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Advanced Critical Reasoning Lesson: RTFQ

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Advanced Critical Reasoning Lesson: RTFQ  [#permalink]

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New post 20 Jan 2015, 05:20
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Advanced Critical Reasoning Lesson: RTFQ


From the Manhattan GMAT Blog


So 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.
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Re: Advanced Critical Reasoning Lesson: RTFQ  [#permalink]

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New post 20 Jan 2015, 05:30
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ADVANCED CRITICAL REASONING, Part II: Deductive Logic


My last article discussed the difference between inductive and deductive arguments. Today’s article will focus mostly on the rules of deductive arguments. I promise to nerd out on inductive reasoning in later articles.

Here’s a quick quiz on the difference between inductive and deductive logic: http://www.thatquiz.org/tq/previewtest? ... 1355243858

To review: In a deductively “valid” argument, if all the premises are true, the conclusion must also be true, with 100% certainty. Luckily, on the GMAT, we should usually act as if the premises of an argument are true, especially when the question specifies, “the statements above are true.”

Deductive reasoning shows up most often on inference (aka “draw a conclusion”) questions and “mimic the reasoning” questions, but it often appears on other types of questions, and even on reading comprehension!

On inference questions, the correct answer will usually be deductively valid (or very very strong, inductively). An incorrect answer will be deductively invalid, with some significant probability that it could be false.

What follows are most of the formal rules of deductive reasoning (from a stack of logic textbooks I have on my shelf), with examples from the GMAT. For shorthand, I’ll label the arguments with a “P” for premise and a “C” for conclusion:

P) premise
P) premise
C) conclusion

Remember: these are not the same kind of conclusions (opinions) you’ll see on strengthen and weaken questions. Deductive conclusions are deductively “valid” facts that you can derive with 100% certainty from given premises.

EASY STUFF: Simplification/conjunction (“and” statements)

This is kind of a “duh” conclusion, but here goes: If two things are linked with an “and,” then you know each of them exist. Conversely, if two things exist, you can link them with an “and.”

Simplification:

P) A and B
C) Therefore, A

Conjunction:

P) A
P) B
C) Therefore, A and B

P) Bill is tall and was born in Texas.
P) Bill rides a motorcycle.
C) Therefore, Bill was born in Texas (simplification).
C) Therefore, at least one tall person named Bill was born in Texas and rides a motorcycle (conjunction).

CAUTION: Fallacies ahead!!

Don’t confuse “and” with “or.” (More about this later.) More importantly, don’t confuse “and” with causality, condition, or representativeness. Bill’s tallness probably has nothing to do with Texas, so keep an eye out for wrong answers that say, “Bill is tall because he was born in Texas” or “Most people from Texas ride motorcycles.”

MEDIUM STUFF: Disjunctive syllogism (“or” statements)

With “or” statements, if one thing is missing, the other must be true.

Valid conclusions:

P) A or B
P) not B (shorthand: ~B)
C) Therefore, A

P) We will go to the truck rally or to a Shakespeare play
P) We won’t go to the Shakespeare play.
C) Therefore, we will go to the truck rally.

CAUTION: Fallacies ahead!!

Unlike in the real world, “or” statements do not always imply mutual exclusivity, unless the argument explicitly says so. For example, in the above arguments, A and B might both be true; we might go to a play and go to the movies. Yes, really. A wrong answer might say “We went to a play, so we won’t go to the movies.” This error is called “affirming the disjunct.”

Invalid:

P) A or B
P) B
C) Not A

GMAT example:

To see this in action, check out your The Official Guide for GMAT Review 13th Edition, by GMAC®*, question 41. This argument opens with an implied “or” statement:

“Installing scrubbers in smokestacks and switching to cleaner-burning fuel are the two methods available to Northern Power…”

The author here incorrectly assumes that by using one method, Northern Power can’t use both methods at the same time. Question 51 does the same thing; discuss it in the comments below?

TOUGH STUFF: Fun with conditional statements

This is important! Keep a sharp eye out for statements that can be expressed conditionally and practice diagramming them. Look for key words such as “if,” “when,” “only,” and “require.”

I use the symbol “–>” to express an if/then relationship, and a “~” to express the word “not.” Use single letters or abbreviations to stand in for your elements.

