Here’s the problem again; if you didn’t read the first article and try the problem already, then try this problem now (2 minutes):

*A contractor combined x tons of gravel mixture that contained 10 percent gravel G, by weight, with y tons of a mixture that contained 2 percent gravel G, by weight, to produce z tons of a mixture that was 5 percent gravel G, by weight. What is the value of x?

(1) y = 10
(2) z = 16

After trying the problem, checking the answer, and reading and understanding the solution (read the original article, linked above), I try to answer these questions:

1. Did I know WHAT they were trying to test?

Was I able to CATEGORIZE this question by topic and subtopic? By process / technique? If I had to look something up in my books, would I know exactly where to go?

• The question is a Data Sufficiency question from the Statistics chapter of my Word Translations book. It’s testing the concept of average (arithmetic mean) and, more specifically, it’s testing the concept of weighted average. The problem never mentions the word “average” but I figured this out because the problem talks about 2 sub-groups that are combined in some way to make a 3rd overall group, or mixture of the original 2 sub-groups.

Did I COMPREHEND the symbols, text, questions, statements, and answer choices? Can I comprehend it all now, when I have lots of time to think about it? What do I need to do to make sure that I do comprehend everything here? How am I going to remember whatever I’ve just learned for future?

• I noticed that the problem has three variables: x, y, and z. It asks me to solve for the value of x. One of the statements gives me the value for y and the other gives me the value for z. I’m already thinking E is probably not the right answer (think about why before you keep reading – I’ll explain this under the “Other Strategies” question, below).

Did I understand the actual CONTENT (facts, knowledge) being tested?

• What kind of average is this problem discussing? Regular average / mean is characterized by the formula A = S/n, where A is the average of the set, S is the sum of the items in the set, and n is the number of items in the set. Is this problem testing “regular” averages? Let’s see: a “regular” average of 10% gravel and 2% gravel would be (10+2) /2 = 6. But the problem says the resulting mixture is 5% gravel, not 6% gravel – so this isn’t a “regular” average.

• That means this problem must be about the more complicated weighted average. In a weighted average, some of the elements are weighed, or counted more heavily, than other elements, so the calculation has to take that into account. (And I have to know how to do that… more on that later.)

2. How well did I HANDLE what they were trying to test?

Did I choose the best APPROACH? Or is there a better way to do the problem? (There’s almost always a better way!) What is that better way? How am I going to remember this better approach the next time I see a similar problem?

• (See the original article, for a detailed discussion of the best approach. Here, I’ll pretend that I didn’t use the best approach.) Weighted average problems can be solved by using the weighted average formula, which is what I tried to do. I got into trouble with it though – I didn’t set it up properly and so I couldn’t finish it to see whether I could solve.

• There’s a shortcut solution method that I could have used, but I forgot about it when I was doing this problem. (See original article for this shortcut solution method.)

Did I have the SKILLS to follow through? Or did I fall short on anything?

• I ended up having to guess because I couldn’t solve the “official math” way and then I forgot to try the easier “shortcut” way. I’m going to redo this problem using the easier shortcut, and I’m also going to go find a couple of additional weighted average problems and do those with the easier shortcut way so that I can make sure that (a) I know how to do it this way, and (b) I remember / recognize when I can do it this way.

• I should still also learn how to do this using the “official math” weighted average formula, just in case I ever have to use the long way.

Did I make any careless mistakes? If so, WHY did I make each mistake? What habits could I make or break to minimize the chances of repeating that careless mistake in future?

• When I tried to use the “official” formula, I couldn’t remember exactly how to set it up, so I ended up setting it up with too many variables, and then of course I couldn’t solve. It’s data sufficiency, so knowing I can’t solve is sufficient… except that I knew I was doing something wrong because I couldn’t really remember the formula. I need to go and study that formula. I should make a flash card with “weighted average formula” on one side, and the couple of different ways the formula can be written on the other side. (Those different ways are listed in my Word Translations strategy guide.)

Am I comfortable with OTHER STRATEGIES that would have worked, at least partially? How should I have made an educated guess?

• I was pretty sure it wasn’t E because it looks like you can set up a three-variable equation, and then we’re supposed to solve for x. Each statement gives us only one of the two remaining variables, so it “looks like” it can’t be done unless you have both of the other variables… which you would for answer choice C. So, at the least, C does work and it’s not E.

