But in mathematics, seemingly basic topics often have broader applications. So let’s consider both simple and complex applications of remainders on the GMAT. The most straightforward scenario is for the question to ask what the remainder is in a given context. We’ll start by looking at an official Data Sufficiency question of moderate difficulty:

*What is the remainder when x is divided by 3?*

*1) The sum of the digits of x is 5*

*2) When x is divided by 9, the remainder is 2*

Pretty straightforward question. In Statement 1, we could approach by simply picking numbers. If the sum of the digits of x is 5, x could be 14. When 14 is divided by 3, the remainder is 2. Similarly, x could be 32. When 32 is divided by 3, the remainder will again be 2. Or x could be 50, and still, the remainder when x is divided by 3 will be 2. So no matter what number we pick, the remainder will always be 2. Statement 1 alone is sufficient.

Note that if we know the rule for divisibility by 3 – if the digits of a number sum to a multiple of 3, the number itself is a multiple of 3 – we can reason this out without picking numbers. If the sum of the digits of x were exactly 3, the remainder would be 0. If the sum of the digits of x were 4, then logically, the remainder would be 1. Consequently, if the sum of the digits of x were 5, the remainder would have to be 2.

Again, in Statement 2, we can pick numbers. We’re told that when x is divided by 9, the remainder is 2. To quickly generate a list of numbers that we might test, we can start with multiples of 9: 9, 18, 27, 36, etc. Then, we can add two to each of those multiples of 9 to get the following list of numbers: 11, 20, 29, 38, etc. All of these numbers will give us a remainder of 2 when divided by 9. Now we can test them. If x is 11, when x is divided by 3, the remainder will be 2. If x is 20, when x is divided by 3, the remainder will be 2. We’ll quickly see that the remainder will always be 2, so Statement 2 is also sufficient on its own. The answer to this question is D, either statement alone is sufficient. That’s not too bad.

But the GMAT won’t always be so conspicuous about what category of math it’s testing. Take this more challenging question, for example:

* **June 25, 1982 fell on a Friday. On which day of the week did June 25, 1987 fall. (Note: 1984 was a leap year.)*

* **A) **Sunday*

*B) **Monday*

*C) **Tuesday*

*D) **Wednesday*

*E) **Thursday*

If you’re anything like my students, it’s not blindingly obvious that this is a remainder question in disguise. But that is precisely what we’re dealing with. Consider a very simple case. Say that June 1 is a Monday, and I want to know what day of the week it will be 14 days later. Clearly, that would also be a Monday. And if I asked you what day of the week it would be 16 days later, you’d know that it would be a Wednesday – two days after Monday. Put another way – because we’re dealing with weeks, or increments of 7 – all we need to do is divide the number of days elapsed by 7 and then find the remainder in order to determine the day of the week. 16 divided by 7 gives a remainder of 2, so if June 1 is a Monday, 16 days later must be 2 days after Monday.

Suddenly the aforementioned question is considerably more approachable. From June 25, 1982 to June 25, 1983 a total of 365 days will pass. 365/7 gives a remainder of 1, so if June 25, 1982 was a Friday, June 25 1983 will be a Saturday. From June 25, 1983 to June 25, 1984, 366 days will pass because 1984 is a leap year. 366/7 gives a remainder of 2, so if June 25, 1983 was a Saturday, June 25, 1984 will be 2 days later, or Monday. We already know that in a typical 365 day year, the remainder will be 1, so June 25, 1985 will be Tuesday, June 25, 1986 will be Wednesday and June 25, 1987 will be Thursday, which is our answer.

Takeaway: the challenge of the GMAT isn’t necessarily that questions are asking you to do difficult math, but that it can be hard to figure out what the questions are asking you to do. When you encounter something that seems unfamiliar or strange, remind yourself that virtually every problem you encounter will involve the application of a concept considerably simpler than the nebulous wording the question might suggest.

*Official Guide questions courtesy of the Graduate Management Admissions Council.

Plan on taking the GMAT soon? We have GMAT prep courses starting all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*By David Goldstein, a Veritas Prep GMAT instructor based in Boston. You can find more articles by him here. *

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However, timing issues should not arise in the Quant section. Your reading speed has very little effect on the overall timing scheme because most of the time during the Quant section is spent in solving the question. So if you are falling short on time, it means the methods you are using are not appropriate. We have said it before and will say it again – most GMAT Quant questions can be done in under one minute if you just look for the right thing.

