Because of this, rate problems that feature two trains (or cars or people or anything else) have a bit of a bum rap.  These questions are seen, unjustly, as difficult, time consuming and complicated.  However, by learning only a few basic rules, you can handle these questions quickly and correctly.

The first step is to make sure the trains leave at the same time.  If one train leaves earlier than the other one, calculate the distance the earlier train will have travelled by the time the later train leaves.  Subtract that distance from the distance originally separating the trains, and use the that new distance as the total distance.

The second step will depend on the exact type of problem.  If the trains are coming towards each other or going away from each other, add their speeds.  If one train is catching up to the other, subtract their speeds.  Use this result as the total speed.

Once you have calculated the total distance and total speed, you can solve for the time as you would on any other rate question.  You just plug these numbers into the same formula you used back in step one to find the earlier trains distance, which is distance = rate x time.

The problem below is a perfect example of this type of question.  While it looks complicated at first, draw a diagram and then follow the steps outlined above to reach the correct answer.

Problem:

Train A left Centerville Station, heading towards Dale City Station, at 3:00 p.m.  Train B left Dale City Station, heading toward Centerville Station, at 3:20 p.m. on the same day.  The trains rode on straight tracks that were parallel to each other.  If train A traveled at a constant speed of 30 miles per hour and Train B traveled at a constant speed of 10 miles per hour, and the distance between the Centerville Station and Dale City Station is 90 miles, when did the trains pass each other?

(A)  4:45 p.m.

(B)  5:00 p.m.

(C)  5:20 p.m.

(D)  5:35 p.m.

(E)  6:00 p.m.

Solution:

Begin as you do for any word problem, by understanding the basic situation.  Two trains, 90 miles apart, start moving toward each other at different times. One train moves at 30 mph, the other at 10 mph. Our task is to determine the times at which the trains pass each other, which is to say when they will be at the same point on these 90-mile tracks.

Our story begins at 3:00 pm when train A leaves.  It is going 30 mph.  The next event happens at 3:20 pm when Train B leaves its station going 10 mph.  In the 20 minutes before train B leaves, train A has travelled 10 miles.  This leaves 80 miles of track between them when train B starts at 3:20.   This is now our total distance.

The question is then, “How fast will the two trains close that distance?”  Here we add the speeds to get total speed: 30 + 10 = 40.

So, at a combined rate of 40 mph, how long will it take them to close an 80-mile gap?  Time = distance/speed.  Thus, 80/40 = 2 hours to close the gap.   It will be 5:20 at that point.  Answer (C) is correct.

“I ate some cake at the birthday party”

“I ate some cakes at the birthday party”

If one of those two sentences sounds fishy, you have a good ear—but I assure you both sentences are grammatically correct. They just mean different things.

The key concept behind those sentences is the grammatical notion of countability, a set of idiomatic rules frequently tested in GMAT sentence correction problems. The English language distinguishes between nouns that can be modified by a number and ones that can’t. For instance, you can have one chair, two chairs, or fifty chairs. But although you have confidence that you’ll do well on the GMAT (as you should!), you can’t have one, two, or fifty confidence in that fact.

If you’ve done many Sentence Correction problems, you’ve probably seen the most common version of this error: the words “many,” “number,” and “few” apply only to count nouns such as “dollar” and “catamaran,” while uncountable things like “money” and “sand” must be described with “much,” “amount,” and “little.” However, you may also need counting rules to discern verb tenses, because only a noun that can pair with a number can agree with a plural verb. To use an Official Guide sentence correction problem as an example, the uncountable group “citrus,” referring to a type of fruit, agrees with the verb “is.” Don’t assume that because there are many types of citrus fruit, citrus itself is plural!

And finally, some words—like cake, in our opening example—have different meanings depending on whether they are treated as a plural noun or as an uncountable one. Saying “I ate some cake” treats cake as a substance; it means you ate some amount of cake, perhaps a few ounces or even a few pounds. But when you say “I ate some cakes,” you are talking about the individual physical objects, whole cakes, frosted on the platter! If you ate more than one of those, you’d be sick to your stomach for sure.

Problem:

Growth in the industry is at an all-time low, with total employment at less than 68,000 people and fewer companies in the field than there have been during any of the past ten years.

(A) at less than 68,000 people and fewer

(B) at fewer than 68,000 people and fewer

(C) lesser than 68,000 people and fewer

(D) fewer than 68,000 people and less

(E) at less than 68,000 people and there are less

Solution:

In this question – and any time you see them on Test Day – “less” and “fewer” should pop out as important words to check.  Are they both used correctly here?   No.  We can count people, so the first part needs to say “at fewer than 68,000 people.” Eliminate (A).

