In the past, we’ve talked about making story problems real. In other words, when the test gives you a story problem, don’t start making tables and writing equations and figuring out the algebraic solution. Rather, do what you would do in the real world if someone asked you this question: a back-of-the-envelope calculation (involving some math, sure, but not multiple equations with variables).

If you haven’t yet read the article linked in the last paragraph, go do that first. Learn how to use this method, then come back here and test your new skills on the problem below.

This is a GMATPrep® problem from the free exams. Give yourself about 2 minutes. Go!

* “Machines X and Y work at their respective constant rates. How many more hours does it take machine Y, working alone, to fill a production order of a certain size than it takes machine X, working alone?

“(1) Machines X and Y, working together, fill a production order of this size in two-thirds the time that machine X, working alone, does.

“(2) Machine Y, working alone, fills a production order of this size in twice the time that machine X, working alone, does.”

You work in a factory. Your boss just came up to you and asked you this question. What do you do?

In the real world, you’d never whip out a piece of paper and start writing equations. Instead, you’d do something like this:

I need to figure out the difference between how long it takes X alone and how long it takes Y alone.

Okay, statement (1) gives me some info. Hmm, so if machine X takes 1 hour to do the job by itself, then the two machines together would take two-thirds…let’s see, that’s 40 minutes…

Wait, that number is annoying. Let’s say machine X takes 3 hours to do the job alone, so the two machines take 2 hours to do it together.

What next? Oh, right, how long does Y take? If they can do it together in 2 hours, and X takes 3 hours to do the job by itself, then X is doing 2/3 of the job in just 2 hours. So Y has to do the other 1/3 of the job in 2 hours. Read more

Stop! Before you dive in and start calculating on a math problem, reflect for a moment. How can you set up the work to minimize the number of annoying calculations?

Try the below Percent problem from the free question set that comes with your GMATPrep® software. The problem itself isn’t super hard but the calculations can become time-consuming. If you find the problem easy, don’t dismiss it. Instead, ask yourself: how can you get to the answer with an absolute minimum of annoying calculations?

* ” The table above shows the results of a recent school board election in which the candidate with the higher total number of votes from the five districts was declared the winner. Which district had the greatest number of votes for the winner?

“(A) 1

“(B) 2

“(C) 3

“(D) 4

“(E) 5”

Ugh. We have to figure out what they’re talking about in the first place!

The first sentence of the problem describes the table. It shows 5 different districts with a number of votes, a percentage of votes for one candidate and a percentage of votes for a different candidate.

Hmm. So there were two candidates, P and Q, and the one who won the election received the most votes overall. The problem doesn’t say who that was. I could calculate that from the given data, but I’m not going to do so now! I’m only going to do that if I have to.

Let’s see. The problem then asks which district had the greatest number of votes for the winner. Ugh. I am going to have to figure out whether P or Q won. Let your annoyance guide you: is there a way to tell who won without actually calculating all the votes?

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We need to know a lot of different facts, rules, formulas, and techniques for the Quant portion of the test, but there are 4 math strategies that can be used over and over again, across any type of math—algebra, geometry, word problems, and so on.

Do you know what they are?

Try this GMATPrep® problem and then we’ll talk about the first of the 4 math strategies.

*If mv < pv < 0, is v > 0?

(1) m < p

(2) m < 0

All set? 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

In honor of the final season of Breaking Bad, we decided to put together our ultimate Breaking Bad GMAT quiz. Those of you who fall in the overlapping section of the “Breaking Bad Fan” “GMAT student” Venn diagram should test your skills below… yo!

1. Data Sufficiency

Does x+4 = Walter White?

(1) x+4 is the danger
(2) x+4 is the one who knocks

A. Statement (1) ALONE is sufficient, but statement (2) ALONE is not sufficient
B. Statement (2) ALONE is sufficient, but statement (1) ALONE is not sufficient
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient
D. EACH statement ALONE is sufficient
E. Statement (1) and (2) TOGETHER are NOT sufficient to answer the question asked, and additional data are needed

2. Discrete Quant

The front portion of Walter White’s Roof is a 7 ‘ by 15’ rectangle. If the diameter of a pizza is 22”, what is the approximate area of the shaded region of this diagram?

A. 13,600 inches sq.
B. 14,740 inches sq.
C. 15,120 inches sq.
D. 15,500 inches sq.
E. 16,640 inches sq.

3. Critical Reasoning

Today, Walter White will cook 100 pounds of methamphetamine.

This argument is flawed primarily because:

A. Cooking methamphetamine presents a moral dilemma for Walter White.
B. Walter White has to prioritize the needs of his wife and children and be a better father.
C. Walter has already paid for his cancer treatment and no longer needs to cook methamphetamine.
D. There is a fly in the laboratory.
E. He was told not to cook that day and is obeying his instructions.

