Patterson CANNOT meet with Upton at which one of the following times?

Skylar on October 5, 2019

@Lucas Happy to help!

We have 6 variables (the 5 given names, and the workout): R, S, T, U, Y, W
We also have 6 slots, labeled from 1:00 to 6:00.

R, S, T, U, Y, W

___ ___ ___ ___ ___ ___
1:00 2:00 3:00 4:00 5:00 6:00

The rules can be broken down and diagrammed as follows:
(1) S - W
(2) W - T
* These first two rules can be combined to create: S - W - T
(3) YW or WY
(4) U - R

Combining these rules further shows us that we will have either:
(1) S - WY - T
(2) S - YW - T

The question asks us which spot U CANNOT occupy. The answer is (C) 3:00. This is because, if U is in spot 3, the only variable that could fill either spot 1 or spot 2 is S. Variables Y and W must be after S and next to each other, so they would have to fill spots 4/5. Variable T would have to fill spot 6 in order to be after W. However, R has to be after U according to our fourth rule, so it would also have to occupy either spot 4, 5,or 6. So, we only have one variable (S) that can occupy spots 1-2, and we have 4 variables (W, Y, T, R) that need to fit in spots 4-6. Therefore, Patterson CANNOT meet with Upton at 3:00.

For sake of explanation, here is a (non-exhaustive) list of valid ways in which U can occupy spots 1, 2, 4, and 5:
(1) U - R - S - W - Y - T
(2) S - U - R - W - Y - T
(4) S - W - Y - U - R - T
(5) S - W - Y - T - U - R

Does this make sense? Please let us know if you have additional questions!

mjt222 on February 20, 2020

The correct answer is C3 but it's being marked wrong I think