Here we have a strengthen with necessary premise question. Remember that a premise is necessary for a conclusion if the falsity of the premise guarantees or brings about the falsity of the conclusion. First we check to see if the answer choice strengthens the passage, and then, if it does strengthen, we negate the answer choice to see if its negation makes the argument fall apart. If the answer choice does both those things then it is our correct answer.
Conclusion: the fact that today 45% of homes now have smoke detectors makes early detection of house fires no more likely.
Why? Even though now there are 45% of homes that have smoke detectors as opposed to 30% 10 years ago, the conclusion holds since over half of the domestic smoke detectors are either without batteries or else inoperative for some other reason.
Answer choice (D) states: "The proportion of domestic smoke detectors that are inoperative has increased in the past ten years."
Does this strengthen? Yes. If the proportion of domestic smoke detectors that are inoperative has increased in the past ten years, then the fact that so many more households have smoke detectors today will definitely not make early detection more likely. We know that normally over half of the domestic smoke detectors are either without batteries or else inoperative for some other reason, and if answer choice (D) is true, then the proportion of these smoke detectors that are inoperative has actually increased from the past ten years. Therefore, answer choice (D) strengthens the conclusion.
Negation: The proportion of domestic smoke detectors that are inoperative has not necessarily increased in the past ten years.
Does this make the argument fall apart? Yes.
Let's use numbers to better visualize. Let's say there are 100 households. Ten years ago 30% of them had smoke detectors. We know that over half of these smoke detectors are inoperative. So, let's say that ten years ago there were a total of 30 households with smoke detectors and 16 were inoperative while 14 worked.
Now we know 45% of households have smoke detectors. That means that out of 45 people who have smoke detectors, 23 people have inoperative smoke detectors while 22 have working ones.
Thus, even though over half are inoperative, it is more likely that today house fires will be detected early than 10 years ago since today there are 22 working smoke detectors while 10 years go there were only 14.
Therefore, if we take the negation of answer choice (D) to be true, then the conclusion no longer necessarily holds.
Hope that clears things up! Please let us know if you have any other questions.
hannahnaylor5August 12, 2019
How are we to assume that the proportion of detectors has increased from ten years ago? the passage doesn't say anything besides the number of detectors increasing and the proportion of them that are inoperable is over half. Couldn't it be that over half were inoperable 10 years ago as well?
ElaFebruary 26, 2020
why would B not be the correct answer? Wouldn't it strengthen ?
