Whenever we see the language must be true in the question text, we know that we can eliminate any answer that is OR could be false. The correct answer will be true in every iteration of the sequence as it conforms to the conditions of the pre-question text AND question text. The most effective strategy for answering questions of this nature is to make all possible deductions and then apply those deductions to the answer choices.

The correct answer for this question is: Sylvia is scheduled to interview on the sixth day. Let's start by seeing what deductions we can make using the language in the question text. 

In this scenario, "neither Chet nor Beulah is scheduled to interview on the sixth day".  Because both Chet and Beulah are mentioned in the conditions of the pre-question text, we can combine this new information with what we already know to further deduce the limitations on which entities can occupy which positions. Let's start with the first pre-question condition.

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

While on its surface this condition might not appear to tell us anything, it actually helps us by imposing a further limitation on the sixth position in the sequence. Because we know that Lester must be interviewed earlier than Sylvia, we also know that he can never occupy the sixth position. This means that we can establish that neither Chet nor Beulah nor Lester is scheduled to interview on the sixth day. Conversely, we can also establish that Sylvia must not occupy the first position. Let's move on to the second condition.

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

This condition will be key in determining the correct answer, as it has effects on both of the entities mentioned in the question text. We already know that neither Chet nor Beulah can occupy the sixth position in the sequence. However, this condition further tells us that Dennis also can't occupy the sixth position, as that would contradict the condition that he precede Chet and Beulah. Because we also know that "Henrietta's interview cannot be scheduled for the sixth day" we now know that the only entity who can occupy the sixth position is Sylvia. Therefore, it must be true that Sylvia is interviewed on the sixth day. Once we have determined this to be true, we should check to see if this is one of the options, and if so, select it as our answer.

Each of the incorrect answers can be eliminated using the rules provided by the stimulus. One incorrect answer is ruled out because Lerder is listed consecutively. One incorrect answer is ruled out because there are not three Lerder employees. One incorrect answer is ruled out because Nickle is not followed by Halley. One incorrect answer is ruled out because Gordon is listed as the seventh company.

Since you know the Nickle employee is interviewed first, you also know the Halley employee is interviewed second, from the rules in the stimulus. This leaves interviews 3-7 open. You also know that the Lerder employees cannot be interviewed consecutively, which leaves only one possible distribution for those three Lerder employees: third, fifth, and seventh. This leaves the fourth and sixth interview slots open, either of which could be occupied by the Gordon or Mack employees. The question asks about Gordon, and sixth is not listed as a possibility - leaving you with "fourth interview" as the only available correct answer.

After you place the Mack employee interview in the last slot, you have the first six slots still open. Where you place the Nickle-Halley block will restrict where the three Lerder employees can fit. If you test the possibilites for the Nickle-Halley block, you will see there are only two possible outcomes: Nickle is second and Halley is third or Nickle is fourth and Halley is fifth. If you fill out these two possible placements for the Nickle-Halley block, you will be able to completely fill out each sequence.

In the first case, Lerder employees must occupy the first, fourth, and sixth spots. In the second case, Lerder employees must occupy the first, third, and fifth spots. You will be able to then fill in the Gordon employee in the fifth spot for the first case, and the second spot for the second case.

It then becomes a matter of process of elimination. Four of the answers CANNOT be true with either of the possible outcomes. Only the correct answer, the Gordon employee being interviewed fifth, can be true (it is true in our first case).

To find the correct answer here, it must be exactly the possibilites for the fourth interview. It cannot list anything less than all possibilites, nor can it list anything extraneous.

First you should write in that one of the Lerder employees is interviewed second. This immediately rules out another Lerder employee being interviewed first or third. If you consider the Nickle-Halley block, you will discover that there are only two possible outcomes: either filling the third and fourth slots or the fifth and sixth slots. Nickle cannot be first, because Halley would be unable to follow as second. Nickle cannot be fourth nor sixth, because there would be no possible outcome in which Lerder employees are interviewed non-consecutively.

