Family Thomas Shawn David Sui Lisa
Number of Consecutive 10 5 8 6 8
Nights
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 Sui family’s stay did not overlap with the Lisa 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) The 2nd (B) The 4th (C) The 5th (D) The 8th (E) The 10th
Since the Sui and Lisa families can't overlap, one of those two occupies the
hotel all 14 nights. The Thomas family spends either nights 1-10,2-11,3-12,
4-13, or 5-14. Therefore regardless of which consecutive 10 nights the Thomas
family spends there, there will always be at least two of the families
overlapping on nights 5-10. Since the other two families stay fewer nights than
the Thomasses, they could both overlap with the Thomasses so as to leave nights
1-4 and 11-14 with only one of the families occupying the hotel. It would be
possible for the other three families to delay their first night until or after
the 5th night. So of the choices listed, both the 2nd and the 4th nights could
be the correct answer, but none of the others could be. You didn't say there
was just one possible choice, so the only answer is to choose both (A) and (B)!
Edwin