In the first part of this article, we talked about how GMAT quant problems are often written to imply a certain approach or solution path that is not actually the best way to do the problem. We want to reorient our view in order to pick an easier, more efficient setup or solution (if at all possible).

We finished off with a homework assignment; here’s the problem I gave you (from the free problems that come with the GMATPrep software):

* ” If , then  =

“(A) –¹/₂

“(B) –¹/₃

“(C) ¹/₃

“(D) ¹/₂

“(E) ⁵/₂   ”

The answers are fractions but they aren’t horrible fractions. They give me a value for x / y. The question is kind of annoying though, because the form doesn’t match x / y.

Or does it? Is there any way for me to rearrange that thing to make it look more like x / y?

Yes! Check it out:

Now, how did I know to do that? I’ve actually seen another problem with the same shortcut: split the numerator into two fractions. The first time I saw that other problem, though, the way I figured it out was that whole “Well, this is annoying, why did they give it to me that way!” And so I started looking at it differently and asking myself some questions:

“They gave me a value for x / y. But the question doesn’t give me x / y. Is there any way I can make x / y? There is an x on top and a y on the bottom; what if I put those two together?

“Oh, yeah, I see! It’s totally legal to split the numerator and get two separate fractions, so that would give me x / y for one of the fractions. Does that make my life any easier, though?

“The other fraction just turns into 1! That’s fantastic! I know what I’m doing now.”

Et voilà ! I know that  , so . Plug that in and get 1 – 1.5 = -0.5.

Note that it’s easier to add and subtract in decimal (or percent) form, so if fractions can be converted easily (as 3/2 can), then consider doing the subtraction in decimal form. You already know that it will be easy to convert back into the final answer because look at the answer options—they’re all easy fractions to convert.

The correct answer is (A).

Quick! Glance at the answer choices for the above problem. If you did no work at all and had 1 second to make a guess, which answer would you NOT pick? Read more

The Quant section of the GMAT is not a math test. Really, it isn’t! It just looks like one on the surface. In reality, they’re testing us on how we think.

As such, they write many math problems in a way that hides what’s really going on or even implies a solution method that is not the best solution method. Assume nothing and do not accept that what they give you is your best starting point!

In short, learn to reorient your view on math problems. When I look at a new problem, one of my first thoughts is, “What did they give me and how could it be made easier?” In particular, I look for things that I find annoying, as in, “Ugh, why did they give it to me in that form?” or “Ugh, I really don’t want to do that calculation.” My next question is how I can get rid of or get around that annoying part.

What do I mean? Here’s an example from the free set of questions that comes with the GMATPrep software. Try it!

* ” If ½ of the money in a certain trust fund was invested in stocks, ¼ in bonds, ¹/₅ in a mutual fund, and the remaining $10,000 in a government certificate, what was the total amount of the trust fund?

“(A) $100,000

“(B) $150,000

“(C) $200,000

“(D) $500,000

“(E) $2,000,000”

What did you get?

Here’s my thought process:

(1) Glance (before I start reading). It’s a PS word problem. The answers are round / whole numbers, and they’re mostly spread pretty far apart. I might be able to estimate to get the answer and I should at least be able to tell whether it’s closer to (A) or (E).

(2) Read and Jot. As I read, I jot down numbers (and label them!):

S = ¹/₂

B = ¹/₄

F = ¹/₅

C = 10,000

(3) Reflect and Organize. Let’s see. The four things should add up to the total amount. Three of those are fractions. Oh, I see—if I had four fractions, they should all add up to 1. So if I take those three and add them, and then subtract that from 1, that’ll give me the fractional amount for the C. Since I know the real value for C, I can then figure out the total.

But, ugh, adding fractions is annoying! You need common denominators. I’m capable of doing this, of course, but I really don’t want to! Isn’t there an easier way?

In this case, yes! Adding decimals or percents is really easy. Adding fractions is annoying. Plus, check it out, the fractions given are all common ones that we (should) have memorized. So change those fractions to percents (or decimals)!

(4) Work. Let’s do it!

S = ¹/₂  = 50%

B = ¹/₄ = 25%

F = ¹/₅ = 20%

C = 10,000

Wow, this is a lot easier. I know that 50 + 25 + 25 would equal 100, but I’ve only got 50 + 25 + 20, so the total is 5 short of 100. The final value, C, then must be 5% of the total.

