#2 - Five years ago, the hair dryer produced by the Wils

[Administrator]

Complete Question Explanation

Flaw in the Reasoning. The correct answer choice is (A)

This is a by-the-book numbers and percentages problem in which a change in percentages without reference to overall quantity leads to an erroneous conclusion. The author concludes that a drop in percentage of Wilson's hair dryer sales versus the total number of all hair dryer sales implies that Wilson's net income must have dropped by the same percentage. While the author does account for a constant net income per hair dryer sold (addressing one potential weakness), the author does not establish that the overall number of Wilson hair dryers has dropped over the same period. Imagine the hypothetical:

• In 2010, Wilson sold 1,000 hair dryers out of 2,000 total hairdryers sold nationwide.
• In 2015, Wilson still sold 1,000 hair dryers out of 4,000 total hairdryers sold nationwide.

Even though Wilson's hair dryers represent a smaller fraction of overall national hair dryer sales, its actual number of units sold has not declined, and neither has Wilson's net income.

A good prephrase will describe how a decrease in percentage does not imply a decrease in number without reference to analogous initial values. In other words, without knowing how many hair dryers were sold in each of the years in question, it is not possible to reach the conclusion the author reaches.

Answer choice (A): This is the correct answer choice. The one curve ball in this answer is the term "market share." Students must recognize that a decline in the percent of sales of a product versus its competitors describes a drop in its "share" of the "market." Otherwise, this answer choice is a clear match for both the prephrase and an accurate description of the flawed reasoning in the stimulus.

Answer choice (B): This choice goes off on a tangent about what the actual profits earned on hair dryer sales for hair dryer manufacturers. It perhaps tries to play off a misunderstanding about the role of the statement about Wilson's constant net income from hair dryer sales. Not part of the flaw, this statement actually makes the argument stronger!

Answer choice (C): This choice introduces revenues from other products perhaps imagining a misreading of the conclusion. If a student were to misinterpret the conclusion to concern Wilson's overall net income, we would care about other products, but in the argument, we are only concerned about net income from hair dryers.

Answer choice (D): This choice introduces irrelevant information about the retail price of the hair dryers. Since Wilson's net income per hair dryer remains unchanged, the retail price, whether different or the same, is immaterial.

Answer choice (E): This choice has a couple problems. First, the validity of the premises is not in question here. No "independent evidence" is needed to corroborate the figures given. Second, neither have we knowledge of Wilson's profitability from hair dryer sales versus other products nor is such information pertinent.

[LawSchoolDream]

I wouldn't have thought about the 1k to 4k example from manufacturing point. The market share did throw me off in answer a and I went with answer d. The reason I chose D was because I crossed all others out and also because I felt the last sentence where it says about net income, even though it's selling much less the net income is remaining the same indicated to me perhaps theres' a price increase involved. Can you please clarify with this thought process?

Also, Would the numbers chapter be good for this Because I don't think flaws chapter is helping

[Jeff Wren]

Hi LawSchoolDream,

To answer your second question first, yes the chapter on Numbers and Percentages in "The Logical Reasoning Bible" is exactly where to look for this concept, specifically under Numbers and Percentages Misconception #2, Decreasing Percentages automatically lead to decreasing numbers. A smaller "slice" (the percentage) of a much larger "pie" may still be more than a larger "slice of a smaller "pie.".To use a rather extreme example, would you rather have 50% of 10 dollars or 25% of 1 million dollars? Without knowing the totals (the sizes of the "pies"), the percentages tells us nothing about the actual quantities of hair dryers sold.

Numbers and Percentages are such important concepts on the LR section that they get their own chapter. Also, while these concepts often appear in flaw questions, they also appear in other LR questions.

As for Answer D, it does not matter if the retail price has increased over 5 years. We are told in the argument that average net income per hair dryer has not changed over 5 years. (This is stated as a premise.) What this means is that even if the retail price did increase over 5 years, the net income per hair dyer that the company receives hasn't changed. In other words, the cost to make each hair dryer may have increased the same amount, so that the higher retail price doesn't make the company more profit.

The flaw in the argument, as described in Answer A, is that even though the company now has a smaller % of the market share, it may still be selling more hair dryers if the total market size has greatly expanded.