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 4th, 2012.
Most people who are studying now arent, of course, worried about changes that arent 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 youre taking the test this week, the Next Gen questions will not impact your real GMAT experience at all the study wont begin until the regular test is concluded.)
So, I thought it would be fun to look at one of these questions in more detail! Theyre planning some pretty interesting things for their Next Gen Integrated Reasoning section. For instance, it looks like theyre going to give us access to a calculator which tells me that theyre emphasizing reasoning much more than brute calculation for this section. It really does seem to be a mix of quant and critical reasoning.
Lets start with the problem. I cant reproduce it here for reasons that will be obvious once you actually start to tackle it yourself. I also cant tell you how much time to give yourself because GMAC hasnt 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 youre 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 youre done. Leave the browser window open! Youre 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, thats a LOT of data, isnt it? But, hey, its sortable we can sort by any of the sub-headers! Also, theres a calculator tab at the bottom; its a basic calculator, but we still have a calculator!
So, theres a bunch of data, and we have to examine it to understand whats going on. Theres 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, Im also told the rank of each airport for the two groups and heres something odd.
Go and sort the table by Passengers Rank. Look down that column theres no 4. Or 12. Or 13! Whats 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 Im ready to start testing the answers. If I hit a roadblock with one, Ill set it aside and come back to it later. Because Im only marking (on the screen) the ones that are true and leaving the ones that are false blank, Im 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 Im 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.
Weve got two statistics here. First, weve got the greatest percent decrease in total passengers from 2007 to 2008. Sort the data by Passengers % Change and see what youve got! Which airport had the greatest percent decrease? (Answer below.)
Next, weve 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 dont 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 theyre 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 youd need to combine the two middle numbers to find the median in an even-numbered set but we cant 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 theyll clean this up before the real test.)
Okay, so whats 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 youre not sure why, count it out. In future, take the odd number, divide it by 2, and add 0.5. Thats 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 its 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 ones 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 dont 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! Beijings movements totaled 431,670 in 2008 oh, but this answer asks me about 2007, not 2008. I knew it couldnt 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. Lets try it. Pull up that handy calculator and multiply 400,000 by 1.08. The answer is 432,000. Thats 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, lets figure this out about Charlotte. I want the biggest positive difference between rank based on movements and rank based on passengers. Charlottes difference is: 26-9 = 17. Are any other airport at or above 17? Whats the fastest way to tell?
Im going to resort by one of the rank columns Im going to do Passengers Rank (though you could choose either one). Now Im going to compare the two rank columns and try to find any that are really far apart maybe 17 or more places apart.
Lets see. Not Atlanta, obviously. Or Chicago, or LondonBeijing? Larger but not 17+. Minneapolis is coming in at 16 and 30! But thats only 14. Yep, Charlotte is it this ones true.
Finally:
* The range of the total numbers of movements is less than 600,000.
If you dont 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? Its because youll 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. Theyre 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?)
Theyre asking me whether this range is less than 600,000. Dont call up that calculator and subtract the exact numbers not unless its 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 Atlantas figure of 978,000, so the range is actually larger than 600,000. This ones false.
Whew! Were done. A lot of work for one problem, wasnt it? At the least, I think we can conclude that well be spending a lot more time per question on this future Integrated Reasoning section.
Key Takeaways for Integrated Reasoning:
(1) If youre planning to take the test before June 4th 2012, you can ignore it! (Unless youre 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 dont have to do as much number crunching as were 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 thats why theyre calling this section integrated reasoning.
* Test questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.