• I ended up guessing C but, in hindsight, that’s a trap too. I could ask my 14-year-old niece: if you have an equation with three variables and you want to solve for one of those variables, what do you need to know? And she’d say “The other two variables.” (And then she’d probably think, “Duh, Aunt Stacey.”) This test isn’t for my 14-year-old niece, though, it’s for people who have already graduated from college. So that’s too easy. And that’s really interesting, because that means that you most likely CAN actually solve given just one statement. Each statement represents one of the two unknown variables, so if one works, it’s fairly likely that the other one works too… so I probably should have guessed D.

Do I understand every TRAP & TRICK that the writer built into the question, including wrong answers?

• See above – I think C and E are both trap answers on this one, and C is especially tempting.

3. How well did I or could I RECOGNIZE what was going on?

Did I make a CONNECTION to previous experience? If so, what problem(s) did this remind me of and what, precisely, was similar? Or did I have to do it all from scratch? If so, see the next bullet.

Can I make any CONNECTIONS now, while I’m analyzing the problem? What have I done in the past that is similar to this one? How are they similar? How could that recognition have helped me to do this problem more efficiently or effectively? (This may involve looking up some past problem and making comparisons between the two!)

• Yes, I did make a connection, but I also missed one. I did recognize that this was a weighted average problem even though it didn’t explicitly mention the word “average,” so I’m happy about that. I didn’t recognize, however, that I could have used a big shortcut that would have saved me a lot of time and frustration. I need to go study that shortcut, how to recognize it, how to use it, etc – and maybe make a couple of flash cards.

HOW will I recognize similar problems in the future? What can I do now to maximize the chances that I will remember and be able to use lessons learned from this problem the next time I see a new problem that tests something similar?

• I need to do everything I already described in my notes above. I’m also going to re-do this problem from scratch– actually make myself write out the best way to do it, alternate ways to do it, how to make a guess, and so on, so that I really remember the lessons. Then, because my big problem on this one was with recognizing that I could use a shortcut and then actually using it, I’m going to find other weighted average problems that I’ve already done in the past and practice: (1) knowing how to recognize that it’s a weighted average and that it qualifies for the “weighted average shortcut,” (2) working through the problem using that shortcut, and (3) thinking about how to make an educated guess. Then I’m going to do new weighted average problems as part of a mixed set of problems consisting of things I’ve messed up recently and other random things (so that I don’t know exactly what I’m getting for each problem) and see whether I can quickly recognize and apply what I just learned.

And that’s it! Note that, of course, the details above are specific to each individual person – such a write-up would be different for every single one of you, depending upon your particular strengths, weaknesses, and mistakes. Hopefully, though, this gives you a better idea of the way to analyze a problem. This framework also gives you a valuable way to discuss problems with fellow online students or in study groups – this is the kind of discussion that really helps to maximize scores.

* GMATPrep® question courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.

Without question, gaining admission at virtually any of the top schools in the third round is more challenging. When mbaMission interviewed J.J. Cutler, Director of Admissions at UPenn-Wharton, he informed us,

…our ability to make decisions in the third round is different than it is in the first round. So my advice is to always use the third round as an absolutely last resort…I think if you’re serious, and if it’s possible, you should apply in Round 1 or 2. Third round is—and we’re very clear about this on our Web site—just significantly less optimal for an applicant than Round 1 or Round 2.

Similarly, Northwestern Kellogg’s Assistant Dean and Director of Admissions Beth Flye told mbaMission,

I would strongly encourage (applicants to) apply in one of the first two rounds. Are we going to shun those who apply in the third round? No, not at all.

While we don’t have the space to go through each and every admissions officer comment we have on Round 3, the theme among them all is that the first and second rounds are generally preferable for a serious candidate. However, what is particularly important to note is Ms. Flye’s final comment: “Are we going to shun those who apply in the final round? No, not at all.” There is a definite difference between a preference—even a strong preference—and a rule that states “don’t bother applying.”

