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# Formal Logic and GMAT Critical Reasoning

I’ll begin with a typical GMAT Critical Reasoning question.  As a case study, consider this question from the OG13e, CR #115 (OG12e, CR #114):

Guidebook writer: I have visited hotels throughout the country and have noticed that in those built before 1930 the quality of the original carpentry work is generally superior to that in hotels build afterwards.  Clearly carpenters working on hotels before 1930 typically worked with more skill, car, and effort than carpenters who have worked on hotels build subsequently.

Which of the following, if true, most seriously weakens the guidebooks writer’s argument?

(A) The quality of original carpentry in hotels is general far superior to the quality of carpentry in other structures, such as houses and stores.
(B) Hotels build since 1930 can generally accommodate more guests than those build before 1930.
(C) The materials available to carpenters working before 1930 were not significantly different in quality from the materials available to carpenters working after 1930.
(D) The better the quality of original carpentry in a building, the less likely that building is to fall into disuse and be demolished.
(E) The average length of apprenticeship for carpenters has declines significantly since 1930.

It may be helpful to think through this question on your own before you read the full analysis below.

## Do you need to study formal logic to master the GMAT Critical Reasoning?

The short answer is: no.   If you have studied formal logic, then chances are good that the “muscles” you developed in those studies also will help you with CR.  But, if you have never studied formal logic, don’t go out of your way to read up on Quine.  It’s somewhat beside the point.

## Formal Logic vs. Contextual Logic

On the GMAT CR, you will not see words like “necessary”, “sufficient”, “if and only if” —- i.e. the words of formal logic.  You will see an occasional if-then statement, and other statements that could be recast as if-then statements, but results of formal logic are very seldom at the heart of what the CR is testing.

CR is all about what I would call contextual logic: here’s a real world scenario, and given the unique particularity of this situation, what would make the most sense in context?  In many CR question, the correct answer provides new information that you have to integrate with the understanding developed from the prompt.  It’s rare that you can “logically deduce” the correct answer purely from the prompt, without any reference to the answer choices.  It’s true that, for certain CR question types, it’s helpful to anticipate the answers before you start analyzing the answer choices, but the point is: pure logic is not enough.  You must be sensitive to the peculiarity of the context.

## An Example of CR Logic

Guidebook writer: I have visited hotels throughout the country and have noticed that in those built before 1930 the quality of the original carpentry work is generally superior to that in hotels build afterwards.  [This is a factual observation.]  Clearly carpenters working on hotels before 1930 typically worked with more skill, car, and effort than carpenters who have worked on hotels build subsequently.  [This is a conclusion that would explain the factual observation.]

We are asked to weaken the argument.  This means, we have to find another explanation for the factual observation (pre-1930 have good carpentry) that would support it even when the conclusion (pre-1930 carpenters were better than carpenters since) is false.  In other words, even if pre-1930 carpenters are no better than later carpenters, why would the critic still observes much higher proportions of good carpentry in pre-1930 hotels?

Notice, some logical reflection has clarified our task for us, but there’s really no glaringly obvious alternate explanation for the higher proportions of good carpentry in pre-1930 hotels.  We will have to look for relevant perspectives among the answer choices.

A. The quality of original carpentry in hotels is general far superior to the quality of carpentry in other structures, such as houses and stores.

True, but not helpful.  Pre-1930 hotels had better carpentry than pre-1930 houses and stores. Post-1930 hotels have better carpentry than post-1930 houses and stores. This fact does not explain why any difference would not be apparent between pre-1930 hotels and post-1930 hotels.

B. Hotels build since 1930 can generally accommodate more guests than those built before 1930.

How many guests a hotel can accommodate has virtually no bearing on the quality of the carpentry.  If the observations about differences in quality of carpentry were made from some kind of survey of hundreds of hotel guests, perhaps we could deduce that more had stayed in pre-1930 hotels simply because those hotels can accommodate more guests.  But, the observation was in fact made by a single guidebook writer, a single person, who presumably stayed in a very large number of hotels.  That persons conclusions presumably would have absolutely nothing to do with how many other people are staying in the hotel.  This fact may well be true, but it’s irrelevant to this argument.

C. The materials available to carpenters working before 1930 were not significantly different in quality from the materials available to carpenters working after 1930.

Same materials in both time periods would not provide an alternative explanation for the difference in quality between pre-1930 and post-1930 hotels.  In fact, arguably, this fact would strengthen the argument, not weaken it.

D. The better the quality of original carpentry in a building, the less likely that building is to fall into disuse and be demolished.

This is fascinating.  Old buildings with fine carpentry are more likely to be around still.  Old buildings with mediocre carpentry are more likely to be no longer with us.  Remember, the guidebook writer was implicitly speaking of proportions.  The factual observation was, essentially: if we look at the proportion of pre-1930 hotel that have fine carpentry, and the proportion of post-1930 hotel that have fine carpentry, then the first proportion is greater than the second proportion.  The guidebook writer argued that differences in the quality of the carpenters caused this difference in proportions.

This new fact provides an alternative explanation.  Suppose carpenters now are just as good, just as skillful and careful, as carpenters from before 1930.  For simplicity, suppose, on average, 3% of hotels built have fine carpentry, and the other 97% have mediocre/substandard carpentry, and assume that was just as true before 1930 as it is now.  For hotels build before 1930, essentially all of those hotels with poor carpentry would have been knocked down, and the only ones still standing would be the 3% that had fine carpentry.  Thus, when the guidebook writer goes to pre-1930 hotels still standing, still in service, the carpentry in almost all of them is of high quality.  By contrast, hotels build in the past decade are all still standing, regardless of the quality of the carpentry.  When the guidebook writer goes to these, only 3% have fine carpentry, and the rest do not.  Thus, the guidebook writer could experience vast differences in the proportion of hotels with fine carpentry, and it would have nothing to do with the inherent quality of the respective carpenters.  This is the correct answer.

E. The average length of apprenticeship for carpenters has declines significantly since 1930.

If anything, this would strengthen the argument.  It would explain why pre-1930 carpenters would be more skillful.  This does not weaken the argument.

Notice that we were asked to weaken the argument, and a couple of the answers did the opposite: provided information to strengthen the argument.  That’s a typical GMAT CR pattern.  Similarly, when you are asked to strengthen an argument, expect to see a couple answer choices that weaken the argument.

Notice, also, in all five answer choices, our reasoning was deeply bound to the context itself.  We had to think through the details of the context to separate what was relevant from what was not relevant.  That is quite different from the exercises of formal logic, which tends toward abstraction.  GMAT CR logic is all about getting our hand dirty in the rough and tumble of real-world issues.  That what the GMAT asks you to do because, once you’re a manager with your MBA and you’re out in the business world making decisions, that’s precisely what you are going to be doing all day every day in your job.

If you want to improve your GMAT CR logic, don’t read textbooks on formal logic.  Read The Wall Street Journal and The Economist magazine: they both elucidate clearly the logic needed in the business world.

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### One Response to Formal Logic and GMAT Critical Reasoning

1. Binit September 4, 2015 at 10:26 pm #

Hi Mike,
A very useful topic, I must say. I always had this doubt, unknowingly residing in my mind. You helped in bringing it up.
I ll take care of the caveat. Thanks a ton.

Binit.

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