The Denial Test: a Must-Know Strategy for CR Assumption Questions

July 22nd, 2011

Critical Reasoning Assumption questions ask you to identify an unspoken assumption made by the argument’s author. On these types of questions, one of the most powerful techniques you have at your disposal is the denial test. Before we go into the details of the test, let’s take a look at some sample Assumption question stems:

“The commentator’s argument relies on which of the following assumptions?”

“The official’s conclusion logically depends on which of the following assumptions?”

“Which of the following is an assumption made in drawing the conclusion above?”

Again, all of these questions are asking you to find an answer choice that contains a missing assumption of the argument.

The denial test allows you to confirm that you’ve chosen the right answer choice. The test is very simple: just negate the answer choice you’ve chosen. The negation of the correct answer must weaken the argument. While it certainly isn’t efficient to negate every answer choice, the denial test can be extremely useful when debating between two tempting answer choices.

Let’s consider the following argument:

Joe is an American. Therefore, Joe probably likes country music.

Let’s say we want to find the missing assumption in this argument. We can use the denial test to evaluate the following two competing assumptions:

a) Some Americans like country music.

b) All Americans like country music.

Both of these choices connect the evidence (“Joe is an American”) to the conclusion (“Joe probably likes country music.”)  But only one of them is a necessary condition, i.e., an assumption, of the conclusion.

Let’s negate statement A first. Be careful: “Some Americans do NOT like country music” is NOT an actual negation of the original statement. Negations must contradict the original statement. The statement “Some Americans do NOT like country music” does not contradict the statement “Some Americans like country music”; in fact, the two statements are compatible. The negation of “some” is “none”, so the negation of Statement A should actually be, “No Americans like country music.” This negation clearly destroys the argument. If not a single American likes country music, then it is definitely flawed to conclude that Joe probably does. Looks like this Statement A is our answer — but let’s check Statement B with the denial test just to be sure.

Again, be careful: the negation of “all” is NOT “none.” Clearly, “none” contradicts “all”, but when doing negations, we want the weakest possible statement that contradicts the original. If I wanted to disprove the second statement, I would not need to learn about the musical tastes of every American. All I would need would be one American who did not like country music, and I would have proved the claim false. So the negation of “All” is “Not all Americans like country music” or “Some Americans do not like country music.” These statements do not destroy the argument, because they still allow for the possibility that a majority of Americans like country music and that the conclusion about Joe is a reasonable one. Therefore, statement B isn’t a correct assumption.

Thanks to the denial test, we can confidently choose statement A as our correct assumption.

Next time, I’ll blog  about negating some actual GMAT answer choices. But for now I hope I’ve given you a little bit of insight to an often overlooked part of mastering the Verbal section.

30 Signs It’s Time to Go to B-School

July 21st, 2011

Not sure whether to apply to MBA programs?

Hint: if you’re yearning for study cohort pals, watching Youtube video after Youtube video of b-school “Follies” performances, and find yourself getting defensive when people bash business degrees… it’s probably time.

10 Inspirational Quotes for EdTech-Friendly Teachers

July 21st, 2011

Mt ShastaIf you’re a teacher — especially one trying to integrate educational technology into your classroom — you’re probably aware of the challenges of the job. Tight budgets, inflexible administration, overcrowded classrooms… the list goes on. Even with all the day-to-day struggles, it’s important to keep the big picture in mind. Here are 10 quotes that we will hope will inspire you and remind you of the importance of your job.

Leave your own favorite inspirational quotes in the comments!

If we teach today as we taught yesterday, we rob our children of tomorrow.

-John Dewey

As educators we should help facilitate goals and help cast a vision for students that will, not only, stretch their imaginations, but also their beliefs regarding what is possible…

-Sam Pabon

After teaching all day, if you didn’t learn anything, you probably didn’t teach anything.

-Don Taylor

The time has never been more ready for systemic change than right now, and we’ve never had better tools to achieve this level of creative disobedience, to successfully prepare our children for the big challenges that lie ahead. It might be uncomfortable and take a bit of work, but our future depends on this radical change in order to survive.

-Andrea Kuszewski

Technology is anything that wasn’t around when you were born.

-Alan Kay

We need to prepare students for their future, not our past.

-Ian Jukes

Practice is the best of all instructors.

-Publilius Syrus

Since we live in an age of innovation, a practical education must prepare a man for work that does not yet exist and cannot yet be clearly defined.

-Peter F. Drucker

When you innovate, you’ve got to be prepared for everyone telling you you’re nuts.

-Larry Ellison

The world we have created is a product of our thinking. It cannot be changed without changing our thinking.