For example, of the four listed numbers below, which number is the greatest and which is the least?

2/3

2^2/3^2

2^3/3^3

Sqrt(2)/Sqrt(3)

Now, how much time you take to solve this depends on how you approach this problem. If you get into ugly calculations, you will end up wasting a ton of time.

2/3 = .667

2^2/3^2 = 4/9 = .444

2^3/3^3 = 8/27 = .296

Sqrt(2)/Sqrt(3) = 1.414/1.732 = .816

So we know that the greatest is Sqrt(2)/Sqrt(3) and the least is 2^3/3^3. We got the answer but we wasted at least 2-3 mins in getting it.

We can do the same thing very quickly. We know that the squares/cubes/roots etc of numbers vary according to where the numbers lie on the number line.

2/3 lies in between 0 and 1, as does 1/4.

The Sqrt(1/4) = 1/2, which is greater than 1/4, so we know that the Sqrt(2/3) will be greater than 2/3 as well.

Also, the square and cube of 1/4 is less than 1/4, so the square and cube of 2/3 will also be less than 2/3. So the comparison will look like this:

(2/3)^3 < (2/3)^2 < 2/3 < Sqrt(2/3)

That is all you need to do! We arrived at the same answer using less than 30 secs.

Using this technique, let’s solve a question:

Which of the following represents the greatest value?

(A) Sqrt(3)/Sqrt(5) + Sqrt(5)/Sqrt(7) + Sqrt(7)/Sqrt(9)

(B) 3/5 + 5/7 + 7/9

(C) 3^2/5^2 + 5^2/7^2 + 7^2/9^2

(D) 3^3/5^3 + 5^3/7^3 + 7^3/9^3

(E) 3/5 + 1 – 5/7 + 7/9

Such a question can baffle someone who believes in calculating everything. We know better than that!

Note that the base values in all the options are 3/5, 5/7 and 7/9. This should hint that we need to compare term to term and not the entire expressions. Also, all values lie between 0 and 1 so they will behave the same way.

Sqrt(3)/Sqrt(5) is the same as Sqrt(3/5). The square root of a number between 0 and 1 is greater than the number itself.

3^2/5^2 is the same as (3/5)^2. The square (and cube) of a number between 0 and 1 is less than the number itself.

So, the comparison will look like this:

(3/5)^3 < (3/5)^2 < 3/5 < Sqrt(3/5)

(5/7)^3 < (5/7)^2 < 5/7 < Sqrt(5/7)

(7/9)^3 < (7/9)^2 < 7/9 < Sqrt(7/9)

This means that out of (A), (B), (C) and (D), the greatest one is (A).

Now we just need to analyse (E) and compare it with (B).

The first term is the same, 3/5.

The last term is the same, 7/9.

The only difference is that (B) has 5/7 in the middle and (E) has 1 – 5/7 = 2/7 in the middle. So (E) is certainly less than (B).

We already know that (A) is greater than (B), so we can say that (A) must be the greatest value.

A quick recap of important number properties:

Case 1: N > 1

N^2, N^3, etc. will be greater than N.

The Sqrt(N) and the CubeRoot(N) will be less than N.

The relation will look like this:

… CubeRoot(N) < Sqrt(N) < N < N^2 < N^3 …

Case II: 0 < N < 1

N^2, N^3 etc will be less than N.

The Sqrt(N) and the CubeRoot(N) will be greater than N.

The relation will look like this:

… N^3 < N^2 < N < Sqrt(N) < CubeRoot(N) …

Case III: -1 < N < 0

Even powers will be greater than N and positive; Odd powers will be greater than N but negative.

The square root will not be defined, and the cube root of N will be less than N.

CubeRoot(N) < N < N^3 < 0 < N^2

Case IV: N < -1

Even powers will be greater than N and positive; Odd powers will be less than N.

The square root will not be defined, and the cube root of N will be greater than N.

N^3 < N < CubeRoot(N) < 0 < N^2

Note that you don’t need to actually remember these relations, just take a value in each range and you will know how all the numbers in that range behave.

