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Complete Question Explanation

Flaw in the Reasoning-#%. The correct answer choice is (B)

In this case the author provides several numerical premises, followed by a flawed conclusion. Out of 1000 workers, an average of 10 are sick each day, a scenario that allows the plant to run produce at its normal rate.

Based on the above information, the author draws the conclusion that 10 employees could be fired without the plant losing productivity. The problem with this logic is this: the author seems to think that having an average of 10 sick is the same as having 10 employees who are sick every day. The author is missing the fact that, based on the statistics provided, an average of 10/1000, which is equivalent to 1/100, or 1%, of the companies employees are sick each day. So in reality, if 10 employees were fired, that would leave 990, and we would still most likely continue see 1%, or about 10 (9.9) sick on average.

Answer choice (A): The author doesn't "ignore" this possibility, as the argument does not require it. Regardless, this would strengthen the author's conclusion, rather than show a vulnerability in the argument.

Answer choice (B): This is the correct answer choice. There is no reason to believe that the percentage of the staff that is sick on any given day will change from the current 1%. If the absentee rate didn't drop, and about 10 people were sick after the firings, there is no way to know whether a loss of productivity would result.

Answer choice (C): The author does not make this presumption. Rather, the author takes the fact that a loss of 10 on any given day is allowable without a drop in productivity, and concludes that firing 10 would also allow for no change in productivity rates.

Answer choice (D): This is not the flaw displayed in this stimulus. The flaw concerns the author's misinterpretation of percentages and statistics.

Answer choice (E): The author certainly does not take this for granted, but instead draws the conclusion in part from the specific fact that 10 could be lost on any given day without a resulting loss in productivity.
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I'm having difficulty understanding what C is saying. Is it saying that it assumes that if 11 or more workers are absent, then the normal rate of production will not be attained? Is this not an assumption he makes because if you negate it to say "the normal rate can be attained even if more than than the average number of workers are absent" it actually strengthens the argument?
 Luke Haqq
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Hi jrc3813,

Happy to try to explain answer (C). As you paraphrase it,
it assumes that if 11 or more workers are absent, then the normal rate of production will not be attained?
This would be diagrammed:

11+ :arrow: ~ NRP

However, answer (C) states, "takes for granted that the normal rate of production can be attained only when no more than the average number of workers are absent." Using the variables from your paraphrase, this should instead be diagrammed:

NRP :arrow: ~11+

The contrapositive of that would be:

11+ :arrow: ~NRP

In other words, (C) could be rephrased as, "If the normal rate of production can be attained, then there are no more than the average number of workers absent," or alternatively, "If there are more than the average number of workers, then the normal rate of production cannot be attained."

(C) isn't a flaw that occurs in the stimulus though. For example, it's consistent with the stimulus that the normal rate of production could be achieved if, say, 15 workers were absent (i.e., more than the average number absent). We just don't know whether or not that's true--it only mentions what happens when exactly 10 are absent. Since this is something we don't know but is still possible, that's why (C) doesn't refer to a flaw made in the stimulus.
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I wanted to check if my understanding of (B) is on the right track. After the firing, if the absentee rate remains the same (10/1000=1% for example), there would still be people on sick leave every day (1%x990=9.9 on average). Therefore, there should be a loss in production. Correct?

Regarding (E), is the rate of production referring to the total production per day instead of [total production/number of workers] per day?

Many thanks!
 Adam Tyson
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Your understanding looks good to me, and I interpret the production rate to be the total production by the plant rather than tvs per worker. Well done!
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Why is E Wrong
 Jennifer Janowsky
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Answer choice (E) states that the author takes it for granted that the rate of production is not affected by the number of workers employed. However, that is not the case. The author observes that the rate of work is not affected when 10 people are missing--rather than an assumption made, this is more of an observation.

The author's real logical flaw was to ignore that there might still be the same amount of absentees after removing workers, and that this when combined with 10 less sets of hands might drop production below the normal rate.
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I understand why B is right, intially choose B. For E however, the way I looked at it was he assumes that firing people won't do anything to the other people. For example firing 10 people could reduce motivation and reduce production. When I went back to review it in eliminated it by saying that it didn't mention anything about them employing would affect it, just the presence. I'm I right with my reasoning?
 Adam Tyson
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I think you got it the second time around, mo_wan! The author doesn't have to assume that the number of workers does not ever affect production, because he might agree that a larger round of firing might reduce production. It's just that he thinks that letting go of just 10, the same number absent on any given day, won't affect it. He might say "firing 100 people would be a problem, because production would go down, but firing just 10 is fine and will have no effect."

He already showed that 10 people absent has no effect on production, so he didn't make any assumptions about that number. That was explicitly stated, a premise, and therefore not an assumption.

I hope that helps clear it up for you!

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