So let’s see… if C = 10,000 = 5%, then 10% would be twice as much, or 20,000. And I just need to add a zero to get to 100%, or 200,000. Done! Read more

Exciting news! GMAC (the owners of the GMAT) announced on Friday that, starting immediately, we’ll get our unofficial IR scores as soon as the test is over. They already do this for our Quant, Verbal, and Total scores, so IR will be added to the mix.

As with the other scores, the IR score will be considered an “unofficial” score until you receive your official score report. You can consider these test-day scores essentially official, though, as it’s incredibly rare for something to change after that day. The folks over at GMAC are professionals; they’re not going to release scores if there’s even a small chance that something could change, upsetting students who thought they had earned a different score.

So now you won’t have to wait to find out how you did on IR. (You’ll still wait for the essay score, of course, but that’s not quite so nerve-wracking, is it?)

Need to practice IR? Try our new free GMAT Interact lessons for Integrated Reasoning.

Happy studying and good luck on test day!

For the past couple of weeks, we’ve been learning the 4-step SC Process. (If you haven’t read that two-part article yet, go do so now!) Also, grab your copy of The Official Guide 13^th Edition (OG13); you’re going to need it for the exercises in this article.

People often ask what they should check “first” in SC, or in what order they should check various potential grammar problems. It would take too long to check for a laundry list of error types every time, though, so what to do? You take a First Glance: a 2-3 second glance at the screen with the goal of picking up a clue or two about this problem before you even start reading it.

Open up your OG13 to the SC section right now—any page will do—and find a really long underline. Now find a really short one.

How would you react to each of these? Each one has its own hints. Think about this before you keep reading.

A really long underline increases the chances that “global” issues will be tested. These issues include Structure, Meaning, Modifiers, and Parallelism—it’s easier to test all of these issues when the underline contains a majority of the sentence.

A really short underline (around 5-6 words or fewer) should trigger a change in strategy. Instead of reading the original sentence first, compare the answers to see what the differences are. This won’t take long because there aren’t many words to compare! Those differences can give you ideas as to what the sentence is testing.

Either way, you’ve now got some ideas about what might be happening in the sentence before you even read it—and that is the goal of the First Glance.

Read a Couple of Words

Next, we’re going to do a drill.  Flip to page 672 (print edition) of OG13 but don’t read anything yet. Also, open up a notebook or a file on your computer to take notes. (Note: I’m starting us on the first page of SC problems because I want to increase the chances that you’ve already done some of these problems in the past. It’s okay if you haven’t done them all yet. You can also switch to a different page if you want, but I’m going to discuss some of these problems below, FYI.)

Start with the first problem on the page. Give yourself a maximum of 5 seconds to glance at that problem. Note the length of the underline. Read the word right before the underline and the first word of the underline, but that’s it! Don’t read the rest of the sentence. Also go and look at the first word of each answer choice. As you do this, takes notes on what you see.

For the next step, you can take all the time you want (but still do not go back and read the full sentence / problem). Ask yourself whether any of that provides any clues. Read more

In the first half of this article, we talked about the 5-step process to answer SC problems:

1. Take a First Glance

2. Read the Sentence

3. Find a Starting Point

4. Eliminate Answers

5. Repeat steps 3 and 4

If you haven’t already learned that process, read the first half before continuing with this part.

Drills to Build Skills

How do you learn to do all of this stuff? You’re going to build some skills that will help at each stage of the way. You might already feel comfortable with one or multiple of these skills, so feel free to choose the drills that match your specific needs.

Drill Number 1: First Glance

Open up your Official Guide and find some lower-numbered SC questions that you’ve already tried in the past. Give yourself a few seconds (no more than 5!) to glance at a problem, then look away and say out loud what you noticed in those few seconds.

As you develop your First Glance skills, you can start to read a couple of words: the one right before the underline and the first word of the underline. Do those give you any clues about what might be tested in the problem? For instance, consider this sentence:

Xxx xxxxxx xxxx xx and she xxx xxxxx xxxx xxxx xxx xxx xxxxx.

