Archive : GMAT

Last week I left you with a conditional probability question. Let’s look at its solution now. This will be my last post on GMAT Combinatorics and Probability (for a while at least) until and unless you want me to take up a particular concept/question related to this topic. Next week, we will start a new topic.

Back to question at hand:

Question 2: Alex has five children. He has at least two girls (you do not know which two of her five children are girls). What is the probability that he has at least two boys too? (The probability of having a boy is 0.4 while the probability of having a girl is 0.6)

If you have not yet encountered the term “intended meaning” in your GMAT study, you are free -and encouraged – to skip this post! But if you have, this point is worth learning. While many GMAT books and websites – including the Official Guide for GMAT Review in some of its solutions – provide as rationale for eliminating answer choices that they “distort the intended meaning” of the sentence, beware that the concept of “intended meaning” is dangerous if you use it to solve problems. Consider, as evidence, the following answer choices from an official GMAT problem:

This week the Graduate Management Admission Council (GMAC) released a new report revealing how much the mix of U.S. and international test takers has changed for the GMAT over the past five years. According to GMAC’s new World Geographic Trend Report, a total of 258,192 GMAT exams were taken in the testing year ending June 30, 2011. That represents a drop of 2.2% vs. the previous year (263,979 tests taken), and a drop of 2.8% vs. two years ago, when a record 265,613 GMATs were taken.

GMAT figures also serve as a good indicator of where interest lies for MBA programs. For the year ending June 30, 2011, test takers sent more than 750,000 test scores to schools, but only 77% of those were sent to U.S. schools, compared to 83% in 2007, reflecting the continuing rise in interest in Asian and European programs.

Let’s look at the concept of conditional probability in detail today. (As if the probability questions weren’t tricky enough!) But since I like to discuss advanced concepts in this blog (in addition to alternative approaches and very important fundamentals), it would not be fair on my part to end the probability discussion without a quick review of conditional probability. Let me start by tossing a question at you.

Question 1: Alex tosses a coin four times. On two of the tosses (we don’t know which two), he gets ‘Heads’. What is the probability that he gets ‘Tails’ on other two tosses?

Like high school seniors across the country, we at Veritas Prep are already well within our countdown-to-June period as we anxiously await the unveiling of the GMAT’s new Integrated Reasoning (IR) section (less than four months to go! Seniors/GMAT enthusiasts whoooo!) If you’re similarly-minded and thinking about the IR section already, the following should help you set your mathematical mind to the right frequency. Remember this: while the numbers in many IR problems might be large and specific, the math is all relative.

I would like to take up a couple of questions on binomial probability today. The concepts of the topic have been covered in detail in the book so I am assuming that you know how to solve questions such as “What is the probability of getting at least 3 heads on 5 tosses of a coin?” etc. Therefore, let’s work on a couple of questions which use the binomial probability with a twist.

Question 1: Martin and Joey are playing a coin game in which each player tosses a fair coin alternately. The player who gets a ‘Heads’ first wins. The maximum number of tosses allowed in a single game for any player is 6. What is the probability that the person who tosses first will win the game?

Solution:

In today’s GMAT Tip of the Week, New England-based blogger and former Tom Brady classmate David Newland explains why New York is Not Sufficient…on the GMAT or in the Super Bowl.

New York is Not Sufficient…on the GMAT or in the Super Bowl

I am writing this from New England — Vermont to be precise — so maybe you think that I am a bit biased as far as the Super Bowl goes. But I KNOW that I am biased when it comes to my LOVE for Data Sufficiency. That love is pure and ever-lasting.

So while I may not be able to convince you that the New York Giants are not sufficient to win the Super Bowl on February 5^th, I bet that I can give you a quick memory device to think about for Data Sufficiency.

As if there weren’t enough good reasons to live in Southern California this time of year, we can officially add “the world’s best GMAT instructors” (at least for 2011) to that list. The 2011 Veritas Prep Worldwide Instructor of the Year winners both teach and reside in the greater Los Angeles area, a treat for those of us at Veritas Prep headquarters but certainly not a reason to infer regional bias in the selection process!

Both Mia Groves and Travis Morgan stand a cut above on their own merits, having posted outlandishly-high student evaluation scores and, more importantly, having delighted dozens of students who have raved about both their experiences and their scores. Without further ado, we present the 2011 Veritas Prep Worldwide Instructors of the Year, Mia and Travis!

