Below is an excerpt from Andrew Yang‘s new book, Smart People Should Build Things: How to Restore Our Culture of Achievement, Build a Path for Entrepreneurs, and Create New Jobs in America, which comes out in February 2014. Andrew was named Managing Director of Manhattan GMAT in 2006, Chief Executive Officer in 2007, and President in 2010. He left Manhattan GMAT in 2010 to start Venture for America, where he now serves as Founder and CEO. 

The Qualities We Need.  

A friend told me about a young Princeton graduate she knew named Cole. Cole studied mathematics and went to work for a hedge fund directly out of school. He’s now making well into six figures at the age of twenty-four. That’s his whole story to date.

That’s success and the American way. And yet how excited are you about Cole’s trajectory? Think about it for a second. I’ll admit that I’m not too psyched about it, even though I have friends at hedge funds who are very intelligent, stand-up guys and even philanthropists, and I know that hedge funds are positive in that they provide diversified investment opportunities to large pools of capital.

My lack of enthusiasm comes down to a few things. If Cole successfully analyzes an opportunity for the hedge fund and it invests slightly more effectively, that will be a win for the fund’s managers and its investors. But there will very likely be an equivalent loss on the other side of the investment (whoever sold it to them makes out slightly less well for having undervalued the asset). It’s not clear what the macroeconomic benefit is, unless you either favor the hedge fund’s investors over others or have a very abstract view toward capital markets working efficiently.

Cole is almost certainly very smart. But what has he done to merit his almost immediately elevated stature in life? He’s never hazarded anything. He hasn’t demonstrated any outstanding character or virtue, unless you consider studying math and being really smart intrinsically virtuous. He’s never had to go against the grain or go out on a limb. His rewards seem a little bit exaggerated for his accomplishments.
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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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My last article discussed the difference between inductive and deductive arguments. Today’s article will focus mostly on the rules of deductive arguments. I promise to nerd out on inductive reasoning in later articles.

Here’s a quick quiz on the difference between inductive and deductive logic: //www.thatquiz.org/tq/previewtest?F/Z/J/V/O3UL1355243858

To review: In a deductively “valid” argument, if all the premises are true, the conclusion must also be true, with 100% certainty. Luckily, on the GMAT, we should usually act as if the premises of an argument are true, especially when the question specifies, “the statements above are true.”

Deductive reasoning shows up most often on inference (aka “draw a conclusion”) questions and “mimic the reasoning” questions, but it often appears on other types of questions, and even on reading comprehension!

On inference questions, the correct answer will usually be deductively valid (or very very strong, inductively). An incorrect answer will be deductively invalid, with some significant probability that it could be false.

What follows are most of the formal rules of deductive reasoning (from a stack of logic textbooks I have on my shelf), with examples from the GMAT. For shorthand, I’ll label the arguments with a “P” for premise and a “C” for conclusion:

P) premise
P) premise
C) conclusion

Remember: these are not the same kind of conclusions (opinions) you’ll see on strengthen and weaken questions. Deductive conclusions are deductively “valid” facts that you can derive with 100% certainty from given premises.

EASY STUFF: Simplification/conjunction (“and” statements)

This is kind of a “duh” conclusion, but here goes: If two things are linked with an “and,” then you know each of them exist. Conversely, if two things exist, you can link them with an “and.”

Simplification:

P) A and B
C) Therefore, A

Conjunction:

P) A
P) B
C) Therefore, A and B

P) Bill is tall and was born in Texas.
P) Bill rides a motorcycle.
C) Therefore, Bill was born in Texas (simplification).
C) Therefore, at least one tall person named Bill was born in Texas and rides a motorcycle (conjunction).

CAUTION: Fallacies ahead!!

Don’t confuse “and” with “or.” (More about this later.) More importantly, don’t confuse “and” with causality, condition, or representativeness. Bill’s tallness probably has nothing to do with Texas, so keep an eye out for wrong answers that say, “Bill is tall because he was born in Texas” or “Most people from Texas ride motorcycles.”

MEDIUM STUFF: Disjunctive syllogism (“or” statements)

With “or” statements, if one thing is missing, the other must be true.

Valid conclusions:

P) A or B
P) not B (shorthand: ~B)
C) Therefore, A

P) We will go to the truck rally or to a Shakespeare play
P) We won’t go to the Shakespeare play.
C) Therefore, we will go to the truck rally.

