LSAT Logic Games : Four- & Five-Variable
Study concepts, example questions & explanations for LSAT Logic Games
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Example Questions
Example Question #61 : Four & Five Variable
On Sunday, Marvin plans his dinners for the following 6 days (Monday-Saturday). He plans 6 main courses and 3 salads. Of the main courses, 3 are pasta dishes—Angel Hair, Fettuccine, and Spaghetti—and 3 are meat dishes—Steak, Chicken Breast, and Pork Loin. The 3 salads are Caesar Salad, Greek Salad, and Garden Salad. All of the following statements are true about the meals Marvin has planned for the week:
- Each main course and each salad will be served exactly once during the week
- A pasta dish is never served on the same night as a meat dish
-
Salad is always paired with either a pasta dish or a meat dish
-
The 3 salads are not always paired with a meat dish nor are they always paired with a pasta dish
-
No two meat dishes are served on consecutive days
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Both Wednesday and Friday have pasta dishes
-
Both Monday and Thursday have salads with dinner
Given the above information, which of the following could NOT be Marvin's planned meal for Thursday night?
Pork Loin with Garden Salad
Chicken Breast with Greek Salad
Angel Hair Pasta and Caesar Salad
Chicken Breast with Caesar Salad
Steak with Greek Salad
Angel Hair Pasta and Caesar Salad
You are told that "No two meat dishes are planned on consecutive days" and that "Both Wednesday and Friday have pasta dinners." Given that this is true, and that each dish mentioned must be served at some point during the week, you can conclude that Thursday night must be a meat dish, as if it were the third pasta dish, the only days of the week left available to serve the three meat dishes would be Monday, Tuesday, and Saturday, and that would break the rule that no two meat dishes are planned for consecutive days. So you can eliminate Angel Hair Pasta as the dish for Thursday night. Any of the other dishes would be possible.
Example Question #62 : Four & Five Variable
On Sunday, Marvin plans his dinners for the following 6 days (Monday-Saturday). He plans 6 main courses and 3 salads. Of the main courses, 3 are pasta dishes—Angel Hair, Fettuccine, and Spaghetti—and 3 are meat dishes—Steak, Chicken Breast, and Pork Loin. The 3 salads are Caesar Salad, Greek Salad, and Garden Salad. All of the following statements are true about the meals Marvin has planned for the week:
- Each main course and each salad will be served exactly once during the week
- A pasta dish is never served on the same night as a meat dish
-
Salad is always paired with either a pasta dish or a meat dish
-
The 3 salads are not always paired with a meat dish nor are they always paired with a pasta dish
-
No two meat dishes are served on consecutive days
-
Both Wednesday and Friday have pasta dishes
-
Both Monday and Thursday have salads with dinner
Given all of the above, suppose you find out that Marvin plans to have Greek Salad with his Wednesday meal. If that is true, which of the following dinners would be impossible?
Chicken Breast and Garden Salad on Thursday
Fettuccine and Greek Salad on Wednesday
Steak and Garden Salad on Tuesday
Pork Loin on Tuesday
Pork Loin on Saturday
Steak and Garden Salad on Tuesday
You are given the information that
-
Both Wednesday and Friday have pasta dinners
-
Both Monday and Thursday have salads with dinner
Which means that, if Marvin plans to eat Greek salad with dinner on Wednesday, he must be eating it with a pasta dish and that the other two salads (Caesar and Garden) must be eaten on Monday and Thursday. Therefore, the only option listed here that would be precluded would be "Steak and Garden Salad on Tuesday," as there are only three salads, and you know that they are planned for Monday, Wednesday, and Thursday.
