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Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom. Five trains are lined up, each a different color. They are, from left to right: Blue, Green, Orange, Red, and Yellow. Each child plays with one train. Caleb doesn't like orange or yellow colors. At most one train separates Everett from his older brother Dan. Amanda sits in between two boys. Dan grabs the blue train right away and won't share.
Who is playing with the yellow train?
Dan is playing with the blue train. Everett is playing with either the green or the orange train. Caleb is playing with the red train. Amanda is in between two boys so she can't be playing with the yellow train on the far right. Beatrice is the only child who could be playing with the yellow train.
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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.
If California is the first tour date, which position(s) can Florida be in?
If California is the first tour date, then Florida cannot be second, third, or fourth. Therefore, Florida may only be in the fifth position.
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Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom. Five trains are lined up, each a different color. They are, from left to right: Blue, Green, Orange, Red, and Yellow. Each child plays with one train. Caleb doesn't like orange or yellow colors. At most one train separates Everett from his older brother Dan. Amanda sits in between two boys. Dan grabs the blue train right away and won't share.
Which train is Caleb playing with?
Caleb doesn't like orange or yellow, so he can't be playing with those trains. Dan is playing with the blue train. Everett must be either next to Dan so that Everett is playing with the green train, or two spaces away, in which case Amanda must be playing with the green train because that would be the only way she could be between two boys. That leaves the red train.
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Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom. Five trains are lined up, each a different color. They are, from left to right: Blue, Green, Orange, Red, and Yellow. Each child plays with one train. Caleb doesn't like orange or yellow colors and refuses to take them. At most one train separates Everett from his older brother Dan. Amanda sits in between two boys. Dan grabs the blue train right away and won't share.
Which train could Amanda be playing with?
Dan is playing with the blue train. Caleb must be playing with the red train. Either Amanda is between Dan and Everett in which case she is playing with the green train, or she is between Everett and Caleb in which case she is playing with the orange train. Only the orange train is listed as an answer choice.
Possibilities that fulfill these conditions if we leave Amanda out for the time being (which keeps things simpler):
Blue: Dan
Green: Everett?/Caleb?/Beatrice?
Orange: Everett?/Beatrice?
Red: Caleb?/Beatrice?
Yellow: Beatrice?
Since Amanda must be between two boys, she cannot take yellow, and since no one else but Beatrice can take yellow, we have to put Beatrice there; since Beatrice has taken yellow, Amanda cannot take red, since she would not be between two boys either, so we now have this situation:
Blue: Dan
Green: Everett?/Caleb?
Orange: Everett?
Red: Caleb? (not Amanda)
Yellow: Beatrice (not Amanda)
Here we see that Caleb is the only option for the red train, so we have to eliminate him from the green train:
Blue: Dan
Green: Everett?
Orange: Everett?
Red: Caleb
Yellow: Beatrice
Now Everett can take either the green or the orange train, and his choice also presents two legal choices for Amanda: orange and green. Orange is the only available choice in the answers.
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Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom. Five trains are lined up, each a different color. They are, from left to right: Blue, Green, Orange, Red, and Yellow. Each child plays with one train. Caleb doesn't like orange or yellow colors. At most one train separates Everett from his older brother Dan. Amanda sits in between two boys. Dan grabs the blue train right away and won't share.
Which is a possible arrangement of children playing with trains?
Dan must be playing with the blue train. Beatrice must be playing with the yellow train. That excludes all other answer choices but one, which also meets all of the conditions.
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Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom. Five trains are lined up, each a different color. They are, from left to right: Blue, Green, Orange, Red, and Yellow. Each child plays with one train. Caleb doesn't like orange or yellow colors. At most one train separates Everett from his older brother Dan. Amanda sits in between two boys. Dan grabs the blue train right away and won't share.
If in addition to the above conditions, Amanda is three spaces away from Beatrice, which kids are playing with with trains?
Dan is playing with the blue train. In order for Amanda and Beatrice to be three spaces apart from each other, they must play with the green and the yellow train. Amanda can't be on the end because she's in between two boys, so Amanda must be playing with the green train and Beatrice must be playing with the yellow train. Everett can't be separated from Dan by more than one train, so he must then be playing with the orange train. That leaves Caleb playing with the red train.
