Articles published in Quant

Everything you need to know about the New Official Guides, Part 3

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I have now done every last one of the new quant problems in both new books—and there are some really neat ones! I’ve also got some interesting observations for you. (If you haven’t yet read my earlier installments, start here.)

In this installment, I’ll discuss my overall conclusions for quant and I’ll also give you all of the problem numbers for the new problems in both the big OG and the smaller quant-only OG.

What’s new in Quant?

Now that I’ve seen everything, I’ve been able to spot some trends across all of the added and dropped questions. For example, across both The Official Guide for GMAT® Review (aka the big book) and The Official Guide for GMAT® Quant Review (aka quant-only or the quant supplement), Linear Equation problems dropped by a count of 13. This is the differential: new questions minus dropped questions.

That’s a pretty big number; the next closest categories, Inequalities and Rates & Work, dropped by 5 questions each. I’m not convinced that a drop of 5 is at all significant, but I decided that was a safe place to stop the “Hmm, that’s interesting!” count.

Now, a caveat: there are sometimes judgment calls to make in classifying problems. Certain problems cross multiple content areas, so we do our best to pick the topic area that is most essential in solving that problem. But that 13 still stands out. :)

The biggest jump came from Formulas, with 10 added questions across both sources. This category includes sequences and functions; just straight translation or linear equations would go into those respective categories, not formulas. Positive & Negative questions jumped by 7, weighted average jumped by 6, and coordinate plane jumped by 5.

Given that Linear Equations dropped and Formulas jumped, could it be the case that they are going after somewhat more complex algebra now? That’s certainly possible. I didn’t feel as though the new formula questions were super hard though. It felt more as though they were testing whether you could follow directions. If I give you a weird formula with specific definitions and instructions, can you interpret correctly and manipulate accordingly?

If you think about it, work is a lot more like this than “Oh, here are two linear equations; can you solve for x?” So it makes sense that they would want to emphasize questions of a more practical nature.

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Everything you need to know about the New Official Guides, Part 2

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OG2016-Ads-2The new Official Guide books are here! Last time, we talked about the Quant portion of The Official Guide for GMAT, aka the OG or the big book. In this installment, we’ll discuss the Verbal section of the big book. Later installments will talk about the Quant Review and Verbal Review (the smaller books), as well as question lists for the new questions.

(Note: I have not yet had time to analyze the IR problems that come via your special online access. I’ll get to that soon—the quant and the verbal are higher priority!)

Part 1 included an overview of the changes to the whole book; I’ve included that overview here as well (the next section!), in case you’re reading this installment first. (The only difference is one sentence in the first paragraph.)

What’s new in OG 2016?

Approximately 25% of the questions are brand new, and there are some beauties in the mix. As I worked through the problems, I marveled anew at the skill with which the test writers can produce what I call elegant problems. On the verbal side, I loved how some of the new questions wove meaning into the issue of Sentence Correction; if you have been focusing on grammar and shortchanging meaning, you’re definitely going to need to change your approach.

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Everything you need to know about the New Official Guides, Part 1

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OG2016-Ads-2The new Official Guide books are here! Aren’t you excited?!?

Okay, I realize that most people probably aren’t as excited as I am. But there are still some interesting and useful things to know about these new books as you get ready to take the GMAT. So let’s talk about it!

In this installment, I’ll discuss additions and changes to quant sections for The Official Guide for GMAT® Review 2016, aka the OG or the big book. Keep an eye out for later installments, in which I’ll discuss the verbal section of the big book, as well as the Quantitative Review and Verbal Review books. I’ll also be providing you with a list of the new questions, in case you decide to study from both the 2015 and 2016 editions.

If you haven’t already bought your official guide books, then do buy these latest editions—sure you might be able to get a discount on the 2015 editions, but since you have to spend money anyway, you might as well work from the latest and greatest.

If you have already bought the older editions and are debating whether to buy the new ones, too, then you’ve got a decision to make. On the one hand, there are a lot of great new questions in the 2016 editions. On the other, the 2015 edition already has a ton of problems; you may not need even more. If it were me, I’d wait until I’d used up the ones in the materials I already have. If I still felt that I needed more beyond that, then I’d consider getting one or more of the new books.

What’s new in OG 2016?