Example Question #63 : Four & Five Variable
On Sunday, Marvin plans his dinners for the following 6 days (Monday-Saturday). He plans 6 main courses and 3 salads. Of the main courses, 3 are pasta dishes—Angel Hair, Fettuccine, and Spaghetti—and 3 are meat dishes—Steak, Chicken Breast, and Pork Loin. The 3 salads are Caesar Salad, Greek Salad, and Garden Salad. All of the following statements are true about the meals Marvin has planned for the week:
- Each main course and each salad will be served exactly once during the week
- A pasta dish is never served on the same night as a meat dish
-
Salad is always paired with either a pasta dish or a meat dish
-
The 3 salads are not always paired with a meat dish nor are they always paired with a pasta dish
-
No two meat dishes are served on consecutive days
-
Both Wednesday and Friday have pasta dishes
-
Both Monday and Thursday have salads with dinner
Which of the following, if true, would give you enough information to determine what day the Spaghetti dinner was planned for?
The Tuesday and Friday dishes would not be paired with a salad
Angel Hair Pasta would be served with the Caesar Salad, Chicken Breast with the Garden Salad
Chicken Breast would be served earlier in the week than Pork Loin and later in the week than Steak
Two pasta meals are paired with salads and one meat meal is paired with a salad
Spaghetti would not be paired with a salad, a salad would be served on Wednesday, a meat dish would be served on Tuesday
Spaghetti would not be paired with a salad, a salad would be served on Wednesday, a meat dish would be served on Tuesday
From the given information, you know that
-
Both Wednesday and Friday have pasta dinners
- Both Monday and Thursday have salads with dinner
From this, you can see that two of the nights that could have Spaghetti are Wednesday and Friday, and that Thursday and Saturday could not have the Spaghetti dinner (because you also know that "No two meat dishes are planned on consecutive days" and therefore, if Wednesday and Friday both have pasta dinners, Thursday and Saturday must both have meat dinners, or two of the meat dinners would have to be consecutive). The only answer choice that gives you enough information to fully determine which night would have Spaghetti is "Spaghetti would not be paired with a salad, a salad would be served on Wednesday, a meat dish would be served on Tuesday." You know that both Monday and Thursday have salads, so Spaghetti would not be served on either of those nights, and if a meat dish would be served on Tuesday, that tells you that the three nights that have pasta dishes are Monday, Wednesday and Friday (or else meat would have to be served two consecutive nights, which isn't allowed). Since you now know that both Monday and Wednesday dinners will be served with salads, that leaves only Friday night as the possible night that Spaghetti will be served.
Example Question #64 : Four & Five Variable
On Sunday, Marvin plans his dinners for the following 6 days (Monday-Saturday). He plans 6 main courses and 3 salads. Of the main courses, 3 are pasta dishes—Angel Hair, Fettuccine, and Spaghetti—and 3 are meat dishes—Steak, Chicken Breast, and Pork Loin. The 3 salads are Caesar Salad, Greek Salad, and Garden Salad. All of the following statements are true about the meals Marvin has planned for the week:
- Each main course and each salad will be served exactly once during the week
- A pasta dish is never served on the same night as a meat dish
-
Salad is always paired with either a pasta dish or a meat dish
-
The 3 salads are not always paired with a meat dish nor are they always paired with a pasta dish
-
No two meat dishes are served on consecutive days
-
Both Wednesday and Friday have pasta dishes
-
Both Monday and Thursday have salads with dinner
Given the above information, which of the following statements is logically valid?
Either a meat dish or a salad is eaten on Friday, but not both.
Either Steak or Chicken Breast is eaten on Thursday.
Either two meat dishes are eaten with a salad, or two pasta dishes are eaten with a salad.
Either Greek Salad or Garden Salad is eaten with a meat dish.
Either a pasta dish is eaten on Tuesday, or a meat dish is not eaten on Monday.
Either two meat dishes are eaten with a salad, or two pasta dishes are eaten with a salad.
When determining the logical validity of "either/or" statements, recall that for the whole statement to be valid, only one of the forks of the statement has to be true. Since you are given the information "Salad is not always eaten with meat AND not always eaten with pasta," and that there are 3 salad dishes in total, you can logically determine that either two of the salads are eaten with pasta dishes, or two of the salads are eaten with meat dishes. You know that at least one salad is eaten with a pasta dish and at least one is eaten with a meat dish, and you know the third must be eaten with either a pasta or a meat dish, because you are told "Salad is always paired with either a pasta dish or a meat dish." The other statements cannot be logically deduced from the information given.