Indeed, Rose Martinelli, Chicago Booth’s associate dean for student recruitment and admissions, recently addressed the myth of the impossible third round (R3) in a blog post, telling readers,

Somewhere along the line, R3 inherited the reputation of being somewhat irrelevant in the overall admissions cycle…The truth is that R3 can be a bit more competitive simply because the majority of applications and acceptances will occur in Rounds One and Two.  However, I’d like to emphasize that a good portion of our class will be admitted from R3…

Ms. Martinelli then added, “R3 exists for a reason… Your dream school should be on your radar no matter what people ‘are saying’!” Indeed, the third round is not a practical joke that schools are playing on applicants. By the time Round 3 rolls around, most admissions committees have been inundated with applications and are exhausted. Yet, they continue to review new candidates and they still grant acceptances. Otherwise, they would just cancel the round and start their vacations. So if you find yourself unable to apply earlier than the third round, you don’t need to take a pass on the year. If you are a standout candidate, apply and see what happens…

Read other Admissions Myths Destroyed:

• Admissions Myths Destroyed: The “Right” Path
• Admissions Myths Destroyed: I Should Quit My Job for the GMAT
• Admissions Myths Destroyed: Title Trumps All!
• Admissions Myths Destroyed: Yikes, a Typo; I am Done!
• Admissions Myths Destroyed: I Must Have Gotten It Wrong!
• Admissions Myths Destroyed: I Have No International Experience
• Admissions Myths Destroyed: I Have a Gap!
• Admissions Myths Destroyed: I Must Interview with the AdCom!
• Admissions Myths Destroyed: Well, I Had My Chance on the GMAT…
• Admissions Myths Destroyed: Why Worried? I Served!

Sometimes an entire passage has a tone. Take this example:

As we approach Earth Day, it is an appropriate time to reflect on our duty to protect the vast natural resources of this country. My imperative today is to show that there are ways to foster economic growth without compromising a healthy, sustainable environment. This nation’s public lands are one of the greatest national resources. They serve as tourist destinations for millions of Americans and generate important activity for many small businesses. We cannot help but feel inspired at their beauty, and afraid of the damage that unsustainable resource-extraction could wreak upon them.

While drilling may be required to meet our energy needs, it must be managed in a way that will not destroy wildlife habitat and diminish the hunting, fishing and grazing opportunities. Even now, unwise use puts these wild places in jeopardy; the need to check this exploitation is pressing. The greedy and malicious see in federal lands a one-time opportunity to fatten their pockets. Allowing the barons of  oil and gas to run rampant will all but assure the destruction of irreplaceable national treasures.

This passage overall has a cautionary tone; it explicitly encourages readers to protect the natural resources against destruction and unsustainable use. The tone is also urgent; words like imperative, must, even now, and pressing help convey the sense that the author’s warnings must be heeded right away.

A single paragraph can also have a tone. The second paragraph of the passage above has an especially negative, critical tone. Members of the oil and gas industry are referred to as greedy and malicious, as barons looking to fatten their pockets. The description of these people as evil tycoons contributes to the author’s case that we need to protect public lands.

Even single words can have significance for tone. Indeed, the associations that individual words call up in readers are the building blocks of tone. Perhaps the most evocative word in the passage above is barons. Barons are generally regarded as cruel despots and heartless opportunists; this word carries strongly negative connotations.

You can find more helpful tips and GMAT Reading Comprehension practice questions here from Knewton.

Question

A circle is inscribed in an equilateral triangle, such that the two figures touch at exactly 3 points, one on each side of the triangle. Which of the following is closest to the percent of the area of the triangle that lies within the circle?

(A) 50%
(B) 55%
(C) 60%
(D) 65%
(E) 70%

Solution

First, draw a picture of the circle and triangle and make up good labels for all points.

We should add one more point: the center of the circle, which will also be the center of the triangle. Let’s call that point O.

In order to deal with the area of the circle, we’ll need a radius (with circles, it should always be your first instinct to draw in a radius). We’ll put in OZ.

Now, because both equilateral triangles and circles are regular, symmetrical figures, and because they’re lined up perfectly in this scenario, we can take advantage of “symmetry arguments.” For instance, it should be obvious that each of the points X, Y, and Z are the midpoints of their respective sides. You don’t need to prove this, nor do you want to under time constraints. Rather, on the exam you should look for regular, symmetrical figures to behave symmetrically, and points that seem like midpoints can actually be proven to be just that. Likewise, we can draw in AO, and we know that this line cuts angle BAC perfectly in half. If you’ve drawn the figure carefully, this conclusion should be apparent. (We almost have the Deathly Hallows here, for you Harry Potter fans).