Let’s take another tricky probability question today and employ two different methods to solve it.

Question: Two couples and one single person occupy a row of five chairs at random. What is the probability that neither couple sits together (the husband and the wife should not occupy adjacent seats)?

(A) 1/5
(B) 1/3
(C) 3/8
(D) 2/5
(E) 1/2

Happy Friday, everyone, and welcome back to the GMAT Tip of the Week! We here on the editorial team would describe ourselves and our roles primarily as “teachers,” and what do teachers do? They teach. And your author plans to spend the weekend teaching, but as a break from teaching Algebra and Data Sufficiency, this weekend he’ll be teaching a 5-year old to ski. And what both of them learn can teach you to be a better GMAT test taker.

There are a few pillars of ski instruction, most notably:

Last week INSEAD announced that it will launch an executive MBA (EMBA) program on its Singapore campus, and that it will introduce its own admissions test for the school’s EMBA program. Built in conjunction with test prep company Prep Zone (which was founded by INSEAD alumni), the exam will mark the first time that a top MBA program has created a proprietary entrance exam for its admissions process.

The new exam will keep some elements of the GMAT, such as questions that measure quant- and verbal-related reasoning skills. (“Higher-order thinking,” anyone?) INSEAD will remove some of the more obscure measures of one’s mathematical ability and grasp of more subtle language nuances, and in their place will introduce “mini case studies” and a a personal interview. In this way, the line will be blurred between the entrance exam and the rest of the admissions process.

Today, as requested by Pratap, we are going to take removal/replacement in mixtures. For those of you who were looking forward to some more tricky probability questions, I will make up for your disappointment next week. Meanwhile, rest assured, replacement is a very interesting, not to mention useful, concept in GMAT. So brace yourself to learn some new things today.

First of all, many “replacement” questions are nothing but the plain old mixture questions, the type we discussed in this post, with an extra step. So don’t flip out the moment you read the word “replace.” Let me show you what I mean:

As you’ve probably already seen this morning, last night the President ba-rocked the Apollo, singing a few bars from Al Green’s “Let’s Stay Together” in front of the soulful reverend himself and complicating the next “2012 Presidential Election” category clue to be aired on Jeopardy.  “Let’s Stay Together” – is it “what is Barack Obama’s campaign song?” or “what is something Newt Gingrich has never said to a wife?”.  Ba-dump-bump.

Today’s headline on Yahoo Finance states that:

Fed’s latest easing could cost $1

Which is pretty surprising.  A dollar?  Sign us up – staplers and trash cans seem to cost the government hundreds a pop.  If we can do anything worthwhile for a dollar, just add it to my tax bill.  Even McDonald’s dollar menu costs more than a dollar when you add tax.  If the government is doing things for a dollar, well, what is Newt going to use as his platform now?  Chalk one up for efficiency.

I hope you have gone through the theory of probability from your book. I will not replicate that theory here but will assume that you already know it. Instead, what we will do now is take some tricky questions on probability and try and find out the various ways in which they can be solved. Hope they give you ideas and takeaways for other questions too!

Question: At the shooting range, the probability that Robert will hit the target in any one shot is 25%. If he takes four shots one after another, what is the probability that he will hit the target?

Would you like to work with an energetic group of really sharp people at a startup-like 10-year-old established company that rivals Google for its smarts, Zappos for its customer focus, and Apple for its elegance (and modesty)? Join our team!

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To break through the average-difficulty GMAT problems and succeed on those upper-level separate-the-700s-from-the-Sixers items, you need to accept that the harder problems offer a unique challenge. They aren’t typically concerned with more obscure information in the way that Jeopardy-style trivia questions get harder the more obscure the information is.  Instead, they challenge you to think more critically about the same fundamental skills that you have mastered in the middle-range problems to even get to that top-shelf point.

The key to success on hard GMAT problems is to accept this quirky challenge — think differently and critically.

Looking for a unique opportunity to meet one-on-one with admissions representatives from both local and international business schools? We always tell applicants that the very best way to get to know an MBA program is to visit the school. The next best thing, however, is when the school visits you!

The upcoming MBA Tour Conferences involve a variety of formats to help you gain a competitive edge in the admissions process. If you’re researching business schools, events like this one are an excellent way to get to know schools better as you narrow down your list of target programs.

