Question

Family	Number 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 familys stay did not overlap with the Benton familys stay, which of the 14 nights could be a night on which only one of the five families stayed at the hotel?

• A. The 3rd
• B. The 5th
• C. The 6th
• D. The 8th
• E. The 10th

Answer 1

The correct option is A The 3rd

$\Rightarrow$ Try stacking all the families other than Liu and Benton all on one side. If you put them all in the first part of the $14$ day period, then the Jackson family would cover all the answer choice days.

$\Rightarrow$ If you put them all at the end of the $14$ day period, then the Jackson family shows up on the $4th$ day, and stays until the end. They don’t need to be there the $3rd$ day, nor does anyone else except either Benton or Liu. That’s why it’s $\left(A\right).$