit into that process.

First, pick up your pen and start drawing! If they give you a diagram, redraw it on your scrap paper. If they don’t (as in the above problem), draw yourself a diagram anyway. This is part of your Glance-Read-Jot step.

Second, identify the “wanted” element and mark this element on your diagram. You’ll do this as part of the Glance-Read-Jot step, but do it last so that it leads you into the Reflect-Organize stage. Where am I trying to go? How can I get there?

Third, start Working! Infer from the given information. Geometry on the GMAT can be a bit like the proofs that we learned to do in high school. You’re given a couple of pieces of info to start and you have to figure out the 4 or 5 steps that will get you over to the answer, or what you’re trying to “prove.”

Let’s dive into this problem. They’re talking about a coordinate plane, so you know the first step: draw a coordinate plane on your scrap paper. The question indicates that there’s a line L, but you don’t know anything else about it, so you can’t actually draw it. You do know, though, that they want to know the y-intercept. What does that mean?

They want to know where line L crosses the y-axis. What are the possibilities?

Infinite, really. The line could slant up or down or it could be horizontal. In any of those cases, it could cross anywhere. In fact, the line could even be vertical, in which case it would either be right on the y-axis or it wouldn’t cross the y-axis at all. Hmm.
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