## Tackling a Next Generation Integrated Reasoning Problem

People have been buzzing about the sample test questions released recently by GMAC. These questions are “under consideration” for inclusion in the Next Generation GMAT, which will launch on June 4^{th}, 2012.

Most people who are studying now aren’t, of course, worried about changes that aren’t coming until 2012. This week, though, people taking the real GMAT will have an opportunity to do an experimental set of Next Gen questions after their real GMAT is finished. (Note: if you’re taking the test this week, the Next Gen questions will not impact your real GMAT experience at all – the study won’t begin until the regular test is concluded.)

So, I thought it would be fun to look at one of these questions in more detail! They’re planning some pretty interesting things for their Next Gen Integrated Reasoning section. For instance, it looks like they’re going to give us access to a calculator – which tells me that they’re emphasizing reasoning much more than brute calculation for this section. It really does seem to be a mix of quant and critical reasoning.

Let’s start with the problem. I can’t reproduce it 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

Scroll down to the bottom of that page and click on the link that says “Question 2.” 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 at the bottom; it’s a basic calculator, 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 6 statements and I have to use the data to figure out which ones are true. 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. Because I’m only marking (on the screen) the ones that are true and leaving the ones that are false blank, I’m also going to make six boxes on my scrap paper, big enough for me to write either T or F inside. As long as a box on my scrap paper is blank, I know I’m not done with that statement.

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 on your scrap paper 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 11^{th} 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 11^{th} best (or worst) by “Passengers Rank” is Amsterdam (with an overall rank of 14).

Next, sort by Movements Rank and find the 11^{th} entry again; this time it’s Frankfurt. False.

Answer 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 myself before I remembered that they gave us a calculator! Hard habit to break.)

Next:

* “The airport with the greatest positive difference between its rank based on total movements and its rank based on total passengers is in Charlotte.”

Hmm. I definitely need info about Charlotte to answer this… but not only Charlotte. First, let’s figure this out about Charlotte. I want the biggest positive difference between rank based on movements and rank based on passengers. Charlotte’s difference is: 26-9 = 17. Are any other airport at or above 17? What’s the fastest way to tell?

I’m going to resort by one of the rank columns – I’m going to do “Passengers Rank” (though you could choose either one). Now I’m going to compare the two “rank” columns and try to find any that are really far apart – maybe 17 or more places apart.

Let’s see. Not Atlanta, obviously. Or Chicago, or London…Beijing? Larger but not 17+. Minneapolis is coming in at 16 and 30! But that’s only 14. Yep, Charlotte is it – this one’s true.

Finally:

* “The range of the total numbers of movements is less than 600,000.”

If you don’t know what the mathematical term “range” means, go look it up. (Do you wonder why I keep telling you to look stuff up and then I tell you what it is in the next paragraph? It’s because you’ll remember a lot better if you make the effort right now to look it up for yourself. You never remember as well when someone just hands you the answer.)

The range refers to the difference between the largest and smallest numbers in the set. They’re asking us specifically about the set of numbers in the “movements” category, so sort by “Movements Number.” Miami is the smallest at 371,000. Atlanta is the largest at 978,000. (Notice the approximating I did there?)

They’re asking me whether this range is less than 600,000. Don’t call up that calculator and subtract the exact numbers – not unless it’s so close that you need to. Just add 600,000 to the smaller number. 371 + 600 = 971 (and now add the “,000” = 971,000). This is smaller than Atlanta’s figure of 978,000, so the range is actually larger than 600,000. This one’s false.

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 4^{th} 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 was simpler than some others because all of the data was in one table; others have a chart, a graph, and a description or scenario all for the same problem. 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.

## 10 comments

Rahul on November 22nd, 2010 at 11:20 am

I have a doubt, If I'm taking the GMAT now, will my score remain vaild after GMAC restructures the GMAT?

Stacey Koprince on November 22nd, 2010 at 11:32 am

Good question. Officially, we don't know - they haven't said whether they'll be making changes.

When you take the test now, though, they do still say that your scores will be valid for 5 years, so I imagine they will leave that in place... otherwise, they're going to have a lot of angry students on their hands. If they start changing that language to say your test will only be valid for 2 years or something... well, then we'll know.

There's also another issue - what the schools will prefer or possibly even require. Schools may eventually require the new test even before all of the old test scores have expired. Or they may just have a preference for the new test that would leave you at a disadvantage if you'd taken the old one.

I would guess that, for at least the first year, the schools aren't going to have a preference for the new over the old. They'll mostly be collecting data and trying to decide whether they should have a preference for the new one. After that... things get murkier.

If you're planning to apply before mid-2013, I think you're almost certainly in the clear. We may start to see some new preferences in the fall of 2013, but even then, I think "old" scores will still be safe / fine during that season. Starting in the fall of 2014, though, I'd expect some schools to start showing a preference for the new test (assuming, of course, that the data bears this out).

Rahul on November 22nd, 2010 at 12:18 pm

Thanks for your insight , Stacey.

I'm planning to apply before mid-2013, So hopefully I expect my score to remain valid till then.

Fingers crossed

a.e. on November 22nd, 2010 at 1:31 pm

I took the experimental section today after my exam and I found it to be really hard. Maybe because there was a million pieces of information thrown at me all at once and my mind was still reeling from 3 and a half hours of testing. Whatever the situation, I am very glad that I have the GMAT behind me (scored a 720) and will never have to learn the new format.

Stacey Koprince on November 22nd, 2010 at 1:33 pm

Congrats - that's great! Yeah, it's tough to do something in a totally new / unexpected format even when you haven't already been taking a test for 3.5 hours right before!

Rahul on November 22nd, 2010 at 10:12 pm

Congrats !! 720 is awesome !!

siddharth on November 24th, 2010 at 1:37 am

hi stacey,

i solved this question and got it right..but it took me 8 long minutes!! Is this a "2min" question...if not, will the official time limit for the quant section be increased from the current 75 minutes?

Stacey Koprince on November 24th, 2010 at 6:49 am

The people taking the extra IR testing session this week have reported being given 15 questions in 30 minutes - so still 2 minutes per question.

I strongly suspect, however, that one of the things they're testing is how much time they ought to give... so I think we're going to see some adjustments there.

Remember, too, that you haven't studied how to tackle these kinds of problems yet. We're going to be slower until we get used to answering questions in this kind of format - but we should speed up as we do get used to them!

siddharth on November 24th, 2010 at 6:59 am

Thanks for the info stacey..

Stacey Koprince on October 26th, 2011 at 9:05 am

As some of you may have seen, they killed the link to the problem a while back. But they put it up again in a new place!

Go here: http://www.mba.com/the-gmat/nex-gen/new-questions.aspx

and click on the Table Analysis problem.

Note that the new version of the problem drops the final two statements discussed in the above article.

Also, the calculator tab is now at the top of the screen, not the bottom.