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by imskpwr » Fri May 09, 2014 8:55 am
Two farmers, who never left their farms their whole lives, were looking at their dogs and observed that all their border collies were black and white. The border collies were the only things that the farmers ever saw as a mix of black and white. Farmer Gil luckily but correctly observed that if something is a border collie then it must be black and white. Farmer Geva then remarked that if something is not black and white, then it is not a border collie.

The argument is flawed primarily because Farmer Geva:

A. fails to realize that there are other dog breeds apart from border collies
B. fails to realize that being black and white is a necessary but insufficient condition to be called a border collie
C. lacks sufficient information on which to base the condition for being a border collie
D. only observes one type of phenomenon-border collies and their color
E. demonstrates only limited knowledge about the world outside
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by [email protected] » Fri May 09, 2014 12:50 pm
Hi imskpwr,

This prompt is an overly-simplified attempt to test your knowledge of what's called a "contra-positive"; it's an LSAT concept that you will probably never see on the GMAT.

Contra-positives are "equivalent" statements.

eg. "If X happens, then Y happens" is equivalent to "If Y doesn't happen, then X doesn't happen"

What is the source of this question?

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by mathrupradeep » Sat May 10, 2014 7:03 pm
Hi Rich,

The answer is D ?
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by Matt@VeritasPrep » Mon May 12, 2014 1:00 pm
This is a strange question with no correct answer, and a little Googling turned up what seems to be its source. (DON'T pay attention to the explanation there, however, as it's incorrect.)

As Rich notes, the contrapositive is an important concept on the LSAT but a minor (perhaps irrelevant) one on the GMAT, which is much more about common sense arguments than about logical deductions. But if we're going to use the contrapositive, we ought to use it correctly, and the OA (which is B) is WRONG.

Here's the gist. The statement "If a, then b" is the SAME as the statement "If not b, then not a". To see why, consider the first statement: if a happens, then b MUST happen. So if b didn't happen, it's impossible for a to have happened: if a had happened, then b would've happened. (For instance, consider the statement "if I win the Nobel Prize, then I'll be famous". I'm not famous, so I must not have won the Nobel Prize.)

Now let's return to this odd argument. If Farmer Gil "correctly" observed that

"If something is a border collie, then that thing must be black and white"

then the obvious contrapositive of this statement is "If something is NOT black and white, then that thing is NOT a border collie". Since we're told Farmer Gil is correct, Farmer Geva has made an astute inference from a correct statement, and is ALSO correct. Nothing is wrong with his argument!

Now what I assume that the author of the question MEANT to have Farmer Geva say was "If something is black and white, then that thing is a border collie". That would be an example of mixing up necessary and sufficient conditions and would be an improper deduction from Farmer Gil's statement ... but if my aunt had a mustache, she'd be my uncle.
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by David@VeritasPrep » Tue May 13, 2014 5:40 pm
Matt said:
(For instance, consider the statement "if I win the Nobel Prize, then I'll be famous". I'm not famous, so I must not have won the Nobel Prize.)
The fact is Matt, that you are famous! You are Matt from G-Matt Mondays! Therefore your argument is false and since you are famous maybe you have won the Nobel Prize as well???

Seriously, though this is a strange question. Best to take Matt's advice and ignore this one.
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