We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:

For how many different pairs of positive integers (a, b) can the fraction  be written as the sum ?

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On the GMAT, you may see a 3 to 5 ratio expressed in a variety of ways:

3:5
3 to 5
x/y = 3/5
5x = 3y (Yes, that’s the same as the other 3. Think about it.)

In the real world, we encounter ratios in drink recipes more often than anywhere else (3 parts vodka, 5 parts cranberry), perhaps explaining why–after drinks that strong–we forget how to handle them.

Keep in mind: ratios express a “part to part” relationship, whereas fractions and percentages express a “part to whole” relationship. So the fraction of the above drink is 3/8 vodka (or 37.5% of the whole). Either way, hold off on mixing that drink until after this post.

I like to set up ratios using a “ratio box.” The box is a variant on the “Unknown Multiplier” technique from page 65 of our FDPs book, but it’s a nice way to visually manage ratios without resorting to algebra.

Let’s take the beginning of a typical ratio question:

“The ratio of men to women in a class is 3:2…”

Instead of doing anything fancy with variables, I just set up a tracking chart:

From this point alone, I have sufficient information to answer a bunch of questions.

-What fraction of the students are men? (3/5)

-What percent of the students are women? (40%)

-What is the probability of choosing a man? (3/5)

-etc.

However, I have nowhere near enough information to answer anything about the REAL numbers of students in this class. Suppose the GMAT were to add a little more information:

“The ratio of men to women in a class is 3:2. If there are 35 students in the class…”

Now we can calculate almost everything about the real numbers of people. First, make a bigger box with 3 lines. The unfilled box looks like this:

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We invite you to test your GMAT knowledge for a chance to win! Each week, we will post a new Challenge Problem for you to attempt. If you submit the correct answer, you will be entered into that week’s drawing for a free Manhattan GMAT Prep item. Tell your friends to get out their scrap paper and start solving!
Here is this week’s problem:

If a, b, and c are integers such that 0 < a < b < c < 10, is the product abc divisible by 3?

(1) If   is expressed as a single fraction reduced to lowest terms, the denominator is 200.

(2) c “ b < b “ a?

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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.

For every five hours of studying combinatorics-type questions, the average GMAT student increases their chances of being able to correctly answer a question type that is found only on the very difficult end of the GMAT spectrum. Meanwhile, the same student will have to compute hundreds of basic computations without the aid of a calculator. For students who know how to quickly do these computations, they are rewarded with extra minutes that can be spent double-checking their work and critically thinking about whether their answers make sense. As BenGMAT Franklin might say, a second saved is a second earned on the GMAT, but it doesn’t matter if those extra seconds come from being faster at doing combinatorics questions or quicker at computations. So check out these five math tricks, learn the ones that you like, and practice them daily to give yourself some extra time to finish off that 37th and final Quant question.

Note: like everything else on the GMAT, being able to do something and being able to do something QUICKLY are two different tasks. If you like any of the following math tricks, make sure you know it inside and out before you try using it during your test. Read more

I’ve spoken with multiple students lately who received a disappointing (lower than they were expecting) score on the Quant section and who all said that the Quant felt relatively easy or straightforward. How is that possible?

First of all, thinking that a test like the GMAT is easy is actually a warning sign: things probably are not going very well. If the test was going very well, then you’d be seeing some seriously hard—next to impossible—problems.

Second, the test writers are phenomenal at writing questions that don’t seem all that complicated but are in fact your worst nightmare. My worst nightmare is not an impossible question—I know I can’t do it, so I just pick and move on. My worst nightmare is a question that I think I can do, and I spend a decent chunk of time doing it, and then I get it wrong anyway—even though I’m sure I got it right! Read more

Most people don’t like weighted averages, and for good reason. The formula is complicated, and these often come in the form of story problems, which are hard to set up. We’re going to talk today about a couple of great little techniques to make these fast and easy well, easier anyway!

First, try this GMATPrep problem. Set your timer for 2 minutes. and GO!

*  A rabbit on a controlled diet is fed daily 300 grams of a mixture of two foods, food X and food Y. Food X contains 10 percent protein and food Y contains 15 percent protein. If the rabbit’s diet provides exactly 38 grams of protein daily, how many grams of food X are in the mixture?

 

(A) 100

(B) 140

(C) 150

(D) 160

(E) 200

Wow. I’m glad I don’t have to feed this rabbit. This sounds annoying. : )
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This week, we’re going to tackle a GMATPrep question from the quant side of things. We’ll tackle a medium-level question this week in order to learn how to master weighted average questions in general, and in the next article, we’ll try a very hard one “ just to see whether you learned the concept as well as you thought you did. : )

Before we begin, I want to mention that every weighted average problem I’ve seen on GMATPrep is a Data Sufficiency question. This doesn’t mean that they’ll never give us a Problem Solving weighted average problem, but it does seem to be the case that the test-writers are more concerned with whether we understand how weighted averages work than with whether we can actually do the calculations. So we’re going to work on that conceptual understanding today and then we’ll discuss a neat calculation shortcut next week (built on the same principles!), just in case we do need to solve.

Let’s start with a sample problem. Set your timer for 2 minutes. and GO!
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Given the statement, the ratio of men to women in the room is 3 to 5, how many men are in the room?

You probably recognize pretty quickly that it is not possible to answer the question above.  Just given a ratio, it is not possible to identify the actual number of men in the room.  At this point we know the number of men in the room must be a multiple of 3, but the actual number could be 3 or 3,000 (although I am not sure I have been in a room that large).

Along with ratios in their traditional form (3 to 5 or 3:5), there are other types of numbers that are ratios, slightly disguised

a) Fractions: The container is 2/3 full.

This statement is expressing that there are 2 full parts for every 3 total parts of the container (a ratio of 2 to 3).

b) Percentages: 33% of company employees have Master’s degrees.

This statement is expressing for every 33 employees with Master’s degrees there are 100 total employees (a ratio of 33 to 100).

c) Percentage or fractional increase: The company’s profits increased 25% (or ¼) from 2010 to 2011.

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Let me start off by saying that hard work and mastering each question topic is the best way to conquer the GMAT. There is no Up-Up-Down-Down-Left-Right-Left-Right B, A, Start cheat code that can replace months of intense studying. That said, getting a 700+ score on the GMAT sometimes means having a few tricks up your sleeves. Here’s a few strategies that I’ve found to be helpful with gaining a few extra points at the very top of the GMAT curve:

1) Know your PEMDAS and your SADMEP

 In other words, you have to know your parenthesis, exponents/roots, multiplication, division, addition, and subtraction, backwards and forwards. For as many students as I have worked with, I have yet to come across a student who can barely work through a multiplication table, yet still manages to consistently finish the quant portion of the GMAT. Even though you only need to answer 37 quantitative questions, this will entail hundreds of math calculations- calculations that far too many of us have left to the machines (I for one welcome our new calculator overlords). If the average straightforward calculation takes five seconds and a student sees two hundred of these calculations over an average test, that’s sixteen minutes and forty seconds of just doing simple arithmetic. And if it takes you twice as long to do each of those calculations, that’s going to take, umm, well, it’s…. it’s going to take a lot longer.

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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.

In a world where we are often carrying at least one device, if not multiple devices, that can complete calculations, there is little need to do calculations manually. For this reason, the lack of a calculator on the GMAT Quantitative section is a significant point of concern—or perhaps even fear—to many test takers, even some with strong quantitative skills. That brings me to some good and some bad news for prospective GMAT takers. Read more