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!*

*Karishma, a Computer Engineer with a keen interest in alternative Mathematical approaches, has mentored students in the continents of Asia, Europe and North America. She teaches the **GMAT** for Veritas Prep and regularly participates in content development projects such as this blog!*

**Essay 1:**

**What matters most to you, and why? (750 words)**

The dreaded Stanford open-ended essay prompt has been one of the most feared parts of the school’s application process for years. For many students the more open the prompt the higher the anxiety – couple this with the inherent pressure that results from applying to Stanford, and many students derail their chances of success before they even put pen to paper. Many students struggle with how to tackle this type of essay question and with Stanford, it’s best to follow the direction provided by the Admissions Committee.

The “what” of your essay is less important than the “why.” Stanford GSB, as much as any other program, truly wants to know who you are. So give them the chance by offering up some direct insight into who you are as a person. Introspection is key in this essay, and walking the AdComm through the “what” of the question, as well as why you are uniquely motivates by this “what”, will serve to humanize your candidacy and make your response more personal. Stanford strives to admit people, not just GMAT scores or GPAs, so make sure you let them into your world. Breakthrough candidates will utilize structured storytelling effects to craft a compelling narrative that brings the Stanford AdComm deep into the candidate’s world.

This essay honestly at its core is about getting to know you, so don’t miss the opportunity by trying to craft the perfect answer for what you feel the AdComm wants to read.

**Essay 2:**

**Why Stanford? (400 words)**

This is a typical “Why School X Question,” however, you will want to avoid the typical boilerplate response with Stanford and dive a bit deeper here. Think of this prompt in two parts: “Why MBA?” and “Why Specifically a Stanford MBA?” Be specific and connect your personal and professional development goals to the unique programs at Stanford that are relevant to your success. Breakthrough candidates will not only select clear, well-aligned goals, but will connect these goals with a personal passion that makes their candidacy feel bigger than just business. Now do not reach here, the more authentic this personal passion is the better it will connect with the AdComm, but for years Stanford has maintained a track record of looking for something a bit different in their candidates.

Just a few thoughts on the new essays from Stanford, hopefully this will help you get started. For more thoughts on Stanfords’s deadlines and essays, check out another post here.

If you are considering applying to Stanford GSB, download our Essential Guide to Stanford, one of our 14 guides to the world’s top business schools. Ready to start building your applications for Stern and other top MBA programs? Call us at 1-800-925-7737 and speak with an MBA admissions expert today. As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Dozie A. is a Veritas Prep Head Consultant for the Kellogg School of Management at Northwestern University. His specialties include consulting, marketing, and low GPA/GMAT applicants. You can read more of his articles here. *

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**1) 1**

1 may be the loneliest number but it’s also a very important number for divisibility! Every integer is divisible by 1, and the result of any integer x divided by 1 is just x (when you divide an integer by 1, it stays the same). On the GMAT, the fact that every integer is divisible by 1 can be quite important. For example, a question might ask (as at least one official problem does): Does integer x have any factors y such that 1 < y < x?

Because every integer is divisible by itself and 1, that question is really just asking, “Is x prime or not?” because if there is a factor y that’s between 1 and x, x is not prime, and there is not such a factor, then x is prime. That “> 1″ caveat in the problem may seem obtuse, but when you understand divisibility by 1, you can see that the abstract question stem is really just asking you about prime vs. not-prime as a number property. The concept that all integers are divisible by 1 may seem basic, but keeping it top of mind on the GMAT can be extremely helpful.

**2) 2**

It takes 2 to make a thing go right…in relationships and on the GMAT! A number is divisible by 2 if that number is even (and a number is even if it’s divisible by 2). That means that if an integer ends in 0, 2, 4, 6, or 8, you know that it’s divisible by 2. And here’s a somewhat-surprising fact: the number 0 is even! 0 is divisible by 2 with no remainder (0/2 = 0), so although 0 is neither positive nor negative it fits the definition of even and should therefore be something you keep in mind because 0 is such a unique number.

The GMAT frequently tests even/odd number properties, so you should make a point to get to know them. Because any even number is divisible by 2 (which also means that it can be written as 2 times an integer), an even number multiplied by any integer will keep 2 as a factor and remain even. So even x even = even and even x odd = even.

