GMAT: Spot the Math Traps in Critical Reasoning

by on March 8th, 2018

write_applicantsAs soon as I saw this question, I knew I had to write about it. The ability to handle this question depends on a certain kind of quantitative reasoning that you’re absolutely going to have to use in business school—indeed, in business in general!

Quantitative reasoning is sort of like math, but not exactly. It’s really about the ability to think about quantitative topics or to understand how to reason around a topic that deals with numbers. That’s pretty much the heart of b-school.

The other nice aspect of this problem is that it’s a somewhat less common Critical Reasoning (CR) question type, so I don’t often get a chance to talk about it. But I think this often represents real-world reasoning that we all have to do, so it’s a great chance to practice getting better.

Okay, without further ado, try this problem from the free GMATPrep® exams and then we’ll talk about how this question works!

“The violent crime rate (number of violent crimes per 1,000 residents) in Meadowbrook is 60 percent higher now than it was four years ago. The corresponding increase for Parkdale is only 10 percent. These figures support the conclusion that residents of Meadowbrook are more likely to become victims of violent crime than are residents of Parkdale.

“The argument above is flawed because it fails to take into account

“(A) changes in the population density of both Parkdale and Meadowbrook over the past four years

“(B) how the rate of population growth in Meadowbrook over the past four years compares to the corresponding rate for Parkdale

“(C) the ratio of violent to nonviolent crimes committed during the past four years in Meadowbrook and Parkdale

“(D) the violent crime rates in Meadowbrook and Parkdale four years ago

“(E) how Meadowbrook’s expenditures for crime prevention over the past four years compare to Parkdale’s expenditures”

Let’s start by talking about what you need to do for Flaw questions in general. Then we’ll tackle the problem.

Flaw questions are part of the Assumption Family (Assumption, Strengthen, Weaken, Evaluate, or Flaw). Any arguments in this family will provide you with some kind of premise(s) and conclusion. The argument will be making at least one assumption—something the author assumes to be true in drawing her conclusion even though she doesn’t explicitly state this assumption in the argument. And that unstated assumption is going to be the key in solving the problem.

Let’s see how this plays out in the above problem.

 Step 1: Identify the Question

How do you know that this is a Find the Flaw question in the first place?

The word flaw in the question stem stands out. :D The fails to take into account language is also a good sign. The question is basically asking you why the argument is poorly constructed (or flawed!).

Step 2: Deconstruct the Argument

Before I even read this, I could see that the text included numbers. There are a few common themes that come up again and again when a CR question includes numbers—and one of these has to do with percents, a characteristic this problem also includes.

The key concept they tend to play off of is the disconnect between percents and real numbers. When someone tells you something about percents, and only percents, you know nothing about the actual underlying (or real) numbers.

For example, if I tell you my pizza consumption increased by 100% last month but my pasta consumption went down 50%, that doesn’t mean I ate more pizza than pasta last month. It might be that my pizza starting point was just 1 slice, so a 100% increase brought me up to 2 slices. And maybe I ate pasta 20 times last month, so a 50% reduction brings me down to 10 bowls of pasta. Really, anything is possible when I only tell you about percentages, not real numbers.

So immediately be skeptical as soon as you see a CR talking about percents. Look for anything they might tell you about real numbers—and, wherever they don’t, think about how you can manipulate the interpretation to give you many possible outcomes.

Okay, let’s talk about the actual argument.

M: VCR = 60% higher

P: VCR = 10% higher

[Thinking to myself: Does this tell me anything about whether M or P has more actual crime? No real numbers. Anything is possible!]

 © M res more VC than P res

And I’m already thinking, Nope! I can’t actually tell that. If P already had a ton of crime, then going up by “only” 10% could still leave the crime rate much higher than it is in M with its 60% increase.

Step 3: State the Goal

On Flaw questions, the goal is to find the answer that explains the flawed reasoning in the argument. What is that on this one?

The author assumes that a higher percentage increase translates to a higher actual number. But it might not.

Now, note the question stem again. The argument fails to take into account (the correct answer). So the argument fails to take into account that P might have had a much higher crime rate to start with or that M had a really low crime rate.

Step 4: Work from Wrong to Right

All right, let’s dive in.

“(A) changes in the population density of both Parkdale and Meadowbrook over the past four years”

The population density alone isn’t the issue. The key point is really around the starting level of crime four years ago or the actual level of crime at any point in this timeframe.

“(B) how the rate of population growth in Meadowbrook over the past four years compares to the corresponding rate for Parkdale”

Again, population growth is not the issue. The level of crime, or crime rate, is the issue.

“(C) the ratio of violent to nonviolent crimes committed during the past four years in Meadowbrook and Parkdale”

This one does mention crime, but they’re trying to distract me. The argument discusses only violent crime, so making a distinction between violent and nonviolent crime is irrelevant to the argument.

“(D) the violent crime rates in Meadowbrook and Parkdale four years ago”

Yes! This is exactly the problem! The author completely fails to address what the actual crime rates were, and that’s why we can’t actually draw any conclusion about the relative levels of crime. All we know is the percentage change—but percentage change of what base number? No idea.

“(E) how Meadowbrook’s expenditures for crime prevention over the past four years compare to Parkdale’s expenditures”

Nope. The argument doesn’t discuss preventing crime or costs for preventing crime.

The correct answer is (D).

What did you learn on this problem? Come up with your own takeaways before you read mine below.

Key Takeaways for Flaw Problems:

(1) Know how to identify the question type. On CR, this usually means some form of the word flaw and the answer should be something that the argument fails to consider in some way.

(2) Lay out the premises and the conclusion so that you can think about the gap between them. The assumption “lives” in that gap—it’s something the author didn’t say but nevertheless must believe in order to get from the premises to the conclusion.

(3) If the concept of percent comes into play, immediately see what real numbers you have actually been given—and what you have not been given. There’s a very good chance that the gap will be around assuming something about the real numbers that may or may not actually be the case. If you can find that, you’ve found your flaw.

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

Ask a Question or Leave a Reply

The author Manhattan Prep gets email notifications for all questions or replies to this post.

Some HTML allowed. Keep your comments above the belt or risk having them deleted. Signup for a Gravatar to have your pictures show up by your comment.