This year MBA Tour features a variety of ways to get to know top business schools:

Dean Nitin Nohria has only been at the top spot at Harvard Business School for about a year, but the effects of his projects and initiatives are already starting to be seen. He has declared that his priorities are around five core themes: Innovation. Intellectual Ambition, Internationalization, Inclusion, and Integration. What does this all mean specifically for you as an HBS applicant?

The visible changes at Harvard that are at least in part due to Dean Nohria’s influence include:

A move beyond the case method
What was sacrosanct at Harvard for generations was that 100% of courses were taught using the case study method. As Veritas Prep predicted when Dean Nohria arrived in Summer 2010, the curriculum is undergoing change. Starting with the class matriculating in Fall 2011, students will now have “field method” experiences as a counterpart to the case-based teaching. The first change to the curriculum is a year-long first-year course called FIELD, for Field Immersion Experiences for Leadership Development. FIELD features small-group opportunities for students to put what they learn into practice. The Class of 2012 will also see a reduction in the number of case-based courses and the introduction of new labs, similar to what schools like MIT have offered for some time.

Now that we have laid the groundwork for permutations and combinations, probability will be a piece of cake. We just need to build up on what we have already learned.

The single most important concept in probability is the following:

The probability of an event A is calculated as P(A) = No. of outcomes when A occurs/Total no. of outcomes.

In this post, we will just extend the combinatorics concepts and apply them to probability. Let me explain how we will do it using some examples.

Happy January 6, or as it is known to many, the day of  the Epiphany…the twelfth day of Christmas.  If your New Year’s Resolution includes getting serious about the GMAT and your  b-school future, epiphanies are a great place to start.

The feast of the Epiphany, in Western Christianity, celebrates primarily the visitation of newborn Jesus Christ by the three kings, who famously bore gifts of gold, frankincense, and myrrh.  And this is a mistake that many GMAT test-takers make when studying – they anticipate “knowledge” as “gifts,” asking questions like “what is the formula?” and “what is the rule?”  But, really, what’s important about the Epiphany is not the gifts themselves, but the revelation (in the Christian tradition of the new Lord to the rest of the world). And for your GMAT study, the revelation/epiphany that comes with newfound (or newly-reviewed) knowledge is exponentially more important than is the knowledge itself.  As you study for the GMAT, allow yourself to have epiphanies and not just “gifts.” 

What do you know… Another year has already gone by. We’re so full of opinion and points of view here at Veritas Prep that we thought we should commit ourselves to another round of prognosticating about what the coming year will bring in the worlds of standardized tests and grad school admissions. It will be fun to check in at the end of the year to see how we did.

Without further ado, here are six things that we predict will happen in 2012:

Happy New Year! Hard to believe a whole year has already gone by again. At this time last year we laid out six predictions for 2011. We exhibited restraint by avoiding predictions about flying cars and holographic teachers, but we did stick out our collective neck on a few matters. Now it’s time to see how we did.

More Schools Will Adopt Video and Other Less Traditional “Essay” Questions
We were at least partly correct here. While at least one school actually backed away from utilizing video response (UCLA Anderson, we’re looking in your direction), other programs embraced Twitter and experimented with ultra-short essay responses. In other cases, schools made iPads an official part of the application review process, paving the way to allowing them to view multimedia responses in coming years. We expect this trend will only continue in the coming year.

If you have been following my last few posts, I am sure you are a little wary of today’s post. They have been a little convoluted lately since we are dealing with permutations and combinations. Next, we will tackle probability but today, I am going to digress (to give you some much needed respite) and take up a simple yet interesting topic. We deal with quadratic equations on a regular basis. Tackling them effectively is pretty much one of the most basic and important skills you need for GMAT Quant. Today we will look at some relationships between the coefficients of quadratic equations and roots.

It’s hard to believe that 2011 has already come and gone. Why do these years seem to keep going by faster and faster? As we at Veritas Prep wind down the year, we thought we’d share some of our most popular posts and most interesting topics from the past 12 months.

We hope that this blog has provided you with some useful insights as you’ve studied for the GMAT or slaved over your grad school applications. Sometimes we have a little fun, and sometimes we veer off topic to talk about what interests us, but everything written here comes from the same place: We want to help you be successful in your pursuit of grad school and in your career overall!

Another popular combinatorics concept deals with letters and envelopes. Let’s look at it today in some detail.