**3) 3**

It’s been said that good things come in 3s, and divisibility rules are no exception! The divisibility rule for 3 works much like a magic trick and is one that you should make sure is top of mind on test day to save you time and help you unravel tricky numbers. The rule: if you sum the digits of an integer and that sum is divisible by 3, then that integer is divisible by 3. For example, consider the integer 219. 2 + 1 + 9 = 12 which is divisible by 3, so you know that 219 is divisible by 3 (it’s 3 x 73).

This rule can help you in many ways. If you were asked to determine whether a number is prime, for example, and you can see that the sum of the digits is a multiple of 3, you know immediately that it’s not prime without having to do the long division to prove it. Or if you had a messy fraction to reduce and noticed that both the numerator and denominator are divisible by 3, you can use that rule to begin reducing the fraction quickly. The GMAT tests factors, multiples, and divisibility quite a bit, so this is a critical rule to have at your disposal to quickly assess divisibility. And since 1 out of every 3 integers is divisible by 3, this rule will help you out frequently!

**4) 4**

Presidential Election and Summer Olympics enthusiasts, be four-warned! You already know the divisibility rule for 4: take the last two digits of an integer and treat them as a two-digit number, and if that’s divisible by 4 so is the whole number. So for 2016 – next year and that of the next presidential election and Brazil Olympics – the last two-digit number, 16, is divisible by 4, so you know that 2016 is also divisible by 4.

If you fail to see immediately that a number is divisible by 4 given that rule, fear not! Being divisible by 4 just means that a number is divisible by 2 twice. So if you didn’t immediately see that you could factor a 4 out of 2016 (it’s 504 x 4), you could divide by 2 (2 x 1008) and then divide by 2 again (2 x 2 x 504) and end up in the same place without too much more work.

**5) 5**

Who needs only 5 fingers to divide by 5? All of us – divisibility by 5 is so easy you should be able to do it with one hand tied behind your back! If an integer ends in 5 or 0 you know that it’s divisible by 5 (and we’ll talk more about what extra fact 0 tells you in just a bit…).

**6) 6**

Your favorite character from the hit 1990′s NBC sitcom “Blossom” is also an easy-to-use divisibility rule! Since 6 is just the product of 2 and 3 (2 x 3 = 6), if a number meets the divisibility rules for both 2 (it’s even) and 3 (the sum of the digits is divisible by 3) it’s divisible by 6. So if you need to reduce a number like 324, you might want to start by dividing by 6, instead of by 2 or 3, so that you can factor it in fewer steps.

**7) 7**

Ah, magnificent 7. While there is a “trick” for divisibility by 7, 7 occurs much less frequently in divisibility-based problems (as do other primes like 11, 13, 17, etc.), so 7 is a good place to begin to think about a strategy that works for all numbers, rather than memorizing limited-use tricks for each number. To test whether a large number, such as 231, is divisible by 7, find an obvious multiple of 7 nearby and then add or subtract multiples of 7 to see whether doing so will land on that number. For 231, you should recognize that a nearby multiple of 7 is 210 (you know 21 is 7 x 3, so putting a 0 on the end of it just means that 210 is 7 x 30). Then as you add 7s to get there, you go to 217, then to 224, then to 231. So in your head you can see that 231 is 3 more 7s than 7 x 30 (which you know is 210), so 231 = 7 x 33.

**8) 8**

8 is enough! As you saw above with 4s and 6s, when you start working with non-prime factors it’s often easier to just divide out the smaller prime factors one at a time than to try to determine divisibility by a larger composite number in one fell swoop. Since 8 = 2 x 2 x 2, you’ll likely find more success testing for divisibility by 8 by just dividing by 2, then dividing by 2 again, then dividing by 2 a third time. So for a number like 312, rather than working through long division to divide by 8, just divide it in half (156) then in half again (78) then in half again (39), and you’ll know that 312 = 39 x 8.

**9) 9**

While “nein” may be German for “no,” you should be saying “yes” to divisibility by nine! 9 shares a big similarity with 3 in that a sum-of-the-digits rule applies here too. If you sum the digits of an integer and that sum is a multiple of 9, the integer is also divisible by 9. So, for example, with the number 729, because 7 + 2 + 9 = 18, you know that 729 is divisible by 9 (it’s 81 x 9, which actually is 9 to the 3rd power).