Now, since any angles in an equilateral triangle is 60°, angle AOZ = 60°/Z = 30°. Moreover, angle AZO is 90° (a radius touches any tangent line, at 90°).

Thus, we know AOZ is 60°, and we have a 30-60-90 triangle. Let’s redraw that triangle by itself:

Now, let’s make up a convenient radius. Say OZ = 1. We quickly get the dimensions of triangle AOZ:

We can now compute the areas of each figure. First, the circle is .

The triangle is a little harder, but we’re almost there. Since AZ = , and Z is the midpoint of AC, we know that AC = .

If you know the formula for the area of an equilateral triangle in terms of its side length, you can plug in right now — or you can figure out the height. Let’s take the latter approach.

Since we know AO = 2, and OY = 1, we know that AY = 3 (again, we don’t need or want a rigorous proof that they form a straight line. Regular figures behave nicely!)

And again by symmetry, this tells us that BZ = 3 as well:

Now we can calculate the area of the triangle, which equals (½)bh = (½)()(3) = . (Incidentally, the area of an equilateral triangle in terms of its side length s is , which in this case gives )

Finally, we compute the ratio of the areas:

. We approximate: ≅ 3.1 and ≅ 1.7, so we get

(Excel gives the ratio as 60.46% to a couple more decimal places, so our approximation didn’t create much of an error).

The correct answer is (C) 60%.

If you get completely stuck on this problem, of course learn the method above. But a scrappy method that’s really not too bad is to draw the picture carefully and try to eyeball the answer. Since the answers only differ by 5%, this might only help you eliminate extremes, but that’s better than nothing. And incidentally, if you must guess at random on such a problem, in which you have to estimate a ratio of areas or lengths that you can draw reasonably approximately, guess toward the middle of the pack. The question writers will have a sequential lineup of answers, and it’s unlikely that the writers would put all the wrong answers on one side of the right answer, because you would be able to knock out the extreme wrong answer or answers more easily. In this case, you’d be unlikely to see the answers as (A) 60% (B) 65% (C) 70% (D) 75% (E) 80% or as (A) 40% (B) 45% (C) 50% (D) 55% (E) 60%.

Again, the correct answer is (C).

Special Announcement: Manhattan GMAT is now offering you a chance to win prep materials by solving the Challenge Problem. On our website, we will post a new question (without the answer) every week. Submit a solution to the problem, and if we pick your name out of those who answer correctly, you could win free prep material from Manhattan GMAT. To view the current question, simply visit our Challenge Problem Showdown.

Admissions officers will consider all of the pieces of your application holistically when making an admission decision.  But in terms of what YOU should focus your time and energy on at this point, focus on the pieces YOU CAN STILL CHANGE.

Your GPA/transcripts?  (For most:) already set in stone.  Your work experience?  Not much you can change there, unless you happen to get a promotion right now, or begin working on a new and exciting project just in time for applications.  Recommendations?  You have a limited amount of influence on these.  The two components of your application that you can STILL CHANGE, and therefore where you can maximize your time and effort: GMAT and application essays.

GMAT test-takers who score higher report studying more hours than lower-scorers, according to GMAC.  Preparation does make a difference—reviewing the math formulas and problems you may not have seen in years; reviewing grammar rules and logical thinking; learning how to approach these new data sufficiency questions; and most importantly, practicing on the computer in a timed, realistic testing environment.  Familiarizing yourself with computer adaptive testing strategy and training with full-length timed practice tests will go far in increasing your comfort level with the exam and allowing you to perform your best on test day.  Given how important the GMAT score can be for admission to top MBA programs, this is an area worth investing your time and resources in.