Which other answers fail to fix the problem?  (E) retains exactly the same problem; (C) uses “lesser” inappropriately (we don’t use it to compare a number to another number). Eliminate it as well.

What distinguishes the final two choices, (B) and (D)?  (B) has “at fewer,” which is needed, because we are saying that total employment is “at” a certain level.  (D) ends with “less,” which cannot be used before the countable noun “companies.”  (B) is the answer.

The tendency to toil away with GMAT concepts and question types that just aren’t clicking can cause grave harm to your potential score on Test Day.  A GMAT score is a scaled, aggregated number ranging from 200 to 800.  Have you ever heard a conversation that goes like this?

X:  “I am so happy!  I scored a 700 on the GMAT!”

Y:  “Oh yeah?  And what are the component parts of that score?  Did you get an equal number of questions correct as per their type and difficulty level?  Because if you didn’t, then your 700 is obviously lopsided, built only on stuff you’re good at, and doesn’t really count.”

Of course you haven’t heard that conversation.  It’s absurd.  It is true that your score report includes a breakdown of your raw quantitative score (0 to 60) and your raw verbal score (0 to 60).  These are then aggregated and scaled to a percentile distribution curve represented by the 200-800 scoring scale in order to communicate your overall performance in relation to your peers.  However, even though schools can see your Quant and Verbal percentiles separately, they can never know how those scores were built.  Plus, what is the number that everyone cares about?  I can tell you definitively that it is not a 44 for Verbal nor a 47 for Quant.

All of the above is background information for the thrust of this post: you absolutely need to schedule a significant proportion of your study time to build upon your strengths.  For the majority of your study schedule, it is advisable to divide each study session at a 1:2 ratio, strengths to weaknesses.  In fact, that is also the preferred order.  Spend the first third of your session working on areas of greatest strength and the next two-thirds working to improve areas of greatest opportunity.  By starting with your strengths, you not only kickoff a study session on a positive note, but you also avoid sacrificing that time at the end because you just had to “get” probabilities or modification errors, for example—which may or may not have actually happened.

Over time and as Test Day draws nearer, you will want to shift that 1:2 ratio to a 1:1 ratio, spending an equal amount of time on strengths and weaknesses.  This should happen at approximately 60% of the way through your total study schedule.   When you have only 20% of your total time left, the ratio shifts one last time to a 2:1, strengths to weaknesses.  Let’s look at a 2.5-month study schedule as an example to illustrate the breakdown:

• Days 1-45             –           1:2, str:wkn
• Days 46-60          -           1:1, str:wkn
• Days 61-75          -           2:1, str:wkn

Imagine a coach assigning her players to their weakest positions for the championship game.  That is essentially what you are doing to yourself if you fail to play your game on Test Day.

Your job is to make sure that you leave absolutely no money on the table when you sit down with the GMAT.  The only way to be sure you squeeze every last point out of that test on Test Day is to build your strengths up as much as possible so that they compensate for your weaker areas.  If you only focus on what isn’t “clicking,” then those lovely muscles slumbering lazily on their laurels will atrophy.

It takes discipline to develop and adhere to a study schedule like the one I’ve outlined above.  However, if you want the score you deserve to get then you must commit to building your strengths.

How many liters of water must be evaporated from 50 liters of a 3 percent sugar solution to get a 5 percent sugar solution?

“This is simple percentages,” I would say. “Just start by taking 3% of 50 liters, which is 3 over 100 times 50, which comes out to 1.5 liters sugar…”

But one day, teaching this same quantitative problem, a student’s hand shot straight up. “Yes, James?” I said. (That wasn’t his real name, by the way, but it will do.)

“Eli, who cares about the sugar?”

I paused. “Well, the sugar will help us figure out the solution.”

“But you don’t need it!” James explained. “I’ve been a chemical engineer for years, so I do this problem all the time. The sugar is a constant. The amount of sugar doesn’t change, and that amount is always equal to the concentration times the volume. So just do CV = CV; 50 times 3 is equal to the final volume times 5!”

I paused, impressed, and amazed—and have taught his timesaving shortcut ever since.

However, there is a bigger lesson here than simple mixture problems.  I had approached that problem uncritically.  I “knew” how to find the right answer, so I never gave it a second thought.  I spent far more time prepping the combination and probability problems given their complexities and hidden challenges.  As a result of my complacency, I made extra work for myself.

