Math question

<p>The question is in the official SAT practice test at this link: <a href="https://satonlinecourse.collegeboard.com/SR/digital_assets/assessment/pdf/F4D31AB0-66B4-CE32-00F7-F5405701F413-F.pdf%5B/url%5D"&gt;https://satonlinecourse.collegeboard.com/SR/digital_assets/assessment/pdf/F4D31AB0-66B4-CE32-00F7-F5405701F413-F.pdf&lt;/a&gt;&lt;/p>

<p>Its on pg. 33, #8 </p>

<p>I got the answer by basically writing out all the possible scenarios there could have been, but is there any easier way to do this? I don't want to consume so much time on 1 single question.</p>

<p>Liu’s stay (6 nights) and Benton’s stay (8 nights) did not overlap, meaning that during each of the 14 nights, the hotel is filled up by 1 family. We need to figure out which of the nights could have had only 1 family.</p>

<p>Now we look at the family that stayed the longest: the Jackson family, which stayed 10 nights. The remaining two families, which stayed fewer nights–5 days and 8 days, could have overlapped with the Jackson family’s stay (completely). So, all 3 families could have filled up at least 1 spot for any given 10 consecutive nights at the minimum.</p>

<p><a href=“A”>b</a> The 3rd** is the answer because the 10 consecutive nights could have been the 5th, 6th, 7th, 8th, 9th, 10th, 11th, 12th, 13th, and 14th nights. The other families, with fewer stays, could have overlapped any of those 10 nights (5-14).</p>

<p>The answer is not the 5th, 6th, 8th, or 10th because it is impossible to distribute the 10 consecutive nights without including those nights.</p>