**10) 10**

We’ve saved the best for last! If a number ends in 0, it’s divisible by 10, giving you a great opportunity to make the math easy. For example, a number like 210 (which you saw above) lets you pull the 0 aside and say that it’s 21 x 10, which means that it’s 3 x 7 x 10.

Working with 10s makes mental (or pencil-and-paper) math quick and convenient, so you should seek out opportunities to use such numbers in your calculations. For example, look at 693: If you add 7, you get to a number that ends in two 0s (so it’s 7 x 10 x 10), meaning that you know that 693 is divisible by 7 (it’s 7 away from an easy multiple of 7) *and* that it’s 7 x 99 because it’s one less 7 than 7 x 100. Because the GMAT rewards quick mental math, it’s a good idea to quickly check for, “If I have to add x to get to the nearest 0, then does that give me a multiple of x?” (297 is 3 away from 300, so you know that 297 = 99 x 3). And since 10 = 2 x 5, it’s also helpful sometimes to double a number that ends in 5 (try 215, which times 2 = 430) to see how many 10s you have (43). That tells you that 215 = 43 x 5 because 215 x 2 = 43 x (2 x 5). Working with 10s can make mental math extremely quick – we’d rate numbers that end in 0 a perfect 10!

*Getting ready to take the GMAT? We have free online GMAT seminars running all the time. And, be sure to find us on Facebook and Google+, and follow us on Twitter!*

*By Brian Galvin*

I’d like to take a look at the other side of this equation and discuss some bad reasons for getting an MBA. Pursuing an MBA can be one of the toughest decisions a young professional has to make, so it is even more important to make it for the right reasons in order to avoid other potentially negative implications.

Consider the three aspects listed below as you decide whether you are at risk of pursuing an MBA for all of the wrong reasons:

**1) Money**

Is the only reason you are applying to business school to make more money? Now, there is nothing wrong with wanting to make more money – this is a legitimate goal for all working professionals – but if that is your primary goal, you may be setting yourself up for disappointment. This goal can be problematic because with business recruiting, there are no guarantees that you will actually make more money in the end. Often times, MBAs who solely focus on making more money target high paying industries such as management consulting and investment banking that may not necessarily fit with their true career development goals or personalities. Not reaching salary goals after business school is a common complaint from alums that pursue MBA degrees for non-holistic reasons.

**2) Prestige**

MBA programs are looking for the best and the brightest young professionals, and many applicants are pursuing the MBA programs with the best reputations. Of course, there is nothing wrong with pursuing top-tier programs, but when interest is more about prestige and arrogance and less about fit, potential issues can arise. My advice here is to focus on the highest ranked programs that align best to your development needs and represent a numerical and cultural fit.

**3) Boredom**

Are you just bored with your current job? This is a very common scenario for many applicants who see business school as a way out. MBA programs are looking for candidates who are running towards something, not away from something. If your interest in truly pursuing an MBA is not honest, no matter the program you attend you will continue to search for “what’s next.”

Utilize the tips above to help you decide if right now is the best time for you to apply to business school.

Considering applying to MBA programs? Call us at 1-800-925-7737 and speak with an MBA admissions expert today. As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

*Dozie A. is a Veritas Prep Head Consultant for the Kellogg School of Management at Northwestern University. His specialties include consulting, marketing, and low GPA/GMAT applicants. You can read more of his articles here. *

Firstly, there has been overall a pretty remarkable downward trend in application volume. This drop in number of applications has put a dent on revenues for schools as well as in the overall quality of the application pool. It makes sense: fewer applicants generally will mean fewer top applicants (not always true, but in this case, the percentage of good, better and best applicants seems to hold pretty constant no matter how many applicants there are in total). Neither result is attractive to these top schools.

One way to combat the drop in application volume is to try and reach outside the normal circles for folks who might think of applying to b-school who perhaps would not have in the past. Accepting the GRE instead of the GMAT is one way top schools have broadened their search. Because the GRE is widely considered a more “accessible” test for the general graduate school population, it has never in the past been given serious consideration by the b-schools, who are in agreement that the GMAT is a better indicator of b-school success. Granted, the GRE does not have a large enough statistical base to test its predictability for b-school success yet, but old traditions die hard.

