Improbable Isn’t Impossible


We had a rough weekend. What should have been a relaxing weekend away was hampered by my wife becoming extremely ill on Saturday night. After a long, slow, traffic-filled car ride home on Sunday, my 11-month old son had a very difficult night of illness. I was recounting the story to my mom and she declared “It’s contagious then.”

My mom’s reasoning follows a version of Occam’s Razor, which states that with competing hypotheses in play, you should choose the one that requires the fewest assumptions. In this situation (one person gets sick then another person gets sick) a contagious bug is the most likely solution. But it’s likely, not certain.

My son’s sickness could have been the result of a long car ride, or a hot day, or some completely unrelated bug. Those aren’t likely solutions, but they are possible. When you’re working on data sufficiency, it’s very important to remember that distinction.

Imagine a problem where you’re asked to determine whether some value is even. Maybe the first three values you check yield 2, 4 and 8 respectively. At that point you can conclude that it’s likely the value will always be even (and given limited time you may just need to select that answer). However, you don’t KNOW the value will always be even. Here are some things to keep in mind:

1. Test fractional values- Positive fractional values get smaller when squared. That’s a unique property that can yield different results and help you find that a statement is insufficient.

2. Test negative values- Don’t forget about the negatives! They often produce different results.

3. Test 0- Zeroes are not only useful to check, they’re usually very easy to calculate!

4. Test 1- Just like 0, ones are easy to plug in and have several properties that can help give you different results.

Remember, just because something is probably true, doesn’t mean it must be true and testing different kids of numbers can help you strengthen your hypothesis.

 Garbage In, Garbage Out


I recently read an article that proclaimed Washington D.C. as the nation’s fittest city. Having lived in DC for three years, I was curious, so I read through the article. The American College of Sports Medicine apparently decided that it would be interesting to figure out which is America’s fittest city. The people running the survey, not wanting to introduce their own personal biases figured that they would come up with an objective list of factors, collect the data, and declare a winner.

One of the factors that seemed to carry heavy weight is spending on parks. The ACSM reasoned that heavy spending on parks makes them attractive and safe places to spend time, and thus would likely lead to a more fit population. They suggest that municipalities target approximately $100 per capita in parks spending. They note to Washington’s great credit that the city spends $398 per capita.

Stop and think about that for a minute. Does that necessarily mean that DC is filled with many beautifully manicured parks where citizens can safely enjoy exercise? No. In fact, as a former resident of the area, I remember many times when we had to scramble to fit some suitable space for a softball game or some pick-up soccer. Very rarely could you find a space big enough to accommodate a good game without being right up against other groups of people or having to deal with concrete walkways cutting through the field.

So how could DC have such great park spending and not have great recreational facilities? Simply speaking, DC’s parks aren’t parks, they’re monuments. The National Mall is a huge park, but it’s not made for fitness and it’s not really made for locals. It’s made for the thousands of tourists that flock to the city. Spending money to repair the Washington Monument doesn’t make DC fitter, but it does go into DC’s park budget.

You get the idea here. The point is that when you put garbage information into your formula, you get garbage out. When you’re working through a math problem making a simple mistake in transcribing the information is just as deadly as a gap in math knowledge. Be diligent, be careful and make sure you’re putting the right information into your formulas, because if it’s not right going in, it’s garbage coming out.

 Something better than practice, practice, practice?


I’ve been blessed to have the opportunity to partner with the business school at a local university to teach a GMAT recently. Although I’m working with the material on a daily basis, I wondered whether the transition from individual tutoring back to teaching in a group setting would be a difficult one. For the most part, it hasn’t been. The most challenging part has been remembering how different each student’s perspective can be.

The benefit to working one-on-one is that I get to adapt to one individual’s learning style and methods. I can adapt my message to the way that I expect it will best be heard, and if that doesn’t work, I can try again. In the classroom setting I’m aiming for the approach that yields the fewest puzzled looks.

This inevitably leads to more questions after class, but the variety of questions is something that I really enjoy. One of the questions I received last week is something that I thought deserved a wider audience: In order to get better at these question types do I just need to practice, practice, practice?

It’s a three-step process that many people are quick to embrace because it implies that there is some amount of work you can do that will eventually conquer the test. But, practice is only half of the story. I would suggest a six-step process: practice, review, learn, practice, review learn.

There are two distinct stages that are necessary beyond just doing problem after problem. The first is review. By reviewing, you take the time to understand why you missed problems, as well as why you got questions correct. You can recognize helpful patterns and gaps in your knowledge.

Once that’s done, the next job is to learn. By learn I mean go back and attack the weaknesses you diagnosed during your review. If you simply keep doing problems, you’re likely to continue to make the same mistakes. Taking the time to diagnose and fix your mistakes before they become habits is what takes process of practice and elevates it.

 The Artist Formerly Known as GPA or How a 10.03 GPA Makes Me Angry


Hold on kids, here comes a rant.

I recently read an article about a Florida high school student who got a 10.03 GPA. Okay, I read seven articles. I kept reading because every article I found was fawning (excellent SAT word) over this amazing accomplishment. It made me angry.

Back in my day (yup, old man tendencies coming through loud and clear), GPA was on a 4.0 scale. Four points for an A, three points for a B, and if I have to keep going any further you’ll never get into a good college and your life is ruined (not really). Sure, we’d fudge those rules every once in a while and give five points for an A in an Advanced Placement class on our college resumés, but that was just to keep up with the kids at the other schools who were going to cheat either way. We couldn’t let them get an unfair advantage, right?

Lo and behold, I’ve come to discover that many schools now give AP classes a six-point weight, and that’s just grade inflation and terrible. And that’s how I feel about that.

But you know what, grade inflation is a minor crime compared to what this Florida high school is doing. You see, rather than use a four-point or five-point or even a six-point scale this Florida school is doing something different. They’re adding. For each half-credit of AP or dual enrollment course one of their students completes they add .08 to that student’s GPA. I can’t tell you how angry that makes me.

Let’s do a quick acronym review. GPA stands for Grade Point Average. Average. You know, that one where you sum all of the terms and then divide. You know, that one THAT ISN’T AN AVERAGE ANYMORE IF YOU START ADDING STUFF TO IT AT THE END. Average.

Think of the consequences: take enough AP classes and your report card of straight B’s could net you a 4.0. Heck, keep at it and you could make a 5.0. Keep going long enough and you could earn a 6.0 GPA without ever receiving a single A. The absurdity goes on and on because there is no cap, it’s not an average anymore!

This school has gone and turned GPA into KFC– formerly Kentucky Fried Chicken, but now just three letters that vaguely stand for a concept. GPA has gone the way of SAT– the artist formerly known as the Scholastic Aptitude Test. Maybe GPA should just follow Prince’s lead and change itself into an unpronounceable symbol because what this school has done has separated all the meaning out of the A.

So yes, I’m angry. I’m angry at high school educators for setting up a stupid system. I’m angry at the media for reporting a story like this with awe and amazement rather than asking the very simple question: How do you get a 10.03 GPA? I’m angry that the simple and pure mathematical concept of average has been so savagely destroyed (okay, maybe that last one took it a bit too far).

There are fundamental mathematical skills that you need to succeed on the SAT or ACT or everyday life (unless your life is being an administrator at this Florida high school). Average is one of those skills. But there’s this other skill: critical thinking. It’s really important too. So the next time you see some outrageous piece of information on the news, I hope you’ll stop and take a minute to think about the implications of what that really means. Taking the time to sharpen your critical thinking skills may occasionally push you into an angry late-night rant about trivial things, but in the long run they’ll be skills you’re glad you have.