If/then statements:

If you jump into that mud, you will get dirty: J –> D

If you don’t stop, I will faint: ~S –> F

I will scream if I hear that Bieber song again: B –>S

I will go only if you buy me dinner: Go –> Din

(Hint, replace the words “only if” with the arrow. See necessary/sufficient below.)

Extreme categorical statements (all, none, every, each, only, always, never):

I always go bowling on Tuesdays: T –> B

Every dog has ears: D –> E

Only teenagers listen to Bieber: B –> T (notice that “only” is backwards from “every”)

No Librarians are Constructivists: L –> ~C

None of my friends eat sushi: F –> ~S

“or” statements:

I will order the cake or the pie: ~C –> P (and ~P –> C)

If you run across the word “unless,” it might help to replace it with “if not”:

I will show up to the barbecue unless its raining.

(“If not” raining, then BBQ): ~R –> B

Necessary/Sufficient statements (need, required, guarantee)

Remember this: Sufficient (guarantee, enough) goes on the left; Necessary (need, requirement) on the right

Sufficient –> Necessary

A good party needs beer: P –> B

A Katy Perry album guarantees a good time: KP –> GT

GMAT example:

Check out CR question 60 from the Official Guide for GMAT Review 13th Edition, by GMAC®. Brackets mine:

“Neither a rising standard of living [RSL] nor balanced trade [BT], by itself establishes a country’s ability to compete[C] in the international marketplace. Both are required simultaneously…”

Diagram this: C –> RSL & BT (both are necessary)

DON’T diagram this: RSL or BT –> C (each is sufficient)

Now, answering the question should be easy. Go for it.

VALID CONCLUSIONS FROM CONDITIONAL STATEMENTS

There are only a few valid deductions one can make from conditionals, and MANY invalid ones. Obviously, you won’t be tested on the Latin names, so worry more about the rules themselves and how they apply

Modus Tollens

Latin for “method that affirms by affirming,” this one more or less repeats the conditional statement as given:

P) A –> B
P) A
C) Therefore, B

If you think that’s too easy, check out Official Guide Question 60 again. It uses Modus Tollens!

P) A –> B & C
P) A
C) Therefore, B & C

Modus Ponens (the “contrapositive”)

EXTREMELY COMMON! Latin for “method that denies by denying,” this shows up all over the GMAT.

P) A –> B
P) ~B
C) Therefore, ~A

P) If you’re in Auckland, you’re in New Zealand
P) You’re not in New Zealand
C) Therefore, you’re not in Auckland

I (and many others) call this the contrapositive. To find the contrapositive, “flip and negate.” Just swap the elements and change negatives to positives:

X –> Y
~Y –> ~X

If you’re a libertarian, you’re not a communist: L –> ~C

Therefore: C –> ~L (If you’re a communist, you’re not a libertarian)

If you jump into that mud, you will get dirty: J –> D

~D –> ~J

If you don’t stop, I will faint: ~S –> F

~F –> S

Try diagramming the contrapositive for all the examples you’ve seen so far.

Advanced note: If a conditional contains an “and” or an “or,” change “and” to “or” and vice versa in the contrapositive. Remember to negate everything.

A –> B or C

(If I get a raise, I’ll go on vacation or buy a car.)

~B and ~C –> ~A

(I didn’t buy a car AND I didn’t go on vacation, so you know I didn’t get a raise.)

This works well with necessary/sufficient reasoning:

A good party needs beer and chips (remember, necessary elements go on the right):

P –> B and C

Therefore, ~B or ~C –> ~P

No beer? Not a good party. No chips? Not a good party.

GMAT example:

The Official Guide for GMAT Review 13th Edition, by GMAC®, question 103. Brackets mine:

“For a trade embargo [TE]…to succeed, a high degree of both international accord [IA] and ability to prevent goods [PG]…must be sustained.”

I diagram it like this: TE –> IA and PG

Then I do the contrapositive: ~IA or ~PG –> ~TE

If one of those elements is missing, you can’t have a trade embargo–much like our party without chips above. Work out the rest of the question for yourself.

