Arithmetic and the GMAT

Random pile of colourful plastic lettersThe branch of mathematics dealing with the basic manipulation of numbers is called “arithmetic.” On the GMAT, Arithmetic questions have to do with solving equations and expressions by moving variables from one side of the equation to the other.

Sometimes this involves conversion, or describing one variable in terms of another. Let’s look at an example from the OG:

Temperatures in degrees Celsius (C) can be converted to temperatures in degrees Fahrenheit (F) by the formula F = 9/5*C + 32. What is the temperature at which F = C?

(A) 20°
(B) (32/5)°
(C) 0°
(D) -20°
(E) -40°


The question is asking what is the temperature at which F = C. For this question if, F = C, then wouldn’t F = (9/5)C + 32 be the same thing as C = (9/5)C + 32?
If C = (9/5)C + 32, we can start to simplify by subtracting (9/5)C from both sides.
C – (9/5)C = 32 is the same thing as:
(9/9)C – (9/5)C = 32
(-4/5)C = 32

Let’s multiply both sides by 5:

-4C = 160
C = -40

The correct answer is (E).


Factorials (!) and Divisibility

exclamationIt’s amazing how something as simple as a (!) symbol can throw us all for a loop, even when really we’re just looking at a very simple divisibility question. This is my own question designed to mimic a GMATPrep question.

Start by setting a timer for 2-minutes and try this one on your own, then scroll down for the explanation!

Which of the following is an integer?

I. 10! / 3!
II. 9! / 8!
III. 13! / 11! 5!

A) I only
B) II only
C) III only
D) I and II only
E) I, II, and III


If the result of a fraction is an integer that means that what is in the denominator divides evenly into what is in the numerator. The question for each of these Roman numerals becomes: will the denominator go evenly into the numerator?

Since we know that 10! = 10 x 9 x 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1, and 3! = 3 x 2 x 1, it is obvious that the denominator of Roman Numeral 1 will go evenly into its numerator.

This same logic can be applied with Roman Numeral 2. As long as the factorial in the numerator is larger than the factorial in the denominator, then we will get a resulting integer.

Roman Numeral 3 is more complex. If we start by cancelling out the 11! from both the numerator and the denominator, the resulting fraction becomes:

(13 x 12) / (5 x 4 x 3 x 2)

Since 4 x 3 = 12, we can cancel those values out:
13 / (5 x 2)

Now we are stuck. 13 is a prime number, so neither 5 nor 2 will divide evenly into it. The result will be a decimal.

The correct answer is (D).


Should You Take a Practice Test the Day Before Your Test?

When setting up a Study Schedule with students, I like to leave an open slot the week before the exam, so we can decide as we get closer to your GMAT test whether you should do another “last minute” CAT. Why? Because in my experience there is no hard and fast rule. Some of my students just need a break the two days before the exam to mentally “rest up,” while others seem to enjoy re-taking a GMATPrep 3 or 4 two days before just to move the flow of “official” questions front-and-center.

So what should YOU do? Ultimately, see how you feel the week of, and make your own decision. If you’re feeling burnt out or worried it might make your anxious, definitely avoid it. There’s nothing you’re really going to be able to cram in the 48 hours before the test that’s going to make that great a difference to your score. So the only benefit to a CAT that close to your exam is if you think of it like a prolonged runner’s stretch.

If you were to take a practice test right before, then I’d do it ONLY to keep your pacing “in shape” and your brain in the GMAT-space, and I’d still NOT suggest doing it the day/night before your exam but rather two days before. If you do decide this is the way to go, I’d suggest a GMATPrep re-take and NOT any new practice tests (such as one from Veritas or MGMAT). There’s no point in taking a brand new practice test if you can’t properly examine the errors, and whatever score that is churned out by the private test prep company could likely unnerve your or undermine your confidence.

If you can take the CAT with a sense of “play” and “muscle-flexing” then go for it, if it seems like a horrible stress nightmare that will lead to sleepless nights, then definitely avoid.

10 Ways to Beat the GMAT This Year!

Preparing for tests, especially the GMAT, is no easy task! In between filling out MBA applications, applying for college scholarships, and researching the Best Business Schools, you have to carve out several months for GMAT test prep. These free GMAT tips will help you jumpstart your GMAT test prep!

