Praetorian wrote:
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. This makes early detection of house fires no more likely, however, because over half of the domestic smoke detectors are either without batteries or else inoperative for some other reason.
In order for the conclusion above to be properly drawn, which one of the following assumptions would have to be made?
(A) Fifteen percent of domestic smoke detectors were installed less than 10 years ago.
(B) The number of fires per year in homes with smoke detectors has increased.
(C) Not all of the smoke detectors in homes are battery operated.
(D) The proportion of domestic smoke detectors that are inoperative has increased in the past ten years.
(E) Unlike automatic water sprinklers, a properly functioning smoke detector cannot by itself increase fire safety in a home.
Source: LSAT
OFFICIAL EXPLANATION
(A) No. Not only is this irrelevant, it is incorrect! Fully one-third of smoke detectors were installed within the last ten years, as they jumped from installations in 30 percent of homes to 45 percent.
(B) No. This is irrelevant. The conclusion concerns the probability of early detection of a house fire, not the total number of such fires.
(C) No. This is irrelevant. The conclusion only concerns the percentage of inoperable smoke detectors, not the reason the detectors are not functioning.
(D) Yes. If the proportion of smoke detectors that are inoperative is the same now as in the past, then the detection of fires would be 50 percent more likely (45 is 50 percent larger than 30). However, if the percentage of inoperable smoke detectors has increased over the last 10 years, then the chance of detecting fires would increase less than 50 percent. In fact, it is possible for so many smoke detectors to have become inoperable that there was no increase in the number of properly functioning detectors.
(E) No. The passage is discussing early detection, not safety per se.
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