Large inequalities in wealth always threaten the viability : GMAT Critical Reasoning (CR)
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# Large inequalities in wealth always threaten the viability

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Large inequalities in wealth always threaten the viability [#permalink]

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07 Jun 2005, 16:18
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Large inequalities in wealth always threaten the viability of true democracy, since wealth is the basis of political power, and true democracy depends on the equal distribution of political power among all citizens.

The reasoning in which one of the following arguments most closely parallels the reasoning in the argument above?

(A) Consumer culture and an emphasis on technological innovation are a dangerous combination, since together they are uncontrollable and lead to irrational excess.
(B) If Sara went to the bookstore every time her pocket was full, Sara would never have enough money to cover her living expenses, since books are her love and they are getting very expensive.
(C) It is very difficult to write a successful science fiction novel that is set in the past, since historical fiction depends on historical accuracy, whereas science fiction does not.
(D) Honesty is important in maintaining friendships. But sometimes honesty can lead to arguments, so it is difficult to predict the effect a particular honesty act will have on a friendship.
(E) Repeated encroachments on oneâ€™s leisure time by a demanding job interfere with the requirements of good health. The reason is that good health depends on regular moderate exercise, but adequate leisure time is essential to regular exercise.
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07 Jun 2005, 18:25
E it is.

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07 Jun 2005, 18:40
Wealth is the basis of political power (A<->B)
Democracy depends on equal distribution of politcial power (C<->B)
So large inequalities in wealth threatens true democracy (A->B)

In E we have:
adequate time is essential to exercise (A<->B)
health depends on regular exercise (C<->B)
so repeated encroachments on oneâ€™s leisure time interfere with the requirements of good health (A->B)

I'll go with E
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07 Jun 2005, 20:01
Another one for "E"
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08 Jun 2005, 04:24
(E) again...
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Re: Large inequalities in wealth always threaten the viability [#permalink]

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21 Jun 2013, 16:34
Large inequalities in wealth always threaten the viability of true democracy,
since wealth is the basis of political power and true democracy depends on
the equal distribution of political power among all citizens.

A) Consumer culture and an emphasis on technological innovation are a dangerous combination, since together they are uncontrollable and lead to irrational excess.

B) If Sara went to the bookstore every time her pocket was full, Sara would never have enough money to cover her living expenses, since books are her love and they are getting very expensive

C) It is very difficult to write a successful science fiction novel that is set in the past, since historical fiction depends on historical accuracy, whereas science fiction does not.

D) Honesty is important in maintaining friendships. But sometimes honesty can lead to arguments, so it is difficult to predict the effect a particular honest act will have on a friendship.

E) Repeated encroachments on one's leisure time by a demanding job interfere with the requirements of good health. The reason is that good health depends on regular moderate exercise, but adequate leisure time is essential to regular exercise.

This one showed up for me on Google. I noticed that no one actually took the time to explain their answer, which leads me to conclude that most people achieved the correct answer either by process of elimination or by guessing. Neither strategy is particularly helpful for learning how to answer these questions, so I will endeavor to explain systematically how to solve these questions.

I realize this is a really long post, but it's important that everyone understands the systematic process for solving these questions. It takes time initially to symbolically represent every argument, but with time and practice your speed will improve, and in some cases you will be able to rule out options without even diagramming them.

The first step is to establish whether we are dealing with an argument or merely a set of facts. This is in fact an argument, which means that it has a conclusion. Isolating the conclusion is the first step to properly understanding the argument.

Large inequalities in wealth always threaten the viability of true democracy,
since wealth is the basis of political power and true democracy depends on
the equal distribution of political power among all citizens.

The conclusion is in fact the first statement: [b]Large inequalities in wealth always threaten the viability of true democracy
.

We know this is the case because all of the other statements in the argument (the premises) support this conclusion. This is also established by "since" at the beginning of the second line. Looking closely, we can identify two premises: (1) wealth is the basis of political power, and (2) true democracy depends on the equal distribution of political power among all citizens.

Having isolated our conclusion and supporting premises, we can now turn the admittedly poorly written english sentences into symbolic logic. The purpose of doing this is to clearly isolate the argument structure, so that we can compare the structure to the structure in the supposed parallel arguments in the answer choices.

The first sentence states that large inequalities in wealth threaten the validity of true democracy. A simple way to think about this statement is that in a true democracy (TD), equality of wealth (EW) is necessary:

TD --> EW
~EW --> ~TD

Here we are applying two basic principles of formal logic: sufficient and necessary, and the contrapositive rule (later, we'll apply a third: transposition). In the interest of brevity I won't explain sufficient and necessary except by way of a simple example. All lawyers have graduated law school. Lawyers is sufficient. Law school is necessary. As such, it is only valid to say that if you did not graduate law school you are not a lawyer. That is,

Sufficient --> Necessary: Lawyer --> Graduate Law School
Contrapositive: ~Graduate Law School --> ~Lawyer

It is NOT correct to say that all graduates of law school are lawyers, nor that those who are not lawyers did not graduate law school. It is perfectly possible and in fact often the case that law graduates obtain careers in other fields. The contrapositive above is the only valid argument we can form from the original sufficient-necessary statement.

