Advanced Critical Reasoning Lesson: RTFQ

Neil Thornton —  January 25, 2014 — 3 Comments

gmat-critical-reasoningSo your Critical Reasoning (CR) score has moved a little, but not enough. Or each question is still taking you 3 minutes to answer. You’ve studied for months, read the Strategy Guides, taken every practice test, and completed every Critical Reasoning question in the big Official Guide and the Verbal Review supplement so many times you have them all memorized. What more can you do? Do more questions? You can probably imagine, more questions will usually mean more of the same issues, and simply reinforce bad habits…

Chances are, despite all your hard work, you’re still using your intuition and “gut feeling” to answer CR questions. Unfortunately, your gut feeling works some of the time, but not 100% of the time. Remember, the test is designed so that the average person picking what “looks right” will get only 50% of the questions correct.

So what to do? For now, stop doing more questions until you 1) learn the formal rules of logic behind how CR works, and 2) deeply analyze all the questions you’ve done for repeating patterns: question types, patterns of reasoning, logical flaws, right and wrong answer types, etc.

So that’s what the next few weeks will be about. Each week, I’ll post an article that goes absurdly in-depth about one aspect of the logic behind CR, along with exercises to apply those lessons. These are the same exercises I do with my tutoring students, who have found them very effective. I’m also interested in your feedback: what worked for you? What didn’t? Questions and concepts you’re still struggling with? I’m open to discussion and debate.

So let’s get started. I’ll start with the essentials and then really nerd out on formal logic, so keep reading to the end.

LESSON ONE: RTFQ

In our classes, we teach a four-step process to answering CR questions:

1) Identify the question (Know what the question is asking and what kind of question it is)
2) Deconstruct the argument (Analyze each piece of the passage for what role it plays)
3) Pause and state the goal (Predict what the correct answer should do)
4) Work from wrong to right (Use process of elimination to get to the right–or “least wrong”–answer.)

Today’s focus: Step one, which I call RTFQ, as in “Read the F___ Question” (F as in Full! Read the Full question. What were you thinking?)

The basics: The GMAT only asks a limited number of questions, with very rare variation. Each type of question implies HOW you should deconstruct the argument and WHAT the right answer will do. If you don’t identify the question properly, you won’t look for the right things, or you’ll waste time reading for things that aren’t there. So…Right now, can you name them all? No really.

Exercise 1: Before you scroll down, get out your notebook and write down as many types of questions as you can think of. Ready? Go.
.
.
.
.
.

How many did you come up with? 5? 6? Depending on how you break them down (what books you’ve read and who taught you), there are anywhere from 10-13 common types of questions. Here’s a list of the 11 most common that I use, grouped by category.

Structure based:
Identify the bolded part (role in the reasoning)
Identify the overall reasoning
Identify the conclusion
Mimic the reasoning (also known as parallel the reasoning)

Reasoning/assumption based:
Assumption
Strengthen
Weaken (and Flaw questions)
Evaluate
Fill in the Blank

Evidence or fact-based questions:
Inference (also known as “Draw a Conclusion” questions)
Resolve or Explain (a paradox or discrepancy)

I’ll explain more about the categories in future articles, but for now… Can you identify them when they show up? One of the most common mistakes you can make on the GMAT is simply misidentifying the question (e.g. mistaking strengthen for inference or strengthen for explain).

Exercise 2: Pick a dozen questions and name them! Take out your Official Guide for GMAT Review and get to work. Let’s pick numbers 50 through 61. If you need help, skim the passage itself to (All questions excerpted from The Official Guide for GMAT Review 13th Edition, by GMAC®)

50. Which of the following, if true, most strengthens the argument above?
51. The argument is most vulnerable to the objection that it fails to
52. Which of the following, if true, most strongly supports Summit’s explanation of its success in retaining employees?
53. Which of the following strategies would be most likely to minimize company X’s losses on the policies?
54. If the statements above are true, which of the following must be true?
55. Which of the following most logically completes the argument given below?
56. The conclusion above would be more reasonably drawn if which of the following were inserted into the argument as an additional premise?
57. Which of the following, if true, most helps to explain the surprising finding?
58. Which of the following, if true, most seriously weakens the conclusion above?
59. Which of the following most logically completes the passage?
60. If the facts stated in the passage above are true, a proper test of a country’s ability to be competitive is its ability to
61. Which of the following, if true, does most to explain the contrast described above?

