Logical Reasoning

PT7 · S4 · Q13 The National Association of Fire

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The National Association of Fire Fighters says that 45 percent of homes now have smoke detectors, whereas only 30 percent of homes had them 10 years ago.

Conclusion

Early detection of house fires is no more likely than it was 10 years ago.

Evidence (because)

45 percent of homes now have smoke detectors, whereas only 30 percent did 10 years ago.

Over half of the domestic smoke detectors are either without batteries or inoperative for some reason.

Evaluate

The author is presenting a statistic that suggests more homes have smoke detectors now than they did ten years ago. This could indicate that early detection of house fires should be more likely. However, the author concludes that early detection is no more likely despite the increase in smoke detectors, because more than half of these smoke detectors are inoperative.

Well, wasn't that true 10 years ago too? If it's a general truth that half of all smoke detectors don't actually function, you'd still have more functioning smoke detectors nowadays. After all, half of 45% is bigger than half of 30%.

Goal

The author must be thinking that the "half of them are inoperative" is a RECENT problem, not an ongoing one. She must be Assuming a Difference. Because if it's always been the case that half of them are inoperative, then her conclusion would just be wrong. We WOULD be more likely to early-detect fires nowadays, because a higher percentage of homes have detectors.

13.

In order for the conclusion above to be properly drawn, which one of the following assumptions would have to be made?

  1. Fifteen percent of domestic smoke

    Irrelevant Quality

    The argument is just about whether we have more functioning smoke detectors now compared to 10 years ago. When these smoke detectors were installed doesn't make any difference to that calculation. We only care about what proportion of homes have smoke detectors and what proportion of those smoke detectors are operable vs. inoperable. If we negate this and say that some other % of smoke detectors were installed in the past ten years, it doesn't change or hurt the argument at all. This answer is just baiting people with 45% - 30% = 15%

    5% picked this

  2. The number of fires per

    Irrelevant Comparison

    The number of fires per year and their relation to homes with smoke detectors does not address the operability of the detectors, which is the main concern in whether early detection is more likely. The argument isn't about actual fires going up or down. It's about whether the proportion of homes with functional smoke detectors has gone up or down.

    10% picked this

  3. Not all of the smoke

    Irrelevant Quality

    It doesn't matter whether 100% of smoke detectors are battery operated or less than 100%. We just care about whether or not they're in operable condition, however it is that they get their power. This is baiting people into inferring from "inoperable because of no batteries or because of some other reason" that some detectors don't use batteries. That's not a valid inference (also not our task on Necessary Assumption). A battery-powered smoke detector can be inoperable for some other reason, such as maybe it got smashed by a basketball and some of its internal circuits have come apart.

    7% picked this

  4. Correct

    The proportion of domestic smoke

    Why this is right

    This gets to the Assumed Difference. If ten years ago we had the same proportion of inoperable smoke detectors (we'll say 50%), then we would currently have more operable smoke detectors than ten years ago, which basically contradicts the conclusion. 50% of 30% is 15%. So ten years ago 15% of homes would have had operable smoke detectors. And 50% of 45% is 22.5%. So now 22.5% of homes would have operable smoke detectors. The author's argument only makes sense if we interpret the "over half are inoperable" premise as a NEW problem. He has to be arguing that "even though a larger proportion of homes have these detectors, there's this new problem where tons of them are inoperable, so that offsets the gain in detectors and leaves us essentially where we were ten years ago."

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

    71% picked this

  5. Unlike automatic water sprinklers, a

    Irrelevant Comparison

    This argument is only about smoke detectors, so we don't have to assume anything about sprinklers. If we negated this and go "a properly functioning smoke detector can by itself increase fire safety", it wouldn't weaken. The author agrees that FUNCTIONING smoke detectors increase safety. Her argument is about how inoperable detectors mean we aren't getting an increase in safety.

    7% picked this

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