Question 1: Robin wrote 3 different letters to send to 3 different addresses. For each letter, she prepared one envelope with its correct address. If the 3 letters are to be put into the 3 envelopes at random, in how many ways can she put

(i) all three letters into the envelopes correctly?
(ii) only two letters into the envelopes correctly?
(iii) only one letter into the envelope correctly?
(iv) no letter into the envelope correctly?

Today’s post is a continuation of last week’s post and heavily refers back to it. I would suggest you to take a quick look at last week’s post again to make sense of this post. Let’s start with the variation question 1a we saw in the last post.

This weekend, there is a high likelihood that you will unknowingly engage in one of the GMAT author’s greatest devices of trickery. Via Christmas shopping (9 days left… thank Heaven for Amazon Prime shipping) you may try to misdirect your gift recipient by bringing home a bag from a different store (He went to Lowe’s? I thought he went to Jared.) or wrapping a tiny gift in a larger box. Or you may wait on the shopping and watch the Tim Tebow vs. New England game, and in doing so watch Tebow’s option-style offense employ all kinds of misdirection tactics to open up running lanes.

However you view misdirection this weekend, bring some of that back to your GMAT studies and notice misdirection wherever it’s employed. Consider, for example, this question:

Today, using some examples, let’s look at different ways of distributing identical/distinct objects among people or in groups. There are some formulas which can be used in some of these cases but I will only discuss how to use the concepts we have learned so far to deal with these questions. I am not a fan of unintuitive formulas since the probability (we will come to this topic soon) that we will get to use even one of them in GMAT is quite low while the effort involved in cramming all of them is humongous. Therefore, I only want to focus on our core concepts which we can apply in various situations. Let’s start with our first example.

Question 1: In how many ways can 5 different fruits be distributed among four children? (Some children may get more than one fruit and some may get no fruits.)

Watching the Republican Party presidential primary race take shape over the past six months, we can’t help but think of one of our favorite GMAT sentence correction lessons. Seemingly forever, Mitt Romney has been the lead horse in the race, but voters have never quite seemed to embrace him. One month it was Michele Bachmann who seemed to be a more popular alternative, the next it was Rick Perry. Then, Herman Cain uttered the phrase “9-9-9″ and became the next candidate to potentially overtake Romney, and now it’s New Gingrich’s turn. Before we finish writing this post, Ron Paul and Jon Huntsman will probably get their turns, too.

There seems to be the pervasive feeling about Romney that, while many Republican voters like him, not many love him as their nominee. They keep one hand on the “Romney” lever in the election booth, but always have an eye out for someone who’s potentially better. If you’ve done enough Sentence Correction problems on the GMAT, this may sound familiar to you.

Now that we have discussed both permutations and combinations independently, it’s time to look at questions that involve both. Mind you, these questions are not difficult -– they just involve both concepts. The first one is a circular arrangement question with a tiny twist. The second one requires us to make some cases. It takes a fair bit of patience to work out one case at a time and I doubt that GMAT will give you such a question since it is a little bit of a bore. (Actual GMAT questions have more entertainment value for the test maker and the test taker. They make you think and are FUN to solve) That said, it is a great question to bind together everything that we have learned till now and strengthen your understanding. Let’s start.

Matt Damon’s character in the poker-themed movie Rounders had a famous line: “If you can’t spot the sucker in the first half-hour at the table, then you are the sucker.”  The same is often true of GMAT questions — on a difficult question, if you can’t spot the sucker choice, the most popular incorrect answer, there’s a high likelihood that you’ll pick it it yourself.

Learning to understand the GMAT’s popular “sucker choice”  techniques can make you a much better test-taker.  It can also be a much more enjoyable way to study — instead of seeing the traps as threats, you can learn to enjoy the process of outsmarting the GMAT authors.  It’s also a great way to learn from your mistakes, noting after you’ve reviewed an error “I see where you tricked me,” a knowing insight into the test and not a criticism of yourself.  The test is cleverly written, so embrace the insights you  gain about it.  Note a few things about trap answers on the GMAT:

Let’s continue our discussion on combinations today. From the previous posts, we understand that combination is nothing but “selection.” Today we will discuss a concept that confuses a lot of people. It is similar to making committees (that we saw last week), but with a difference. Read the two questions given below:

Question 1: In how many ways can one divide 12 different chocolate bars equally among four boys?