Hypothetical Syllogism

Easy enough. You can chain if/then statements if they work out left to right:



P) A –> B
P) B –> C
C) Therefore, A –> C

GMAT Example:

This is a free question from the GMATPrep® software v.2.1*:

Increases in the level of high-density lipoprotein (HDL) in the human bloodstream lower bloodstream-cholesterol levels by increasing the body’s capacity to rid itself of excess cholesterol. Levels of HDL in the bloodstream of some individuals are significantly increased by a program of regular exercise and weight reduction.

Which of the following can be correctly inferred from the statements above?

(A) Individuals who are underweight do not run any risk of developing high levels of cholesterol in the bloodstream.
(B) Individuals who do not exercise regularly have a high risk of developing high levels of cholesterol in the bloodstream late in life.
(C) Exercise and weight reduction are the most effective methods of lowering bloodstream cholesterol levels in humans.
(D) A program of regular exercise and weight reduction lowers cholesterol levels in the bloodstream of some individuals.
(E) Only regular exercise is necessary to decrease cholesterol levels in the bloodstream of individuals of average weight.

You can chain the premises using conditionals as follows

Premise) incHDL –> lowBCL (B –> C)
Premise) someEX –> incHDL (A –> B)
Conclusion) Therefore, someEX –> lowBCL (A –> C)

Which is, more or less, the correct answer a nutshell. Work it out for yourself.

(Keep an eye out for words like “some” and “most” by the way)

CAUTION: Fallacies ahead!!

One common way the GMAT constructs wrong answers (and incorrect assumptions) is to mess up conditional logic in some way or another. Wrong answers will flip without negating, negate without flipping, confuse necessary with sufficient, mess up syllogisms, and make a series of either/or mistakes.

Flipping without negating (Affirming the consequent)

Invalid:

P) A –> B
P) B
C) Therefore, A

If you’re in Auckland, you’re in New Zealand. You’re in New Zealand. Therefore, you must be in Auckland.

(Nope, you might be in Auckland, but there are lots of other places you could be in New Zealand other than Auckland: Wellington, Nelson, Hobbittown, etc.)

This one is common in politics as well as on the GMAT:

No democrats are republicans (D –> ~R). You’re not a republican, so you must be a democrat (R –>~D).

(Nope, there are a lot of other political parties in the world…)

Negating without flipping (Denying the antecedent)

Invalid:

P) A –> B
P) ~A
C) ~B

If you’re in Auckland, you’re in New Zealand. You’re not in Auckland, so you can’t be in New Zealand.

No democrats are republicans (D –> ~R). You’re not a democrat, so you must be a republican (~D –> R).

Confusing necessary with sufficient or sufficient with necessary:

A good party needs chips and beer. We have chips and beer, so it’s going to be a good party.

(Nope, there may be other necessary requirements to a good party, such as music, a place to have the party, actual other people…)

Chopping off your leg is a guarantee that you’ll lose 30 pounds. Bill lost 30 pounds, so he must have chopped off his leg.

(There are other sufficient ways to lose 30 pounds.)

GMAT examples:

The Official Guide for GMAT Review 13th Edition, by GMAC®, question number 103: Remember this?

“For a trade embargo [TE]…to succeed, a high degree of both international accord [IA] and ability to prevent goods [PG]…must be sustained.”

One of the wrong answers says:

(B) As long as international opinion is unanimously against Patria, a trade embargo is likely to succeed.

Which is a whole lot like saying: “I have chips, so it’s going to be a good party!”

Even on other kinds of questions, the GMAT will confuse necessary/sufficient in wrong answers:

From the GMATPrep® 2.1 CAT exam practice test*, on one assumption question, the argument states:

“The interview is an essential part of a successful hiring program”

(Interview is necessary: SHP –> Int.)

Whereas one of the wrong answers states:

“A hiring program will be successful if it includes interviews.”

(An interview is sufficient: Int. –> SHP)

Syllogism Fallacies:

Be careful how you link syllogisms. Make sure they chain up correctly.

Invalid:

P) A –> B
P) A –> C
C) B –> C

Many wrong answers do this in weird ways. See Official Guide question 103:

“(E) For a blockade of Patria’s ports to be successful, international opinion must be unanimous.”

Either/Or fallacies (Affirming the disjunct)

We’ve covered this already, but to sum up: When you see “or” statements on the GMAT, pay attention to the precise phrasing.