CAUTION: Fallacies ahead!!

Unlike in the real world, “or” statements do not always imply mutual exclusivity, unless the argument explicitly says so. For example, in the above arguments, A and B might both be true; we might go to a play and go to the movies. Yes, really. A wrong answer might say “We went to a play, so we won’t go to the movies.” This error is called “affirming the disjunct.”

Invalid:

P) A or B
P) B
C) Not A

GMAT example:

To see this in action, check out your The Official Guide for GMAT Review 13th Edition, by GMAC®*, question 41. This argument opens with an implied “or” statement:

“Installing scrubbers in smokestacks and switching to cleaner-burning fuel are the two methods available to Northern Power…”

The author here incorrectly assumes that by using one method, Northern Power can’t use both methods at the same time. Question 51 does the same thing; discuss it in the comments below?

TOUGH STUFF: Fun with conditional statements

This is important! Keep a sharp eye out for statements that can be expressed conditionally and practice diagramming them. Look for key words such as “if,” “when,” “only,” and “require.”

I use the symbol “–>” to express an if/then relationship, and a “~” to express the word “not.” Use single letters or abbreviations to stand in for your elements.
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Below is an excerpt from Andrew Yang‘s new book, Smart People Should Build Things: How to Restore Our Culture of Achievement, Build a Path for Entrepreneurs, and Create New Jobs in America, which comes out in February 2014. Andrew was named Managing Director of Manhattan GMAT in 2006, Chief Executive Officer in 2007, and President in 2010. He left Manhattan GMAT in 2010 to start Venture for America, where he now serves as Founder and CEO. 

Entrepreneurship Isn’t About Creativity.  

There is a common and persistent belief out there that entrepreneurship is about creativity, that it’s about having a great idea. But it’s not, really. Entrepreneurship isn’t about creativity. It’s about organization building—which, in turn, is about people.

I sometimes compare starting a business to having a child. You have a moment of profound inspiration, followed by months of thankless hard work and waking up in the middle of the night. People focus way too much on the inspiration, but, like conception, having a good idea isn’t much of an accomplishment. You need the action and follow-through, which involves the right people, know-how, money, resources, and years of hard work.

I learned this the hard way. Here’s a list of things you can reasonably do on the side as you’re working a full-time job to explore an idea for a great new business:

1. Research your idea (figure out the market, talk to prospective customers about what they would like, see who your competitors are, and so forth).

2. Undertake legal incorporation and trademark protection (the latter when necessary; most companies don’t need a trademark at first).

3. Claim a web URL and build a website or have it built; get company e-mail accounts.

4. Get a bank account and credit card (you’ll generally have to use personal credit at first).

5. Initiate a Facebook page, a blog, and a Twitter account if appropriate.

6. Develop branding (e.g., get a logo designed, print business cards).

7. Talk it up to your network; try to find interested parties as cofounders, staff, investors, and advisers.

8. Build financial projections and draft a business plan (if necessary).

9. Engage in personal financial planning (e.g., cut back on expenses, budget for startup costs, and so on.)

10. Create a mock prototype and presentation for potential investors or customers.

If all of this sounds like a lot of work to do before you’ve even really gotten started, you’re right. Getting this stuff done while holding down a job would be a significant commitment. You might not have time to hang out with friends and family and do the things people like to do when they’re not at work.  It is doable, though; I’ve seen it done or done it myself.

You’re just getting started. There’s a big jump in difficulty when it comes to the next things:

1. Raise money. In my experience, fledgling entrepreneurs focus way too much on the money—you can get most things done and figure out a lot without spending much. That said, most businesses require money to launch and get off the ground. For example, the average restaurant costs about $275,000 in construction and startup costs.  Finding initial funds is the primary barrier most entrepreneurs face. Many people don’t have three or six months’ worth of savings to free themselves up to do months of unpaid legwork.

2. Develop the product. Product development is a significant endeavor. Even if you’re hiring someone to build your product, managing them to specifications is a huge task in itself. You can expect vendors to take twice as long and cost twice as much as you’ve planned for. Think of the last home improvement project you paid a contractor for; most experiences are like that. Depending on the product, you may need to travel to find the right ingredients, partners, and suppliers. This phase might require raising additional money as well. In some cases, you might want to patent your product, which will involve a patent search and thousands of dollars in patent attorney fees.
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Sequence problems aren’t incredibly common on the test, but if you’re doing well on the quant section, be prepared to see one. Now, you’ve got a choice: do you want to guess quickly and save time for other, easier topics? Do you want to learn some “test savvy” techniques that will help you with some sequence questions but possibly not all of them? Or do you want to learn how to do these every single time, no matter what?