Approximately 25% of the questions are brand new, and there are some beauties in the mix. As I worked through the problems, I marveled anew at the skill with which the test writers can produce what I call elegant problems. On the quant side, I saw example after example in which the problem can be solved with little to no computation as long as you can decode and understand the fundamental concept underlying the problem—that’s the real test-taking skill!

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New Edition of GMAT Advanced Quant: Study the Hardest Quant Questions

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GMAT Advanced Quant Now AvailableI am super excited to announce a new edition of our GMAT Advanced Quant Strategy Guide! We worked hard on this book all of last year (yes, it takes a long time make a book!) and we hope that you find it to be a valuable addition to your GMAT preparation.

What is the Advanced Quant guide?

We created the Advanced Quant (AQ) guide a few years ago for people who want to get a top score (50 or 51) on the quant section of the GMAT.

Here’s the interesting thing: it doesn’t teach you a bunch of really hard math concepts. We teach all of those concepts in our five regular strategy guides (Algebra, Geometry, Word Problems, Number Properties, and Fractions, Decimals, & Percents). Instead, the AQ guide teaches you the next level of GMAT study: how to think your way through really hard quant problems.

What’s new in this edition?

A bunch of things! First, there are more than 50 brand-new, extremely hard problems. We actually removed some old ones that we thought were a bit too easy and replaced them with harder problems.

But that’s not all. Since the entire point of this book is how to solve better, we’ve updated some solutions to existing problems because we’ve discovered an even more efficient or effective way to solve.

We’ve also introduced a new organization method for working your way systematically through any quant problem. We’ve added or expanded lessons on test-taking strategies, such as testing cases on both problem solving and data sufficiency problems.

One student, who has already used the old version of AQ, asked whether we would provide a list indicating which questions are the new ones. I told him no. Not because I’m lazy or I don’t care, but because you don’t need such a list! If you’ve already tried the first edition and want to try this one, too, just start going through the book. If you hit a problem you remember, feel free to skip it. (Although maybe this is a chance to see if you really do remember what to do…and remember that we may offer an updated solution that you haven’t seen before.) If you hit a problem you don’t remember, then it doesn’t matter whether it’s old or new. It’s new to you right at this moment!

Who should use the AQ Strategy Guide?

First, you should have mastered most (if not all) of the material in our five main quant Strategy Guides. As I mentioned earlier, we do not actually teach you that math in this guide. We assume that you already know it.

As a general rule, we recommend that people avoid using this book until they’ve gotten to a score of at least 47 on a practice CAT. (Seriously. We say so right in the first chapter of the book!) I might let that slide a bit for certain students, but someone scoring below 45 likely does not have the underlying content knowledge needed to make the best use of the Advanced Quant lessons.

Note that, from an admissions standpoint, you may not necessarily need to score higher than 47. The scoring scale tops out at 51, so 47 is already quite high. Do a little research to see what you may need for the specific schools to which you plan to apply.

All right, that’s all I’ve got for you today. I’d love to hear what you think about the book. Which problem is your favorite? And which one do you think is the absolute hardest, most evil thing we could have given you? Let us know in the comments!

Check out our store to learn more about the new GMAT Advanced Quant Strategy Guide.

GMAT Problem Solving Strategy: Test Cases

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3-19-TestCasesIf you’re going to do a great job on the GMAT, then you’ve got to know how to Test Cases. This strategy will help you on countless quant problems.

This technique is especially useful for Data Sufficiency problems, but you can also use it on some Problem Solving problems, like the GMATPrep® problem below. Give yourself about 2 minutes. Go!

* “For which of the following functions f is f(x) = f(1 – x) for all x?

(A) f(x) = 1 – x
(B) f(x) = 1 – x2
(C) f(x) = x2 – (1 – x)2
(D) f(x) = x2(1 – x)2
(E)  f(x) = x / (1 – x)”

 

Testing Cases is mostly what it sounds like: you will test various possible scenarios in order to narrow down the answer choices until you get to the one right answer. What’s the common characteristic that signals you can use this technique on problem solving?

The most common language will be something like “Which of the following must be true?” (or “could be true”).

The above problem doesn’t have that language, but it does have a variation: you need to find the answer choice for which the given equation is true “for all x,” which is the equivalent of asking for which answer choice the given equation is always, or must be, true.
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When Your High School Algebra is Wrong: How the GMAT Breaks Systems of Equations Rules

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2-17-HighSchool-2If you have two equations, you can solve for two variables.

