Because P focuses on health it must come before Q and R. And because Q is both energy focused and scientist there are no employees allowed to use the lab after Q. The game can thus be written three ways:

P __ __ __ Q

__ P __ __ Q

__ __ P R Q 

In the first way, R, S, T are interchangeable and can all be placed second. The second way shows P can go second. Thus, the only employee to not be able to go second is Q.

All the incorrect answers are wrong for the following reasons:

P, Q, R, S, T (Since Q and R are both energy focused, and Q is a scientist and R is a engineer R must use the lab before Q)

P, Q, T, S, R (Since Q and R are both energy focused, and Q is a scientist and R is a engineer R must use the lab before Q)

P, S, T, Q, R (Since Q and R are both energy focused, and Q is a scientist and R is a engineer R must use the lab before Q)

T, S, R, P, Q (P is health focused, whereas R is energy focused, thus P must use the lab before R)

If Violet performs after Blue, but Violet must be in Act I, then Blue must also be in Act I. That means that Blue can go first, second, or third in the lineup.

• If Blue goes first, Yellow must go third because there is exactly one act between them.
• If Blue goes second, Yellow must go fourth for the same reason.
• If Blue goes third, Yellow must go first for the same reason.

There is no possible case, then, in which Yellow goes second.

If Blue performs second, and there is exactly one act between Blue and Yellow, then Yellow must perform fourth. Since Violet performs after Blue but still performs in Act I, yet there are only four acts in Act I, Violet must perform third.

Since Katie graduated after Lou, and Katie graduated in 2006, Lou must have graduated in 2005. Therefore, Lou did not graduate in 2008.

Since Red performs last, and Green can only perform first or last in the lineup, Green must go first. Therefore, Green performs in Act I.

In order to solve this problem, simply go through each answer and apply each individual condition from the pre-question text. If the answer violates any of the conditions, then you can eliminate it. If the answer does not violate any conditions, then you know it is correct. A question like this will typically be the first in its set, and is an opportunity to solidify your knowledge of the conditions governing the game. 

For this problem, the correct order is: Henrietta, Lester, Dennis, Sylvia, Chet, Beulah

Let's go through the list of conditions to see why:

"Lester must be scheduled to interview earlier than Sylvia." TRUE

"Dennis must be scheduled to interview earlier than both Chet and Beulah." TRUE

"The interviews scheduled for the second and third day cannot be for either Chet, Beulah, or Henrietta." TRUE

"Henrietta's interview cannot be scheduled for the sixth day." TRUE

This is the only provided sequence that satisfies every condition of the game, and is therefore the correct answer. 

The key to finding the correct solution to this problem is drawing additional deductions from the question text. In addition to the conditions given to us in the pre-question text, we know that in the sequence we are solving for, neither Chet nor Beulah nor Henrietta can occupy the fourth position. This will allow us to make secondary deductions about their relative positions in the sequence by combining this information with the previous conditions. Let's start by looking at the third condition from the pre-question text:

"The interviews scheduled for the second and third day cannot be for either Chet, Beulah, or Henrietta."

When we combine this condition with the new information in the question, we see that neither Chet nor Beulah nor Henrietta can occupy the second, third, or fourth positions in our sequence. This leaves only the first, fifth, and sixth positions to place these three entities. Next, let's look at the second condition.

"Dennis must be scheduled to interview earlier than both Chet and Beulah."

We now know that Chet, Beulah, and Henrietta must occupy the first, fifth, and sixth positions in the sequence. However, when we apply the second condition of the pre-question text, we see that neither Chet nor Beulah may occupy the first position, as this would make it impossible for the second condition to be true. This leaves only Henrietta to fill the first position in the sequence, meaning that it must be true that Henrietta is interviewed on the first day. Therefore, this is the answer we are looking for.

Now, questions like this can get confusing because of their phrasing. After all, through our own deductions we have established that Chet could be interviewed on the fifth day, and that Beulah could interview on the sixth day. However, for the answer to this question to be considered correct, it is not sufficient that an answer could be true. Rather, the answer must be true in every possible iteration of the sequence. Chet and Beulah are interchangeable in the fifth and sixth positions, and therefore do not meet the criteria for a correct answer.

The answer to this problem will be a condition that must be true. Therefore, this condition will always be true, in any viable iteration of the sequence of interviews. Any answer that does not meet this criteria can be automatically eliminated. 

The correct answer from the options provided is: Lester is scheduled to interview earlier than Chet.

We need to look at the conditions from the pre-question text to determine why this is correct. Let's start with the second condition:

"Dennis must be scheduled to interview earlier than both Chet and Beulah."

Because we know that at least one entity (Dennis) must precede Chet in the sequence, we know with certainty that he cannot occupy the first position. Now let's combine this information with the third condition:

"The interviews scheduled for the second and third days cannot be for either Chet, Beulah, or Henrietta."

When we add this information from the third condition into the mix, we see that Chet cannot occupy either the first, second, or third positions in the sequence. Conversely, this means that Chet can only occupy the fourth, fifth, or sixth positions. Now that we've established Chet's potential positions in the sequence, let's look at the first condition, which concerns Lester.

"Lester must be scheduled to interview earlier than Sylvia."

Because we know that Lester must precede at least one entity (Sylvia) in the sequence, we can deduce that he cannot occupy the sixth position in the sequence. Since we also already know that Chet can only occupy the fourth, fifth, or sixth position in the sequence, we can further deduce that the only conceivable way for Chet to precede Lester in the sequence would be for Chet to occupy the fourth position and Lester to occupy the fifth. If this sequence violates any of the other conditions, then we will know that we've found the correct answer. Let's test it out. 

_ _ _ C L _

Since the first condition tells us that Lester must precede Sylvia, we know that Sylvia must occupy the sixth position in the sequence.

_ _ _ C L S

Furthermore, we know from the third condition that the only remaining position for Henrietta to occupy is the first. She must occupy this position.

H _ _ C L S

This is where the sequence breaks down. According to the third condition, neither Chet nor Beulah nor Henrietta can occupy the second or third positions of the sequence. However, with Beulah as one of our remaining entities, our only remaining positions in the sequence are the second and third. Since we have determined through our deductions that this is the only conceivable way for Chet to precede Lester in the sequence, it is impossible for Chet to come before Lester. Therefore, it must be true that Lester is scheduled to interview earlier than Chet.

The phrasing of the question text is intended to make this question more difficult. Before looking at the answer choices, we should take a second to parse what the question is really asking, and what will determine a correct answer. Because the question is asking us for an order that CANNOT work within the conditions of the game, the correct answer will contain an error. Apply each condition to each potential answer. The first time you encounter an error, you will know you have found your correct answer. 

The correct choice for this question is: Lester, Chet, Sylvia.

Let's apply the conditions from the pre-question text to this response to see why it is the right choice.

"Lester must be scheduled to interview earlier than Sylvia."

No error so far. In this sequence, Lester is scheduled to interview earlier than Sylvia. Let's go on to the second condition.

"Dennis must be scheduled to interview earlier than both Chet and Beulah."

This is where we encounter a problem. Because Lester, Chet, and Sylvia occupy the fourth, fifth, and sixth positions (respectively), we know that the only remaining positions to fill are the first, second, and third. No matter which remaining position Dennis occupies, he will always precede Chet, so that's not the problem. The problem is that Dennis must also precede Beulah, meaning that Beulah must occupy either the second or third position. However, as we know from the third condition:

"The interviews scheduled for the second and third days cannot be for either Chet, Beulah, or Henrietta."

Therefore, it is impossible for Beulah to occupy either of the remaining positions, and this response CANNOT be true.