Articles published in Fractions, Decimals, Percents

Here’s How to do GMAT Unit Conversions Like a Pro


blog-metricsSometimes the whole point of a specific GMAT problem is to convert between miles and kilometers, or meters and centimeters. In other problems, you’ll need to do a unit conversion as part of a longer solution. It’s easy to mess up unit conversions, and the GMAT writers know this — they include them on the test in order to test your level of organization and your ability to double-check your work. Here’s how to add fast unit conversions to your repertoire of skills.   Read more

Three things to love about GMAT Roman numeral problems


blog-numeralsI. Roman numeral Quant problems aren’t a whole lot of fun.

II. A lot of my students choose to skip them entirely, which is much smarter than wasting five minutes wondering what to do!

III. However, it’s possible to turn this rare and tricky problem type into an opportunity.

Read on, and learn why many GMAT high-scorers love Roman numeral problems. Read more

Here’s why you should interleave your GMAT studies (and what that means)


Blog-InterleaveRecently, I wrote a post about how to get the most out of Official Guide (OG) problems during your studies. In that article, I discussed the concept of Interleaving your studies and I’ve got more to say on this strategy that’s of crucial importance to your studies.

What is Interleaving?

In a nutshell, interleaving is a way of mixing up your studies. For example, let’s say that you’re about to start studying the Fractions chapter of our Fractions, Decimals, & Percents (FDP) Strategy Guide. It’s only 8 pages long, so you should just read the whole thing straight through, right? (Note: if you actually have this guide,  pull it out right now and follow along below.) Read more

Manhattan Prep’s GMAT® study app is now available!


I am very excited to announce that our new GMAT® study app is available on both iOS and Android!

Download now!



Read more

GMAT Data Sufficiency: Ratio Stories – Part 2


Social-RatioStoriesRecently, we took a look at a story problem dealing with ratios, and I finished up by giving you a second problem to test your skills. How did you do?

If you haven’t already, try the GMATPrep® problem below and then we’ll talk about it. Give yourself about 2 minutes. Go! Read more

The Importance of Getting to No on the GMAT — Part 2


Last time, we talked about how crucial it is to develop the instinct to go for the “No” when taking the GMAT. If you haven’t read the first installment, do so right now, then come back here to learn more.

I left you with this GMATPrep® problem from the free exams.

“*If 0 <r< 1 <s< 2, which of the following must be less than 1?

“I. r/s

“II. rs

“III. sr

“(A) I only

“(B) II only

“(C) III only

“(D) I and II

“(E) I and III”

Let’s talk about it now!

Read more

The 4 Math Strategies Everyone Must Master, Part 1


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 four strategies.

* ” If mv < pv < 0, is v > 0?

“(1) m < p

“(2) m < 0”

All set?

How did you do the problem? Most quant questions have more than one possible approach and this one is no exception—but I want to use this problem to talk about a particular technique called Testing Cases.

This question is called a “theory” question: there are just variables, no real numbers, and the answer depends on some characteristic of a category of numbers, not a specific number or set of numbers. When we have these kinds of questions, we can use theory to solve—but that can get very confusing very quickly. Instead, try testing real numbers to “prove” the theory to yourself.

(Note: I chose a particularly tough question for this exercise; testing cases can also be useful and fast on easier questions!)

This problem gives one inequality:

“mv < pv < 0″

The test writers are hoping that you’ll say, “Oh, let’s just divide by v to get rid of it, so the equation is really m < p < 0.” But that’s a trap! Why?

When you divide an inequality by a negative, you have to flip the signs. But you don’t know whether v is positive or negative, so you don’t know whether to flip the signs! Never divide an inequality by a variable if you don’t know the sign of the variable.

The question itself contains a clue (two, actually!) pointing to this trap. The given inequality asks about “< 0” and the question also asks whether v > 0? Less than zero and greater than zero are code for “I’m testing you on positives and negatives.”
Read more

GMAT Challenge Problem Showdown: October 14, 2013


challenge problem
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 acdx, and y are positive integers such that ay < x and  is the lowest-terms representation of the fraction , then c is how much greater than d? (If  is an integer, let d = 1.)

(1)  is an odd integer.

(2) a = 4

Read more

GMAT Challenge Problem Showdown: September 30, 2013


challenge problem
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 (ab) can the fraction  be written as the sum ?

Read more

Ratios: Box ‘Em Up (Or Just Pour A Drink)


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

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),don't drink and derive 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:

Men Women Total
Ratio 3 2 5

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)


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:

Read more