Are the two things mutually exclusive (Cats and Dogs)? If so, do those two categories account for everything in the universe? Or are there possibilities of being other things? If so, you might want to diagram it as follows:

C –> ~D
D –> ~C

So it would be invalid to say: “That’s not a dog, so it must be a cat.” (~D –> C). You never know, it might be a wombat or the Empire State Building.

Seems obvious, but people do it all the time: (You’re not a democrat, so you must be a republican.)

On the other hand, is it a simple “or” statement that leaves the possibility of both things being true? (See disjunctive syllogism way earlier). “A or B” should be diagramed as:

~A –> B
~B –> A

Premise: My light doesn’t work. Either the power is out or the bulb is blown.

(~P or ~B)

Valid conclusion: The power is working, so the bulb must be blown. (P, so ~B)

Invalid conclusion: The bulb is blown, so the power must be working. (~B, so P) (Both things could be true)

Again, check out Official Guide questions 41 and 45!

IN CONCLUSION

Overwhelmed? Don’t be. The most important rule to remember is this:

Premise) A –> B
Conclusion) ~B –> ~A
Wrong) B –> A, ~A –> B

Otherwise, I just wanted to expand your mind a little, make you aware of the ways in which the GMAT construct right and wrong answers, and to give you some tools to deeply analyze tough Critical Reasoning questions.

From now on when you struggle with a CR question, try to figure out which logical fallacy the test writers used to construct each wrong answer (during the review process, NOT on the test itself).

For example: take the HDL problem we discussed earlier. You now know how the correct answer was written. What about the incorrect ones? Can you spot the fallacies at work? Please discuss in the comments section.

Increases in the level of high-density lipoprotein (HDL) in the human bloodstream lower bloodstream-cholesterol levels by increasing the body’s capacity to rid itself of excess cholesterol. Levels of HDL in the bloodstream of some individuals are significantly increased by a program of regular exercise and weight reduction.

Which of the following can be correctly inferred from the statements above?

(A) Individuals who are underweight do not run any risk of developing high levels of cholesterol in the bloodstream.
(B) Individuals who do not exercise regularly have a high risk of developing high levels of cholesterol in the bloodstream late in life.
(C) Exercise and weight reduction are the most effective methods of lowering bloodstream cholesterol levels in humans.
(D) A program of regular exercise and weight reduction lowers cholesterol levels in the bloodstream of some individuals.
(E) Only regular exercise is necessary to decrease cholesterol levels in the bloodstream of individuals of average weight.

Have fun! There’s a cool quiz here: http://www.think-logically.co.uk/lt.htm

More to come. If there are specific issues or questions you want me to cover, let me know.

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

* The text excerpted above from The Official Guide for GMAT Review 13th Edition is copyright GMAC (the Graduate Management Admissions Council). The short excerpts are quoted under fair-use statutes for scholarly or journalistic work; use of these excerpts does not imply endorsement of this article by GMAC.

Primary source: Critical Thinking, by Jamie Carlin Watson and Robert Arp. Continuum International Publishing.
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Re: Advanced Critical Reasoning Lesson: RTFQ  [#permalink]

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Advanced Critical Reasoning, Part 3: Strike a P.O.S.E.



My last two articles (part 1 and part 2) gave you some advanced tools to analyze deductive reasoning. Now it’s time to dive into the wonderful world of inductive reasoning, which appears much more often, especially in the following GMAT question types:

• Assumption
• Strengthen
• Weaken
• Evaluate
• Fill in the blank
• Identify the role
• Identify the overall reasoning
• Identify the conclusion
• Mimic the reasoning (sometimes)

According to Wikipedia:

“Inductive reasoning (as opposed to deductive 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.”

Therefore, in inductive arguments, conclusions are a matter of opinion, some more strongly supported than others.

Beyond the basics: P.O.S.E.

First, from class and your own study, you should be able to DECONSTRUCT arguments–in other words, identify the background, conclusion, premises, counterpoint, and counter premises of all inductive arguments. Our books cover that skill thoroughly if you need more work.

Next, you should learn to categorize each conclusion by type.

Fortunately, the GMAT uses only a few basic argument patterns, with similar assumptions and a limited number of ways to strengthen or weaken those assumptions. If you can spot and name those patterns, you’re well on your way to drastically improving your CR score.

