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- Fri Jan 21, 2011 12:00 am
#23441
Complete Question Explanation
Assumption-#%. The correct answer choice is (D)
The argument is that since over half of smoke detectors are inoperative or without batteries, the fact that there has been a 15% increase in the number of homes with smoke detectors does not improve the likelihood of early house-fire detection.
The argument seems to imply that since there is currently at least a 50% disuse rate, a 15% increase cannot compensate. However, that only makes sense if we assume that, 10 years ago, there was a significantly lower disuse rate. For example, if 10 years ago the disuse rate was also around 50%, the 15% increase in the number of houses with smoke-detectors does change the likelihood of early detection. The question asks you to identify that assumption.
In attacking this question, consider the nature of the ideas in play. You have a discussion about percentages in the premises and conclusion of the stimulus, and then you are asked for an Assumption of the argument. Chances are extremely high that the assumption revolves around what's been happening with the percentages. Answer choices (B) and (C) are about actual numbers, and thus less likely here to be the assumption. (A) is about installation, and thus not all that likely to be correct. Answer choice (E) is about a comparison to water sprinklers, which the author didn't address and so this is unlikely to be an assumption. Thus, just from surveying the answers and thinking about what types of things the author has to be thinking, answer choice (D) is the most promising answer.
If you are looking for a full numerical confirmation of how the problem works, one of our instructors provided the following scenario:
Answer choice (A): Homes can have multiple smoke detectors, so this 15% is not necessarily the same as the 15% in the stimulus. If 15% of domestic smoke detectors were installed less than 10 years ago, that could make early detection more likely, since the equipment would be newer and possibly in better repair. Also, adding multiple detectors could increase the probability of detection. Either that is the case, or the 15% corresponds to nothing more but the increase in homes with smoke detectors. This response could attack or restate the stimulus, depending on some suppositions, but cannot provide support.
Answer choice (B): This does not support the conclusion that the likelihood of early detection has not increased. Since the fire has to occur before it can be detected, you should not conclude that more fires means less detection. This response gives you no reason to suppose that the fires were undetected and became severe.
Answer choice (C): This choice could be damaging to the stimulus, so you should eliminate it. If some of the detectors are not battery operated, a significant proportion of detectors without batteries might still be operational.
Answer choice (D): This is the correct answer choice. For the argument's conclusion to follow, it must be true that 10 years ago the proportion of inoperative smoke-detectors was lower than it was at the time of this argument.
Answer choice (E): Since the stimulus was about early detection, not overall fire safety, this response is irrelevant, and incorrect.
Assumption-#%. The correct answer choice is (D)
The argument is that since over half of smoke detectors are inoperative or without batteries, the fact that there has been a 15% increase in the number of homes with smoke detectors does not improve the likelihood of early house-fire detection.
The argument seems to imply that since there is currently at least a 50% disuse rate, a 15% increase cannot compensate. However, that only makes sense if we assume that, 10 years ago, there was a significantly lower disuse rate. For example, if 10 years ago the disuse rate was also around 50%, the 15% increase in the number of houses with smoke-detectors does change the likelihood of early detection. The question asks you to identify that assumption.
In attacking this question, consider the nature of the ideas in play. You have a discussion about percentages in the premises and conclusion of the stimulus, and then you are asked for an Assumption of the argument. Chances are extremely high that the assumption revolves around what's been happening with the percentages. Answer choices (B) and (C) are about actual numbers, and thus less likely here to be the assumption. (A) is about installation, and thus not all that likely to be correct. Answer choice (E) is about a comparison to water sprinklers, which the author didn't address and so this is unlikely to be an assumption. Thus, just from surveying the answers and thinking about what types of things the author has to be thinking, answer choice (D) is the most promising answer.
If you are looking for a full numerical confirmation of how the problem works, one of our instructors provided the following scenario:
- Let's say we have 100 homes. 10 years ago, only 30 of them had smoke detectors; today, that number is 45:
TOTAL # of houses: 100
% of houses with detectors: 30% in 2002 vs. 45% in 2012
# of houses with detectors: 30 vs. 45
Because over half of them are inoperative, however, the author is concluding that detection of house fires today is no more likely than it was ten years ago (i.e., that the number of houses with operative detectors has not changed significantly over the years).
This is a horrible argument, because we don't know how the ratio of operative vs. inoperative smoke detectors has changed over the last 10 years. If the proportion of inoperative detectors remained the same (let's say a little over 50% for both years), only 15 houses would have been safe ten years ago, vs. 23 houses today. Clearly, early detection of house fires would be more likely today than it was in the past, weakening the conclusion of the argument:
Hypothetical 1:
% of houses with inoperative detectors: 50%+ in 2002 and in 2012
# of unsafe houses: 15 in 2002 vs. 23 in 2012
# of safe houses: 15 in 2002 vs. 22 in 2012 (i.e. early detection is more likely today than before)
For the conclusion to be valid, we need to rule out the possibility of the above-mentioned hypothetical. To do so, we need to assume that the proportion of inoperative detectors has actually increased, while the proportion of operative detectors decreased. That way, the number of "safe houses" can remain the same despite the increase in the total number of houses equipped with detectors. Here's a hypo that would satisfy the provisions in this argument:
Hypothetical 2:
% of houses with inoperative detectors: 50%+ in 2002 vs. 67% in 2012
# of unsafe houses: 15 in 2002 vs. 30 in 3012
# of safe houses: 15 in 2002 vs. 15 in 2012 (i.e. early detection is no more likely today than before)
Bottom line is, unless the percentage of inoperative detectors increases, the number of "safe houses" is bound to increase with the increased number of detectors installed. This is why answer choice (D) states an assumption of the argument. If you negate (D), you'll end up with Hypo 1, which undermines the conclusion of the argument.
Answer choice (A): Homes can have multiple smoke detectors, so this 15% is not necessarily the same as the 15% in the stimulus. If 15% of domestic smoke detectors were installed less than 10 years ago, that could make early detection more likely, since the equipment would be newer and possibly in better repair. Also, adding multiple detectors could increase the probability of detection. Either that is the case, or the 15% corresponds to nothing more but the increase in homes with smoke detectors. This response could attack or restate the stimulus, depending on some suppositions, but cannot provide support.
Answer choice (B): This does not support the conclusion that the likelihood of early detection has not increased. Since the fire has to occur before it can be detected, you should not conclude that more fires means less detection. This response gives you no reason to suppose that the fires were undetected and became severe.
Answer choice (C): This choice could be damaging to the stimulus, so you should eliminate it. If some of the detectors are not battery operated, a significant proportion of detectors without batteries might still be operational.
Answer choice (D): This is the correct answer choice. For the argument's conclusion to follow, it must be true that 10 years ago the proportion of inoperative smoke-detectors was lower than it was at the time of this argument.
Answer choice (E): Since the stimulus was about early detection, not overall fire safety, this response is irrelevant, and incorrect.