And for good measure, identify number 66.

66. Which of the following conclusions about Country Z’s adversely affected export-dependent industries is best supported by the passage?

Write down what you think each one is.

Ready for your answers? Here’s how I identified them, with commentary.

50. Strengthen: Pretty straight up. The correct answer will strengthen the argument above.
51. Weaken: Or more specifically, identify the flaw in the reasoning. The words “it fails to” mean that the right answer, when considered, will damage the argument.
52. Strengthen: Don’t let the word “explain” fool you. The explanation is already in the argument; in fact the explanation may be the conclusion of the argument. Your job is to find an additional piece of evidence to strengthen that explanation.
53. Resolve/Explain: This one was tough. The question implies that there’s a problem (losses) to be solved (“minimize[d]“), which is what many resolve/explain questions do. Also, the argument itself describes a pretty clear contradiction: how does X keep its prices low, but also make enough income to pay for claims? The answer will resolve this. Feel free to argue with me in the comment section, though.
54. Inference (also known as “draw a conclusion”): Notice how “the statements above are true.” That mean you WON’T be looking for premises and conclusions, just putting facts together to find out what else must be true. More about this later in the section about “Deductive Reasoning.”
55. Fill in the Blank: note that the blank part starts with the word “because____” so you’ll be providing a premise that helps the conclusion. So, in a way, you can look at this as a strengthen question, too.
56. Assumption: Yes, assumption, though if you named this as a strengthen question, you’ll probably get it right. Technically, though, when the GMAT asks for an additional or unstated premise that makes the argument “more reasonably drawn” or that is “required,” it’s asking you for the assumption. But it’s interesting to note that assumption and strengthen questions both do the same thing: support the reasoning of an argument.
57. Resolve/explain: NOT strengthen. Imagine walking into your house to find your favorite chair is broken. Explaining WHY it’s broken is far different from Strengthening or fixing the chair with additional support.
58. Weaken: fair enough, easy to spot.
59. Fill in the blank: and with the word “since____” leading off the blank, it’s another strengthen.
60. Inference: Again, “if the statements above are true…” your reading for facts, not arguments.
61. Resolve/explain: again

aaaaand #66?

66. Inference: Yes. Inference. NOT STRENGTHEN! For more about how to differentiate between Inference and Strengthen questions, see our Critical Reasoning Strategy Guide, chapter 6.

So, how’d you do? If you were less than 100%, spend some time with the strategy guide, focusing on how to identify question types. Write down several examples of each question type and quiz yourself some more. You can use the Official Guide Problem Sets in the back of the CR Strategy Guide to see whether you were right or not. Keep working until you’re 100%.

NERDING OUT ON LOGIC

Critical reason is a test of LOGIC. So, with a big stack of logic books next to me, I’m going to discuss some of the formal rules behind the what GMAT writes questions. Ready?

The GMAT uses the word conclusion in two different ways. Most of the time, the GMAT is referring to an “inductive” conclusion, but occasionally, it’s asking about a “deductive” conclusion. Don’t confuse them!
So to explain: There are two kind of reasoning in the word: deductive reasoning and inductive reasoning.

Deductive reasoning is more concrete, more mathematical, more “true.”

Wikipedia’s definition of deductive reasoning: “Deductive reasoning links premises with conclusions. If all premises are true, the terms are clear, and the rules of deductive logic are followed, then the conclusion reached is necessarily true.”

In other words, if the premises are true, then the conclusion must be true. Does this sound like a common question type? (Hint: it starts with an “I____”)

Here are some examples of deductively valid arguments.

Premise: Sally is taller than Frank.
Premise: Frank is taller than William
Conclusion: Sally must be taller than William.
(Other deductively valid conclusions: Frank is shorter than Sally. William is not the same height as sally.)

Premise: All cats are persnickety
Premise: Mr. Whiskers is a cat.
Conclusion: Mr. Whiskers is persnickety.
(Other deductively valid conclusions: Some persnickety things are cats. At least one cat is named Mr. Whiskers.)

Inductive reasoning is a little softer, and much more common on the GMAT and in the real world. Science, economics, medicine, and our justice system are largely based on induction.