Example Question #65 : Solving Four And Five Variable Logic Games
On Sunday, Marvin plans his dinners for the following 6 days (Monday-Saturday). He plans 6 main courses and 3 salads. Of the main courses, 3 are pasta dishes—Angel Hair, Fettuccine, and Spaghetti—and 3 are meat dishes—Steak, Chicken Breast, and Pork Loin. The 3 salads are Caesar Salad, Greek Salad, and Garden Salad. All of the following statements are true about the meals Marvin has planned for the week:
- Each main course and each salad will be served exactly once during the week
- A pasta dish is never served on the same night as a meat dish
-
Salad is always paired with either a pasta dish or a meat dish
-
The 3 salads are not always paired with a meat dish nor are they always paired with a pasta dish
-
No two meat dishes are served on consecutive days
-
Both Wednesday and Friday have pasta dishes
-
Both Monday and Thursday have salads with dinner
Which of the following statements would not be possible given that the above information is all true?
Neither Pork Loin nor Chicken Breast will be served on Monday.
Friday night has Spaghetti dinner with Greek Salad.
Neither Pork Loin nor Chicken Breast will be served on Tuesday.
Niether Tuesday nor Saturday has a salad.
Neither Monday nor Tuesday has a pasta dinner.
Neither Monday nor Tuesday has a pasta dinner.
If all the given information is true, either Monday or Tuesday night must have a pasta dinner. Since you know that:
-
No two meat dishes are planned on consecutive days
-
Both Wednesday and Friday have pasta dinners
you can determine that meat dishes must be served on Thursday and Saturday, which means there is only one remaining night for a meat dish to be served. If Monday AND Tuesday did not have pasta dishes, they would both have to have meat dishes, which would be impossible. (Also, this would violate the "no meat dishes on consecutive days" rule.)
Example Question #66 : Solving Four And Five Variable Logic Games
On Sunday, Marvin plans his dinners for the following 6 days (Monday-Saturday). He plans 6 main courses and 3 salads. Of the main courses, 3 are pasta dishes—Angel Hair, Fettuccine, and Spaghetti—and 3 are meat dishes—Steak, Chicken Breast, and Pork Loin. The 3 salads are Caesar Salad, Greek Salad, and Garden Salad. All of the following statements are true about the meals Marvin has planned for the week:
- Each main course and each salad will be served exactly once during the week
- A pasta dish is never served on the same night as a meat dish
-
Salad is always paired with either a pasta dish or a meat dish
-
The 3 salads are not always paired with a meat dish nor are they always paired with a pasta dish
-
No two meat dishes are served on consecutive days
-
Both Wednesday and Friday have pasta dishes
-
Both Monday and Thursday have salads with dinner
Which of the following pieces of information would allow you to determine whether the Chicken Breast would be eaten with a salad?
A pasta dish is served on Monday.
Spaghetti is served on Friday, Fettuccine is served with Greek salad.
Steak is served on Tuesday and Pork Loin is served later in the week than every pasta dish
The Caesar Salad is served with either Angel Hair Pasta or Pork Loin.
Angel Hair Pasta is served earlier in the week than Fettuccine or Spaghetti.
Steak is served on Tuesday and Pork Loin is served later in the week than every pasta dish
You know that
-
No two meat dishes are planned on consecutive days
-
Both Wednesday and Friday have pasta dinners
-
Both Monday and Thursday have salads with dinner
By process of elimination, you can infer that Thursday and Saturday have meat dishes for dinner. The answer choice "Steak is served on Tuesday, Pork Loin is served later in the week than every pasta dish" tells you that Pork Loin is served on Saturday, which means the only meat dish left to be eaten on Thursday would be Chicken Breast, and it would be eaten with a salad. The other answer choices do not provide enough relevant information to help you determine this.