In other words, the takeaway is this: don’t focus exclusively on your mistakes. Review your correct answers as carefully as your errors. There might be a time-saving shortcut that you missed the first time through. Or better yet, you might have used such a technique that you can notice, reconstruct, and repeat! It’s very tempting to spend all of your time studying those red X’s on your quizzes and CATs. But avoid that trap; looking at your right answers as well as your errors will help you stay positive, and more importantly, will give you many opportunities to raise your score.

One of the most important skills to master for the GMAT is prime factorization.  Finding prime factors can be useful on many different types of questions.  On test day, if you are stuck on a question and unsure of how to solve, remember the big number rule.  The big number rule is simply this: if you see a big number, one that is so large it is unreasonable to work with, find its prime factors.  Once you have those factors, you should be able to simplify.

Every positive integer that is not prime, with the exception of 1, can be broken down into a series of prime numbers multiplied together.  Additionally, each series of primes is unique and will only result in a single integer.

For example, let’s say you want to find the prime factors of 20.  Start by identifying any two numbers that multiply to equal 20.  We will choose 4 x 5.   5 is prime, so we cannot break it down further, but 4 is not, so we repeat the process.  If you try to think of two numbers that multiply to equal 4, you will only come up with 2 x 2, which are both prime.  Thus, the prime factorization of 20 is 2 x 2 x 5.

Now let’s say that instead of choosing 4 x 5, you choose 2 x 10.   2 is prime, so we leave it alone, but we need to break down 10.  10 equals 2 x 5, thus we again find the prime factorization of 20 is 2 x 2 x 5.  Notice that no matter what numbers we choose, as long as the math is correct, we reach the prime factors.

Try the question below and see if you can figure out how prime factorization can help you solve.

Problem:

Is q a multiple of 48?

(1) q is a multiple of 6.

(2) q is a multiple of 8

Solution:

The stem asks whether q is a multiple of 48. It’s a yes/no question so you should see if you can answer the question with both a yes and a no.  The prime factorization of 48 is 2 x 2 x 2 x 2 x 3, so we need four 2’s and one 3 to know that q is a multiple of 48.

Statement 1: This tells you that q is a multiple of 6. The prime factorization of 6 is 2 x 3, so we know q has one 2 and one 3, but we do not know if it has the additional three 2’s we need, so this statement is not sufficient.

Statement 2: If q is a multiple of 8, we know that it must include the prime factors 2 x 2 x 2, which gives us three 2’s.  Since we do not know if it will have the additional 2 and one 3, it is insufficient.

Statements 1 & 2: If q is a multiple of 6 and 8, it must have one 2 and one 3 in its prime factors, so it will divide by 6, and three 3’s in its prime factors, so it will divide by 8.  This means that q must have three 2’s and one 3.  Note that one of those 2’s is being used to divide by 6 and by 8, since we need to be able to divide by both, but not at the same time.  However, to reach 48 the prime factors would need to include one additional 2.  Since we do not know if q would include a fourth 2 or not, the statements are still not sufficient.  Therefore, the answer is (E).

In an earlier post, we kicked off a Kaplan GMAT student success story series.  We want to share our students’ successes to inspire you to reach for your goals because they are attainable.  In fact, your goals are so important to us that you can win cash and prizes just by telling us about them!  We want to know: 

Jeff Gibbard never had a problem with creativity. But in order to get his social business agency off the ground, he needed to give himself a left-brain advantage. After preparing for the GMAT with Kaplan, he got a scholarship to Drexel’s fast-track MBA program and eventually founded his own social business agency.

Q: Why did you decide to get an MBA?

My undergrad degree was in film and media arts. During my studies I explored other creative outlets such as photography, graphic design and basic web development. I tried to start a few businesses, and it quickly became very clear that, in order to reach my full potential, I needed a business education.

Q: So after you decided to go for an MBA, what was the biggest surprise about what it takes to get into business school?

I can’t say that anything really “surprised” me, but it was definitely an adjustment trying to juggle work, a relationship, studying for the GMAT and getting everything together for my MBA application. I had done my research, so I knew what to expect, but knowing what needs to get done, and actually doing it, are not the same thing. I was also a bit nervous about how competitive my top schools were.

Q: What did you do to become competitive?

In all honesty, Kaplan helped a lot. My first GMAT score prior to my GMAT course did not cut it.  A strong GMAT score was necessity to get into my top choice schools. I knew I could get a good enough score, but I also knew I needed help to get there. It was honestly the best decision I made on the road to business school. Kaplan’s GMAT prep course allowed me to raise my score to such an extent it translated into not only admission into the program of my choice, but also a scholarship to go there.