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Amanda, Beatrice, Caleb, Dan, and Everett are five toddlers who go to Big Bean Playroom. Five trains are lined up, each a different color. They are, from left to right: Blue, Green, Orange, Red, and Yellow. Each child plays with one train. Caleb doesn't like orange or yellow colors. At most one train separates Everett from his older brother Dan. Amanda sits in between two boys. Dan grabs the blue train right away and won't share.
If Dan and Everett are playing immediately next to each other, then which train is Everett playing with?
This is an easy question. Dan must be playing with the blue train. The green train is next to the blue train.
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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:
Given the above information, which of the following could NOT be Marvin's planned meal for Thursday night?
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.
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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:
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?
You are given the information that
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.
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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:
Which of the following, if true, would give you enough information to determine what day the Spaghetti dinner was planned for?
From the given information, you know that
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.
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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:
Which of the following pieces of information would allow you to determine whether the Chicken Breast would be eaten with a salad?
You know that
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.
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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:
Given the above information, which of the following statements is logically valid?
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.
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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:
Which of the following statements would not be possible given that the above information is all true?
If all the given information is true, either Monday or Tuesday night must have a pasta dinner. Since you know that:
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.)
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The directors of a movie festival are deciding the lineup of their six films: Causes, Brothers, Willow, Above, Forged, and Monarchy. The festival will span Friday, Saturday, and Sunday evenings. At least one movie must be played each night, and there can be no more than three played the same evening. No movie is played more than once. The directors have decided on the following:
Monarchy is played on the night directly after Brothers.
Willow is played on the same night as Above.
If Causes is played on Saturday, then Above is played on Friday.
Brothers and Forged do not play on the same night.
Forged does not play by itself.
What is the possible order of the six films?
First, consider what we're given. Forged cannot be played on a night by itself; we can delete that answer. Willow and Above must be played on the same evening, so we can delete the answer where they're not. Monarchy must be played directly after Brothers, so delete the answer where that is not the case. And lastly, Brothers and Forged cannot be played on the same evening. Delete that. We are left with the correct answer choice.
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The directors of a movie festival are deciding the lineup of their six films: Causes, Brothers, Willow, Above, Forged, and Monarchy. The festival will span Friday, Saturday, and Sunday evenings. At least one movie must be played each night, and there can be no more than three played the same evening. No movie is played more than once. The directors have decided on the following:
Monarchy is played on the night directly after Brothers.
Willow is played on the same night as Above.
If Causes is played on Saturday, then Above is played on Friday.
Brothers and Forged do not play on the same night.
Forged does not play by itself.
If Forged plays on Friday, what must be true?
Let's look at the question. It asks what must be true, not what can be true. In this scenario, Willow can be played on any of the days, so it does not have to be played on Friday. The same goes for Causes: it can be played on Friday or Saturday, so does not have to be played on Friday specifically or on Saturday specifically. Based on the information, because Brothers cannot play on the same night as Forged, it cannot play Friday night. But it must play one night before Monarchy, so it cannot play on Sunday night either, and it must be played on Saturday. Thus, Monarchy can and must be played on Sunday night since it must be played the night directly after Brothers.
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The directors of a movie festival are deciding the lineup of their six films: Causes, Brothers, Willow, Above, Forged, and Monarchy. The festival will span Friday, Saturday, and Sunday evenings. At least one movie must be played each night, and there can be no more than three played the same evening. No movie is played more than once. The directors have decided on the following:
Monarchy is played on the night directly after Brothers.
Willow is played on the same night as Above.
If Causes is played on Saturday, then Above is played on Friday.
Brothers and Forged do not play on the same night.
Forged does not play by itself.
If Causes is played on Saturday, what could be true?
Let's look at the question. It asks which of the answers has the posibility of being true; it does not ask which of the answers must be true. We know that Causes is played on Saturday. Given our guidelines, that means that Above must be played on Friday. So Willow must also be played on Friday night; it cannot be played on Saturday. We can delete that answer. We know that Brothers must play on the night directly before Monarchy, so we know that Monarchy can thus not play on the first night of the festival. So Monarchy cannot be played on Friday. Delete that answer.
We know so far that Above and Willow play on Friday night and that Causes plays on Saturday night. Say Brothers plays on Friday night. Then Monarchy must play on Saturday night and Forged must play on Sunday night by itself, but that is impossible, so we can delete that answer choice. Say Forged plays on Saturday night, instead. Then Monarchy must play on Sunday night and Brothers must play on Saturday night, but that is impossible because Brothers and Forged cannot play on the same night. Delete that answer.