I combed through every available CR question I could find, and discovered that the GMAT only writes 4 types of conclusions: predictions, opinions, solutions, and explanations (acronym P.O.S.E.)

Predictions: Something that “will” happen sometime in the future, using past or present circumstances to make that prediction.

Opinions: Interpretations of facts or data–often value judgments (good/bad/true false). I use “opinion” as a catchall category for anything that doesn’t fall under the other three.

Solutions: Plans, recommendations, solutions to problems, strategies, or suggestions of what someone “should” or “must” do.

Explanations: WHY something happened, or the cause of some phenomenon.

In future articles, I’ll divide the pie even more, showing you how the GMAT uses logical fallacies so common that they have Latin names, but for now let’s just stick to the big four.

P.O.S.E. Exercise:

The following are conclusions quoted from The Official Guide for GMAT Review 13th Edition, by GMAC®, questions 27 – 42. Name the TYPE. Is it a solution, prediction or explanation? If you can’t name it as one of those three, just call it an opinion for now. If you want more information, open your book and look at the whole argument, including the question stem. Write down your ideas before you look at mine.

27. “Clearly, therefore, insurance companies are making a greater profit on collision-damage insurance in Greatport than in Fairmmont.”
28. “Clearly, it can be concluded that the number of new jobs created this year will fall short of last years record.”
29. “The government ministry plans to reassure worried gardeners by…”
30. “To help track the ruffle’s spread, government agencies have produced wallet-sized cards about the ruffle.”
31. “This fact, however, does not indicate that most chickens are immune to the virus…”
32. “We can conclude that inflation is on an upward trend and the rate will still be higher next year. ”
33. “This proposal, however, is ill conceived.”
34. “…for economic reasons alone the board should be disbanded.”
35. “Thus, the loss to the industry is quite small…”
36. “That assumption, however, is evidently false.”
37. “Therefore, the decrease in coffee consumption must have been caused by consumer’s awareness of the harmful effects of coffee.”
38. “It should be expected that…”
39. “Thus, Sviatovin must have been written between 1165 and 1167…”
40. “The Mooreville Transit authority plans to…Officials predict that…”
41. “Therefore, by installing scrubbers, Northern Power will be doing the most that can be done…”
42. “Therefore, to reduce shipping time, Trancorp plans to switch to trains…”

Answers: (If you saw something different, let me know in the comments section, and we can debate!)

27. Opinion (interpretation of studies)
28. Prediction
29. Solution/Plan. Check out the word “plan” in the question, too!
30. Solution/Plan. Check out the word “action” in the question…
31. Opinion. If you said explanation, I’ll accept that.
32. Prediction. The word “will” is a big hint.
33. Solution (or rejection of a solution). “Proposal” is usually some kind of solution or recommendation.
34. Solution
35. Opinion
36. Opinion
37. Explanation! The words “caused by” are a big hint.
38. Prediction
39. Opinion
40. Solution (“plans to”) AND prediction.
41. Opinion. Not quite a prediction of the future, despite the word “will.”
42. Solution

How’d you do? You can do this exercise with the WHOLE official guide in less than an hour. I highly recommend it!

But why?

Wouldn’t it be nice, on the real GMAT, to see a dozen arguments you’ve seen a hundred times already? Similar conclusions have similar assumptions. And similar assumptions have similar ways to strengthen, weaken, and evaluate. If you can categorize using P.O.S.E, you can answer everything faster and more accurately.

ANALYSIS WITH REAL GMAT QUESTIONS

Here are the basics of how to analyze and answer using P.O.S.E.:

OPINIONS

As I said before, every inductive conclusion is an opinion. Therefore, I’m going to start here. The generic pattern is as follows:

Conclusion: Opinion, interpretation, declarative statement, or judgment call.
Premises: Facts, information, data, statistics, circumstances, etc.
Assumptions: The author is assuming that the facts are RELEVANT to his or her conclusion, the facts are SUFFICIENT to prove the conclusion (with a high probability), and there are NO OTHER FACTORS that would decrease the probability of the conclusion.

Strengthen: Add factual evidence that increases the probability of the conclusion. Conversely, you can remove/disprove a factor that would decrease the probability of the conclusion.