-Albert Einstein

Future MBAs Eager for Tech Jobs

July 20th, 2011

Google HQTech jobs are hot again.

The bubble may have burst years ago, but b-school students aren’t holding that against today’s hottest tech companies. A new survey of 6,297 MBA students from 72 top b-schools found that Google was the #1 most attractive employer among students. Apple (#3), Facebook (#7), and Amazon (#8) also made the top 10 — which was rounded out by more traditional names like McKinsey, Goldman Sachs, the Boston Consulting Group, and J.P. Morgan.

To be fair, Amazon, Google, Facebook, and Apple are all very well-established companies, meaning that MBAs won’t be risking too much more by joining their ranks. Karl-Johan Hasselström, the regional manager for Universum, the company behind the survey, told CNN Money that MBAs are looking for challenging work environments that are far removed from the aftermath of the financial crisis. Read more in this report from CNN Money.

What would be your ideal job post b-school? Let us know in the comments!

EdTech Tweets You May Have Missed: Classroom Microblogging, Why Teachers Love Blended Learning, and Great Tech Expectations

July 20th, 2011

In this week’s edition of EdTech Tweets, check out articles about cheating, blended learning, crossword puzzles, and more!

Law School Admissions Tip: Academic Strengths

July 20th, 2011

This admissions tip comes to us from our friends at Clear Admit. For more expert admissions advice, check out their blog.

While we’ve previously offered advice on addressing weaknesses in one’s academic record, today we wanted to explore the other side of the issue: your undergraduate record’s strengths.

1. The undergraduate GPA is, alongside the LSAT score, one of the most important elements of the law school application. Therefore an impressive college GPA is crucial to be competitive at the leading law schools – the average GPA of students in the Class of 2013 at many top schools like Yale, Stanford and Penn was well over 3.8, while students at Columbia, NYU, and Chicago needed GPAs above 3.7.

2. The undergraduate institution attended can have a slight, yet positive impact on a student’s chance of admission. For example, students who went to college at Harvard, Yale, Princeton, and Stanford receive a small bump at the law schools at Harvard, Yale, and Stanford. Similarly, undergraduates from Penn are somewhat favored in Penn Law’s admissions process.

3. “Hard majors” (i.e. math, engineering, natural sciences) carry extra weight in the evaluation process, although the GPA must be very strong in order for the hard major to have an impact.

4. Although doing well in graduate school(s) is a nice addition to any profile, it will not make up for a less than average undergraduate GPA.

5. In addition, for applicants who held a part-time job or were involved in a number of extracurricular activities during college, high grades might be taken as a sign of a solid work ethic and strong organizational or time management skills. Finally, because many college students don’t take their studies seriously for some or all of their time at college, consistently strong grades could be taken as a sign of maturity and responsibility at an early age.

As you can see, there are a number of things that the adcom could conclude about an applicant’s general qualities and characteristics simply by looking at his or her transcript. This should encourage you to think about the more abstract ways that your academic record reflects your positive qualities and consider ways that you could convey this information in your application.
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More Fun with Weighted Averages

July 19th, 2011

In last week’s post, I discussed how weighted averages are often tested conceptually and thus show up on Data Sufficiency problems. However, even when weighted average problems appear on the more results-oriented Problem Solving questions, this conceptual understanding can be mighty handy. As I said in a previous post, the GMAT is not a speed calculation test, but that doesn’t mean the test won’t reward you if you can find conceptual shortcuts!

If you think I have another official GMAT problem handy, you are right :-) . Feel free to give it a shot before reading my explanation.

Last year Manfred received 26 paychecks. Each of his first 6 paychecks was $750; each of his remaining paychecks was $30 more than each of his first 6 paychecks. To the nearest dollar, what was the average (arithmetic mean) amount of his paychecks for the year?

(A) $752
(B) $755
(C) $765
(D) $773
(E) $775

You could certainly solve this problem the standard way: his first 6 paychecks average $750, meaning that they total $750*6 = $4500, then you’d calculate the total of the remaining paychecks and find an overall average. But instead, let’s have some fun and try to short-circuit the problem using weighted averages:

According to the problem, 6 of Manfred’s paychecks averaged $750 and the other 20 averaged $780. First of all, notice that the $780 group carries much more weight, because there are 20 paychecks versus only 6 in the other group. This means the overall average will be closer to $780 than to $750. Guess what? That means right away, we say goodbye to answers A, B, and C. So if you end up having to guess, you’ve got a 50-50 shot. Not bad!

