Logical Reasoning

PT3 · S2 · Q12 Photovoltaic power plants produce electricity

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Photovoltaic power plants produce electricity from sunlight.

Conclusion (thus)

PV plants offer a less expensive approach to meeting demand than traditional plants do.

Evidence

Cost of producing electricity at photovoltaic (PV) plants is now one-tenth of what it was 20 years ago.

Cost of producing electricity at traditional (fossil-fuel) plants has increased over the same period.

Evaluate

There is a subtype of Sufficient Assumption questions where the conclusion is some mathematical comparison. These arguments are rarely about missing links. They're more about missing info when it comes to comparing two different things or time periods. In many cases we might want to make a little table of values so that we can better see what's missing. Or we need to think of a mathematical scenario that would break the conclusion, so that our correct answer can make that sort of scenario impossible.

We know that the cost of PV has gone down while the cost of traditional plants have gone up.

But the cost of Ferrari's could go down while the cost of a Nissan Altima goes up, but that doesn't mean that a Ferrari is less expensive than an Altima.

If we made a table, we wouldn't really know any values to start with other than the 1/10, sot if we assigned variables everywhere it would look something like this:

OLD NEW cost of PV x 1/10 x cost of trad a b

The evidence tells us that a < b (the cost of traditional has gone up).

Does that mean that (1/10) x < b?

No, we have no way to compare them.

Goal

We need to be guaranteed that the new cost of PV is lower than the new cost of trad, knowing only that the former has decreased by a tenth and the latter has gone up.

12.

The conclusion of the argument is properly drawn if which one of the following is assumed?

  1. The cost of producing electric

    Premise Support

    This basically restates the premise that the cost of producing electric power at traditional plants has increased over the past 20 years. Restating a premise has no impact on the answer, so this can't be correct. It certainly us any way to prove that the current cost of PV is less than the current cost of traditional.

    7% picked this

  2. Twenty years ago, traditional power

    Irrelevant Quality

    This is about the relative output (how much electric power) of the two plant types 20 years ago, not about the relative cost. We only care about how much PV and traditional used to cost and how much they currently cost. Telling us the volume of output doesn't tell us anything about the cost of producing that output.

    3% picked this

  3. None of the recent technological

    Irrelevant Relationship

    This has nothing to do with the cost of power at PV versus traditional. It's a non-financial fact about what type of technology can / can't be used.

    18% picked this

  4. Correct

    Twenty years ago, the cost

    Why this is right

    Before we get into the nitty gritty math of how this answer mathematically works, let's think about why we'd probably guess this answer, even if we didn't have time to math it out. We know we need a mathematical comparison between PV and traditional. We're trying to prove a mathematical comparison between them, but the evidence didn't provide any comparison between PV and traditional (the evidence compared old PV to new PV and compared old traditional to new traditional). This is the only answer that's providing a mathematical comparison between PV and traditional, so we'd pick it! Onto the actual math. Here's our old table: OLD NEW cost of PV x 1/10 x cost of trad a < b This is saying that x < 10a. The old cost of PV is less than 10 times the old cost of traditional. The conclusion is trying to prove that (1/10) x < b If we multiply both sides by 10, the conclusion is trying to prove that x < 10b Since a < b, if we multiply both sides by 10, 10a < 10b Since we know that x < 10a, that means x < 10a < 10b So we have proven the conclusion, that x < 10b, or alternatively that 1/10(x) < b. Got all that? (Sorry, anyone who thought they would never have to deal with algebra again in their lives) Most of us would be better off trying numbers. Say that PV power used to cost $100 and now costs $10 (its current cost is 1/10 its old cost). OLD NEW cost of PV $100 $10 cost of trad ? < ? This answer tells us that $100 is less than ten times the old-Traditional cost. So the old-Traditional cost would have to be bigger than $10, in order for ten times the old-Traditional to be bigger than $100. And if we know that the old-Traditional has to be bigger than $10, and the new-Traditional has to be even bigger than that, then we know that new-Traditional will be bigger than New-PV (which is $10).

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

    62% picked this

  5. The cost of producing electric

    Out of Scope

    Future trends do not establish the current cost comparison. The conclusion is about which is less expensive now, based on trends comparing old prices and current prices. Information about future prices won't be useful in proving where the costs are currently at.

    10% picked this

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