Weaken: Add evidence (another factor) that decreases the probability of the conclusion.

GMAT example: Art’s Decline from GMATPrep® practice test software.

Reviewer: The book Art’s Decline argues that European painters today lack skills that were common among European painters of preceding centuries. In this the book must be right, since its analysis of 100 paintings, 50 old and 50 contemporary, demonstrates convincingly that none of the contemporary paintings are executed as skillfully as the older paintings.

Which of the following points to the most serious logical flaw in the reviewer’s argument?

(A) The paintings chosen by the book’s author for analysis could be those that most support the book’s thesis.
(B) There could be criteria other than the technical skill of the artist by which to evaluate a painting.
(C) The title of the book could cause readers to accept the book’s thesis even before they read the analysis of the paintings that supports it.
(D) The particular methods currently used by European painters could require less artistic skill than do methods used by painters in other parts of the world.
(E) A reader who was not familiar with the language of art criticism might not be convinced by the book’s analysis of the 100 paintings.

Analysis:

1) RTFQ
Some LSAT teachers might call this a “flaw” question, but since the correct answer will attack the conclusion, you can just call it a “weaken” question.

2) Deconstruct
Conclusion: “In this [painters today lack skills] the book must be right.”
Notice how this is more of a value judgment than a prediction, explanation, or solution, so we can just call it a general “opinion.”

Premise: In the 100 paintings in the book, the 50 old ones were more skilled than the 50 contemporary.

With any opinion, ask yourself the following questions:

Are the premises RELEVANT? Are these 100 paintings representative of ALL old and contemporary paintings?
Are the premises SUFFICIENT? Are 100 paintings enough to prove a blanket statement about all European artists?
Could there be OTHER FACTORS? Are there other paintings not in the book that might disprove this conclusion?

3) State the goal:
We need to find an answer that proves these 100 paintings are irrelevant/unrepresentative, or that there’s another factor that makes contemporary painters just as skilled, if not more skilled, than the old ones.

4) POE (Process Of Elimination)
The correct answer (A) indicates that the paintings might have been selected to prove the thesis (an unrepresentative sample), and suggests there may be other paintings that disprove the conclusion.

PREDICTIONS

Key words: predict, will, probably, future, trend, etc.

Conclusion: Something “will” happen in the future.

Premises: A description of past events, or a description of the present.

Assumptions: The past (or present) is the same as the future, with no significant differences. Nothing will change to affect the future.

To strengthen: Show that nothing will change, that trends occurring in the present will continue in the same direction.

To weaken: Show that something significant is going to change.

GMAT Example: Gortland from GMATPrep® practice test software.

Gortland has long been narrowly self-sufficient in both grain and meat. However, as per capita income in Gortland has risen toward the world average, per capita consumption of meat has also risen toward the world average, and it takes several pounds of grain to produce one pound of meat. Therefore, since per capita income continues to rise, whereas domestic grain production will not increase, Gortland will soon have to import either grain or meat or both.

Which of the following is an assumption on which the argument depends?

(A)The total acreage devoted to grain production in Gortland will soon decrease.
(B)Importing either grain or meat will not result in a significantly higher percentage of Gortlands’ incomes being spent on food that is currently the case.
(C)The per capita consumption of meat in Gortland is increasing at roughly the same rate across all income levels.
(D)The per capita income of meat producers in Gortland is rising faster than the per capita income of grain producers.
(E) People in Gortland who increase their consumption of meat will not radically decrease their consumption of grain.

Analysis:

1) RTFQ:
First of all, this is an assumption question. The answer will support the argument. In fact, the argument won’t hold up without this assumption.

2) Deconstruct:
Conclusion: “Gortland will soon have to import grain or meat or both.”
AHA! The word “will” indicates the author is making a prediction.

Predictions often make the assumption that nothing else will change. We know consumption of meat is in the rise, so the author is assuming that consumption of grain will stay the same.

3) State the goal:
I predict that the answer will say something to the effect of “nothing else changes.”

4) POE (Process Of Elimination)
The only two answers that imply, “things WON’T change” are (B) and (E). But (B) mentions income, which is irrelevant to the prediction. And if people did decrease their grain consumption, the conclusion would fall apart. (E) must be the answer.