Create an Error Log. An Error Log is a spreadsheet designed to help you track your incorrect questions for later review. Add to it on an ongoing basis. You will want to re-take GMAT practice questions multiple times to make sure you do not get them incorrect a second or third time. This will improve your GMAT score more than you think! Free GMAT Error Logs are available online at GMAT websites such as Beat the GMAT and GMAT Club.

Practice online. The GMAT is an online exam, so to ace the GMAT you will need to become an expert at negotiating between the screen and your scratch pad. GMAT test prep books such as the OG, or those made by Kaplan, Powerscore, and MGMAT are excellent sources of GMAT practice questions, but make sure you also do a significant amount of studying for the GMAT online. Mimic the test-taking environment as best you can as you study. Websites such as Grockit and MGMAT offer six free GMAT practice tests with their membership or purchase of one of their books. Ideal for adjusting to an online format!

Learn your grammar. Success on the SC portion of the GMAT entirely depends on your ability to recognize the most-tested grammatical errors. Use a good English-grammar book or a reputable GMAT online SC resource to review the basics of subject-verb agreement, independent/dependent clauses, and grammatical construction.

Take full-length tests. The GMAT requires a great deal of stamina. Even if you have limited resources, most test-prep companies such as Knewton, MGMAT, Kaplan, etc. offer one free GMAT practice test online.

Understand why you get questions wrong. Some students believe that more questions answered = better scores on the GMAT. Fundamentally, answered a ton of GMAT practice questions will only lead to faster pacing, but without solid strategies and disciplined reviewing, your overall score will not improve. Don’t be a lazy reviewer!

Study in shorter blocks. Don’t burn yourself out as you aim for better GMAT scores. It’s better to study in shorter 2-3 blocks, taking frequent breaks to eat, stretch, and exercise, rather than to park yourself in front of your computer and books for 10 hours at a time. The GMAT takes commitment, but you don’t want to become a GMAT zombie.

Don’t neglect AWA. Read through the free GMAT list of essay topics for each AWA essay provided for free on You will want to practice writing at least 3 of each so that you are comfortable with the timing guidelines. Have a template in mind for each GMAT essay and get feedback from other GMAT students.

Take notes as you read RC passages. Keep it short and simple, but make sure to extract and write down the important information in each GMAT passage: topic, scope, author’s tone, function of each paragraph, and main idea. That way you already have predictions for most of the GMAT RC questions and you will save time by not having to constantly re-read the passage.

Use “12TEN” for Data Sufficiency. Instead of writing down ABCDE for the answer choices on your scratch pad. Use the acronym “12TEN” to represent each choice. T = together. E = either. N = neither. This will help you keep straight what each GMAT answer choice means, and allow you to cross off the options quickly and efficiently as you evaluate the statements.

Backsolve and Pick Numbers. Use these GMAT Quant strategies as much as possible on the more difficult GMAT Math practice questions. Remember that there is often more than one way to get the correct answer! Choose the method of least resistance.

GMAT Quant: Question of the Day!

Try Picking Numbers with the GMAT practice problem of the day!

Last year the price per share of Stock X increased by k percent and the earnings per share of Stock X increased by m percent, where k is greater than m. By what percent did the ratio of price per share to earnings per share increase, in terms of k and m?

A. k/m
B. (k – m)
C. [100 (k – m)]/ (100 + k)
D. [100 (k – m)]/(100 + m)
E. [100 (k – m)]/ (100 + k + m)

If the original price per share of Stock X = 100
Let’s say k = 20
New price per share = 120

Original earnings per share of Stock X = 100
Let’s say m = 5 (since k > m)
New earnings per share = 105

Old ratio of price/earnings = 100/100 = 1
New ratio of price/earnings = 120/105 = approx 1.14

The percent increase is approx 14%.

Plug in our numbers into the answer choices, and look for the choice that also yields 14%:

A. k/m = 20/5 = 4 too small

B. (k – m) = 20 – 5 = 15 too big

C. 100 (15) / 100 + 20 = 1500 / 120 = 12.5 too small

D. 100 (15) / 100 + 5 = 1500/105 = approx 14. CORRECT!

E. 100 (15) / 100 + 20 + 5 = 1500/125 = 12

The answer is (D).

Learnist: 7 Ways to Make Studying for the GMAT Fun!