Enter Harvard, Stanford and Wharton, the first and last bastion of high quality business school reputations. Certainly if you are Harvard, Stanford or Wharton, your reputation will not be dampened using any test for admission (even “guess how many fingers I am holding up behind my back?”) — the point is, no matter what these super elite schools do, their rankings will likely not suffer. So, they started accepting GRE scores in lieu of GMATs. This did indeed give them a broader look at those interested in graduate school and has enticed more students to choose b-school as their graduate education path. As could probably have been predicted, so goes H/S/W, so goes the rest of the b-school world, and sure enough, over the past several years, more and more schools have been quietly accepting GRE scores.

So which test should you use as part of your application package? If your target school accepts the GRE, should you use that instead of the (some argue more difficult) GMAT? This is indeed the question. In some respects, the GRE is a tempting alternative. For starters, it’s about $100 cheaper to take the test, which for some post-college, recession-damaged applicants, is real money. Additionally, the test is not quite as rigorous on the quantitative side, making it for some, a less punishing preparation process.

There is also the argument that it could help you stand out in the crowd, since with fewer applicants submitting GRE scores, you force yourself out of the general application pool and into a category which will require the admissions committee to consider you separately from the crowd. Is this true? The Admissions Director I spoke with said it makes no difference whether someone submits the GMAT or the GRE, but I argued that simply due to the new nature of the discussion, there will naturally be more attention drawn to applicants with GREs.

This could be simply a psychological phenomenon, and of course the risk is that the lack of reliable data out there with which to compare scores could put applicants in a no-man’s land without any real evidence of aptitude. At least with the GMAT, the scores are very well established and everyone knows what a 550 means vs. a 650 or 750. As more GRE scores show up in admissions committee evaluations, we will begin to establish some better standards for exactly what a good score is as compared to the GMAT, but as for now, it’s really anybody’s guess what that score should be.

The other challenge for b-schools who are now accepting the GRE is what to do with the scores when the time comes to tally statistics for rankings. The GMAC as well as the BW and US News rankings boards have indicated that schools need only list whether or not they accept the GRE, and are presently not required to report their average scores (which in the case of some schools, could be the average of as few as one or two applicants’ scores).

Again, as more data comes online, we may start seeing a dual category, with schools listing both their GMAT average and their GRE average. I wouldn’t bet on this, however. The same b-school traditions and history which established the GMAT in the first place will be hard to sway in another direction. The computer adaptability of the GMAT test and other technological advances it has made vs. the GRE is keeping it in a position of superiority for now.

In the final analysis, I would say that if the GMAT is kicking your tail, you might at least try your hand at the GRE, just to see if perhaps the test better meets with your abilities. If your target schools accept the GRE for admission and your score on the GRE is impressive, who knows? You might just be able to “slip in through the back door” while other applicants who are relying on mediocre GMAT scores get lost in the proverbial shuffle.

Applying to business school? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter.

*Bryant Michaels has over 25 years of professional post undergraduate experience in the entertainment industry as well as on Wall Street with Goldman Sachs. He served on the admissions committee at the Fuqua School of Business where he received his MBA and now works part time in retirement for a top tier business school. He has been consulting with Veritas Prep clients for the past six admissions seasons. See more of his articles here.*

**Essay 1:**

**What are you most proud of and why? How does it shape who you are today? (400 words)**

This is a typical “accomplishment” essay, and with the limited word count it would be wise to focus on one accomplishment in the most direct fashion possible.

Dig deep as you identify what topic to discuss as these types of open-ended questions give applicants an opportunity to really differentiate themselves from the competition. Breakthrough applicants will align their personal, professional, or academic stories around some of the relevant values expressed by the Ross MBA.

Don’t be afraid to select a topic that extends outside of your professional career. Many candidates will opt to go the professional route, so consider “zigging” when the rest “zag.” Remember admissions committees will be reading a lot of essays so stand out by allowing them to explore a topic a bit more unique then the mundane. Also, keep in mind that you will have time to talk about your professional career and highlight some of your past accomplishments via the second essay.

Finally, don’t think if your accomplishment does not involve $100 million in savings or climbing Mount Kilimanjaro that your response will not be well received. What makes your response to this question relevant is the impact this accomplishment had to YOU.

**Essay 2:**

**What is your desired career path and why? (400 words)**

This is a traditional “career goals” essay. This type of question should come as no surprise to any candidate applying to business school. In fact, your response to this question should involve what initially drove your interest in business school to begin with, so Ross will be expecting a pretty polished essay here.