This rule is a cornerstone of algebra. It’s how we solve for values when we’re given a relationship between two unknowns:

If I can buy 2 kumquats and 3 rutabagas for $16, and 3 kumquats and 1 rutabaga for $9, how much does 1 kumquat cost?

We set up two equations:

2k + 4r = 16

3k + r = 9

Then we can use either substitution or elimination to solve. (Try it out yourself; answer* below).

On the GMAT, you’ll be using the “2 equations à 2 variables” rule to solve for a lot of word problems like the one above, especially in Problem Solving. Be careful, though! On the GMAT this rule doesn’t always apply, especially in Data Sufficiency. Here are some sneaky exceptions to the rule…

2 Equations aren’t always 2 equations
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Tackling Max/Min Statistics on the GMAT (part 3)

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2-12-MinMaxP3

Welcome to our third and final installment dedicated to those pesky maximize / minimize quant problems. If you haven’t yet reviewed the earlier installments, start with part 1 and work your way back up to this post.

I’d originally intended to do just a two-part series, but I found another GMATPrep® problem (from the free tests) covering this topic, so here you go:

“A set of 15 different integers has a median of 25 and a range of 25. What is the greatest possible integer that could be in this set?

“(A) 32

“(B) 37

“(C) 40

“(D) 43

“(E) 50”

Here’s the general process for answering quant questions—a process designed to make sure that you understand what’s going on and come up with the best plan before you dive in and solve:

gmat1

Fifteen integers…that’s a little annoying because I don’t literally want to draw 15 blanks for 15 numbers. How can I shortcut this while still making sure that I’m not missing anything or causing myself to make a careless mistake?

Hmm. I could just work backwards: start from the answers and see what works. In this case, I’d want to start with answer (E), 50, since the problem asks for the greatest possible integer.
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Tackling Max/Min Statistics on the GMAT (Part 2)

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minLast time, we discussed two GMATPrep® problems that simultaneously tested statistics and the concept of maximizing or minimizing a value. The GMAT could ask you to maximize or minimize just about anything, so the latter skill crosses many topics. Learn how to handle the nuances on these statistics problems and you’ll learn how to handle any max/min problem they might throw at you.

Feel comfortable with the two problems from the first part of this article? Then let’s kick it up a notch! The problem below was written by us (Manhattan Prep) and it’s complicated—possibly harder than anything you’ll see on the real GMAT. This problem, then, is for those who are looking for a really high quant score—or who subscribe to the philosophy that mastery includes trying stuff that’s harder than what you might see on the real test, so that you’re ready for anything.

Ready? Here you go:

“Both the average (arithmetic mean) and the median of a set of 7 numbers equal 20. If the smallest number in the set is 5 less than half the largest number, what is the largest possible number in the set?

“(A) 40

“(B) 38

“(C) 33

“(D) 32

“(E) 30”

 

Out of the letters A through E, which one is your favorite?

You may be thinking, “Huh? What a weird question. I don’t have a favorite.”

I don’t have one in the real world either, but I do for the GMAT, and you should, too. When you get stuck, you’re going to need to be able to let go, guess, and move on. If you haven’t been able to narrow down the answers at all, then you’ll have to make a random guess—in which case, you want to have your favorite letter ready to go.

If you have to think about what your favorite letter is, then you don’t have one yet. Pick it right now.

I’m serious. I’m not going to continue until you pick your favorite letter. Got it?

From now on, when you realize that you’re lost and you need to let go, pick your favorite letter immediately and move on. Don’t even think about it.
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Tackling Max/Min Statistics on the GMAT (Part 1)

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1-20-StatisticsBlast from the past! I first discussed the problems in this series way back in 2009. I’m reviving the series now because too many people just aren’t comfortable handling the weird maximize / minimize problem variations that the GMAT sometimes tosses at us.

In this installment, we’re going to tackle two GMATPrep® questions. Next time, I’ll give you a super hard one from our own archives—just to see whether you learned the material as well as you thought you did. :-)

Here’s your first GMATPrep problem. Go for it!

“*Three boxes of supplies have an average (arithmetic mean) weight of 7 kilograms and a median weight of 9 kilograms. What is the maximum possible weight, in kilograms, of the lightest box?