4. Critical Reasoning

Hank’s collection of rocks includes over 400 different items. Hank’s rock collection is clearly the most impressive in New Mexico.

This argument is flawed primarily because:

A. Rock collections are not judged by the total number of rocks but by the rarity of each item included.
B. Rock collections are not impressive to anyone.
C. Hank’s rock collection is a metaphor and therefore cannot be judged against other rock collections.
D. Hank’s wife stole most of the rocks and it is therefore ineligible for any superlatives.
E. They aren’t rocks, they are minerals.

5. Discrete Quant

Walter Junior eats 3 eggs for breakfast every morning. Given that Walter Junior never misses breakfast, how many eggs does Walter Junior consume in March?

A. 60
B. 74
C. 82
D. 93
E. 107

Answers are after the jump…

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If you’ve read my previous post you know I got married very recently. When I asked my new wife the other day to name her favorite celebrity, she said Ryan Gosling; unfortunately I look nothing like him “ so I’m not quite sure where that leaves me. As a form of revenge I’ve decided to use Mr. Gosling to demonstrate some key insights in the commonly misunderstood topic of Weighted Average. Ryan will never forgive me!

For the purpose of this blog post let’s assume that Ryan Gosling made $10M per movie in 80% of his movies and $20M per movie in 20% of his movies. His average paycheck would have been $15M if his salary were distributed evenly between $10M and $20M “ but an 80-20 distribution means we’ll have to put a little more thought into the situation. If we want to know how much Mr. Gosling made on average per movie, we have no choice but to calculate the weighted average.

Some math lovers might use an algebraic formula to calculate the weighted average, but I believe using a visual approach for this calculation will drive a deeper level of understanding for us regular folks.

Use your intuition and try a visual approach

If I asked you for a range of the weighted average of Ryan Gosling’s paychecks, your intuition would probably suggest between $10M and $20M. You might even propose that the weighted average be closer to $10M than to $20M (since $10M has a heavier weight “ 80% vs. 20%). You would be absolutely correct!

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We’ve got another GMATPrep word problem on tap for today, but this one’s in the area of divisibility (number properties). These kinds of problems often include a lot of math vocab; we need to make sure both that we understand the precise words used and concepts being described and that we don’t forget or overlook any of the pieces.

Set your timer for 2 minutes and GO!

If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers?
(1) m is not divisible by 3.
(2) m is not divisible by 5.

Read more

In this article, we’re going to tackle a challenging GMATPrep problem solving question from the topic of Percents.  (The GMATPrep software can be downloaded for free at MBA.com)

Let’s start with the problem.

Set your timer for 2 minutes… and… GO!

*Before being simplified, the instructions for computing income tax in country R were to add 2 percent of one’s annual income to the average (arithmetic mean) of 100 units of country R’s currency and 1 percent of one’s annual income. Which of the following represents the simplified formula for computing the income tax, in country R’s currency, for a person in that country whose annual income is I?

Read more

This week, we’re going to tackle a challenging GMATPrep problem solving question from the topic of Rates & Work.

Let’s start with the problem. Set your timer for 2 minutes. and GO!

*Circular gears P and Q start rotating at the same time at constant speeds. Gear P makes 10 revolutions per minute, and gear Q makes 40 revolutions per minute. How many seconds after the gears start rotating will gear Q have made exactly 6 more revolutions than gear P?

(A) 6

(B) 8

(C) 10

(D) 12

(E) 15

Given info about two different gears, P and Q, we have to figure out something about how quickly they move relative to each other. In particular, we’re supposed to figure out when this is true: (# of Gear Q revolutions) = (# of Gear P revolutions) + 6.

Read more

About 2 years ago, one of our L.A. Instructors, Mike Kim, suggested that we provide a math curriculum  for students who want a refresher on fundamental math topics (e.g.  fractions, algebra, etc.).  We thought it was a fantastic idea.  Being an extraordinarily productive guy, Mike went on to author the Foundations of GMAT Math Workshops I and II which take place online (it turns out there are too many fundamental math topics to teach in one sitting).

Now, the Foundations of Math Workshops will be available for free to any Manhattan GMAT course student.  If you are a course student, you can simply go to the website and add the Foundations workshops to your account.  You will immediately receive access to dozens of practice problems in your student center as well as class recordings, and you can attend the next scheduled Foundations workshops live.

For non-students, the Foundations of Math Workshops will each be available for only $95.  Additionally, if you end up signing up for a course after taking the Workshops, we’ll credit you whatever you spent on the workshops, so they’ll essentially wind up being free for you too.

Remember, these workshops review foundational math topics such as algebra, basic geometry, fractions, etc.  They’re very useful if you need a refresher because you haven’t seen the math in a long while, but if you’re comfortable with the math already you can feel free to go straight to the Official Guides, Strategy Guides, etc.

P.S.  The Foundations of GMAT Math Book is due out this Fall, as Mike’s original idea is taking multiple forms to reach as many people as possible.