EXPLANATIONS

(By the way, I plan a whole future article on causal/correlation flaws, so this is just an intro.)

Key words: due to, result of, cause, because, reason why, etc.

Conclusion: Event A caused Event B (causation).

Premises: Event A occurred. Event B also occurred (correlation).

Assumptions: Event A is the only cause. There are no other causes. Event B did not cause event A (not reversed). It’s not a coincidence.

To strengthen: Provide evidence for a causal link. Eliminate potential other causes. Show that the purported cause happened first (and very close in time). With a control group, show what happens when you remove the proposed cause (no cause = the effect should go away).

To weaken: Show evidence another cause. Prove it was a coincidence. Show the cause without the effect. Show the effect without the cause. Show that B was actually the cause of A.

GMAT Example: Sea Otters from GMATPrep® practice test software.

In the late 1980s, the population of sea otters in the North Pacific began to decline. There are two plausible explanations for the decline: predation, possibly by killer whales, or disease. Of these two, disease is the more likely, since a concurrent sharp decline in populations of seals and sea lions is believed to have been caused by disease, and diseases that infect these creatures are likely to be able to infect sea otters also.

Which of the following, if true, most seriously weakens the reasoning?

(A) Killer whales in the North Pacific usually prey on seals and sea lions but will, when this food source is scarce, seek out other prey.
(B) There is no indication that the sea otter population at any North Pacific location declined in the 1980s because of substantial numbers of sea otters migrating to other locations.
(C) Along the Pacific coast of North America in the 1980s, sea otters were absent from many locations where they had been relatively common in former times.
(D) Following the decline in the population of the sea otters, there was an increase in the population of sea urchins, which are sea otters’ main food source.
(E) The North Pacific populations of seals and sea lions cover a wider geographic area than does the population of sea otters.

Analysis:

1) RTFQ
This is a weaken question. The answer will provide evidence against the conclusion.

2) Deconstruct
“There are two possible explanations […] Of these two, disease is more likely.”
Hey! Looks like we have an “explanation” argument.
In this case, we need to weaken the explanation of disease. The best way to weaken an explanation is to provide evidence of alternative cause–in this case, killer whales.

3) State the goal.
We’re looking for an answer that suggests killer whales are killing the otters.

4) POE
The only answer that even mentions killer whales is (A). And if seals and sea lions are dying of disease, then the killer whales will be going after other food, namely the otters! The answer must be (A).

SOLUTIONS/PLANS

Key words: plan, strategy, proposal, policy, solution, recommendation, action, must, should, profit, etc.

Conclusion: Solution, Plan, or recommendation.

Premises: Problem or situation that need to be improved. Reasons the plan will work.

Assumptions: The solution is effective and complete. It will actually work to cure causes of the problem. The benefits of the solution outweigh the costs, downsides, and side effects. The solution won’t be worse than the problem itself.

To Strengthen: Provide evidence that support the above assumptions.
To Weaken: Show that the costs or side effects outweigh the benefits. Prove the solution is ineffective or incomplete.

GMAT Example: Seaweed solution from GMATPrep® practice test software.

Scientists are discussing ways to remove excess carbon dioxide from the atmosphere by increasing the amount that is absorbed by plant life. One plan to accomplish this is to establish giant floating seaweed farms in the oceans. When the seaweed plants die, they will be disposed of by being burned for fuel.

Which of the following, if true, would indicate the most serious weakness in the plan above?

(A) Some areas of ocean in the Southern Hemisphere do not contain sufficient nutrients to support large seaweed farms.
(B) When a seaweed plant is burned, it releases an amount of carbon dioxide comparable to the amount it has absorbed in its lifetime.
(C) Even if seaweed farms prove effective, some people will be reluctant to switch to this new fuel.
(D) Each year about seven billion tons of carbon dioxide are released into the atmosphere but only about five billion tons are absorbed by plant life.
(E) Seaweed farms would make more money by farming seaweed to sell as nutritional supplements than by farming seaweed to sell as fuel.

Analysis:

1) RTFQ
This is a weaken question. The answer will provide evidence against the conclusion.