“(A) 1

“(B) 2

“(C) 3

“(D) 4

“(E) 5”

When you see the word maximum (or a synonym), sit up and take notice. This one word is going to be the determining factor in setting up this problem efficiently right from the beginning. (The word minimum or a synonym would also apply.)

When you’re asked to maximize (or minimize) one thing, you are going to have one or more decision points throughout the problem in which you are going to have to maximize or minimize some other variables. Good decisions at these points will ultimately lead to the desired maximum (or minimum) quantity.

This time, they want to maximize the lightest box. Step back from the problem a sec and picture three boxes sitting in front of you. You’re about to ship them off to a friend. Wrap your head around the dilemma: if you want to maximize the lightest box, what should you do to the other two boxes?

Note also that the problem provides some constraints. There are three boxes and the median weight is 9 kg. No variability there: the middle box must weigh 9 kg.

285 image 1The three items also have an average weight of 7. The total weight, then, must be (7)(3) = 21 kg.

Subtract the middle box from the total to get the combined weight of the heaviest and lightest boxes: 21 – 9 = 12 kg.

The heaviest box has to be equal to or greater than 9 (because it is to the right of the median). Likewise, the lightest box has to be equal to or smaller than 9. In order to maximize the weight of the lightest box, what should you do to the heaviest box?

Minimize the weight of the heaviest box in order to maximize the weight of the lightest box. The smallest possible weight for the heaviest box is 9.

If the heaviest box is minimized to 9, and the heaviest and lightest must add up to 12, then the maximum weight for the lightest box is 3.

The correct answer is (C).

Make sense? If you’ve got it, try this harder GMATPrep problem. Set your timer for 2 minutes!

“*A certain city with a population of 132,000 is to be divided into 11 voting districts, and no district is to have a population that is more than 10 percent greater than the population of any other district. What is the minimum possible population that the least populated district could have?

“(A) 10,700

“(B) 10,800

“(C) 10,900

“(D) 11,000

“(E) 11,100”

Hmm. There are 11 voting districts, each with some number of people. We’re asked to find the minimum possible population in the least populated district—that is, the smallest population that any one district could possibly have.

Let’s say that District 1 has the minimum population. Because all 11 districts have to add up to 132,000 people, you’d need to maximize the population in Districts 2 through 10. How? Now, you need more information from the problem:

“no district is to have a population that is more than 10 percent greater than the population of any other district”

So, if the smallest district has 100 people, then the largest district could have up to 10% more, or 110 people, but it can’t have any more than that. If the smallest district has 500 people, then the largest district could have up to 550 people but that’s it.

How can you use that to figure out how to split up the 132,000 people?

In the given problem, the number of people in the smallest district is unknown, so let’s call that x. If the smallest district is x, then calculate 10% and add that figure to x: x + 0.1x = 1.1x. The largest district could be 1.1x but can’t be any larger than that.

Since you need to maximize the 10 remaining districts, set all 10 districts equal to 1.1x. As a result, there are (1.1x)(10) = 11x people in the 10 maximized districts (Districts 2 through 10), as well as the original x people in the minimized district (District 1).

The problem indicated that all 11 districts add up to 132,000, so write that out mathematically:

11x + x = 132,000

12x = 132,000

x = 11,000

The correct answer is (D).

Practice this process with any max/min problems you’ve seen recently and join me next time, when we’ll tackle a super hard problem.

Key Takeaways for Max/Min Problems:

(1) Figure out what variables are “in play”: what can you manipulate in the problem? Some of those variables will need to be maximized and some minimized in order to get to the desired answer. Figure out which is which at each step along the way.

(2) Did you make a mistake—maximize when you should have minimized or vice versa? Go through the logic again, step by step, to figure out where you were led astray and why you should have done the opposite of what you did. (This is a good process in general whenever you make a mistake: figure out why you made the mistake you made, as well as how to do the work correctly next time.)

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

GMAT Data Sufficiency Strategy: Test Cases

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DS StrategyIf you’re going to do a great job on Data Sufficiency, then you’ve got to know how to Test Cases. This strategy will help you on countless DS problems.

 

Try this GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!

* “On the number line, if the number k is to the left of the number t, is the product kt to the right of t?