Many candidates will write generic essays outlining their career goals that could be relevant to any MBA program. What will separate breakthrough candidates from the masses is how personalized the essay reads. Ross will be looking for you to combine your well thought out career goals with specifics on how you plan to utilize their program to reach these goals. Also, if relevant, connect your goals to an underlying passion you have for the role or industry. This will make your interest more tangible and highlight underlying elements of your personal story.

Just a few thoughts on the new batch of essays from Ross that should help you get started.

If you are considering applying to NYU Stern, download our Essential Guide to NYU Stern, one of our 14 guides to the world’s top business schools. Ready to start building your applications for Stern and other top MBA programs? Call us at 1-800-925-7737 and speak with an MBA admissions expert today. As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

The Basics:

A triangle has three sides and three angles. All the interior angles of a triangle add up to 180 degrees. In math speak : A + B + C = 180. This means if you have two angles of any triangle, you can always find the third (something that comes up frequently on the SAT). The largest side is opposite the largest angle and the smallest side is opposite the smallest angle.

Pythagorean Theorem:

This is only useful for right triangles, but right triangles are great on the SAT because they give you all the information needed to find the area of a triangle (which, of course, is ½ A *B, or ½ base * height). The pythagorean theorem states: A² + B² = C², which means if you have two sides of a right triangle, you can always find the third. Common right triangles that have easy to remember side ratios are triangles with a 3x-4x-5x relationship, and a 5x-12x-13x relationship. These Pythagorean triples are useful because if two of the sides of a right triangle have this side relationship, the third must follow suit. For example if two sides of a right triangle are 10 and 8, then the third side must be 6 {6-8-10 is the same as 3(2) – 4(2) – 5(2), hence the “x” in the paragraph above}.

Special Triangles:

Identifying these special triangles saves a step when doing the work of the Pythagorean theorem. An equilateral triangle, when split in half, becomes a 30 – 60 – 90 triangle, which has the side relationship shown above of X – X √3 – 2X, where X is the side opposite the 30 degree angle.

If you cut a square in half you get an isosceles, right triangle or a 45 – 45 – 90 triangle. This has the side relationship S – S – S√2, where is one of the sides opposite the 45 degree angle. These special triangles are given on the formula sheet of the SAT but it is very useful to commit them to memory, as it is quite time consuming to constantly refer to the formula sheet when you think you have encountered a special triangle.

An interesting characteristic of the sides of triangles is as follows:

If A=5 and B= 8, then 3 < C < 13. C must be between 3 and 13.In triangle ABC, |B-C| < A < |B+C|. This is to say, any side on a triangle must be between the absolute value of the sum and the difference of the other sides of the triangle.

Here is an example question that will use some triangle knowledge:

“A rectangular pasture has twelve equally spaced poles on its southern border, and sixteen equally spaced poles on its eastern border. A diagonal pathway from the eastern corner of the pasture to the center of the pasture is 40 ft. How many feet of fencing would be required to build a fence around the entire pasture?”

The first step is always to draw and label what is given. We are given a rectangular pasture that has twelve equally spaced poles on its southern border, and sixteen equally spaced poles on its eastern border. We label the distance between poles as X and we notice that we now have two sides of a triangle, one 12x and one 16x.

We remember the rules of Pythagorean triples and deduce that the diagonal of this triangle would have to be 20x. We then look for what the problem is asking us to find. We have to find the perimeter of the pasture, but all that is given is the length of a pathway from the eastern corner of the pasture to the center of the pasture.

AHA! We now know the length of HALF of the distance of the diagonal of the rectangular pasture! We also know that the FULL diagonal is 20x. We set up a simple equation to solve for X, remembering to double the length given from the center to the corner of the field.

2(40) = 20x

80 = 20x

x = 4

We then use our answer for X to find the length and width of the pasture and add everything together, remembering to multiply the length and width by two, to find the perimeter.

16 (4) = L = 64

12 (4) = W = 48

2W +2L = 2(64) + 2(48) = 224

Voila! The perimeter of the whole field is 224ft, so that is how much fencing will be needed.

Triangles are a very useful tool that is often used in tandem with other math shapes and concepts on the SAT. Through an understanding of triangles, one can develop a greater understanding of many difficult problems on the SAT.

