Political theorist_LSAT CR.

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gmat_perfect: Legendary Member; Posts: 1083; Joined: Wed Feb 24, 2010 9:38 pmFollowed by: 14 members; Thanked: 127 times

by gmat_perfect » Thu Jun 03, 2010 11:54 am

Political theorist: The chief foundations of all governments are the legal system and the police force; and as there cannot be a good legal system where the police are not well paid. It follows that where the police are well paid there will be good legal system.
The reasoning in the argument is not sound because it fails to establish that:
(A) many governments with bad legal systems have poorly paid police forces
(B) bad governments with good legal systems must have poorly paid police forces
(C) a well-paid police force cannot be effective without a good legal system
(D) a well-paid police force is sufficient to guarantee a good legal system
(E) some bad governments have good legal systems

I can easily eliminate A, B, and E. I am in confusion between C and D.

please explain.

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Source: Beat The GMAT — Critical Reasoning | Thu Jun 03, 2010 11:54 am

stephen@knewton: GMAT Instructor; Posts: 22; Joined: Mon Mar 15, 2010 2:42 pmFollowed by: 4 members; Location: Brooklyn, NY; Thanked: 14 times

by stephen@knewton » Thu Jun 03, 2010 1:34 pm

As both an LSAT and GMAT teacher, let me see if I can use this as an excuse to shed a bit of light ... and by light, of course I mean formal logic!

This question contains CONDITIONAL statements, and such questions are best attacked by "translating" the English sentences into formal logic ... or "if/then" statements. This happens with enough frequency on the GMAT to make it worth knowing how to do. The first sentence is essentially background: these two things, a police force and a legal system, are the foundations of government. The substance of the question deals with how they relate to each other.

Let's try translating; I've come up with "symbols" but you can use whatever makes sense to you.

EVIDENCE:

"... there cannot be a good legal system (L) where the police are not well paid (WP) ..."

This translates to something like "If no well paid police, then no legal system" (if ~WP then ~L)
From which we can correctly infer: "if there is a legal system, there MUST be a well paid police force" (if L then WP)

The inference we've made is called the CONTRAPOSITIVE, and it can be made from any "if/then" statement. To form it, we reverse the conditional, AND negate the terms. We must do BOTH, and this is the ONLY valid inference that can be made (in formal logic) from a conditional.

Now, these two statement each contain a SUFFICIENT and NECESSARY condition. In short, sufficient on the left, necessary on the right. In other words, ~WP is sufficient to tell us ~L, and L is sufficient to tell us WP.

So what is the flaw in the CONCLUSION??

The (flawed) conclusion states that it follows, or that we can INFER, that:

"... where the police are well paid there will be good legal system ..."

In other words, "If WP then L, " ... which is NOT a valid inference. In that FLAWED inference, WP would be a sufficient condition!!! In other words, we CANNOT infer that a well paid force is SUFFICIENT to provide us with a good legal system. It's the other way around ... if we have a good legal system, we MUST have a well paid force! So answer choice (D) correctly describes the problem!

Hope that helps!

Oh, and two additional side notes:

1) Some folks will have seen "if/then" statements written as L --> WP, which is perfectly correct and a useful shorthand. This is NOT the same as causality, and sometimes we DO use arrows to denote causality, so just don't mix them up!

2) If you had trouble translating the first piece of evidence, try an intermediate translation of "... there cannot be a good legal system UNLESS the police ARE well paid ..." (which should make sense, I hope). Then you can ALWAYS form the "if/then" by crossing out the "cannot" and the "unless" and drawing an arrow in the direction of causality. Little LSAT trick that sometimes comes in handy!!

Stephen
GMAT Instructor
Knewton Inc.

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martin.jonson007: Master | Next Rank: 500 Posts; Posts: 226; Joined: Wed Jun 02, 2010 1:46 am; Thanked: 2 times

by martin.jonson007 » Fri Jun 04, 2010 2:54 am

IMO C

Plz don forget 2 put ans wid ques...

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stephen@knewton: GMAT Instructor; Posts: 22; Joined: Mon Mar 15, 2010 2:42 pmFollowed by: 4 members; Location: Brooklyn, NY; Thanked: 14 times

by stephen@knewton » Fri Jun 04, 2010 3:06 am

Hi Martin (and to the OP),

I'm sorry for not giving a more detailed explanation of why (C) isn't correct. The problem with that answer choice is actually rather simple, but for that reason it CAN be easy to overlook, so I certainly understand the confusion.

The problem is that nothing in the prompt concerns the EFFECTIVENESS of the police force in any way. We are given evidence, and make a conclusion, about only two things - a GOOD legal system and a WELL PAID police force - and the conditional relationship between them. Whether that force is effective does not impact the conclusion at all.

I'd be curious as to the source as well, but you can be confident about answer choice D ...

Hope that helps!

Stephen
GMAT Instructor
Knewton Inc.

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sanp_l: Master | Next Rank: 500 Posts; Posts: 160; Joined: Sun May 03, 2009 1:17 amFollowed by: 1 member; Location: Rourkela/Hyderabad; Thanked: 4 times

by sanp_l » Fri Jun 04, 2010 3:10 am

I would go with D.High pay of police ensures good legal system. that nothing else is required for that is an assumption here.

Sandy

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CaptainM: Senior | Next Rank: 100 Posts; Posts: 46; Joined: Wed Mar 10, 2010 8:54 amFollowed by: 1 member

by CaptainM » Sun Oct 31, 2010 1:41 am

stephen@knewton wrote:
Now, these two statement each contain a SUFFICIENT and NECESSARY condition. In short, sufficient on the left, necessary on the right. In other words, ~WP is sufficient to tell us ~L, and L is sufficient to tell us WP.

Could you Please explain how did you derive ~WP sufficient to tell us ~L ? So can I generalize that: IF the argument says there cannot be X where Y is not present that means ~Y is suff to tell us ~X.For example there cannot be Dog food in a house if there is no Dog in the house.=> According to the logic:~Dog in the house is sufficient to tell us ~Dog food.
Now you say that ~WP is sufficient to tell us ~L but how can it be sufficient as there may be some more stuffs that may be required as well to make ~L.To me the situation looks like necessary but not sufficient.I mean no dog in the house is not sufficient to tell ~dog food in the house, as there may be dog food for street dogs...

I am not sure that I could articulate my question better than crap so lemme ask you a favor Please help me understand SUFFICIENT vs NECESSARY condition.

So what is the flaw in the CONCLUSION??

The (flawed) conclusion states that it follows, or that we can INFER, that:

"... where the police are well paid there will be good legal system ..."

In other words, "If WP then L, " ... which is NOT a valid inference. In that FLAWED inference, WP would be a sufficient condition!!! In other words, we CANNOT infer that a well paid force is SUFFICIENT to provide us with a good legal system. It's the other way around ... if we have a good legal system, we MUST have a well paid force! So answer choice (D) correctly describes the problem!

Hope that helps!

Oh, and two additional side notes:

1) Some folks will have seen "if/then" statements written as L --> WP, which is perfectly correct and a useful shorthand. This is NOT the same as causality, and sometimes we DO use arrows to denote causality, so just don't mix them up!

2) If you had trouble translating the first piece of evidence, try an intermediate translation of "... there cannot be a good legal system UNLESS the police ARE well paid ..." (which should make sense, I hope). Then you can ALWAYS form the "if/then" by crossing out the "cannot" and the "unless" and drawing an arrow in the direction of causality. Little LSAT trick that sometimes comes in handy!!

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