Lin-tegrated Reasoning

by on July 29th, 2012

Back in February, the entire sporting world succumbed to (Jeremy) Linsanity. But, alas, the GMAT world was months away from the perfect Lin-guistic technique, using “Lin” as a Lintroductory term for “Integrated Reasoning.” So it was with great fanfare last week that Jeremy Lin leaped right back to the top of the news wire, signing with the Houston Rockets and not only creating an opportunity for a fantastic pun with Lintegrated Reasoning, but demonstrating  how to think strategically on Integrated Reasoning questions.

Many IR questions will involve the use of not just math, but “strategic math.” The Houston Rockets’ offer sheet to Lin – a sheet that could have been matched by the Knicks – was not  entirely noteworthy in its size. $25 million over 3 years is not at all an unconscionable contract for a starting point guard, and Lin is a special case in his marketability. Overseas broadcast rights, jersey sales, ticket sales – Lin has the potential to recoup that investment quickly.

So why didn’t the Knicks match the offer? Diehard New Yorkers might answer, simply, “idiocy”, but the business reason ties back directly to Integrated Reasoning (and even Data Sufficiency) strategy. The contact was structured such that the majority of the payment would come in year three – a year in which the Knicks are already projected to be over the NBA’s salary cap and any additional salaries would also incur a hefty “luxury tax” payment, driving the price of Lin’s $14.8 million contract for that year up to reportedly over $40 million for the Knicks.

What was the Rockets’ genius here? Using the minimum/maximum, strategic-math skills that will help you directly on the GMAT. For example, consider this sample Integrated Reasoning situation:

A national consumer publication recently ranked five national airlines in five separate categories: Safety, Punctuality, Comfort, Affordability, and Destinations Offered. Each airline was ranked 1st to 5th in each category, with no ties, then awarded points according to the following scale: 5 points for each 1st place finish, 4 points for each 2nd place finish, 3 points for each 3rd place finish, 2 points for each 4th place finish, and 1 point for each 5th place finish. The following facts are also true:

  • Horizons finished with a total of 24 points.
  • CaribAir finished 1st in Comfort and 3rd in Affordability.
  • Aviata Pacifica directly ahead of Northern Flights, which finished two spots above CaribAir.

For the following conclusions, indicate whether the conclusion is logically true, logically false, or cannot be determined:

1) Northern Flights finished with 15 points.
2) The lowest-ranked airline finished with less than 10 points.

Now, this situation appears quite involved, but you do know a few things to be sure. If Horizons finished with 24 points, it must have finished first in four categories (4 firsts * 5 points per first place = 20 points) and second in the fifth (4 points, which would sum to 24). And since there are 75 total points available (15 in any given category, times 5 categories), that leaves 51 points left for the remaining four airlines.

You also know the finish order: Because Horizons finished with nearly the maximum number of total points, it must have finished first. And since we know that Aviata finished ahead of Northern, then one more airline finished next just ahead of Carib, we know that the order is:

1. Horizons
2. Aviata
3. Northern
4. (unnamed)
5. Carib

With all this said, you can attack the questions, again thinking strategically. You know which airline finished last – Carib – so you can investigate. Could it have finished with less than 10 points? The stimulus states that it earned a first-place finish in one category (good for 5 points) and a third in another (good for 3 points). Which means that, with a minimum of three points left (last place in any category still accumulates one point), Carib must finish with a minimum of 11 points. Much like the Jeremy Lin situation – the hand is forced…we have established a minimum amount and can use it to our advantage. The answer to #2 is “must be false.”

This also helps with a minimum/maximum situation to answer the first question. We now know that first place finished with 24, and last place with at least 11. That leaves a maximum of 40 points left for the 2nd, 3rd, and 4th place finishers. And because there is a distinct finish order, there can be no ties. In order for Northern (third place) to finish with 15, then Aviata would have had to finish with at least 16. And 16 + 15 is 31 – leaving only 9 left for the fourth place finisher, which is impossible since we know that last place had 11. So we can use this information to guarantee that Northern finished with less than 15 points.

The lesson here? On integrated reasoning questions, you won’t just use “math” but instead “strategic math” — often using situations to determine whether something is possible, or finding relationships between numbers to determine that something is impossible. And notice this about integrated reasoning – it is business math, the kind of math that allows your organization to destroy a competitor by using strategic, min/max value math to your advantage.

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