# LSAT Logic Games : Determining sequence in linear games

## Example Questions

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### Example Question #261 : Determining Sequence In Linear Games

A restaurant manager is scheduling interviews for an Executive Chef at her new business. Interviews for six applicants--Chet, Sylvia, Dennis, Beulah, Henrietta, and Lester--will be scheduled, one interview per day for the next six days. The schedule for the interviews is subject to the following conditions:

Lester must be scheduled to interview earlier than Sylvia.

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

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

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

If neither Chet nor Beulah is scheduled to interview on the sixth day, which one of the following must be true?

Possible Answers:

Sylvia is scheduled to interview on the sixth day.

Dennis is scheduled to interview on the third day.

Henrietta is scheduled to interview on the fourth day.

Lester is scheduled to interview on the second day.

Chet is scheduled to interview on the fifth day.

Correct answer:

Sylvia is scheduled to interview on the sixth day.

Explanation:

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.

### Example Question #261 : Sequencing

During a job fair, Caroline will interview exactly seven candidates for an upcoming position at her company. She will interview candidates who currently work at five different companies: Gordon, Halley, Lerder, Mack, and Nickle. No two candidates will be interviewed simultaneously. The following constraints determine the order of Caroine’s interviews:

She will interview one candidate from each company, except Lerder, from which she will interview three candidates.

She will interview the Halley employee immediately following her interview with the Nickle employee.

Her interviews with Lerder employees are never consecutive.

The Gordon employee is neither the first nor the last interview.

Which of the following shows an acceptable order of the companies from which Caroline interviews candidates?

Possible Answers:

Lerder, Nickle, Gordon, Lerder, Halley, Mack, Lerder

Lerder, Nickle, Halley, Gordon, Lerder, Lerder, Mack

Lerder, Mack, Nickle, Halley, Lerder, Gordon, Mack

Lerder, Nickle, Halley, Lerder, Mack, Lerder, Gordon

Lerder, Mack, Lerder, Gordon, Lerder, Nickle, Halley

Correct answer:

Lerder, Mack, Lerder, Gordon, Lerder, Nickle, Halley

Explanation:

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.

### Example Question #263 : Determining Sequence In Linear Games

During a job fair, Caroline will interview exactly seven candidates for an upcoming position at her company. She will interview candidates who currently work at five different companies: Gordon, Halley, Lerder, Mack, and Nickle. No two candidates will be interviewed simultaneously. The following constraints determine the order of Caroine’s interviews:

She will interview one candidate from each company, except Lerder, from which she will interview three candidates.

She will interview the Halley employee immediately following her interview with the Nickle employee.

Her interviews with Lerder employees are never consecutive.

The Gordon employee is neither the first nor the last interview.

If the first interview is with the Nickle employee, then Caroline’s interview with the Mack employee could be the

Possible Answers:

fourth interview

second interview

third interview

first interview

fifth interview

Correct answer:

fourth interview

Explanation:

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.

### Example Question #264 : Determining Sequence In Linear Games

During a job fair, Caroline will interview exactly seven candidates for an upcoming position at her company. She will interview candidates who currently work at five different companies: Gordon, Halley, Lerder, Mack, and Nickle. No two candidates will be interviewed simultaneously. The following constraints determine the order of Caroine’s interviews:

She will interview one candidate from each company, except Lerder, from which she will interview three candidates.

She will interview the Halley employee immediately following her interview with the Nickle employee.

Her interviews with Lerder employees are never consecutive.

The Gordon employee is neither the first nor the last interview.

If the last interview is with the Mack employee, then which of the following could be true?

Possible Answers:

Caroline’s fourth interview is with the Halley employee.

Caroline’s first interview is with the Gordon employee.

Caroline’s fifth interview is with the Gordon employee.

Caroline’s third interview is with the Gordon employee.

Caroline’s second interview is with the Halley employee.

Correct answer:

Caroline’s fifth interview is with the Gordon employee.

Explanation:

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).

### Example Question #265 : Determining Sequence In Linear Games

During a job fair, Caroline will interview exactly seven candidates for an upcoming position at her company. She will interview candidates who currently work at five different companies: Gordon, Halley, Lerder, Mack, and Nickle. No two candidates will be interviewed simultaneously. The following constraints determine the order of Caroine’s interviews:

She will interview one candidate from each company, except Lerder, from which she will interview three candidates.

She will interview the Halley employee immediately following her interview with the Nickle employee.

Her interviews with Lerder employees are never consecutive.

The Gordon employee is neither the first nor the last interview.

If Caroline interviews a Lerder employee second, then which of the following is a complete and accurate list of companies, any one of which could be the company from which the fourth person interviewed comes?

Possible Answers:

Gordon, Mack, Nickle

Gordon, Halley

Lerder, Halley

Lerder, Halley, Mack

Mack, Nickle

Correct answer:

Lerder, Halley

Explanation:

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.

### Example Question #266 : Determining Sequence In Linear Games

During a job fair, Caroline will interview exactly seven candidates for an upcoming position at her company. She will interview candidates who currently work at five different companies: Gordon, Halley, Lerder, Mack, and Nickle. No two candidates will be interviewed simultaneously. The following constraints determine the order of Caroine’s interviews:

She will interview one candidate from each company, except Lerder, from which she will interview three candidates.

She will interview the Halley employee immediately following her interview with the Nickle employee.

Her interviews with Lerder employees are never consecutive.

The Gordon employee is neither the first nor the last interview.

If the Halley employee is interviewed immediately before the Mack employee, then which of the following must be true?

Possible Answers:

Caroline’s first interview is with Nickle.

Caroline’s second interview is with Nickle.

Caroline’s seventh interview is with Lerder.

Caroline’s fifth interview is with Lerder.

Caroline’s sixth interview is with Mack.

Correct answer:

Caroline’s seventh interview is with Lerder.

Explanation:

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.

### Example Question #267 : Determining Sequence In Linear Games

During a job fair, Caroline will interview exactly seven candidates for an upcoming position at her company. She will interview candidates who currently work at five different companies: Gordon, Halley, Lerder, Mack, and Nickle. No two candidates will be interviewed simultaneously. The following constraints determine the order of Caroine’s interviews:

She will interview one candidate from each company, except Lerder, from which she will interview three candidates.

She will interview the Halley employee immediately following her interview with the Nickle employee.

Her interviews with Lerder employees are never consecutive.

The Gordon employee is neither the first nor the last interview.

If Caroline’s interview with the Gordon employee occurs immediately following the interview with the Mack employee, then the fourth person interviewed must come from which company?

Possible Answers:

Gordon

Mack

Lerder

Halley

Nickle

Correct answer:

Lerder

Explanation:

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.

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