The application essays are the one component of your application where you create something FROM SCRATCH to represent who you are as a person.  You have the opportunity to convey what you will bring to the program, and what the program will do for you in the context of your career goals.  In some cases, the essays can make or break an admissions decision, and can balance out a weaker aspect elsewhere on the application.  Be sure to devote sufficient time to crafting these essays, something that many applicants unfortunately fail to do.  Admissions officers can tell when you threw something together at the last minute, and usually the quality of hastily written essays without much thought or effort will not stand up to competing applicants’ applications at top ranked schools.  Set aside time to brainstorm for your essays, to organize and plan them, to draft them (possibly multiple times), and to proofread and edit them.

Sample Argument:

The copy machine is broken. I need to photocopy a document, so I should buy a new copy machine.

Argument Analysis:

C: I should buy a new copy machine.

NOTE: “So” is a claim indicator and “should” is a strong word—two major tip-offs that this is our Conclusion (C). Another way to check is by using the “Why Test.” If we’ve correctly identified the Conclusion, we should be led logically to the Premises (P) if we ask the question, “WHY should I buy a new copy machine?” Because “the copy machine is broken” and because “I need to photocopy a document” are logical answers to this question. Thus, the “Why Test” shows us that we have indeed correctly identified the author’s Conclusion.

P1: The copy machine is broken. (See above NOTE; this is a stated fact in the Argument.)

P2: I need to photocopy a document. (See above NOTE; this is the other stated fact in the Argument.)

Now for the toughest part—identifying the Assumptions (A). The Conclusion that “I should buy a new copy machine” may not be the best solution in the world, but what things need to be true in order for this Argument to hang together/make sense? In other words, in coming up with the Argument’s Assumptions, you need to think of things that would make the Argument fall apart if they were shown to be false.

A1: The copy machine can’t be repaired. (If the copy machine could be repaired, it wouldn’t make any sense to buy a new one.)

A2: No other copy machines are available. (If another copy machine(s) was available, it wouldn’t make any sense to buy a new one.)

NOTE: That’s all. When you’re doing GMAT CR, always remember that you must accept the Premises as true, so you don’t need to consider external possibilities. Given that it’s true that “the copy machine is broken” and that “I need to photocopy a document,” these are the only two Assumptions necessary to the internal consistency of the Argument—i.e., these are the only two things that would make the Argument fall apart if they were shown to be false.

The key Premise is that “the copy machine is broken.” In finding the Assumptions, we want to stay within the topics implicit in that statement. The opposite of a broken copy machine is one that has been fixed (dealt with in A1) or one that works properly (dealt with in A2).

Appendix: Beyond the Scope of the Argument

Examples of issues that are irrelevant to the internal consistency of the Argument are things like why I need to copy a document, why I should bother copying a document at all, or why the copy machine is broken. (Notice that these are all “why” questions concerning the Premises–these questions are irrelevant because you must accept the Premises of the Argument.)

Examples of Assumptions that cover territory beyond the scope of the Argument include the following:

1. The author assumes that documents can be copied. (If documents can’t be copied, it wouldn’t make any sense to buy a new copy machine. True, but this begs the question—if documents couldn’t be copied, we’d never have been in this situation in the first place.)
2. The author assumes that the document can’t be copied by hand. (If the document could be copied by hand, it wouldn’t necessarily make sense to buy a new copy machine. True, but this again begs the question, and remember, we must accept the Premise that “I need to photocopy a document.”)
3. The author assumes that buying a new copy machine is the only way to get a new one. (If one could obtain a new copy machine by some other method, it wouldn’t make any sense to buy a new one. True, and this is a bit closer than #1 or #2, but we’ve already covered this issue with the more comprehensive, correct Assumption that “no other copy machines are available.”)

For fun, think about what would happen if we were to consider #3 above an Assumption. If we did, we’d have to anticipate a plethora of peripheral possibilities—e.g., we could then also say that the author assumes that we can’t steal a copy machine, or that the author assumes that we can’t build a copy machine, etc., ad infinitum. Thus, once again, we’d essentially be begging the question.

Keep in mind that it’s a happy, everyday world on the GMAT—in other words, don’t get too creative when you’re coming up with the author’s Assumptions. In fact, staying within the scope of the Argument is the key to attacking Assumption, Identify-the-Reasoning, and Inference questions. If you followed our discussion above, you’re ready to translate your Argument analyses into an approach to CR questions. Stay tuned!

I = iPt

In basic terms, the above equation tells us the amount of interest that would be earned on a principle amount invested (P), for a given time (t) at a given interest rate (i).