Let's return to the question. We've established that TD --> EW, and, therefore, ~EW --> ~TD. Remember, this is the conclusion of the argument. Now lets examine the premises to determine the validity of the argument, and dissect its structure.

"wealth is the basis of political power"

If wealth is the basis of political power, that means that wealth is necessary for political power. Since we know our conclusion is talking specifically about equality of wealth, we'll be consistent and say that if we have political power, then we have equality of wealth:

PP --> EW
contrapositive: ~EW --> ~PP

"true democracy depends on the equal distribution of political power among all citizens"

The word depends informs us that equal distribution of political power (PP) is necessary. That means that true democracy (TD) is sufficient.

(If you're having trouble with sufficient and necessary think about to our lawyer-law school example. This premise simply says that if you have a true democracy then you have equal distribution of political power. If equally distributed political power does not exist, then you don't have a true democracy.)

TD --> PP
~PP --> ~TD

Great. We've now symbolically established our conclusion and our supporting premises. Let's put them together so we can get a better sense of what we're dealing with.

P1: PP --> EW
~EW --> ~PP

P2: TD --> PP
~PP --> ~TD

C: TD --> EW
~EW --> ~TD

If you're keen to these sorts of questions, you'll notice that a pattern exists here. If the argument is valid, the premises will necessarily inform the conclusion. And that's the case with this question. Using transposition (all dogs are cats, all cats are frogs, therefore all dogs are frogs), we can combine the premises in order to assert the conclusion:

TD --> PP and PP --> EW

Put it together:

TD --> PP --> EW

Using the rules of transposition (see the dog example above), we can conclude that TD --> EW.

And that is the argument's original conclusion, which we identified above. That means the argument is valid. More specifically, we have a valid transposition argument. (Note: in this example, we didn't need to rely on the contrapositives, but often we do need the contrapositives to properly transpose, which is why we've taken that step).

Great, we've symbolically established the argument. Now let's move on to the answer choices and evaluate them in the same manner:

A) Consumer culture and an emphasis on technological innovation are a dangerous combination, since together they are uncontrollable and lead to irrational excess.

P: CC & TI --> U
~U --> ~ CC or TI

P: U --> IE
~IE --> ~U

C: CC & TI ---> DC
~DC--> CC & TI

We can see that not only does A not show the same argument structure, but it's not even a valid argument. The answer is NOT A.

B) If Sara went to the bookstore every time her pocket was full, Sara would never have enough money to cover her living expenses, since books are her love and they are getting very expensive

P: B --> L
~L --> ~B

P: B --> $~$ --> ~B

C: BS --> ~M
M --> ~BS

B doesn't show the right argument structure. The premises also don't necessarily lead to the conclusion, so it isn't a valid argument. B is out.

C) It is very difficult to write a successful science fiction novel that is set in the past, since historical fiction depends on historical accuracy, whereas science fiction does not.

P: HF --> HA
~ HA --> ~HF

P: SF --> ~HA
HA --> ~SF

C: SFNP --> D
~D --> ~SFNP

Even if we take there to be an implied premise that historical accuracy is difficult to achieve (these questions don't typically rely on an implied premise; the lack of the premise invalidates the argument), the argument structure simply doesn't match our original argument. Delete C.

D) Honesty is important in maintaining friendships. But sometimes honesty can lead to arguments, so it is difficult to predict the effect a particular honest act will have on a friendship.

P: H some A
(cannot apply the contrapositive here)

P: H ??? MF

C: MF --> H
~H --> ~MF

Clearly this argument structure is not analogous to our original question. That it is difficult to predict the effect of honesty on maintaining friendship reveals that we cannot properly transpose this argument. That means that it absolutely cannot be the correct answer.

By process of elimination we've determined that E is the correct answer, but let's break down the argument structure to verify that it is the case.

E) Repeated encroachments on one's leisure time by a demanding job interfere with the requirements of good health. The reason is that good health depends on regular moderate exercise, but adequate leisure time is essential to regular exercise.

Note: in some cases, it's easier to symbolically represent the argument by starting with the negation. That's what we'll do in this case. Then we can use the contrapositive rule to get our positive statement, correctly showing our sufficient and necessary conditions.

The conclusion basically states: no leisure time --> no good health

C: ~LT --> ~GH
GH --> LT

Now, let's evaluate the premises:

P: GH --> RME
~RME --> ~GH

P: RME --> LT
~LT --> ~RME

Notice that we can transpose these premises. GH --> RME and RME --> LT. Therefore, GH --> RME --> LT. Finally, we can conclude that GH --> LT. Unsurprisingly, this is the conclusion of the argument. We have therefore identified the only other valid argument among the answer choices, and like the original argument it was identified via transposition.

In order to solve these questions effectively, you need to be able to easily identify sufficient and necessary conditions. You need to understand the contrapositive rule and its nuances (MOST negates to SOME, for example). And, you need to be able to take descriptive phrases and break them down into simple acronyms. It takes a lot of effort to work through these questions, but unlike most question types you can almost certainly find the correct answer. Only the correct answer will show the same argument structure, and in most cases the other choices will be invalid (assuming the original argument was valid).

Good luck!
Re: Large inequalities in wealth always threaten the viability   [#permalink] 21 Jun 2013, 16:34
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