GMAT Question Breakdown: Probability
June 11, 2013
All right, listen up. Here’s the deal. We know you guys are out there tearing it up and studying hard for the GMAT, so each week we’re going to break down a tough GMAT problem for you here on the blog. This will be straight to the point, outcomes-focused practice. No fluff. Let’s get down to business.
Question:
Each person in Room A is a student, and 1/6 of the students in Room A are seniors. Each person in Room B is a student, and 5/7 of the students in Room B are seniors. If 1 student is chosen at random from Room A and 1 student is chosen at random from Room B, what is the probability that exactly 1 of the students chosen is a senior?
(A) 5/42
(B) 37/84
(C) 9/14
(D) 16/21
(E) 37/42
Solution:
For those of you who love probability, you are rejoicing at this question. For everyone else, you are thinking something closer to “Sh@*, I hate these!” Whatever perspective you’re starting with, we’re going to get you over the finish line.
This is a complex question for sure, but it can be broken down into simple steps. As with any probability question, we must first consider all of the scenarios in which the desired outcome can be true. In this question, there are two different ways in which exactly one of two students chosen is a senior. Either (i) a senior is chosen from Room A and a non-senior is chosen from Room B or (ii) a non-senior is chosen from Room A and a senior is chosen from Room B. What we need to do is to determine the probabilities of the two scenarios above and add them together.
Let’s start with (i) and find the probability that a senior is chosen from Room A and a non-senior is chosen from Room B. To do this we’ll find the probability of each and multiply them together (the “and” tells us to multiply here).
The probability that the student chosen from Room A is a senior is 1/6. The probability that the student chosen from Room B is not a senior is 1 – 5/7 = 2/7. So the probability that the student chosen from Room A is a senior and the student chosen from Room B is not a senior is (1/6) x (2/7) = 2/42.
Let’s not simplify this yet, because we can expect that the probability we will find when working with (ii) will also have a denominator of 42.
Now let’s work with (ii). Let’s find the probability that a non-senior is chosen from Room A and a senior is chosen from Room B. To do this we will, again, find the probability of each and multiply them together (the “and” tells us to multiply here).
The probability that the student chosen from Room A is not a senior is 1 – 1/6 = 5/6. The probability that the student chosen from Room B is a senior is 5/7. So the probability that the student chosen from Room A is a not a senior and the student chosen from Room B is a senior is (5/6) x (5/7) = 25/42.
Now we sum the total desired outcomes (the “exactly one” wording in the original question tells us that this is an “or” situation – either this event or that. The “or” tells us to add here).
The probability that exactly one of the students chosen is a senior is (2/42) + (25/42) = 27/42 = 9/14.
(C) is correct.
GMAT Math Shortcuts: Percents
June 10, 2013
28% of 25 = 25% of 28 = 2.8 x 2.5 = 7
This always works.
30% of 50 = 50% of 30 = 3 x 5 = 15
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During my time as a GMAT instructor for Kaplan Test Prep, I have had the great pleasure to work with a select few individuals who display such foresight and reason as they stare down the barrel of their future that I hold a special place of respect and admiration for them. Taken individually, they comprise a highly diverse group, but the one thing all have in common is that they are fresh out of undergrad and studying for the GMAT.
I know what happens after undergraduate commencement: life. The vast majority of my aspirant MBAs are 3-5 years into their professional lives by the time they start positioning themselves for b-school. As the reality of the GMAT sets in, these individuals are soon overwhelmed and questioning how they might be able to pull off GMAT study in addition to all of the other things that were already too much to juggle effectively. Many discover that they simply cannot make it all happen. Balls and batons must be sacrificed for the show to go on, so the GMAT and b-school take a backseat to work and life. Maybe later, maybe next year.
The GMAT is the big obstacle for most people interested in attending business school. They already have their undergraduate GPA; they have long-since established relationships with those who will write letters of recommendation; work experience is exactly what they’ve been building since they last left university life; essays must be written, sure, but the source material from which content will be derived has already been lived through. What must be started from scratch, strived for, and completed successfully is the Graduate Management Admission Test.