Q: And now?

Now I run my own company, doing exactly what I dreamed of doing one day. My company, TrueVoiceMedia, lets me apply my creative skills everyday while using everything I learned in graduate school to grow my business by virtue of helping others grow theirs. I love what I do, and I know I couldn’t have gotten here without getting my MBA degree. I also know that I wouldn’t have been able to receive that education if I hadn’t made the choice to get competitive and raise my GMAT score. So, sincerely, thank you for the role you played in my success. I am very grateful.

Now that you’ve read about where Jeff took himself, we’d like to hear from you! Where will you take yourself? Tell us what lies in your future, what your ambitions are, how you’re going to leave your mark on this world. In short, tell us what and who you’re going to be. We want to hear the story of the “future you”—in 120 characters or less—and give you the chance to win cash and a free Kaplan course. Click here to enter.

Here’s a fun fact:

Here’s another fun fact:  A computer can score 16,000 essays in 20 seconds (and does it just as accurately as the human).

A new study out of the University of Akron published some very intriguing findings on the efficiency and accuracy of automated readers (aka, robo-readers, e-Raters, e-graders, etc.).  A team of researchers used more than 20,000 essays across eight different prompts and nine different programs to evaluate our electronic counterparts and the algorithms that govern them.  Turns out, not only are these programs staggeringly more efficient, but they are also just as accurate as their human workmates.  Sorry, John Henry.

So does this mean that GMAC is keeping mere mortals on the payroll out of pity?  Or perhaps to protect themselves from the wrath of an angry mob of Luddites?  An MIT researcher says no.  According to Les Perelman, the e-grader’s most significant problem is its inability to identify truth.  He also claims that while a robo-reader may be extremely accurate in giving scores as compared to human derived scores, it is both possible and easy to game the system.  In other words, you can learn to write in the way a computer is designed to reward.  [And, by the way, Kaplan can teach you how to please both circuitry and gray matter.]

For now, the world—and the GMAT—still need a human touch.  Bear in mind, though, that while you may spend thirty minutes toiling and sweating over your Argument or Issue essay, that ‘human touch’ will spend just 120 seconds skimming your creation.  I’ll leave you with an insightful quote from a Discover article:

“And as for human essay graders, they have only a couple minutes to come up with a score. When you’re under that kind of pressure, machine-like behavior is the best you can hope for.”

A permutation problem will ask you to determine the number of ordered subsets of a certain size that exist in a group.  If we move away from GMAT speak, this means permutations will occur when you must perform two actions.  First, you will be creating groups.  In our example of a baseball team in a gym class, the class may have 30 students, but you need to select nine.  Second, you will put the selected entities in an order.  On our baseball team, you can think of this as the batting order.  If A is first, B is second, and C is third you have a different outcome than if C is first, B is second, and A is third.  However, A, B, and C may not even be on the team – you will have lots of other outcomes in which they are left out.

Thus, we need to both select nine players to be on the team AND put those players in an order.  On GMAT test day, when we must perform both of these actions, we will have a permutations problem.  The formula to determine the number of permutations is n!/(n – k)!, where n is the number of total entities, in our example 30, and k is the number of entities we want to select, in our example nine.

See how you do on this next problem, and ask questions if you have them… 

Problem:

Kim has four trophies which she wishes to display in a cabinet with five shelves, with only one trophy to a shelf.  How many different ways are there to arrange the trophies?

(A) 4

(B) 5

(C) 20

(D) 24

(E) 120

Solution:

This is an arrangement question. Often you can simply count the different possible arrangements, making sure to do so systematically, but it is usually easier to remember that the number of ways of arranging x objects is x !

There are too many arrangements here to count by simply writing them out, so you will have to use factorials to count the arrangements.

In this case you have 4 objects, but 5 spaces. So you have five possibilities for each shelf-it could contain one of the four trophies, or it could be empty. So the number of possible arrangements is 5! = 120. The answer is (E)

For the purposes of this post, I’m going to move beyond the money issue and speak about what going full-time meant to my experience as compared with the many part-time students I worked with while in school.  Then I’ll kick it over to my colleague, Jonathan Wylie (a current part-time MBAer) to see what he has to say about his experience as he finishes up his first year in Berkeley’s program.  I’ll begin at the beginning…

Upon entering business school in pursuit of an MBA, the “non-traditional” label fit me like an old pair of jeans.  My undergraduate degree was in fine arts with a concentration in sculpture.  I spent most of my twenties working as a studio artist and craftsman in various small businesses from North Carolina all the way up to Alaska.  I made my money with my hands and my eyes.  I saw myself as a journeyman: out to learn all I could about materials and the processes for working with them, creating designs and writing proposals, managing client expectations with the realities of a project, and developing a small business while keeping the creative fires burning and, well, creating.

