Logical Reasoning

PT148 · S1 · Q2 Five years ago, the hair dryer

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Five years ago, the hair dryer produced by the Wilson Appliance Company accounted for 50 percent of all sales of hair dryers nationwide.

Conclusion

The company's net income from sales of the product must be only half of what it was 5 years ago.

Evidence (because)

5 yrs ago, 50% of all hair dryers purchased nationwide were Wilson's. Now, only 25% of all hair dryers purchased nationwide are Wilson's. The average net income that Wilson receives per hair dryer has not changed over the last 5 years.

Evaluate

This is a very math-y argument, so the flaw is probably related to math. When we see arguments involving percentages, they often involve an illicit switch between percentages and numbers.

For example, if an author saw that a certain company went from being 40% female to being 50% female, they would assume that there were more females than before. But just because a percentage went up doesn't mean the raw number went up. It could be like this:

THEN NOW 4 women 4 women 6 men 4 men 40% women 50% women

In this argument, Wilson went from being 50% of hairdryers sold to 25%. Is the author assuming that since the percentage went down, the raw number went down?

Yes! And if the raw number did go down, then the conclusion is totally valid.

If Wilson sold a smaller number of hairdryers last year, compared to five years ago, but they still make the exact same net income (i.e. profit) per hairdryer, then they would be making less net income from that product. Again, let's consider numbers.

5 yrs. ago Now

sold nationally 100 100 % that are Wilson 50% 25% # that are Wilson 50 25

If they make $10 of profit off each hairdryer, then five years ago they made $500 and now they made $250.

But let's not play the author's game. How could a smaller percentage not be a smaller number? If the total number of hairdryers sold nationally has doubled, then Wilson would be selling the same number of hairdryers.

5 yrs. ago Now

sold nationally 100 200 % that are Wilson 50% 25% # that are Wilson 50 50

Now, the author's conclusion is wrong. They sold 50 hair dryers in both cases, so their net income from that product hasn't changed.

Goal

In order for the author's conclusion to be valid, we need there to be the same number of hairdryers sold nationally, now vs. 5 yrs ago.

If that number is different nowadays, then Wilson won't be selling exactly half as many hairdryers and so their profit from hairdryers won't be exactly half of what it was 5 years ago.

2.

The reasoning in the argument is flawed because the argument

  1. Correct

    mistakes a decline in the

    Why this is right

    Any time a Flaw answer is structured like confuses X with Y mistakes X for Y we want to see if X seems to be referring to what the evidence talked about and if Y seems to be referring to what the author concluded/assumed. The evidence was indeed talking about market share. 5 yrs ago, Wilson had 50% of the national hairdryer market. Nowadays, that share has shrunk to 1/4, to 25% of national hairdryers. But that doesn't mean that there has been any decline in total sales, in the number of hairdryers sold. As we showed before, if the number of hairdryers sold nationally changed, then you can't make that "1/2 as big a percent = 1/2 as big net income" inference. Even a modest increase makes the conclusion wrong. 5 yrs. ago Now sold nationally 100 120 % that are Wilson 50% 25% # that are Wilson 50 30 net income $500 $300 ($10 / each) The conclusion said that net income was only half, but here is a possibility where the net income was 3/5 as big (more than 1/2). Since the author goes from establishing that market share got cut in half to concluding that net income got cut in half, he must assume that sales volume got cut in half. This answer is saying that he's conflating what happened to market share with what he assumes also happened to sales volume.

    Skill tested: Flaw · how this choice captures the argument's function is the move to repeat next time.

    80% picked this

  2. does not provide specific information

    Not a Valid Objection

    This sort of answer, which asks for specific values / measurements / names / definitions, is never right on Flaw. We aren't ever complaining in the answers that we don't have precise data. We're complaining about the reasoning. It doesn't matter what the specific profit amount (net income amount) is. If I tell you that Company X sold 1/2 as many hamburgers as last year, and that their net income per burger is the same, then we can validly derive that they made 1/2 as much net income from burgers.

    1% picked this

  3. fails to discuss sales figures

    Out of Scope: other products

    The conclusion is only about "the product", only about hair dryers. Information about other products has no bearing on how much net income they made specifically from hairdryers.

    6% picked this

  4. overlooks the possibility that the

    Not a Valid Objection

    Would it hurt the argument if we said that the price of Wilson's hair dryer increased? Couldn't we then argue that, "even though they're selling fewer hair dryers, they're still making around the same amount of money because they raised the price on those hair dryers"? No, we can't, because we have a factual premise that net income per hair dryer has stayed the same. If it used to be sold for $20, but it cost $15 to make each one, then the company had $5 of net income on the sale of each hair dryer. If over the past 5 years the price as been raised to $25, but the company still has $5 of net income on the sale of each hair dryer, that means that costs have gone up to $20. There's no way to use more revenue as a way to mess with the author's math, because the author has already established that net income, which balances revenue and costs, is the same.

    13% picked this

  5. provides no independent evidence that

    Not Assumed Too Strong: least profitable

    When an answer starts off like presumes / takes for granted / fails to establish / provides no evidence that, it's trying to name something the argument needed to state but didn't. In other words, it's trying to name a necessary assumption of the argument. Did this argument need to assume that Wilson's hair dryer is one of the company's least profitable products? Not at all. It doesn't make a difference how the profitability of hair dryers compares to that of any other of Wilson's products. All we care about is whether the profitability of hair dryers changed at all since 5 years ago, but there's a premise telling us directly that it did not.

    0% picked this

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