The GMAT demands time and hard work. I tell all of my students that the best way to frame GMAT prep is to treat it as a part-time job. Set up a schedule and make it the rule, not the exception. The problem for so many GMAT students is that they are already on full-time-plus work schedules and often have partners—even children—that need these would-be GMATers involved in their lives. Furthermore, with respect to timing GMAT prep, all will agree that no aspect of their professional lives has helped prepare them for a test that is valid only to predict academic success.
Now, let’s pan back to the determined clairvoyants I love so much…
GMAT scores are valid for a full 5 years after Test Day. Closing out undergrad marks a time when the brain is fully engaged in student/study-mode and the responsibility payload is never going to lessen. The decision to tackle the GMAT now with the expressed intention of holding the score in your pocket until needed is a tremendous revelation indeed. Even for those that are well beyond their bachelor’s but nonetheless can see a window of relative downtime in the summer, taking on the GMAT before it is required can be a huge boon not only to your score, but also your general well-being.
Summer time is a wondrous time. Vacations, warm weather, long daylight hours… so much of the season is a recipe for joy. But, can you see how The Long Game unfolds? Do you have the dedication, commitment, and discipline to play it? If so, the rewards will be tremendous.
GMAT Bootcamp: Are you tough enough?
May 8, 2013
Date: Tuesday, May 14, 2013
Time: 9:30pm-11:00pm ET/6:30pm-8:00pm PT
What: GMAT Bootcamp
Hosts: Kaplan GMAT Instructor Team — Justin Doff, Teresa Rupp, and Lucas Weingarten
Why: To learn the strategies you need to build the speed and accuracy to tackle the most advanced content on the test.
Listen up, people! You’ve got somewhere to be on Tuesday, May 14, 2013! One of Kaplan’s Elite GMAT instructors, Justin Lawrence Doff (shown here), will be on-camera and coming to you live from Los Angeles, CA dead-set on a singular agenda: arming you with what you need to conquer the most advanced attacks the GMAT has to throw at you. Learn how to set the pace on the climb to the top scoring tiers and, most importantly, how to maintain that level of performance to the end.
It’s bootcamp*. Expect to work hard and to make gains. No matter where you are in your GMAT prep cycle, Kaplan GMAT Bootcamp is designed for the GMAT warrior within us all.
We are saying ‘JUMP!’ and you are saying ‘HOW HIGH?’ See ya Tuesday.
*But don’t worry. We aren’t going to yell at you.
GMAT Fluency
April 29, 2013
From The Free Dictionary:
flu·ent (flnt)
adj.
1.
a. Able to express oneself readily and effortlessly
b. Flowing effortlessly; polished
2. Flowing or moving smoothly; graceful
3. Flowing or capable of flowing; fluid
fluen·cy n.
fluent·ly adv.
When I teach people how to beat the GMAT a common refrain of mine during class #1 goes something like this:
“It is not enough to study content. It’s not enough to study methods and strategies. It’s not enough to merely understand how to get the right answer to a GMAT question. If you truly want to dominate this test, which is entirely possible for you to do, then you must attain GMAT fluency. You must be fluent in all aspects of the GMAT: content, methodology, strategy, timing, what the GMAT is, what the GMAT is built to test, why you have to take it, what the scores communicate, the levels and types of stress it cultivates, etc., etc., etc. Fluency is the key.”
In Kaplan GMAT courses, we begin our conversation about the Quant and Verbal sections of the test by discussing what we call the GMAT’s four Core Competencies. These core skills are what the GMAT is designed to test and every single question you will face on test day will leverage each of these competencies in some way. A particular problem solving question, for example, may lean heavily on critical thinking and pattern recognition, and less so on paraphrasing and attention to the right detail. The next one, though, might be built almost entirely around one tucked away, camouflaged detail that most test takers brush right by on their way to getting the right answer to the wrong question—a common GMAT mistake. However, the other three central competencies will still lurk within this question and the test will reward those who exercise those skills.