Question 2: In how many ways can one divide 12 different chocolate bars into four stacks of 3 bars each?

It’s the day after Thanksgiving, so as you read this you are probably eating a leftover turkey sandwich and hoping that there’s still a slice of your favorite pie left when you get back to the fridge.  Us, too – having slept off our turkey coma it’s time to make something of the leftovers…namely the problem posted here yesterday about Thanskgiving.

That problem involved what looks on the surface to be a messy, messy algorithm involving fractions and multiple exponents (with variables in them!).  But a closer inspection reveals at least a few things to be thankful for – common GMAT-style exponent “tells” that allow you to get to work:

Happy Thanksgiving! Hopefully today you are enjoying good food and good company (and copious amounts of both). Even if you’re not in the United States, we hope you are eating well and enjoying the company the others!

Doing GMAT math may not be your ideal way to pass the time on a holiday, but if you’re reading this, then maybe it is your idea of fun! So, without further ado, let’s carve up the following GMAT like a Thanksgiving turkey:

In the well-known Thanksgiving equation below, M = the number of minutes after dinner until a person falls asleep, t = the ounces of turkey consumed by that person, s = the ounces of stuffing consumed by that person, c = the number of cocktails consumed by that person, v = the ounces of total vegetables consumed by that person, and K is a constant. Last year, Aunt Jane fell asleep exactly 17 minutes after dinner and she consumed 8 ounces of turkey, 6 ounces of stuffing, 5 cocktails, and 10 ounces of vegetables. This year Lauren is planning on eating 10 ounces of turkey, 6 ounces of stuffing, and 14 ounces of vegetables, while drinking 7 cocktails.

Last week, we discussed the basics of combinations. Until and unless you have worked a decent bit with combinatorics in high school, the formula of combinations will not be very intuitive. We have already discussed how you can easily think of “selection” in terms of basic counting principle and un-arranging instead of the formula, if you so desire. Today, I would like to discuss some combination questions with constraints. A very common type of such questions asks you to make a committee of r people out of n people under some constraints. Let me show you what I mean with the help of some examples.

Question 1: If a committee of 3 people is to be selected from among 6 married couples such that the committee does not include two people who are married to each other, how many such committees are possible?

Do you remember that Tag Team song “Whoomp! (There It Is)” from the early 1990s?  Are you still bumping the ESPN Jock Jams CD in your car?  If so, you’ll know what we’re talking about.  One of the funnier-if-you-listen-closely lyrics in world history is this gem from the one-hit-wonder:

This is a big week here at Veritas Prep! We’ve just announced the availability of our new GMAT on Demand app for the iPad, the first full GMAT course from an established GMAT prep company that can be completed on any iOS device! There is no shortage of flashcard apps and games for people who want to study for standardized tests on their mobile devices, but this is the first real, complete GMAT course for the iPad.

Veritas Prep has been a pioneer in the mobile prep space. We launched our free GMAT Practice Quiz app in early 2009, and to this day it remains the most widely download GMAT prep app of its kind. That app is great for practice — as are many other apps on the market — but it doesn’t provide real instruction, which is where our new GMAT on Demand app comes in. Our new app covers the same exact content that we cover in our 42-hour Veritas Prep on Demand^TM self-paced online GMAT course. This is the real deal.

We will start with Combinations today. The moment we start talking about Permutations and Combinations, the first question many people ask is: “How do I know whether the given problem is a combinations problem or a permutations problem?”

My answer is: “Focus on what you have to do. Do you have to just SELECT some friends/toys/candies/candidates etc or do you have to ARRANGE them in distinct seats/among some children/in distinct positions etc too. If you have to only select, it is a combinations problem; if you have to only arrange, it is a permutations problem; if you have to first select and then arrange, it is a combinations and permutations problem. But if you are not using the formulas (nPr and nCr), you don’t have to think in terms of permutations and combinations. Just think in terms of selecting and arranging.” In the discussion below, I will start with an explanation of how we can make selections and how we can work on combinations without using the formula. We will also take a quick look at the formula and why it is what it is. Then we will move on to some examples.

Would you like to work with an energetic group of really sharp people at a startup-like 10-year-old established company that rivals Google for its smarts, Zappos for its customer focus, and Apple for its elegance (and modesty)? Join our team!

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