Wikipedia’s definition again: “Inductive reasoning is reasoning in which the premises seek to supply strong evidence for (not absolute proof of) the truth of the conclusion. While the conclusion of a deductive argument is supposed to be certain, the truth of an inductive argument is supposed to be probable, based upon the evidence given.”

In other words, if the premised are true, then the conclusion has a probability of being true, but also a probability of being false.

I’m usually sleepy after 11:00pm.
It’s past midnight.
I must be sleepy.

3 out of 4 dentists recommend chewing OctiDent after meals.
You should chew Octident after every meal.

After I cut bacon out of my diet, I lost 5 pounds.
If you want to lose weight, you should cut bacon out of your diet.

Inductively valid arguments have a very high probability of being true, with little chance of contradictory evidence (good scientific theories). Inductively invalid arguments have a high probability of being false (horoscopes). The dividing line between valid and invalid arguments can be shady and can depend on context. 90% certainty would be a great bet at a casino, but a lousy bet on airplane guidance systems.

We’ll get more into how to evaluate inductive reasoning vs. deductive reasoning in later articles, but for now, lets just learn to spot it.

Exercise: peruse the Official Guide questions 50-61 again. Decide whether the question and argument will be based on induction or deduction (Hint: if the argument can be helped or hurt, it’s probably induction. In the conclusion must be true, it’s deduction.)

50. Which of the following, if true, most strengthens the argument above?
51. The argument is most vulnerable to the objection that it fails to
52. Which of the following, if true, most strongly supports Summit’s explanation of its success in retaining employees?
53. Which of the following strategies would be most likely to minimize company X’s losses on the policies?
54. If the statements above are true, which of the following must be true?
55. Which of the following most logically completes the argument given below?
56. The conclusion above would be more reasonably drawn if which of the following were inserted into the argument as an additional premise?
57. Which of the following, if true, most helps to explain the surprising finding?
58. Which of the following, if true, most seriously weakens the conclusion above?
59. Which of the following most logically completes the passage?
60. If the facts stated in the passage above are true, a proper test of a country’s ability to be competitive is its ability to
61. Which of the following, if true, does most to explain the contrast described above?

Answer Key:

50. Induction
51. Induction
52. Induction
53. Induction
54. DEDUCTION
55. Induction
56. Induction
57. Induction (The explanation will be inductively valid.)
58. Induction
59. Induction
60. DEDUCTION
61. Induction

What do you think about question 66? Discuss and debate it in the comments below!

Take some time looking up deductive reasoning vs. inductive reasoning on the web. Wikipedia is a good place to start. Then, start analyzing other questions for the kind of reasoning tested on each. You may find that a lot of the questions you got wrong were one type or the other.

For an advanced drill, dig up all the Inference questions you can find. (I’ll give you a few: 66, 91, 103, and 104) Some of them are asking you for deductively valid conclusions, while others are asking for inductively valid conclusions. Can you determine which is which? Again, post your results in the comments section below.

Get to work, and for now just focus on those questions! See you in future articles.

Neil Thornton

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As the son of an engineer father and English-teaching mother, Neil Thornton has developed a unique ability to break down tough math for poets, as well as to get mathematicians excited about grammar. Neil started teaching SAT classes in 1991 while in college and learned to love beating test-writers at their own game. He’s coached hundreds (thousands?) of students through the GMAT, LSAT, MCAT-verbal, and SAT subject tests (Math level 2 is his favorite) and trained instructors all over the United States. He has scored 99th percentile on the GMAT, LSAT and GRE. Other than teaching, writing, and performing stand-up comedy, Neil spends his free time reading, running, camping, cooking, snowboarding, and juggling fire.

3 responses to Advanced Critical Reasoning Lesson: RTFQ

  1. Correction/Clarification!

    According to some books (i.e. the one I read last night after posting this article), there’s no such thing as a “valid” inductive argument. Because all inductive arguments have a probability of being false (however slight), they are all, technically “invalid.”

    From not on, when discussing inductive reasoning, I’ll be using “strong” inductive reasoning to refer to arguments with a high probability of being true, and “weak” inductive reasoning to refer to arguments with a significant probability of being not true. Again, the difference between strong and weak will depend on context…

  2. Thank you – It’s a fine line of differentiation between inductive & deductive reasoning that takes CR question identification a step further!

    66 – Induction
    91 – Induction
    103 – Induction
    104 – Deduction

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