That isn’t a trick question. Every good business person knows that there’s a point of diminishing returns: if you don’t actually need a 51, then you may study for a lower (but still good!) score and re-allocate your valuable time elsewhere.

Try this GMATPrep® problem from the free test. After, we’ll talk about how to do it in the “textbook” way and in the “back of the envelope” way.

* ”For every integer k from 1 to 10, inclusive, the kth term of a certain sequence is given by . If T is the sum of the first 10 terms in the sequence, then T is

“(A) greater than 2

“(B) between 1 and 2

“(C) between 1/2 and 1

“(D) between 1/4 and 1/2

“(E) less than 1/4”

First, let’s talk about how to do this thing in the “textbook math” way. If you don’t want to do this the textbook math way, feel free to skip to the second method below.

Textbook Method

If you’ve really studied sequences, then you may recognize the sequence as a particular kind called a Geometric Progression. If not, you would start to find the terms and see whether you can spot a pattern.

Plug in k = 1, 2, 3. What’s going on?

What’s going on here? Each time, the term gets multiplied by -1/2 in order to get to the next one. When you keep multiplying by the same number in order to get to the next term, then you have a geometric progression.

This next part gets into some serious math. Unless you really just love math, I wouldn’t bother learning this part for the GMAT, because there’s a very good chance you’ll never need to use it. But, if you want to, go for it!

When you have a geometric progression, you can calculate the sum in the following way:

Next, you’re going to multiply every term in the sum by the common ratio. What’s the common ratio? It’s the constant number that you keep multiplying each term by to get the next one. In this case, you’ve already figured this out: it’s – 1/2.

If you multiply this through all of the terms on both sides of the equation, you’ll get this:

Does anything look familiar? It’s basically the same list of numbers as in the first sum equation, except it’s missing the first number, 1/2. All of the others are identical!

Subtract this second equation from the first:

The right-hand side of the equation is always going to be just the first term of the original sum. The rest of the terms on the right-hand side of the two equations are identical, so when you subtract, they become zero and disappear.

Solve for s:

This value falls between 1/4 and 1/2, so the answer is (D).

Back of the Envelope Method

There is another way to tackle this one. At the same time, this problem is really tricky—so this solution is still not an “easy” solution. Your best choice might be just to guess and move on.

Before you start reading the text, take a First Glance at the whole thing. It’s a problem-solving problem. The answers are… weird. They’re not exact. What does that mean?

Read the problem, but keep that answer weirdness in mind. The first sentence has a crazy sequence. The question asks you to sum up the first 10 terms of this sequence. And the answers aren’t exact… so apparently you don’t need to find the exact sum.

Take a closer look at the form of the answers. Notice anything about them?

They don’t overlap! They cover adjacent ranges. If you can figure out that, for example, the sum is about 3/4, then you know the answer must be (C). In other words, you can actually estimate here—you don’t have to do an exact calculation.

That completely changes the way you can approach this problem! Here’s the sequence:

According to the problem, the 10 terms are from k = 1 to k = 10. Calculating all 10 of those and then adding them up is way too much work (another clue that there’s got to be a better way to do this one). So what is that better way?

Since you know you can estimate, try to find a pattern. Calculate the first two terms (we had to do this in the first solution, too).

What’s going on? The first answer is positive and the second one is negative. Why? Ah, because the first part of the calculation is -1 raised to a power. That will just keep switching back and forth between 1 and -1, depending on whether the power is odd or even. It won’t change the size of the final answer, but it will change the sign.

Okay, and what about that second part? it went from 1/2 to 1/4. What will happen next time? Try just that part of the calculation. If k = 3, then just that part will become .

Interesting! So the denominator will keep increasing by a factor of 2: 2, 4, 8, 16 and so on.

Great, now you can write out the 10 numbers!

… ugh. The denominator’s getting pretty big. That means the fraction itself is getting pretty small. Do I need to keep writing these out?

What was the problem asking again?