“(1) t < 0

“(2) k < 1”

 

If visualizing things helps you wrap your brain around the math (it certainly helps me), sketch out a number line:

GMAT_Chart

k is somewhere to the left of t, but the two actual values could be anything. Both could be positive or both negative, or k could be negative and t positive. One of the two could even be zero.

The question asks whether kt is to the right of t. That is, is the product kt greater than t by itself?

There are a million possibilities for the values of k and t, so this question is what we call a theory question: are there certain characteristics of various numbers that would produce a consistent answer? Common characteristics tested on theory problems include positive, negative, zero, simple fractions, odds, evens, primes—basically, number properties.

“(1) t < 0

This problem appears to be testing positive and negative, since the statement specifies that one of the values must be negative. Test some real numbers, always making sure that t is negative.

Case #1:

t k Valid case? Is kt > t?
-1 -2 Valid: t < 0 and k < t 2 > -1? Yes.

Testing Cases involves three consistent steps:

First, choose numbers to test in the problem

Second, make sure that you have selected a valid case. All of the givens must be true using your selected numbers.

Third, answer the question.

In this case, the answer is Yes. Now, your next strategy comes into play: try to prove the statement insufficient.

How? Ask yourself what numbers you could try that would give you the opposite answer. The first time, you got a Yes. Can you get a No?

Case #2:

t k Valid case? Is kt > t?
-1 2 Invalid! k is not less than t!

 

Careful: this is where you might make a mistake. In trying to find the opposite case, you might try a mix of numbers that is invalid. Always make sure that you have a valid case before you actually try to answer the question. Discard case 2.

Case #3:

t k Valid case? Is kt > t?
-1 -5 Valid: t < 0 and k < t 5 > -1? Yes.

Hmm. We got another Yes answer. What does this mean? If you can’t come up with the opposite answer, see if you can understand why. According to this statement, t is always negative. Since k must be smaller than t, k will also always be negative.

The product kt, then, will be the product of two negative numbers, which is always positive. As a result, kt must always be larger than t, since kt is positive and t is negative.

Okay, statement (1) is sufficient. Cross off answers BCE and check out statement (2):

“(2) k < 1”

You know the drill. Test cases again!

Case #1:

k t Valid case? Is kt > t?
0 1 Valid: k < 1 and k < t 0 > 1? No.

 

You’ve got a No answer. Try to find a Yes.

Case #2:

k t Valid case? Is kt > t?
-1 1 Valid: k < 1 and k < t -1 > 1? No.

 

Hmm. I got another No. What needs to happen to make kt > t? Remember what happened when you were testing statement (1): try making them both negative!

In fact, when you’re testing statement (2), see whether any of the cases you already tested for statement (1) are still valid for statement (2). If so, you can save yourself some work. Ideally, the below would be your path for statement (2), not what I first showed above:

“(2) k < 1”

Case #1:

k t Valid case? Is kt > t?
-2 -1 Valid: k < 1 and k < t Same case, still Yes.

All you have to do is make sure that the case is valid. If so, you’ve already done the math, so you know that the answer is the same (in this case, Yes).

Now, try to find your opposite answer: can you get a No?

Case #2: Try something I couldn’t try before. k could be positive or even 0…

k t Valid case? Is kt > t?
0 1 Valid: k < 1 and k < t 0 > 1? No.

 

A Yes and a No add up to an insufficient answer. Eliminate answer (D).

The correct answer is (A).

Guess what? The technique can also work on some Problem Solving problems. Try it out on the following GMATPrep problem, then join me next week to discuss the answer:

* “For which of the following functions f is f(x) = f(1 – x) for all x?

“(A) f(x) = 1 – x

“(B) f(x) = 1 – x2

“(C) f(x) = x2 – (1 – x)2

“(D) f(x) = x2(1 – x)2

“(E) prob

Key Takeaways: Test Cases on Data Sufficiency

(1) When DS asks you a “theory” question, test cases. Theory questions allow multiple possible scenarios, or cases. Your goal is to see whether the given information provides a consistent answer.

(2) Specifically, try to disprove the statement: if you can find one Yes and one No answer, then you’re done with that statement. You know it’s insufficient. If you keep trying different kinds of numbers but getting the same answer, see whether you can think through the theory to prove to yourself that the statement really does always work. (If you can’t, but the numbers you try keep giving you one consistent answer, just go ahead and assume that the statement is sufficient. If you’ve made a mistake, you can learn from it later.)

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

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