<p>I am not the greatest at problems like these...
Family # of consecutive nights
Jackson 10
callan 5
epstein 8
liu 6
benton 8
The table above shows the number of consecutive nights that each of five families stayed at a certain hotel during a 14-night period. If the liu family's stay did not overlap with the benton family's stay, which of the 14 nights could be a night on which only one of the five families stayed at the hotel?
a. 3rd the answer is 3rd...
b. 5th
c. 6th
d. 8th
e. 10th</p>
<p>Challenging question, and I'm going to type as I think. If the Jackson Family stayed for 10 nights, then you have certain possibilities. Weeks 1-10, 2-11, 3-13, and 4-14. THERE IS NOTHING AFTER 4, they have to begin in weeks 1-4. Notice how 10 is in all of them? No way that 10 is right since then the two 8 families couldn't come as well. You have to go lower. There is NO WAY that the Jackson family, who stays 10 nights, could go after 5 nights. They can't just go from 1-4 and then have another family stay alone for the 5th and go 10 straight. In other words, the Jackson Family can not go 10 straight if a family stayed on the 5th night, there is no 10 straight from 5. I know this is sounding confusing, but 3 is the only one that works because that gives the Jackson family the ability to stay 10 weeks, because they can start their 10 week process on week 4. Any other week would not allow them to reach 14 after going 10 straight. To be honest, you don't need the other families, and the fact about how liu doesn't overlap with benton is also superfluous if you ask me. </p>
<p>Challenging question, under SAT conditions. Normally, people would be thinking so quickly and frantically, and would not realize such things. I'm in the comfort of my recliner watching TV, so I'm very relaxed. Having my thought process on a real test day is the real challenge of the SAT.</p>
<p>Since the nights the Liu and Benton families stay don't overlap, either Liu stays days 1-4 and Benton 5-14 OR Benton 1-8 and Liu 9-14. Because the Jackson family needs to stay for ten days in a row, he must at the latest enter the hotel on the 5th day, to stay from 5-14. From days 5-14, we already know that Jackson and one of Liu(or)Benton stay, so only from days 1-4 can there be a single family at the hotel. The only answer choice less than 5 is A.</p>
<p>So the Liu and Benton weren't necessarily superfluous, but they did make it a little more complicated. Amber's method is still great, but the key is to know that there are always many different methods to solve a problem. The 10/14 was the key though in both methods. It's not really challenging as you think it through, but on test day, you need to try to be calm because usually it's hard not to be in a rush.</p>
<p>thanks for the responses guys</p>
<p>A clearer way of putting it is that the answer is either between 1-4 or 11-14, because the Jackson's 10 day stay is consecutive, and there's at least 1 family staying there at all times (because of the Liu Benton non-overlap thing).</p>
<p>If 11th 12th 13th or 14th were answer choices, they would work as well, but none of those appear, but rather 3rd, which lands inbetween 1-4.</p>
<p>sorry for the necro, but is this question ‘omit-worthy’?</p>