I am fundamentally bent toward immersion, and after a path that took me across the oceans and around the globe, I made the decision to get a Master’s in Business Administration about 3 months before applications were due.  For me, attending part-time was never an option.  I knew that this would represent a sea-change in my life and I had every intention of making the most of it.  I took the GMAT, applied, and, when the time came, was glad to leave the job I held.  I was excited to get back into academia with the drive and purpose only a graduate student can muster.

Choosing to go full-time presented me with options I would never have had otherwise.  It began with a graduate assistantship position (one of few offered and only offered to full-timers) and a scholarship (again, only offered to full-time students and although it was not comprehensive, it did pay for approximately my first year of classes).  What’s more, as a full-time student I was able to exploit the incredible array of opportunities one can only find either in or by way of an institution of higher learning.  Classes were important for me, to be sure, but what I did outside of class was just as valuable, if not more so.

For example, I am a diehard advocate of experiential learning.  Business competitions require an immense time commitment.  I was able to participated in three.  I also led 50 MBA students on three separate economic development service trips on the back of $60,000 in university funding.  Those programs remain in place to this day and are specifically reserved for the school’s full-time learners.  Beyond that, internships and study abroad programs (both highly valuable learning opportunities) are often out of reach for many part-time students due to their continuous professional commitments.

Upon completing the first year of core curriculum, my full-time cohort went their separate ways in order to pursue individual concentrations.  During year 2, the majority of my classmates were part-time students and full-time professionals.  While I was taking a full class load, working on a project with a Rwandan co-op, banging out the final version of a presentation for a conference, and writing a business plan, my new-found colleagues were using toothpicks to hold their eyes open during the lecture.  I often spoke of all I did at the school when the tie-in was clear and relevant (something which happened with notable frequency).  These instances were often met with lament: “That would be nice if I had any extra time.”

After enough of those conversations, I took on the task of building bridges between our university’s full- and part-time students.  I made it a point to offer up opportunities that came my way to everyone.  I remember holding a meeting with the assistant dean of the business school to figure out why taking one part-time student out of a group of twenty with me on a trip to New Orleans was met with so much resistance.  In the end, he allowed the student to go, but he conveyed the strategic importance of building a strong F/T program and, thus, of exhausting opportunities in that pursuit first.

All the way to graduation, I maintained the call for my part-time colleagues to do what they could to involve themselves in whatever possible outside of scheduled classes.  I still sound that drum when I stand in front of them as their MGT500 instructor and bang it frequently for my Kaplan students who will soon be at graduate school themselves.  In the end, I am much more concerned with expanding what graduate school has to offer beyond the classroom.

I am an advocate of choosing to attend full-time if that is a viable option for you.  This will very likely be your last gulp of academia, and I implore you to drink every last drop.   What do you think Jonathan?

Two: If the number is even, it is divisible by 2.

Three: Add up all of the digits.  If the result is divisible by 3, then the original number is divisible by 3.  For example, 534 is divisible by 3 because 5 + 3 + 4 = 12, which is divisible by 3.

Four: Look at the last two numbers.  If that two digit number is divisible by 4, then the entire number is divisible by 4.  For example, 544 is divisible by 4 because 44 is divisible by 4.

Five: If the units digit is either 0 or 5, then the number is divisible by 5.

Six: Check if the number is divisible by both 2 and 3, using the rules described above.  If it is, then it is also divisible by 6.

Seven: Just do the long division.  While you may have learned another way to check if a number is divisible by 7, it will be more time consuming than doing the actual math.

Eight: This one is tricky, because it is conditional.  Always start by looking at the hundreds digit of the number.  If the hundreds digit is even, the final two digits need to be a two digit number that is divisible by 8.  Thus, 5,248 is divisible by 8 because 2 is even and 48 is divisible by 8.  If the hundreds digit is odd, however, the final two digits need to be a two digit number that is divisible by 4, but not by 8.  Thus, 5,344 is divisible by 8 because 3 is odd and 44 is divisible by 4, but not by 8.

Nine: The rule for 9 is similar to the rule for 3.  Add up the digits.  If the result is divisible by 9, then the number itself is divisible by 9.  For example, 486 is divisible by 9 because 4 + 8 + 6 = 18, which is divisible by 9.

Ten: If the units digit is a 0, then the number is divisible by 10.