Still need to take the SAT? We run a free online SAT prep seminar every few weeks. And, be sure to find us on Facebook and Google+, and follow us on Twitter!

*David Greenslade** is a Veritas Prep SAT instructor based in New York. His passion for education began while tutoring students in underrepresented areas during his time at the University of North Carolina. After receiving a degree in Biology, he studied language in China and then moved to New York where he teaches SAT prep and participates in improv comedy. Read more of his articles **here**, including **How I Scored in the 99th Percentile** and **How to Effectively Study for the SAT**.*

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Mini-stories are a great way to ensure you are capturing all of the most interesting and engaging aspects of your profile. The thought behind these mini-stories is that they should be designed to be independent of the essay questions asked by schools. Select stories that reflect the four dimensions of Leadership, Innovation, Teamwork and Maturity emphasized by many MBA programs that you can later apply to the specific essay questions asked from each school. The focus should be on highlighting your strongest and most in-depth personal, professional, and extra-curricular life experiences.

One of the most valuable aspects of creating mini-stories is that you don’t necessarily need any external information. The process is entirely about you and your background, so whether it is in the heart of application season or during a quieter period like the springtime, a candidate can create these valuable anecdotes.

When identifying these stories, don’t limit them to only one aspect of your profile. Include anecdotes from undergrad, extra-curricular activities, work experience, and personal life to develop a diverse array of talking points for potential essay responses. Aim for 5-8 mini-stories covering a diverse set of experiences.

With each story, include a short description and some supporting bullets describing some of the players involved and why the situation was transformative to you, focusing especially on its impact and what you learned from the experience. Remember, what is most important in these mini-stories is the “how” and not just the “what”. Think critically about your thought process in each scenario and the impact of your decisions.

The best essays combine multiple personal elements and touch on different characteristics and skills developed. For the sake of this exercise you want to briefly summarize how the main takeaways and characteristics are represented in the story. Once these mini-stories are completed and the essay topics are available, the next step is to match relevant stories to essay topics.

Utilize this structured and creative approach to most effectively tackle those daunting business school essays and create breakthrough essays that will stand out in the application process.

Considering applying to MBA programs? Call us at 1-800-925-7737 and speak with an MBA admissions expert today. As always, be sure to find us on Facebook and Google+, and follow us on Twitter!

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Broadly speaking, schools don’t really care how many times you take the test, and will only consider your highest score. Know that they won’t combine separate components into one score, but will consider your best overall score from one sitting as your “application score.”

Having said that, it is also generally agreed upon that schools don’t want to see applicants taking the exam a dozen times. This can communicate negative qualities to the admissions committee such as poor time management skills, slow learner syndrome, or good old fashioned poor judgment or misalignment of priorities.

So how many times? Three is the number we hear most often as acceptable or reasonable. Schools tend to think that if you haven’t achieved your max or close to it in three tries, you may be left behind in a typical b-school curriculum. Now, don’t panic if you have already taken the test four or five times. This is not the kind of thing that will get you rejected. If a candidate who has taken the GMAT five times is not admitted, I can almost guarantee it was for other reasons. Still, schools like to see folks practicing within conventions, just like they want to see that you can craft a one page resume or stay within the word count on an essay.

While the most common question on this topic is about how many times are too many, there can also be a big question around whether or not taking the exam only once is enough. This question must focus a bit more on one’s score. If you exceeded the average for the school to which you are applying, you’re “done with one.” But if your score came in under the average, or you felt you did worse than your true potential, you should consider re-taking. We don’t like to tell clients that the average GMAT score at a particular school is a mandatory hurdle, and actually point most often to the 80% range of scores at the schools as a better measure, but if you only take the test once and score noticeably below the average, it may be sending the message that you are not up for the challenge, or cannot manage your time well enough to prepare to do better.

In short, you should take the GMAT at least twice if your score is below your target school’s average, but no more than three times unless there are extenuating circumstances. If your score still falls short in your mind, it’s time to move on to other ways you can offset it in your application.

Applying to business school? Call us at 1-800-925-7737 and speak with an MBA admissions expert today, or click here to take our Free MBA Admissions Profile Evaluation! As always, be sure to find us on Facebook and Google+, and follow us on Twitter.