Next, we’re relating 6 paychecks to 20 paychecks. That’s not an easy ratio to use for weighted averages. But let’s fudge things a bit and pretend that there are 6 paychecks in the $750 group and 18 in the $780 group.

In that case, we would have an 18:6 = 3:1 ratio in favor of the $780 group, which is a much cleaner ratio for dealing with weighted averages. Here’s the cool thing: numerically, that means that the overall average would be 3 times closer to $780 than to $750. Represented on a number line, it would look something like this,

750———–o———–o———–X———–780

where the X marks our final average. Again, think of the relative sizes of the groups as “weights” that pull the overall average away from the average of 750 and 780. Since there are three times as many entries in the 780 group, the overall average is pulled towards 780 and ends up three times closer to 780 than to 750.

Now, notice that the distance of our whole number line is 30. That distance of 30 is divided into 4 equal segments; thus, each marking is 30/4 = 7.5 apart. That means our “fudged” final average (X) is 780-7.5 = 772.5.

Of course, now we have to readjust for the actual problem. There are 20 entries in the $780 group, not 18. But those extra two entries mean the average is bumped up just a tiny smidge from 772.5, and thus we know that D is the final answer!

In addition, you could eliminate E, because an average of $775 would be too neat for the numbers involved. $780-$775 = $5, and $775-$750 = $25, which means that there would be 5 times as many entries in the $780 group. Obviously, it’s not that neat, since the actual ratio is 20:6 = 10:3.

TAKEAWAY: When you see a problem involving multiple sets of numbers, each of which has a unique average and each of which has a different number of entries (“weight”), you should immediately think of weighted averages and see if this conceptual approach can get you to the answer faster.

Okay, now I have a tricky problem for you. But this time, try it on your own! And remember, try to use the strategies we just talked about in this post. Feel free to list your step-by-step solutions in the comments, and be sure to apply the concepts behind weighted averages!

A certain balloon is packaged only in small cases of 40 balloons or in large cases of 100 balloons. A certain stock room has a total of 70 cases of these balloons, and the average number of balloons for each case is 88. A supervisor plans to remove some of the larger cases from the stock room without removing any of the smaller cases. How many of these larger cases must be removed such that the average number of balloons for the remaining boxes is reduced to 70?

A) 28
B) 32
C) 35
D) 40
E) 42

MBA Roundup: Free B-School Courses, Kenan-Flagler Online, and How to Prepare for Bschool Life

July 18th, 2011

Welcome to another installment of Knewton’s MBA News Roundup! This week, check out articles on free courses from top b-schools, Kenan-Flagler’s new online program, and how to prepare for your new life in b-school.

1. Free Courses from Top B-schools

From podcasts to opencourseware, get a taste of Booth, Wharton or Kellogg for free and from the comfort of your home! A must-read for serious applicants.

2. Kenan-Flagler Takes Its Brand Online

This is a first in the MBA world: a world-class business school decides to go online and confront all the branding risks involved. Check out this article for all the facts and read our take on it here.

3. 6 Popular Business Books Adapted as Graphic Novels

Are you a big fan of business books? Check out this clever, artistic re-envisioning of some of the most popular business bibles of all time.

4. Do Techies Need an MBA?

What business opportunities await the serious programmer? Whether your aim is to enhance your “customer dating” or “strategic management” ability, rounding out technical skills with a knowledge of business fundamentals can add tremendous momentum to your career.

5. The MBA Advantage: Companies Run by MBAs are Better Managed

In this age, where instant wins and wunderkind successes get all the spotlight, the MBA degree and the sound business judgment, experience, and training it reflects continues to be essential in many companies. Find out why here.

6. Ready, Set, B-school: How to Prepare For Your New Life

With the hoopla that surrounds the process of getting in, one would think it’s professional happily-ever-after after gaining admittance. However, there are some practical matters that need to be addressed before the acceptance party can begin. Businessweek‘s new series will give you concrete tips on how to smoothly navigate the lifestyle change.

7. SBC Scoop: A Nonprofit Success Story

Are you a non-traditional applicant looking to apply to b-school? Have a dearth of good role models who started off in a creative profession and got into a top program? Check out this success story as well as my list of tips for non-traditional applicants.

7 Benefits of Online GMAT Prep

July 18th, 2011

Working on assignment in the gardenFiguring out how to structure your GMAT prep can be a tough decision. Some people are sure that they need private tutoring or in-person prep classes; others are confident that an online course or self-studying is the only way for them.

Still trying to decide? Here are some of the benefits of online prep to help give you a more detailed picture of the options out there.