I can’t know for sure, but I have a strong suspicion that this problem might test parallelism, because the word and falls immediately before the underline. When I read the sentence, I’ll be looking for an X and Y parallelism structure.

At first, you’ll often say something like, “I saw that the underline starts with the word psychologists but I have no idea what that might mean.” (Note: this example is taken from OG13 SC #1!) That’s okay; you’re about to learn. Go try the problem (practicing the rest of the SC process as described in the first half of this article) and ask yourself again afterwards, “So what might I have picked up from that starting clue?”

The word psychologists is followed by a comma… so perhaps something will be going on with modifiers? Or maybe this is a list? The underline is really long as well, which tends to go with modifiers. Now, when you start to read the sentence, you will already be prepared to figure out what’s going on with this word. (In this case, it turns out that psychologists is followed only by modifiers; the original sentence is missing a verb!)

Drill Number 2: Read the Sentence

Take a look at some OG problems you’ve tried before. Read only the original sentence. Then, look away from the book and articulate aloud, in your own words, what you think the sentence is trying to convey. You don’t need to limit yourself to one sentence. You can also glance back at the problem to confirm details.

I want to stress the “out loud” part; you will be able to hear whether the explanation is sufficient. If so, try another problem.

If you’re struggling or unsure, then one of two things is happening. Either you just don’t understand, or the sentence actually doesn’t have a clear meaning and that’s why it’s wrong! Decide which you think it is and then look at the explanation. Does the explanation’s description of the sentence match what you thought—the sentence actually does have a meaning problem? If not, then how does the explanation explain the sentence? That will help you learn how to “read it right” the next time. (If you don’t like the OG explanation, try looking in our GMAT Navigator program.)

Drill Number 3: Find a Starting Point

Once again, open up your OG and look at some problems you have done before. This time, do NOT read the original sentence. Instead, cover it up. Read more

Last time, we talked about how to make story problems real; if you haven’t read that article yet, go take a look before you continue with this one.

I’ve got another one for you that’s in that same vein: the math topic is different, but the “story” idea still hold in general. This one has something extra though: you need to know how a certain math topic (standard deviation) works in general. Otherwise, you won’t be able to think your way through the problem.

Try this GMATPrep® problem:

* ” During an experiment, some water was removed from each of 6 water tanks. If the standard deviation of the volumes of water in the tanks at the beginning of the experiment was 10 gallons, what was the standard deviation of the volumes of water in the tanks at the end of the experiment?

“(1) For each tank, 30 percent of the volume of water that was in the tank at the beginning of the experiment was removed during the experiment.

“(2) The average (arithmetic mean) volume of water in the tanks at the end of the experiment was 63 gallons.”

Standard deviation! Ugh. : )

Okay, it’s no accident that they’re using a DS-format problem for this one. It’s not possible to calculate a standard deviation in 2 minutes without a calculator (unless, perhaps, that standard deviation is zero!). They never expect us to calculate standard deviation on this test, but they do want to know whether we understand the concept in general.

So what is standard deviation? Try to answer—aloud—in your own words before you continue reading.

(Why did I say “aloud”? Often, we tell ourselves that we can explain something, but not until we actually try do we realize that we need a refresher on the concept. Giving an explanation aloud forces you to prove that you really do know how to explain the concept. If you don’t, you’ll hear your uncertainty in your own explanation.)

Standard deviation is the measure of how spread apart a set of data points is. For example, let’s say you have the following 5 numbers in a set: {3, 3, 3, 3, 3}. The standard deviation is zero because the numbers are all exactly the same—there is no “spread” at all in the set.

Which of the following two sets has a larger standard deviation?

{1, 2, 3, 4, 5}

{1, 10, 20, 80, 2,000}

The second one! The numbers are much more spread apart than in the first set.

Right now, some of you are wondering: okay, but what’s the actual standard deviation of those two sets?

I don’t know. I could calculate it—I’m sure there are many online “standard deviation” calculators I could use. But I don’t care. The real test is never going to make me calculate this! (And that’s why I haven’t gotten into the actual calculation method here… nor will I.)

There are a few concepts that we should know, though, in terms of how changes to sets can affect the standard deviation. Read more

I’ve been on a story problem kick lately. People have a love / hate relationship with these. On the one hand, it’s a story! It should be easier than “pure” math! We should be able to figure it out!

