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If y is 45 percent of x and z is 25 percent of x , what is y + z in terms of x ?
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LSAT: Logical Reasoning Question #6

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One morning, George Petersen of Petersen's Garage watches as a 1995 Da Volo station wagon is towed onto his lot. Because he knows that nearly 90% of the 1995 Da Volo station wagons brought to his garage for work in the past were brought in because of malfunctioning power windows, he reasons that there is an almost 9 to 1 chance that the car he saw this morning has also been brought in to correct its faulty power windows.

Question: Which one of the following employs flawed reasoning most similar to that employed by George Petersen?

Choices:
A. Mayor Lieberman was reelected by a majority of almost 75%. Since Janine Davis voted in that mayoral election, the chances are almost 3 to 1 that she voted for Mayor Lieberman.
B. Each week nine out of 10 best-selling paperback books at The Reader's Nook are works of fiction. Since Nash's history of World War II was among the ten best-selling paperback books at The Reader's Nook this week, the chances are 9 to 1 that it is a work of fiction
C. 90% of those who attempt to get into Myrmidon Military Academy are turned down. Since the previous 10 candidates to the academy were not accepted, Vladimir's application will almost certainly be approved.
D. Only one out of 50 applications for bypassing zoning regulations and establishing a new business in the Gedford residential district is accepted. Since only 12 such applications were made last month, there is virtually no chance that any of them will be accepted
E. Nearly 95% of last year's Borough High School graduating class went on to some type of further schooling. Since only a little more than 5% of that graduating class took longer than the usual four years to graduate, it is probable that everyone who did graduate within four years went on to further schooling.



George Petersen gives us a little lesson on how not to use statistics. He knows that 9 out of 10 Da Volos are brought to his shop because of malfunctioning windows, so he reasons that this particular Da Volo, which is being towed in, has probably also been brought in for malfunctioning windows. Surely the fact that the car is being towed indicates that there must be some more serious problem. Petersen has mindlessly applied a numerical formula while ignoring additional information. Where else do we see such reasoning?

(B) uses previous figures to conclude that there's a 9 to 1 chance that Nash's history of World War II is a work of fiction. (B) ignores the compelling contrary evidence (that this book is a history) and mindlessly applies a numerical formula where it clearly shouldn't be applied.

(A)'s use of statistics is reasonable. We don't know anything special about Janine Davis; she's just a voter. Therefore, since almost 3 out of 4 voters chose Lieberman, there's an almost 3 out of 4 (or 3 to 1) chance that Janine voted for Lieberman.

(C) reasons that Vladimir's chances of being admitted into the academy have been improved by the rejection of the previous candidates. That's not a persuasive line of argumentation, but it's nothing like the stimulus.

(D) is a straight numerical argument. The conclusion seems overstated (even a 1 out of 50 chance isn't "virtually no chance"), but it's not at all like the stimulus; we're not shown a particular case with special information that goes against the numbers.

(E)'s mistake is to assume that all those who took more than four years to graduate did not go on to further schooling; this allows (E) to conclude that the 95% who graduated in four years did go on. It's statistically flawed, certainly, but no special case is discussed, and therefore there's no similarity to the stimulus.
 

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