Which one of the following is an acceptable schedule for the performance of the songs, in order from the first to las...

Payton on August 31, 2020

Set Up

I would also like an explanation to the set up of this question please.

Victoria on September 16, 2020

Hi @Payton,

Happy to help!

We know that six songs will be performed at the concert: O, P, T, X, Y, and Z.

Each song will be performed by one of three vocalists: G, H, and L.

Each song will be performed exactly once.

Song: _ _ _ _ _ _
Singer: _ _ _ _ _ _

Now let's go through our rules.

Rule 1 - Y must be performed earlier than both T and O

> T
Y
> O

Rule 2 - P must be performed earlier than Z and later than O

O > P > Z

We can connect these rules to make a larger sequence.

> T
Y
> O > P > Z

Rule 3 - G can perform only X, Y, and Z

Rule 4 - H can perform only T, P, and X

Rule 5 - L can perform only O, P, and X

These rules mean that G must perform Y and Z, H must perform T, and L must perform O.

X can be performed by any of the three singers. P can be performed by either H or L.

Rule 6 - the vocalist who performs first must be different from the vocalist who performs last.

The question stem asks us to select the answer choice which could be an acceptable schedule. This means that the correct answer choice could be true while the remaining answer choices cannot be true.

Let's start by eliminating answer choices using only the sequencing rules as these are easier.

We can eliminate answer choice (A) because Rule 1 tells us that Y must be performed earlier than T and earlier than O. This schedule has Y performing after T.

We can eliminate answer choice (B) because it violates the sequence imposed by Rule 2: O > P > Z. This answer choice schedules Z earlier than both O and P.

We can eliminate answer choice (D) because it violates the sequence imposed by Rule 2: O > P > Z. This answer choice schedules P earlier than both O and Z.

This leaves us with answer choices (C) and (E). Let's assign singers to each of the schedules based on Rules 3 through 5 to see which one must be correct.

Y O P X T Z
G L H/L any H G

Y X O P Z T
G any L H/L G H

Notice that answer choice (C) violates Rule 6. We know from Rules 3 through 5 that G must perform Y and Z. Rule 6 tells us that the vocalist who performs first must be different from the vocalist who performs last. Answer choice (C)'s schedule both starts and ends with G.

Answer choice (E), on the other hand, starts with G and ends with H. Does this setup meet all of our rules? Yes

1) Y is performed earlier than T and earlier than O
2) P is performed earlier than Z and later than O
3) G performs Y and Z
4) H performs T
5) L performs O
6) The first vocalist is G and the last vocalist is H

Any of the vocalists can perform X and either H or L can perform P.