<p>Question from the Free SAT Practice Test (Online) from the CollegeBoard. I read the explanation online, but its still confusing/the explanation doesn't help me...</p>
<p>Note that the Liu family’s and the Benton family’s stays do not overlap, yet they add to 14 (the length of the interval). This means that exactly one of these families stays at the hotel for each of the 14 nights.</p>
<p>We want to make it possible so that exactly one of the five families is at the hotel for some night. To do this, we “pack” the other three families towards the beginning or end of the 14-night interval (since the Liu or Benton family must be there on any given night). It is possible for nights 1,2,3,12,13,14 to have exactly one family given this algorithm. 3 is the only answer choice listed so the answer is A) 3.</p>
<p>Since Liu’s stay + Benton’s stay = 14 total days, and they don’t overlap, you know that on each of the 14 days, at least 1 family stayed at the hotel, since we are only given 14 days.</p>
<p>Now let’s forget about the Lius and Bentons. The significance of this is that the question is now reduced to: Which of these nights could be a night on which no family stayed at the hotel?</p>
<p>Now, consider the Jackson family. They can start their stay on any of the days 1, 2, 3, 4, or 5. This means that their stay ends on days 10, 11, 12, 13, or 14, respectively. Thus, the Jacksons necessarily stay from days 5 to 10. The other families are less restricted.</p>
<p>Look at the answer choices. Remember our reduced question: Which of these nights could be a night on which no family stayed at the hotel (remembering that we pretend that Benton’s and Lius don’t exist anymore)? Since the Jacksons have to stay from days 5 to 10, you can cross B, C, D, and E off. The answer is A.</p>
<p>edit: sniped yet again…</p>
<p>I remember doing this exact question in one of my practice tests. The above response is right.</p>