1. Increased flexibility

With 60+ hour work weeks, networking events, volunteer commitments, hobbies, travel, and family obligations, the last thing you want to add to your plate is a time-intensive GMAT prep course. “Rigorous,” “challenging,” and “effective,” perhaps — but not all-consuming. After all, your time is precious, and with the demands of the application process, you may need time to research programs and reflect on your professional goals. You don’t want to spend your out-of-work hours trudging off to class! The benefit of online prep is that it allows for flexible scheduling, so you can prep anytime and anywhere (think cafes and the comfort of your home). After all, the GMAT is only one part of the grueling application process.

2. Targeted approach

In order to cut down on the time you spend prepping, you want the time you do spend to be effective. But it can be tricky to figure out how to target your weaknesses, maintain your strengths, and get the most mileage out of your studying on your own. With an online course, technology streamlines the process for you. By employing adaptive technology, online prep courses can generate a stream of learning material that pinpoints your weaknesses and allow you to eliminate them quickly. As a result, you get a course that adapts continuously to you and gets you aggressive results.

3. Cost effective

With price tags around $300 a course, online prep offers a great opportunity to save money, nail that stellar GMAT score, and save the rest of your cash for expensive applications (that can cost as much as $275 a pop), an admissions consultant, a new suit, a flight to the interview… The MBA admissions process is expensive, so don’t burn through your pre-MBA budget with in-person prep when you can get a targeted, effective online course instead. Concerned that it won’t work for you? Pick a course with a higher score guarantee.

4. Quality content

Online prep harnesses the power of the collective; data scientists and product developers can use real-time performance data to continually improve the effectiveness of the content and the scoring algorithms of the practice tests. Thus, the quality of the content (questions, explanations, reading passages, videos) is exceptional and reflects perpetual improvement. If developers find that an educational item isn’t test-like or isn’t up to snuff in some way (too hard or too easy), the problem can be fixed in a few minutes. No expensive printing and shipping costs, and customer feedback can be addressed with a simple click.

5. Social and interactive

You might not think of online prep as social and interactive, but in many ways, they are more so than in-person prep alternatives. Social features like message boards, forums, groups, and private chats give you more ways than you would expect to interact with instructors, assistants, and other students. You might even find yourself asking questions you would be too embarrassed to bring up in a classroom.

6. Environmentally friendly

Though saving the environment may not be on your list of priorities when choosing a GMAT class, you can rest assured that you won’t be adding to your carbon footprint by choosing an online prep course (think: no commuting; no hefty books). Bottom line: you get what you want at minimum cost to the planet.

7. Test-like environment

The GMAT itself is a computer adaptive test. Regardless of whether you enjoy this approach or prefer underlining, dog-earing, and highlighting your way through exam booklets, the GMAT is taken on the computer. In this sense, it makes sense to prep on the computer. You’ll get used to reading passages on screen, working on your scratch paper (instead of in the margins), and not flipping back and forth through the test or underlining key words. On test day, this comfort could make all the difference.

Must-Follow EdTech Tumblrs: In the Cloud, The EdTech Tumble Zone, EdTech SandyK

July 18th, 2011

In this post, read about three more must-follow edtech tumblrs from educational technology enthusiasts and professionals. Miss our first post in this series? Check it out here.

1. In the Cloud

Gwen Mueller, the blogger behind “In the Cloud,” describes herself as an “IT professional, strategist, creative thinker, gamer, [and] nerd in secondary education.” In the Cloud encompasses all these personas, providing fun and helpful edtech resources along with “1/4 cup of fun.” Just as visually appealing as it is fun to read, In the Cloud is a great resource for relevant edtech links (not to mention fun pictures and cartoons).

2. The EdTech Tumble Zone

The EdTech Tumble Zone is curated by Sam Pabon, a IT Professional currently in the process of pivoting into the educational realm (he’s completing a Master’s in Educational & Instructional Technology). His stated philosophy on education is inspirational and in itself worthy of discussion: “As educators we should help facilitate goals and help cast a vision for students that will, not only, stretch their imaginations, but also their beliefs regarding what is possible.” The EdTech Tumble Zone is worth following not only for its many links to helpful edtech-related articles, but also for its fun/inspirational quotes (“Stop worrying so much. Worrying is using your imagination to create things you don’t want”), cartoons, recipes, and more.

3. EdtechSandyK

Though the instructional technology specialist behind Edtech SandyK insists that her tumblr is just an “experiment,” we certainly hope it’s one that lasts! Edtech SandyK has curated a great collection of articles, videos, and other links that speak to education’s changing landscape, the importance of being a responsible digital citizen, and more. Be sure to check out EdTechSandyK’s blog too, which features more long-form posts on tech integration, learning tools, and other educational approaches.