Logical Reasoning

PT143 · S1 · Q19 Economist: Although average hourly

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Economist: Although average hourly wages vary considerably between different regions of this country, in each region, the average hourly wage for full-time jobs increased last year.

Given that ...

In every region of the country, the average hourly wage for full-time jobs increased last year.

How is it that ...

In the country as a whole, the average hourly wage for full-time jobs decreased last year?

Evaluate

This is a tricky mathematical paradox. If the average wage went up in each region, then how could the average wage go down nationally?

Normally, we don't spend too much time up front on Paradox questions trying to guess the answer because there could potentially be a lot of ways to resolve the Paradox. But when it's mathematical, there is often only one way.

In this case, in order for every region's average to go up while the national average went down, we need there to be a net effect of people moving out of regions whose average is higher than the national average into areas whose average is lower than the national average.

Say that the average wage nationally is $25 / hr. Some regions, like San Francisco, will have regional average wage of $30 / hr. Some regions like, like Oklahoma City, will have a regional average wage of $20 / hr.

Let's say, last year, OKC's average rose to $21 / hr and SF's average rose to $31 / hr.

We'd expect the national average to start creeping towards $26 / hr. But now consider the effect if tons of people move from SF to OKC.

Someone who used to be making $30 / hr in SF now lives in Austin and makes $21 / hr.

When it comes to the national average hourly wage, people who made $30 / hr last year but make $21 / hr this year are going to bring that average down.

Or in case this makes more sense, suppose that SF is a region with a $30 / hr average wage. OKC is a region with a $20 / hr average wage. Bob lives in SF and makes $28 / hr.

Now he moves to OKC and makes $25 / hr. What has he done to the average wage in SF, OKC, and nationally?

He raised the average wage in SF, because if the average is 30 and you get rid of a data point that is 28, then that will boost the average. (If you kick a teenager off your team, then the average age of your team will go up).

He raised the average wage in OKC, because the average there was $20, but he makes $25. And he lowered the national average, because he went from making $28 to $25.

Goal

We need to hear that people moved out of higher paying areas into lower paying areas.

19.

Which one of the following, if true of the economist's country, most helps to resolve the apparent paradox in the economist's statements?

  1. In the country as a

    No Impact

    We don't care whether 2 and 3 years ago the national average also decreased. We're trying to explain how this past year the national average could have decreased, given that this past year, every regional average increased.

    2% picked this

  2. Correct

    Last year, to reduce costs,

    Why this is right

    This is what we were looking for. We need people from areas that pay higher than the national average to move to areas that pay lower than the national average. That's the only mathematical way we can get every region's average to increase while the overall average decreases. This answer doesn't in any way "settle the math" and guarantee a lower national average, but it reflects the right type of movement that could potentially reconcile the math paradox.

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

    83% picked this

  3. The year before last, the

    No Impact

    We don't care about the unemployment rate. We're only looking at a paradox that deals with average hourly wages, so by definition we only care about those who are employed.

    2% picked this

  4. Last year, the rate at

    No Impact

    The fact that wages went up 3% in this region and 52% in this other region doesn't help to resolve our Paradox. Since all the regions went up to some degree, shouldn't the national average have also gone up?

    8% picked this

  5. Last year, hourly wages for

    No Impact

    We don't care about specific sectors of the economy. This paradox is about the geographical patchwork of the national average, not the categories-of-employment patchwork. No matter which sectors won or lost, we still know that all regions experienced a rise in average hourly wages, so we still need a way to understand how the national average could go down.

    4% picked this

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