Right, find the sum of these 10 numbers. Let’s see. The first number in the sequence is 1/2 and the second is -1/4, so the pair adds up to 1/4.

Right now, the answer would be right between D and E. Does the sum go up or down from here?

The third number will add 1/8, so it goes up:

But the fourth will subtract 1/16 (don’t forget that every other term is negative!), pulling it back down again:

Hmm. In the third step, it went up but not enough to get all the way to 1/2. Then, it went down again, but by an even smaller amount, so it didn’t get all the way back down to 1/4.

The fifth step would go up by an even smaller amount (1/32), and then it would go back down again by yet a smaller number (1/64). What can you conclude?

First, the sum is always growing a little bit, because each positive number is a bit bigger than the following negative number. The sum is never going to drop below 1/4, so cross off answer (E).

You keep adding smaller and smaller amounts, though, so if the first jump of 1/8 wasn’t enough to get you up to 1/2, then none of the later, smaller jumps will get you there either, especially because you also keep subtracting small amounts. You’re never going to cross over to 1/2, so the sum has to be between 1/4 and 1/2.

The correct answer is (D).

As I mentioned above, you may decide that you don’t want to do this problem at all. These aren’t that common—many people won’t see one like this on the test. Also, you don’t have to get everything right to get a top score. Just last week, I spoke with a student who outright guessed on 4 quant problems, and she still scored a 51 (the top score).

Key Takeaways for Advanced Sequence Problems

(1) Do you even want to learn how to do these? Don’t listen to your pride. Listen to your practical side. This might not be the best use of your time.

(2) All of these math problems do have a textbook solution method—but you’d have to learn a lot of math that you might never use if you try to learn all of the textbook methods. That’s not a problem if you’re great at math and have a great memory for this stuff. If not…

(3) … then think about alternate methods that can work just as well. Certain clues will indicate when you can estimate on a problem, rather than solving for the “real” number. You may already be familiar with some of these, for instance when you see the word “approximately” in the problem or answer choices that are spread pretty far apart. Now, you’ve got a new clue to add to your list: answers that offer a range of numbers and the different answer ranges don’t overlap.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

Below is an excerpt from Andrew Yang‘s new book, Smart People Should Build Things: How to Restore Our Culture of Achievement, Build a Path for Entrepreneurs, and Create New Jobs in America, which comes out in February 2014. Andrew was named Managing Director of Manhattan GMAT in 2006, Chief Executive Officer in 2007, and President in 2010. He left Manhattan GMAT in 2010 to start Venture for America, where he now serves as Founder and CEO. 

Professional Services as a Training Ground.  

As we’ve seen, one of the most frequently pursued paths for achievement-minded college seniors is to spend several years advancing professionally and getting trained and paid by an investment bank, consulting firm, or law firm. Then, the thought process goes, they can set out to do something else with some exposure and experience under their belts.  People are generally not making lifelong commitments to the field in their own minds. They’re “getting some skills” and making some connections before figuring out what they really want to do.

I subscribed to a version of this mind-set when I graduated from Brown. In my case, I went to law school thinking I’d practice for a few years (and pay down my law school debt) before lining up another opportunity.

It’s clear why this is such an attractive approach. There are some immensely constructive things about spending several years in professional services after graduating from college. Professional service firms are designed to train large groups of recruits annually, and they do so very successfully. After even just a year or two in a high-level bank or consulting firm, you emerge with a set of skills that can be applied in other contexts (financial modeling in Excel if you’re a financial analyst, PowerPoint and data organization and presentation if you’re a consultant, and editing and issue spotting if you’re a lawyer). This is very appealing to most any recent graduate who may not yet feel equipped with practical skills coming right out of college.
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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.

How do you study? More importantly, how do you know that the way in which you’re studying is effective—that is, that you’re learning what you need to learn to improve your GMAT score? Read on! Read more

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.

Whether you’ve been studying for a while or are just getting started, let’s use the New Year as an opportunity to establish or renew your commitment to getting your desired GMAT score. Read more

We invite you to test your GMAT knowledge for a chance to win! The second week of every month, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that month’s drawing for free Manhattan GMAT prep materials. Tell your friends to get out their scrap paper and start solving!

Here is this month’s problem:

If p, q, and r are different positive integers such that p + q + r = 6, what is the value of x ?

(1) The average of x^p and x^q is x^r.

(2) The average of x^p and x^r is not x^q.

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