On the other hand, we have to figure out what they’re talking about, and then we have to translate the words into math, and then we have to come up with an approach. That’s where story problems start to go off the rails.

You know what I mean, right? Those ones where you think it’ll be fine, and then you’re about 2 minutes in and you realize that everything you’ve written down so far doesn’t make sense, but you’re sure that you can set it up, so you try again, and you get an answer but it’s not in the answer choices, and now you’re at 3.5 minutes or so… argh!

So let’s talk about how to make story problems REAL. They’re no longer going to be abstract math problems. You’re riding Train X as it approaches Train Y. You’re the store manager figuring out how many hours to give Sue so that she’ll still make the same amount of money now that her hourly wage has gone up.

Try this GMATPrep® problem:

* ” Six machines, each working at the same constant rate, together can complete a certain job in 12 days. How many additional machines, each working at the same constant rate, will be needed to complete the job in 8 days?

“(A) 2

“(B) 3

“(C) 4

“(D) 6

“(E) 8”

Yuck. A work problem.

Except… here’s the cool thing. The vast majority of rate and work problems have awesome shortcuts. This is so true that, nowadays, if I look at a rate or work problem and the only solution idea I have is that old, annoying RTD (or RTW) chart… I’m probably going to skip the problem entirely. It’s not worth my time or mental energy.

This problem is no exception—in fact, this one is an amazing example of a complicated problem with a 20-second solution. Seriously—20 seconds!

You own a factory now (lucky you!). Your factory has 6 machines in it. At the beginning of the first day, you turn on all 6 machines and they start pumping out their widgets. After 12 continuous days of this, the machines have produced all of the widgets you need, so you turn them off again.

Let’s say that, on day 1, you turned them all on, but then you turned them off at the end of that day. What proportion of the job did your machines finish that day? They did 1/12 of the job.

Now, here’s a key turning point. Most people will then try to figure out how much work one machine does on one day. (Many people will even make the mistake of thinking that one machine does 1/12 of the job in one day.) But don’t go in that direction in the first place! If you were really the factory owner, you wouldn’t start writing equations at this point. You’d figure out what you need by testing some scenarios. Read more

Some interesting —and alarming—articles have been making the rounds lately, following on the heels of an academic study published by professors at the University of Akron and Cleveland State University. The more reputable articles report such sweeping conclusions that I actually wondered whether the journalists got it wrong, so I went to the source (I can link only to the abstract here, but I did read the full study).

When I read the study’s methodology, I knew I had my next article topic. We’re going to test our Critical Reasoning (CR) skills on an actual academic study! You might have to do something similar in business school (admittedly with a business case, not an academic study), so let’s test your b-school readiness now!

(Note: I refer to the “more reputable articles” because some blogs have picked this up and publishing under headlines such as “Is the GMAT the root of all evil?” As much as you may hate studying for this test, I think we can agree that this characterization is a bit over the top. : ) )

Correlation vs. Causation

We need to define a couple of terms first. You may already have learned about correlation and causation in your CR studies; here’s a refresher.

Correlation: two phenomena tend to occur or appear at the same time or in conjunction with one another

Causation: one phenomenon causes another phenomenon

Correlation does not imply causation. One of two correlated phenomena could cause the other but those two things could also have absolutely no causation between them. Alternatively, the two things could both be caused by a third thing. The two things could even cause each other! (Predator-prey dynamics are an example of this kind of two-way dependency.)

For example, have you ever noticed how, when the ground is wet, people often seem to be carrying around umbrellas? Those two phenomena are correlated. Which one causes the other? Read more

In the first part of this article, we took a look at how to read MSR passages and take some light notes. We finished off with a problem—now let’s talk about the solution! (Note: click on the link earlier in this paragraph; you’re going to want the tab text when reading through the solution.)

Here’s the problem again:

 “Based on the information in the passage and tables, it can be determined that the average monthly meat consumption, in pounds, by the residents of Barras in the AD 1000s was which of the following?

“(A) 9,600

“(B) 10,000

“(C) 16,000

“(D) 17,400

“(E) 18,000”

How did it go? Our first task is to figure out where to go. Which tab is likely to be most useful in answering this question? They ask about meat consumption and also specify Barras in the AD 1000s.

