Tackling a Next Generation Integrated Reasoning Problem

Note: This is an updated version of an article posted last year.

As GMAC gears up to release the Next Generation GMAT in June of 2012, we’ve been taking a look at the four sample questions posted on the mba.com website.

Let’s look at the hardest one of these questions in more detail! I can’t reproduce the problem here for reasons that will be obvious once you actually start to tackle it yourself. I also can’t tell you how much time to give yourself because GMAC hasn’t given us any timing guidelines. Just take whatever time you need. (Note: all excerpts or quotes from the problem are copyright GMAC.)

First, click on this link: GMAC Question Formats Under Consideration

Click on the link for the “Table Analysis” problem. This will open up a new browser window with the question. Make sure you’re on the right one: you should see a table with a bunch of data on airports, passengers and “movements.”

Okay, now go work on that and come back here when you’re done. Leave the browser window open! You’re going to need to go back and forth between it and this article in order to follow the discussion.
Some cool things to notice about this problem – and maybe some scary things, too. First, that’s a LOT of data, isn’t it? But, hey, it’s sortable – we can sort by any of the sub-headers! Also, there’s a calculator tab; it’s pretty basic, but we still have a calculator!

So, there’s a bunch of data, and we have to examine it to understand what’s going on. There’s also a question. In this case, I read the question first to see what I would need to do. Hmm. They gave me 4 statements and I have to use the data to decide whether each one is true or false. Okay.

Next, I read the description of the table, which appears below the table itself. The table has 2008 data on the number of passengers and the number of “movements” (an aircraft moving) for a bunch of airports. In addition, the table includes a “percentage change” column for each group (passengers and movements) and the percentage change is year-over-year, from 2007 to 2008. Finally, I’m also told the rank of each airport for the two groups – and here’s something odd.

Go and sort the table by “Passengers Rank.” Look down that column – there’s no 4. Or 12. Or 13! What’s going on? The description below the table says that these 21 airports are “among the busiest 30 airports” so not all of the 30 airports are represented – some are skipped. That means every rank from 1 to 21 is not represented, and there are some ranks higher than 21 (all the way up to 30, potentially). I made a note about that on my scrap paper.

Okay, now I feel like I’m ready to start testing the answers. If I hit a roadblock with one, I’ll set it aside and come back to it later. I’m also going to make four boxes on my scrap paper, big enough for me to write either T or F inside, so that I can keep track of my answers.

The first statement says:

*“The airport experiencing the greatest percent decrease in total passengers from 2007 to 2008 also experienced the greatest decrease in the percent of movements.”

We’ve got two statistics here. First, we’ve got “the greatest percent decrease in total passengers from 2007 to 2008.” Sort the data by “Passengers % Change” and see what you’ve got! Which airport had the greatest percent decrease? (Answer below.)

Next, we’ve got “the greatest decrease in the percent of movements.” What should you sort the data by now? And which airport had the greatest percent decrease in this category?

For the first sort, Chicago is the airport with the greatest percent decrease in passengers. For the second sort, we sort by “Movements % Change” and Los Angeles is the airport with the greatest percent decrease. Are those two airports the same? Nope, of course not – so this one is false. Mark the first box with an F.

Next, we have:

* “The airport with the median rank based on total number of passengers is the same as the airport with the median rank based on total number of movements.”

If you don’t know what median is, go look it up. I can wait.

The median number is the middle number in a set of numbers written in increasing order. In the set {1, 3, 6}, the number 3 is the median. Also, this is a bit tricky. Am I looking for the median of the 21 airports listed? Or am I looking for the median of all 30 airports, even though they’re not all on the list?

Look at the instruction right up above the answers: answer “based solely on the information given in the table.” That seems to point to the median of the 21 given data points. Also, there is one distinct median for an odd number of numbers in a set, but you’d need to combine the two middle numbers to find the median in an even-numbered set… but we can’t “average” the names of two airports. So common sense also tells us to find the median just of the 21 given. (Possibly this was just loose wording on the part of the test writer and they’ll clean this up before the real test.)

Okay, so what’s our first sorting? “Passengers Rank.” There are 21 entries (they told us this already), so the median number in a set of 21 is the 11th number. (If you’re not sure why, count it out. In future, take the odd number, divide it by 2, and add 0.5. That’s where the median number will be located in the set. 21/2 = 10.5 + 0.5 = 11.)

The 11th best (or worst) by “Passengers Rank” is Amsterdam (with an overall rank of 14).

Next, sort by Movements Rank and find the 11th entry again; this time it’s Frankfurt. False.
Question three is:

* “Exactly 50% of the airports that experienced an increase in both total number of passengers and in total number of movements are located in the United States (USA).”

First, I need to figure out which airports fall into the described category: an increase in both total number of passengers and in total number of movements.” In which column or columns can I find that data?

Percent change! First sort by “Passengers % change.” We want the airports that have a positive percent change. That list starts with Atlanta and goes all the way down to the last one, Charlotte. Now, I need to narrow that list – I have to knock out all of the ones that show a negative percent change in the “Movements % Change” column. Atlanta and Miami are gone but the rest are still in. There are 6 airports left on the list. How many list USA as the country? 3. Hey, so this one’s actually true! Check the little box on your screen (and write a T in the box on your scrap paper).

Next:

* “ The total number of movements at the airport in Beijing in 2007 was approximately 400,000.”

I don’t need to sort for this one – I just need to find Beijing. Hold your finger or a sheet of paper up to the screen to make sure you look at the right row all the way across! Beijing’s movements totaled 431,670 in 2008… oh, but this answer asks me about 2007, not 2008. I knew it couldn’t be that easy.

That 430,000 (approximately – they told me I could approximate!) represents an 8.0% increase over the 2007 figure. The answer is asking me whether 400,000 is that figure. Let’s try it. Pull up that handy calculator and multiply 400,000 by 1.08. The answer is 432,000. That’s almost exactly what it really was in 2008 – this one ‘s true too. (Confession: I did the math on my scrap paper before I remembered that they gave us a calculator! Hard habit to break.)

Whew! We’re done. A lot of work for one problem, wasn’t it? At the least, I think we can conclude that we’ll be spending a lot more time per question on this future Integrated Reasoning section.

Key Takeaways for Integrated Reasoning:

(1) If you’re planning to take the test before June of 2012, you can ignore it! (Unless you’re interested or work for a test prep company.)

(2) You still need to know math terms and you need to know how formulas and other things work – other questions do require us to, for example, choose the correct formula to calculate a specific probability. But you don’t have to do as much number crunching as we’re used to doing for quant.

(3) Get used to working with tables, graphs, and information presented in multiple formats (even within the same problem). The one we did above had only one table; it’s possible that, for others, we’ll have multiple charts or graphs. I guess that’s why they’re calling this section integrated reasoning.

* Test questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.