In filling out the first possibility, the Lerder employees must occupy the fifth and seventh slots, leaving Mack to the first slot. In filling out the second possibility, the Lerder employees must occupy the fourth and seventh slots, again leaving Mack to the first slot.

Going back to the question, either a Halley or Lerder employee may be interviewed fourth. So the correct answer lists only and exactly those two options.

You already know, from the global rules, that Nickle must precede Halley. Adding the conditional rule here that Halley must precede Mack creates a Nickle-Halley-Mack block. If you attempt to place this block through the sequence, you will discover that it can only occur in two possible outcomes: second, third, and fourth or fourth, fifth, and sixth. Nickle cannot be placed first, third, or fifth because that would force consecutive Lerder interviews. Nickle cannot be placed sixth or seventh, because there would not be enough spaces for Halley and Mack to immediately follow.

With the block being second, third, and fourth, Lerder employees must be interviewed first, fifth, and seventh to keep them non-consecutive. The Gordon interview, then, must take place sixth. With the block being fourth, fifth, and sixth, Lerder employees must be interviewed first, third, and seventh to keep them non-consecutive. The Gordon interview, then, must take place second.

The question is asking for which must be true, meaning we are looking for something that is true in both possible sequences. Proceeding by eliminating incorrect answers, you will discover that Nickle's interview can never be first. For the other three incorrect answers, the outcomes are only sometimes true; they are not true of both sequences. Nickle's interview does not have to be second, Lerder's interview does not have to be fifth, and Mack's interivew does not have to be sixth.

In both cases, Lerder's interview must be seventh, making it the correct answer.

The conditional rule in this problem sets up a Mack-Gordon block, and you have the Nickle-Halley block from the global rules. Since the question is asking which must be true, there is only one possible outcome for the fourth position: if you discover a company that will fit into the fourth position and allow for a correct sequence, that is your correct answer.

Testing each possible answer in the fourth position should allow you to quickly determine the correct answer by process of elimination. Halley cannot be in the fourth position, because after you fill in the Nickle-Halley block, no matter where you place the Mack-Gordon block, there is no way to keep Lerder employees non-consecutive. The same is true if Nickle is in the fourth position, ruling it out as correct.

You run into the same problem if you place either Mack or Gordon in the fourth spot: after you fill in the Mack-Gordon block, no matter where you place the Nickle-Halley block, there is no way to keep Lerder employees non-consecutive.

This leaves you with the correct answer: Lerder. You can prove this answer by placing Lerder in the first, fourth, and seventh positions, leaving room for the Nickle-Halley and Mack-Gordon blocks in between.

Any option without Mildred being first or last is immediately taken out. Any option without one space between Nancy and Quentin is taken out, and any option that has Quentin appearing before Nancy is taken out. Any option that doesn't have Lily appearing before Nancy is taken out, leaving only the correct answer as an option.

If Nancy is second, we can immediately put Quentin in the fourth spot. Since Lily must come before Nancy, her portrait must be first. With Lily occupying the first spot, Mildred then must be last. We are left with Owen and Peter to fill out the thrid and fifth spots, in either order. Therefore, every answer given must be true EXCEPT that Peter is third - he could be, but he doesn't have to be. 

This gives us a new rule, namely that Quentin must come before Peter. We already know that Nancy must appear exactly two spots before Quentin. We also know that Lily has to come somewhere before Nancy. Our complete new rule states that Lily must come somewhere before Nancy, who must appear exactly two spots before Quentin, who must appear somewhere before Peter. When we add all of these up (including the blank spot between Nancy and Quentin) we have already filled out five of the six possible spots. When we take into account that Mildred must be in either the first or last spot, we are left with two options for this super block. Lily, starting off the block, can either go in the first spot and Mildred in the last, or in the second spot with Mildred in the first. In both scenarios Owen fills in the missing spot between Nancy and Quentin. Therefore, there are only two possible solutions that adhere to all of the given rules and the new added rule.