(No, really!) Here’s how to dance, snack, and gamify your way to a 700+ GMAT score.

Tip #1 – Use Music As Motivation (Exhibit A: The USC Marshall School of Buiness doing the “Harlem Shake”)

In this video the MBA candidates of the Class of 2013 and Class of 2014 at the University of Southern California Marshall School of Business decided to do the Harlem Shake.

And while you may not want to waste a precious study-hour making your own Harlem Shake dance-video with your GMAT study group (but by all means, please feel free to do so!), you CAN and SHOULD use music as motivation while you study for the GMAT.

If you’re someone who needs to have background noise as you study, assign a genre of music to each GMAT question-type. Planning to do 20 minutes of Sentence Correction? It’s Britney Spears and Katy Perry! Moving on to Data Sufficiency? It’s Macklemore-time.

Check out Tips #2-7 on Learnist to learn more ways to make studying for the GMAT fun!

3 Ways of Looking at “Profit” Questions on the GMAT

As someone who is about to shell out hundreds of dollars in MBA application fees, you know that money makes the GMAT-world go round. Profit is an essential concept for any aspiring MBA admissions applicant. The GMAT tests this concept in both Problem Solving and Data Sufficiency questions in three main ways. Let’s examine the need-to-know formulas with three GMAT practice questions.

1. A firm increases its revenues by 10% between 2008 and 2009. The firm’s costs increase by 8% during this same time. What is the firm’s percent increase in profits over this period, if profits are defined as revenues minus costs?

(1) The firm’s initial profit is $200,000.

(2) The firm’s initial revenues are 1.5 times its initial costs.

In this question from Grockit, we can start with our most basic Profit formula:

Profit = Revenue – Cost

Using Statement (1), we can say that 200,000 = R – C.
(1.1)r – (1.08)c = 200,000(1 + x), where x equals the amount of the increase. We still do not know R and C so we can’t find x. Insufficient.

Using Statement (2), 1.5c – c = p and (1.1)(1.5)c – (1.08)c = (1 + x)P. Here we can simplify.

.5c = p

.57c = (1 + x)p
Without continuing to solve, we can see that we can solve for x using substitution. .57c = (1 + x)(.5c), and dividing both sides by c will cancel out that variable and allow us to isolate x. Statement 2 is sufficient. Now to a more challenging question!

2. A store purchased 20 coats that each cost an equal amount and then sold each of the 20 coats at an equal price. What was the stores gross profit on the 20 coats?

(1) If the selling price per coat had been twice as much, the store’s gross profit on the 20 coats would have been $2400.

(2) If the selling price per coat had been $2 more, the store’s gross profit on the 20 coats would have been $440.

This GMAT Prep question asks about gross profit.

Gross Profit = Selling price – Cost

For the value Data Sufficiency question, we need to know the price of each coat and the selling price of each coat. From the given information, we can use our known formula to set us the equation: P = 20 (s – c). So either we’ll need a value for s and a value for c, or we’ll need the value of (s – c).

Statement (1) tells us that $2400 = (20(2s – c)) or 2400 = 40s – 20c. We can divide both sides by 20 and simplify it to: 120 = 2s – c. We still don’t know s and c. Insufficient.

Statement (2) tells us that 440 = 20(s + 2 – c). Let’s simplify: 440 = 20s + 40 – 20c. 400 = 20s – 20c. 400 = 20 (s – c). 20 = s – c. Sufficient. Even though we didn’t solve for s and c separately, we were able to find the value of (s – c). Sometimes DS will surprise you!

3. If the cost price of 20 articles is equal to the selling price of 25 articles, what is the % profit or loss made by the merchant?

A. 25% loss
B. 25% profit
C. 20% loss
D. 20% profit
E. 5% profit

Profit/Loss % = (Sales Price – Cost Price) / Cost Price x 100

The question asks about % profit or loss. It tells us that 20c = 25s, or 4c = 5s. So the ratio of the sales price to the cost price is 4/5.

Let’s simplify our Profit/Loss % formula by dividing each term by the cost price:

Profit/Loss % = (S/C – C/C) x 100

P/L% = (S/C – 1) x 100
We know that S/C = 4/5 for this problem. So we can plug in and solve:

P/L% = (4/5 – 1) x 100

P/L% = (-1/5) x 100

P/L% = -20%. The answer is a 20% loss.