The point of this conversation about what skills the GMAT cares most about, despite my best efforts to make it intriguing, is very often lost on many. I try my best to describe that the GMAT is a definable thing and it belongs in a particular box and that the walls of this box are created by these core competencies. I try my best… but, despite my effort, I watch so many who are new to the game inherit only the most superficial appreciation of these concepts. I move on because there is always so much to do in a Kaplan class, always so much to cover, and I must trust that at some point on their trip down Preparation Road each will, in turn, have their own “a-ha moment” and perhaps revisit the big ideas again. (Admittedly, I help ensure these revelations by consistently tracking the competencies throughout the course.)
Possibly, what makes it a difficult sell initially is that the GMAT will never test whether someone knows what the four core competencies are or what aspects of a particular question pertain to which. Similarly, it is hard for some to remember the names of the Critical Reasoning or Reading Comprehension question types. After all, that terminology will never actually be tested. Yet, the ability to spot and accurately identify these question types is monumentally crucial to test day success. How a question ought to be approached and answered is inextricably tied to its type. Nonetheless, it is a common occurrence in my line of work to engage a seasoned GMAT prep student in conversation over a troublesome question and during that discussion I inquire as to the type of question we are talking about. Promptly, I am then met with a coy smile followed by, “I dunno… assumption? Inference?”
It is not that the student can’t understand the difference between an assumption question vs. an inference question. It is not even that they can’t articulate that difference if really pressed. The problem is that understanding is not enough. This knowledge must be at the very front of your mind. It must flow out of you so effortlessly it is as if you aren’t really even thinking at all—you are just doing.
Fluency is the key. It is difficult to acquire, though entirely possible, and it must be continuously worked in order to maintain once achieved. We most often use and think of fluency in regard to language—of which all of us are fluent in at least one. So, to stick with this line of thinking, I ask you:
Can you speak GMAT? Can you speak it fluently?
B-School degree trends: Europe
April 22, 2013
MBA degrees are increasingly global in scope; after all, a degree based on commerce must be so. US schools are shaping curriculum to reflect the mechanics of the global economy, and these schools continue to attract more foreign MBA-degree seekers than any other continental graduate management programs. However, data from GMAC gives an interesting story about education trends across the Atlantic.
According to the 2013 annual ranking report of European business schools by Bloomberg Businessweek, in collaboration with QS Quacquarelli Symonds, publisher of the TopMBA website, European-born GMAT test takers are increasingly choosing to remain on EU soil rather than seek admission to US graduate programs. Further, US-born GMAT test takers appear to be ever more interested in obtaining their MBA and related management degrees from European business schools.
Other recent reports found on Bloomberg’s website help flesh out the EU b-school picture. Young European professionals, like their Asian counterparts, are trending younger and proving more and more interested in specialized master’s degree programs in lieu of an MBA. Interestingly, the underlying driver of the rising numbers of European master’s seekers is something known as the Bologna Process.
The Bologna declaration, the primary guiding document of the Bologna process, was signed in 1999. Several ministerial meetings and agreements among European countries have taken place since then, all with the expressed intention of ensuring comparability in standards and quality of higher education. One result of the Bologna process has been a shift in the duration and dissemination of academic degrees in Europe.
Traditionally, a university student would study for five years and emerge with a bachelor’s and a master’s degree. Now, the bachelor’s and master’s degrees have been separated. Students must now more concertedly navigate the rigors of admission to graduate school if they seek the training and employability benefits a graduate degree can bestow. Thus, a boon in EU GMAT test takers has been observed. What is more, in a time that Europe finds itself deeply mired in unemployment, the next generation of business leaders are hoping to use the shelter of academia to whether this economic storm and emerge into a heartier labor market.
If you are considering a European business school or have attended or are attending one, please share your thoughts and experiences in the comments below!
Kaplan GMAT Blog: Post #150
March 28, 2013
My last retrospective was when I hit fifty. Number one hundred was overshadowed by the test change so there was not an opportunity for much fanfare. However, Elite GMAT Instructor, Justin Doff, asked me what some of my favorite posts were just after I told him that #149 was up on the blogroll. “Geez, that’s a tough one… but it’s a great idea for #150!” I replied.