Example:

If you invested $1,000 (P = your principle) for one year (t = one year) at 6% simple interest (i = given interest rate), you would get $60 in interest at the end of the year and would have a total of $1,060.

For compound interest, you would earn slightly more.

Let’s look at similar type problem, though this one involves compound interest.

Mr. Riley deposits $500 into an account that pays 10% interest, compounded semiannually. How much money will be in Mr. Riley’s account at the end of one year?

For compound interest, first you need to divide the interest rate by how many compound periods there are. So for the above question, because we are compounding semiannually, we need to divide 10% by 2 (because of 2 compounding periods), and if we were compounding quarterly, we would need to divide 10% by 4.

In the above question, Mr. Riley deposited $500 into his account at a rate of 10% compounded semiannually and the bank will divide his interest into two equal parts. They will pay 5% interest (10%/2) at the end of six months, and then will pay another 5% at the end of the year. Compound interest can essentially be translated into “interest paid on interest”, meaning that after one period, you are paid interest on the interest that was paid in prior periods, hence the phrase “compounding”.

So at the end of the six months, Mr. Riley has $525 because the bank paid $25 in interest ($500*5%) into his account. For the second half of the year, Mr. Riley is then paid 5% on the $525 balance that was in his account at the end of the first six months. This interest is equal to $525*5% = $26.25. Therefore, at the end of the year, Mr. Riley has $551.25, which is equal to his balance of $500, plus the $25 interest paid at the end of 6 months, plus $26.25 paid at the end of the year. Mr. Riley earns $1.25 more with this compound interest than he would have been paid if he were paid only 10% simple interest (would have been only $550). The lesson? Compound interest always pays more!

Let’s look at another similar type of problem that involves interest.

Money invested at x%, compounded annually, triples in value approximately every 112/x years. If $2500 is invested at a rate of 8%, compounded annually, what will be its approximate worth in 28 years?

A. $3,750
B. $5,600
C. $8,100
D. $15,000
E. $22,500

At first glance, this one seems pretty tricky because you are given x% as the interest rate and it asks you about compounding and it might seem difficult where to find a starting point for this. For this one, it might be a bit easier to think about this without the use of compound interest, which might unnecessarily confuse you. Here, we are given x% as 8%, so all we need to do is take 112/8 = 14. Thus, we know that the money triples in value every 14 years. Further, we know that the money will triple exactly twice in 28 years, once in 14 years and one more time at the 28^th year. So first we need to multiply the original $2500 invested by 3 to get the balance at the end of year 14 (because it triples), to get $7,500 (or $2,500*3). Now, we know that this balance of $7,500 will triple again, so the final balance at the end of the next 14 year period will be $22,500 (or $7,500*3). The correct answer choice is E.

Overall, the three types of interest problems you will most likely encounter come test day will be simple interest, compound interest, and word problems involving the mention of interest, but that can be solved without the application of interest or compound interest methods. The key to deciphering between compound interest and simple interest is to see how many periods the interest is paid….interest paid in one period is simple interest and interest “paid on interest” in multiple periods is compound interest. Finally, remember that some questions can be solved intuitively.

It’s time to gain a little perspective.

Sulk, mope, cry, exercise—do whatever you need to release your frustration, and then move on.

Take a deep breath and coolly analyze your situation. What are your qualifications for the schools you applied to? Were you competitive at those schools? Did you demonstrate fit? Did you do something wrong in presenting your qualifications, either in your application or during your interview? Is it possible that you aimed too high?

If the answer to the last question is “yes,” then I urge you to not give up the fight and consider applying this year ASAP (if your target programs are still accepting applications) or next year to schools that are ranked a little lower than this round’s choices. Broaden your horizons to the top 30, for example; not everyone will get into the top 10 b-schools.

Schools ranked lower than spot 15 always expect a surge of applications during the later rounds from applicants who have been rejected from the top 15. They do not count this against you. In fact, a few years ago, the then director of admissions at Georgetown told me that he was quite pleased that Wharton rejects immediately turned to Georgetown as their runner-up option. And the admissions director at UNC’s Kenan Flagler expressed a similar sentiment, saying that she also welcomes highly qualified third round applicants, even those who apply as late as late February or March.