We are left with one choice. If Forged plays on Sunday night, Monarchy can also play on Sunday night, and Brothers can play on Saturday night. This is possible, and thus this is the correct answer.
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The directors of a movie festival are deciding the lineup of their six films: Causes, Brothers, Willow, Above, Forged, and Monarchy. The festival will span Friday, Saturday, and Sunday evenings. At least one movie must be played each night, and there can be no more than three played the same evening. No movie is played more than once. The directors have decided on the following:
Monarchy is played on the night directly after Brothers.
Willow is played on the same night as Above.
If Causes is played on Saturday, then Above is played on Friday.
Brothers and Forged do not play on the same night.
Forged does not play by itself.
If Monarchy plays the same night as Above, what could be true?
Let's look at the question. It asks us which answer choice has the possibility of being true, not which one must be true. We know so far that Monarchy, Above, and Willow must all play on the same night. Given that Monarchy cannot be played on the first night (since Brothers must be played before it), these movies must be played on either Saturday or Sunday night. Thus Willow cannot be played on Friday night. Delete that answer.
Now, if Monarchy, Above, and Willow do not play on Saturday, they play on Sunday night, and thus Brothers must play on Saturday night. But Forged cannot play on the same night as Brothers, so it cannot be played on Saturday night. Also, since Forged cannot be played by itself, Causes must always be played with Forged, and thus Causes cannot be played the same evening as Brothers. Delete that answer.
Causes can either be played on Friday or on Sunday. We have our answer.
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The directors of a movie festival are deciding the lineup of their six films: Causes, Brothers, Willow, Above, Forged, and Monarchy. The festival will span Friday, Saturday, and Sunday evenings. At least one movie must be played each night, and there can be no more than three played the same evening. No movie is played more than once. The directors have decided on the following:
Monarchy is played on the night directly after Brothers.
Willow is played on the same night as Above.
If Causes is played on Saturday, then Above is played on Friday.
Brothers and Forged do not play on the same night.
Forged does not play by itself.
If Sunday night is cancelled, but the same restrictions apply, what could be the possible order of the six films?
Looking at our restrictions, we know that there can be no more than three movies played each night. We can delete the answer choice with four movies on Saturday night. We also know that Monarchy must be played directly after Brothers. Delete the answer where it is not. Willow and Above must be played the same night. Delete the answer where they are not. And lastly, Brothers and Forged cannot be played the same night. Delete that answer choice. We are thus left with one answer choice, and it abides by all of our restrictions.
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There are five students sitting in a row while eating ice cream in the cafeteria. The students are Abby, Ben, Connie, David, and Emma. Each is eating a different flavor of ice cream. The order of the ice cream flavors is: vanilla, chocolate, mint chocolate chip, strawberry, and coffee.
Abby is not eating either mint chocolate chip or coffee ice cream.
Ben is sitting next to Emma and is not sitting next to Connie.
David is separated from Connie by exactly one person.
David is eating the coffee ice cream.
Which ice cream is Emma eating?
We know that David is eating coffee ice cream, so we can rule that answer out. Also, we know that Connie is separated from David by exactly one person, so she must be eating the mint chocolate chip ice cream. Ben and Emma are sitting next to one another, so they must be in the first two spots. Since Ben is not sitting next to Connie, he must be first in line. So, Emma must be the second in line. Thus she is eating the chocolate ice cream.
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There are five students sitting in a row while eating ice cream in the cafeteria. The students are Abby, Ben, Connie, David, and Emma. Each is eating a different flavor of ice cream. The order of the ice cream flavors is: vanilla, chocolate, mint chocolate chip, strawberry, and coffee.
Abby is not eating either mint chocolate chip or coffee ice cream.
Ben is sitting next to Emma and is not sitting next to Connie.
David is separated from Connie by exactly one person.
David is eating the coffee ice cream.
Who is eating the strawberry ice cream?
We know that David is eating the coffee ice cream, so we can immediately rule him out. We also know that Connie is exactly one seat away from David, so she must be eating the mint chocolate chip. We can rule her out. Ben and Emma are seated beside each other, so they must be the first two in line. The person seated between David and Connie must then be Abby, meaning that she is eating the strawberry ice cream.
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