Nineteen months and one hundred fifty posts later… Here is a list of some of my favorites, or at least these are posts GMAT blog readers might find interesting.
Cheers.
Student Loan Debt Market: Too Big To Fail
March 5, 2013
On Wednesday, February 27, 2013, the student loan ombudsman at the recently minted Consumer Finance Protection Bureau (CFPB), Rohit Chopra, declared yet another systemwithin the U.S. economy ‘too big to fail.’ While Sen. Warren is grilling Ben Bernanke on what exactly the Federal Reserve is doing to remedy the unacceptable influence big banks wield on the health and state of our economy, the student loan debt market, comprised of public and private lenders, has shot past $1 trillion and continues its relentless climb.
Last year, students borrowed $117 billion from the federal government alone—our most inexpensive and forgiving education creditor. [Although, if our ever-competent and productive legislators [sic] fail to reach an agreement by July 1st of this year, interest rates on subsidized Stafford loans will be hiked to 6.8%.]But, is this any surprise? The cost of college is increasing at a rate of 8% per year, five times the current national rate. This tuition inflation rate translates to a doubling of tuition every nine years. Of course, tuition is nowhere near the entirety of the cost of higher education. In fact, an investigation by Business Insider estimates an average of $70,000 in additional costs above the tuition sticker price, and that is just an undergrad number.
Some are lucky enough to be able to cover the cost of undergraduate and graduate degrees, but more are unable to do so without incurring debt.As you look toward your MBA degree and the multi-faceted investment it involves, take the time to objectively evaluate where a graduate management degree from your targeted institution(s) have the potential to take you. Do not sell yourself short or the institution, but approach this analysis soberly. It may well be that you conclude that you need to set your sights higher and, therefore, incur even more cost in order to track your future in the direction it needs to go. If you have the drive and are willing to make the commitment to do what it takes to get into a top tier school, then go after it. If that does not make sense for your career path and goals, however, then get what you need at less cost.
The numbers surrounding student loan debt are terrifying, both macro and micro (I speak from experience here). But, just as a fledgling company needs investment to grow and prosper, so do individuals. If you decide to take the plunge, then go all in. Sign up for a GMAT class, take trips to universities, apply for scholarships and grants, accept loans if necessary. After all, where is the reward without the risk? Just be sure to do all of these things prudently and with a clear head. Do not be duped into a system that will not reward your risk.Defaults will hurt us all.
GMAT Prep: Attitude is critical
February 15, 2013
Due to some recent student interaction that is disturbingly similar and concentrated with respect to my total student body as well as a conversation I had this morning with my wife in regard to a few students in her Psych 101 class, it is time to resurrect an old post on the importance of your attitude during GMAT prep. Take a moment to click that link and read the story told therein.
Now, admittedly, upon reread, the story is pretty vague. What I was attempting to get across is that your perception of what you can do is a tremendously important variable in the type of score improvement you can yield with a GMAT test prep regimen.
I am often asked, “How much can I expect my score to increase after taking this class?” This is a valid query to pose, but one that simply cannot be answered with any precision. A score increase is a factor of several variables. Here’s a simplified equation:
Final GMAT Score = Diagnostic Score + Target Score + Quality of Prep + Quantity of Prep + Attitude
I call this a simplified equation because many of these variables are comprised of several other variables. Take, for example, Quantity of Prep. On its surface, this appears to be a straight forward, easily quantifiable metric. However, you can further break down quantity by total hours of study time spread over a total days of study time. A good rule of thumb is 120 to 150 hours spread across about three months. Then, of course, you can look at how many days per week and how many hours per day and the typical duration of a study session (note the implications of the word “typical”). At this point, it is easy to see how Quantity of Prep inevitably influences Quality of Prep. Like I said… it’s a simplified equation.
Despite the inherent complexity of the preparation levers mentioned above, let us focus on the final one listed: Attitude.