Example Question #65 : Four & Five Variable
A popular band is preparing for a nationwide music tour. The tour must include the following five states: California, Florida, Illinois, New York, and Texas. The tour will conclude in one state before moving to the next state. The following restrictions apply to the tour dates:
The tour must start in New York or California.
Texas cannot be the final state.
Texas and Illinois must be consecutive, with either coming first.
Florida must be after New York.
New York and California must not be consecutive to each other.
How many possible positions in the tour sequence can New York be in?
Three
One
Four
Five
Two
Two
New York cannot be second. If New York is second, California must be first and the two cannot be consecutive. New York cannot be third because then California would be first, and either Texas and Illinois would not be consecutive, or Florida would not be after New York. New York also cannot be fifth because Florida must come after New York. Thus, New York can be first or fourth only.
Example Question #66 : Four & Five Variable
Over the course of four weeks, each of seven television programs will be aired to a focus group for help in coming up with a title. The programs are identified as G, H, J, K, L, M, and O. A different pair of these programs will be aired each week. Exactly one of the programs will be a member of two of these four pairs. The following constraints must be observed:
J is not aired during a given week unless H is aired during the week immediately preceding J’s airing.
The show that is aired during two of the weeks is aired during week 4 but is not aired during week 3.
G is not aired during a given week unless either J or else O is also aired during that week.
K is aired during one of the first two weeks.
O is one of the programs aired during week 3.
Which one of the following is a pair of programs that CANNOT be aired during the same week as each other?
K and L
H and M
L and M
H and K
J and O
J and O
Best to start with the rule that G must be aired with either J or O. From this we can infer that J and O can never be aired together. If J and O are aired together, the pairing of J and O must occur in week 3, but then neither J nor O could be doubled, and one of J and O would have to be doubled in order to go with G. That line of reasoning indicates that the credited response is “J and O.”
Example Question #69 : Solving Four And Five Variable Logic Games
Over the course of four weeks, each of seven television programs will be aired to a focus group for help in coming up with a title. The programs are identified as G, H, J, K, L, M, and O. A different pair of these programs will be aired each week. Exactly one of the programs will be a member of two of these four pairs. The following constraints must be observed:
J is not aired during a given week unless H is aired during the week immediately preceding J’s airing.
The show that is aired during two of the weeks is aired during week 4 but is not aired during week 3.
G is not aired during a given week unless either J or else O is also aired during that week.
K is aired during one of the first two weeks.
O is one of the programs aired during week 3.
Which one of the following must be aired during week 2?
K
L
G
J
M
J
In a question that asks what MUST be in a particular slot, it is extremely helpful to look at the answer tied to the acceptability question. In that question, we see that week 2 involves G and J. Since we know that week 2 MUST have a particular entity in it, we now know that this particular entity must be either G or J. Eliminate all other answer choices and simply do a trial-and-error test to determine whether G or J can be omitted from week 2. That test reveals that J must always be in week 2.
Example Question #70 : Solving Four And Five Variable Logic Games
Over the course of four weeks, each of seven television programs will be aired to a focus group for help in coming up with a title. The programs are identified as G, H, J, K, L, M, and O. A different pair of these programs will be aired each week. Exactly one of the programs will be a member of two of these four pairs. The following constraints must be observed:
J is not aired during a given week unless H is aired during the week immediately preceding J’s airing.
The show that is aired during two of the weeks is aired during week 4 but is not aired during week 3.
G is not aired during a given week unless either J or else O is also aired during that week.
K is aired during one of the first two weeks.
O is one of the programs aired during week 3.
Which one of the following CANNOT be the show that is aired during two of the weeks?
M
G
K
H
L
G
If a show is aired during two weeks, then, according to the second rule, that show must be aired during week 4. Making appropriate deductions (see below), we can see that G, J, and O cannot be aired in week 4.
Note: H cannot be aired in weeks 2 or 3 due to the second rule. J cannot be doubled since that would also require H to be doubled (no two doubles). Therefore, J can be eliminated from weeks 1, 3, and 4. Since G must be aired with either J or O, and since J and O cannot be doubled, G must be aired during week 2 or 3 but not week 1 or 4.
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