This is a classic example of "LSAT Math," which almost always deals with percentages, proportions, ratios, etc.
Let's consider our premises. 1. A higher percentage of homes today have smoke detectors than did homes 10 years ago.
2. Over 50% of smoke detectors today are inoperative.
Conclusion: Early detection of fires is no more likely than it used to be.
On "strengthen with necessary assumption" questions, it often helps to criticize the argument before looking at the answer choices. Try to identify a gap in the reasoning.
Here is my complaint. We know the current percentage of broken smoke detectors. However, we do not know that number for 15 years ago. It could have been the same or worse, which is a huge gap in the argument! Because a greater percentage of households have smoke detectors today, early detection of fires would be more likely... unless more of them are broken today than 15 years ago. This is why answer choice D is correct.
Answer choice E is not relevant because we have no information about water sprinklers. Maybe some of these houses have both smoke detectors and sprinklers? Also, this answer choice relates to both houses today and houses 10 years ago. Therefore, it does nothing to explain the difference between these eras. Remember, our conclusion is that early fire detection has not improved.