Both tables (in tabs 2 and 3) talk about Barras and meat consumption, but this question asks about pounds—that sends us to tab 3.

Read the key up at top. The table shows average monthly meat consumption (good, that’s what we want!) in pounds for a 4-person family. We want pounds. Do we want a 4-person family?

Nope. The question asks about the total consumption in pounds for the residents of Barras. We’re going to need to do a little calculating here.

In the 1000s, Barras’s average monthly consumption per 4-person family was 160 pounds. Per person, then, consumption was 160 /4 = 40 pounds. Hmm, now what?

We need to know the total number of residents in Barras in the 1000s. Where did they tell us that?

Right! Tab 1 gave some information about population at the end of the paragraph about Barras. The passage says that there were 400 residents, on average, in the AD 1000s.

400 residents multiplied by 40 pounds per resident is a total of 16,000 pounds.

The correct answer is (C).

What did you learn about MSRs from this problem? I think there are 3 key takeaways, which I list at the end of this article; try to come up with your own before you read them.

Let’s try another problem from this MSR; give yourself about 1.5 to 2 minutes total to answer all three parts of this problem.

Read more

Given that Integrated Reasoning may become more important for those who want to go into consulting or banking, let’s take a look at a Multi-Source Reasoning (MSR) problem!

In this first part, we’re going to take a look at how to read and take notes on the MSR text. In the next article, we’ll do a problem that goes with the text. This MSR is from the free GMATPrep test, so if you have not yet taken GMATPrep, don’t read this article yet! Put it away and come back to it after you’ve seen the problem yourself.

MSRs appear as three tabs of information. I can’t format things into tabs here, so I’ll just show it all to you one after the other. You have about 2.5 minutes per question on IR. This MSR has a total of 3 associated questions, but I’m only giving you one in this article. Spend about 2 to 2.5 minutes on the read-through, leaving yourself about 1.5 to 2 minutes to spend on each question.

Tab 1

“An archaeological team has been excavating three ancient village sites—Barras, Agna, and Cussaia—looking in particular at kitchen waste dumps as a way to understand the villages’ dietary patterns and trading relationships. What follows are brief summaries of their findings.

“Barras: The best data come from stratified finds in this oceanside village, which was inhabited from AD 600 to 1300 and was the only one of the three villages to produce seafood, its main dietary item. Though Barras residents hunted on land and raised crops, this provided relatively small amounts of food. As Barras’s overall prosperity rose, there was more food available per person, and its population increased from an average of 100 residents in the AD 600s to 400 residents in the AD 1000s to 600 residents in the AD 1200s.

“Agna: Agna was established in an inland forest around AD 800 and its residents mainly hunted but also ate considerable amounts of fruit, nuts, and other forest-vegetable products. They also traded meat to Barras for other goods. With no open fields, Agna grew no grain.

“Cussaia: Predating Barras, Cussaia depended heavily on raising grain crops and eventually obtained seafood and meat via trade. It traded directly only with Barras, because a mountain range separated it from Agna, though some products may have been traded between Agna and Cussaia via Barras.

“Additionally, there is no evidence that any other village traded with Barras, Agna, or Cussaia prior to AD 1300.”

—

Tab 2

“Barras: Percentages, by Estimated Weight, of Dietary Items Consumed per Person per Month”

Century	Seafood	Meat	Grains	Other
600s	65%	10%	10%	15%
700s	65%	10%	15%	10%
800s	60%	15%	15%	10%
900s	45%	30%	12%	13%
1000s	45%	30%	12%	13%
1100s	60%	10%	20%	10%
1200s	55%	25%	10%	10%

—

Tab 3

“Barras, Agna: Estimated Average Monthly Meat and Seafood Consumption (lb per 4-Person Family)”

Century	Barras		Agna
	Seafood	Meat	Seafood	Meat
600s	240	37	not applicable	not applicable
700s	250	38	not applicable	not applicable
800s	275	70	60	240
900s	258	172	66	180
1000s	240	160	66	186
1100s	275	45	8	240
1200s	265	120	45	240

—

That’s a lot to read through in only 2 minutes or so. The key is to be able to divide the info into three categories:

Read more