2) Deconstruct
“One plan to accomplish this is to establish giant seaweed farms… ”
The word “plan” tells us we have a “solution” argument.
Problem: excess carbon dioxide.
Solution: giant floating seaweed farms to absorb carbon dioxide.

Whenever you’re confronted with a plan or solution, you have to weigh the benefits of the plan against the costs, side effects, and potential downsides.
To weaken a plan, you need to suggest that there’s an unconsidered BAD thing about the plan…

3) State the goal.
We’re looking for an answer that says the seaweed farms are a BAD idea for some reason, especially related to CO2…

4) POE
(A) This seems to suggest that the plan won’t work in some places. This weakens a little, but not enough. We can just put the seaweed farms in a place where they will grow.
(B) HEY! This suggests that burning the plants will release ALL the C02 back into the atmosphere, a serious drawback to the plan to reduce CO2.
(D) This, in a way, actually strengthens the argument…

Looks like (B) shows a big negative side effect of the plan. This must be the answer.

Wrapping up:

Try this on your own with 100 more GMAT examples, especially ones you’ve gotten wrong in the past. Keep track of ways the GMAT likes to strengthen and weaken each type of P.O.S.E conclusion–you’re almost guaranteed to see it again.

Have fun! See you in the land of formal fallacies next!

* The text excerpted above from The Official Guide for GMAT Review 13th Edition is copyright GMAC® (the Graduate Management Admissions Council). The short excerpts are quoted under fair-use statutes for scholarly or journalistic work; use of these excerpts does not imply endorsement of this article by GMAC.

* GMATPrep® questions courtesy of the Graduate Management Admissions Council. Usage of this question does not imply endorsement by GMAC.
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Re: Advanced Critical Reasoning Lesson: RTFQ  [#permalink]

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New post 20 Jan 2015, 15:57
Killer post. Much appreciated, and a well deserved Kudos!
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Re: Advanced Critical Reasoning Lesson: RTFQ  [#permalink]

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New post 14 Feb 2015, 08:23
I have tried implementing the logic explained above; good explanation BUT I need clarification in few things -
1- While reading the "question stem" I infer that it involves deductive logic but the question itself requires us to use Inductive reasoning to get to the correct answer. For example Q 41 from OG 13 is an "Assumption" question, so from question stem I would be ready to go ahead with a mind set that I would use Inductive reasoning to solve this question; but, the answer comes out as a process of applying Deductive Logic??? Big mess at this time - which way to attack the question?? Please help peers...
2- Would it take more time if I start categorizing the problems, even if I practice more than 50 problems?

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Re: Advanced Critical Reasoning Lesson: RTFQ  [#permalink]

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New post 18 Apr 2016, 14:19
Guess what?
Out-of-this-world level of questions!
Should we be clapping or what?
This is nowhere near the hard questions Manhattan or GMAC throws at you.
Ugly Boldfaces, Copy sneaky logics, Irreconcilable differences and lot more are the questions GMAC steadily throws at you when you prove you know one 600level questions too well.

Just look at that lesson above.
It started well like it was going to flummox us with hardcore CR questions.
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Re: Advanced Critical Reasoning Lesson: RTFQ  [#permalink]

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New post 10 Dec 2016, 13:13
Great articles. If anyone is interested for more, thesetwo playlists also provide approachable introduction to formal logic.

I think that in second post Modus Ponens and Modus Tolens should be reversed (Modus Ponens, not Modus Tollens is the “contrapositive”).

Yet, I find it very hard (impossible?) to analyse argument this way in two minutes. I always revert back to usual way of solving the question (i.e. check the reverse causation and other factors for weaken, etc...). But this is useful to know in order to avoid errors when mapping arguments.

souvik101990 wrote:
Syllogism Fallacies:

Be careful how you link syllogisms. Make sure they chain up correctly.


“(E) For a blockade of Patria’s ports to be successful, international opinion must be unanimous.”


I am unable to see how would I show that this is wrong, can anyone help?
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Re: Advanced Critical Reasoning Lesson: RTFQ  [#permalink]

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New post 19 Dec 2016, 13:27
Hi ,

Could you suggest the link for the next article in this topic please ? Great article.

Thanks
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Re: Advanced Critical Reasoning Lesson: RTFQ   [#permalink] 19 Dec 2016, 13:27
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