Coincidentally, in my last post about how Benjamin Franklin would kill the GMAT I included a quote by Henry Ford that says, “Whether you think you can or can’t, you’re right.” The inimitable and profound truth in this statement cannot be overstated. I have seen, and am currently seeing, way too many students engaged in depressing self-fulfilling prophecies that involve their steadfast disbelief in their ability to learn something. Topics range from the micro, like learning how to set up the ever-useful chart for combined work problems, to the ultimate macro: the GMAT itself.
I have said before in uncountable forums that one’s success on the GMAT is borne of tenacity above all else. And tenacity, as it happens, is built on the back of a positive attitude. So, the next time you find yourself engaged in self-deprecation and making defeatist proclamations, STOP! Remind yourself, instead, that you are highly educated, highly intelligent, and eminently capable of beating the GMAT, for it is the truth.
Ben Franklin would kill the GMAT
February 8, 2013
Read this article. It’s about how Benjamin Franklin, a notable and influential founding father of the United States, structured his life so as to be as productive as possible and always live knowing tomorrow is, in fact, today. In the article, the author, Samuel Bacharach, a labor management professor at Cornell University, lists five habits Franklin employed to ensure procrastination was not part of his personal description.
In this post, I will apply each habit as listed by the author of the article in order to provide a framework for a productive GMAT study schedule—one that begins today and does not relent until Test Day!
1. Start a group and share knowledge. GMAT study is too often a very lonely endeavor. Despite my encouragement, it is with rare frequency my students organize study groups. I could speculate reasons as to why—busy schedules, different strengths/weaknesses, not wanting to exhibit weakness in front of others, lack of an idea about how to actually structure group study—and all are totally understandable. However, I really wish this were not the case. I have had groups jump at the chance to meet with their peers and have received a lot of positive feedback about the benefits.
Surrounding yourself with others plodding along a similar road to yours helps stimulate ideas, expand understanding, derive opportunities to learn by teaching, and motivate you to show up and get to work. Create a GMAT Junto!
2. Attack opportunities. You will never recognize opportunities if you do not look for them. A constructive attitude about what constitutes an opportunity during GMAT prep is a wondrous and invaluable thing. Really, several items on this list are opportunities all GMAT test preppers can expect to find. Starting a study group, making mistakes, and planning are all opportunities to get the most out of your study time.
As we discuss each, view them through the lens of opportunity and continue to approach GMAT prep in this way. For example, freaking out during a practice test gives you the chance to learn to recognize stress when it arises and devise a plan to overcome it. Test prep classes and the resources that accompany them are an opportunity to learn how to get the score you deserve to get. A previous misstep in calculating the tremendous challenge of the GMAT is an opportunity to make sure round two is the last round.
3. Time is a commodity in short supply. Time management, study schedules, and respect for the test are common themes in my writing on Kaplan’s GMAT Blog. For some thoughts on the matter, read these three posts: The GMAT Needs a Runway, How to Get Ready for the GMAT, and MBA Decision: The Financial Times Explores the Process.
4. Make a list. Beyond the pro-and-con list described in the article, plan out everything with regard to GMAT prep. So you can see for yourself, definitely take the time to list the good and bad aspects of a top notch study regimen, but continue to utilize lists during the prep cycle to maintain momentum and efficiency.
Something I tell all of my students to do is take the last 5-10 minutes of every study session to plan what they will do when they sit down for the next session. Doing this ensures you will hit the ground running and not be overwhelmed under the weight of all the stuff you could be doing. The latter situation usually results in a useless foray of social voyeurism on Facebook—something that definitively will NOT help improve your GMAT score.
5. Fail often; fail hard; but don’t expect to. Quite simply, celebrate mistakes. Each stumble on Preparation Road makes it that much more likely you will not make the same mistake on the only day it matters: Test Day. A mistake is an opportunity to learn.
Did you get it wrong because you got the right answer to the wrong question? Did you miss it because you searched outside the scope of the passage or argument? Did you run out of time because you gave two “tough nut” questions ten minutes of effort?
If I have said it once, I’ve said it a thousand times: tenacity is what builds high GMAT scores. After all, in the immortal words of Henry Ford:
”Whether you think you can or can’t, you’re right.”