If these non-top-10 options support your goals and you still have time to apply, why not go for it? Otherwise, if you’re not ready to give up on your HBS or Wharton dream, you can use the next six months to improve your qualifications and determine how to present yourself more persuasively.

Not sure if you can evaluate your application and qualifications objectively? Consider investing in a professional MBA Application Review. An Accepted.com professional can analyze your qualifications, evaluate your application, and provide advice for future reapplications.

For excellent reapplication resources, please see:

• Take 2: How to Reapply Right to Business School Webinar, a recorded webinar.
• “MBA Admissions: Application Advice for Reapplicants,” an article.
• Create a Better Sequel: How to Reapply Right to Business School, an ebook.

The GMAT gives you similar opportunities to glean information from a specific case and extrapolate it to another, perhaps more complicated situation.  In fact, while many questions may seem to require you to have memorized a variety of specific tricks, formulas, and rules, the GMAT will reward you for being able to derive these rules from specific cases, and may even punish you for memorizing-without-understanding.  Consider the question:

What is the sum of the even integers between 300 and 400, inclusive?

There are a few “rules” that can help you solve this question efficiently:

1. For evenly-spaced sets (like a set of consecutive even integers), the mean and median of the set will be the same.  In this case, the middle number, 350, will be the average of all the values in the set.
2. To find the number of values in an inclusive set, take the range of (usable) values, then add one.  (The counterpart to this is that, for exclusive sets, you subtract one).
3. So here, knowing that we can only use the even numbers – every second number will count – we’d take the range (100) divide by 2 (to eliminate the non-useful odd numbers), and then add one (because it’s an inclusive set) to note that there are 51 terms with an average of 350.  Accordingly, the answer will be 350*51, or 17,850.

Now, that seems like a lot of memorization needed for a fairly unique question type.  Furthermore, memorization can be tough to implement – you will likely remember that for inclusive/exclusive sets, you add one in one case and subtract one in the other, but it may be tough when you are under pressure to remember exactly which is which.  So keep in mind that you can use small cases in which you can prove rules like the above to prove your point, then extrapolate it to the question at hand – like your own personal GMAT “case method”:

1. The range 300 to 400 is pretty vast, but once you recognize that it is an evenly spaced set of consecutive even integers, you can recognize that it will react similarly to any other set of similar numbers.  If you take a more manageable set of consecutive even integers, like 2 through 10, you can experiment to see if a pattern exits. In that case, there are 5 values:  2, 4, 6, 8, and 10.  Playing with those values, you’ll find that the ends (2 and 10) add to 12, and the next values inward (4 and 8 ) do the same, but that 6 won’t have a pair.  The sum, then is, 12+12+6, or 30, a multiple of 6.  Looking for patterns in these numbers, you may well find that the average value is the same as the middle value, or at least that you can find pairs to add to the same thing (12) unless there is an odd-man-out middle value, in which case it will be half the value of each pair (the same logic, just without mathematical terminology like “mean” and “median”).  If you extrapolate this pattern to a larger set of consecutive even integers like 300-400, you can determine that they’ll have an average value of 350, or that each pair (other than the middle number) will add to 700.
2. You are probably at least aware that there is a rule for inclusive and exclusive sets, but it comes up so infrequently that you may not have it down cold when the time comes to use it.  That’s okay!  It’s more important to know that a rule exists than to know the specifics of the rule! If you know that a rule exists for inclusive/exclusive sets, you can just prove it to yourself using a set like 1, 2, and 3.  The range of that set is 3-1 = 2, but you can clearly see that if you include all numbers, there are 3 total. Accordingly, the rule for inclusive sets is to add one to the range.  Similarly, if you excluded the ends of the range (1 and 3) there is only one value left, so you would have to subtract one from the range.

Many a GMAT student has read an explanation to a question like the one above and thought to himself “sure, that’s great if you remember the rule, but there are so many rules to remember”.  When you recognize, however, that you can pretty quickly prove to yourself any rule that you know (or even suspect) exists, you can use small-number case methods to do for you what your memory just may not be able to.

Don’t worry, this is not nearly as complicated as it sounds. Knewton instructor Cole Entress lays it all out for you in this short lesson.