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A professor is selecting students to work in pairs on four separate parts of a final presentation. There are eight students in the class. Lisa, Marc, Nina and Oliver are seniors; William, Xavier, Yolanda and Zoe are juniors. The pairs will present their sections in a specific order, first through fourth. The assignments of partners and sections must conform to the following restrictions:
Each pair must consist of one senior and one junior
Lisa must be paired with William
Nina cannot be paired with Yolanda
William must present in an earlier group than Zoe
Marc can only present first if Oliver presents third
Which of the following is a complete and accurate list of how the final could be presented?
We can eliminate any answer that fails to pair Lisa and William. We can then eliminate any answer that has Zoe presenting before William. Then we eliminate any answer that pairs Nina with Yolanda. We then eliminate any answer that has Marc presenting first without Oliver presenting third. By going through all of the rules and eliminating in this fashion we are left with only the correct answer.
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A professor is selecting students to work in pairs on four separate parts of a final presentation. There are eight students in the class. Lisa, Marc, Nina and Oliver are seniors; William, Xavier, Yolanda and Zoe are juniors. The pairs will present their sections in a specific order, first through fourth. The assignments of partners and sections must conform to the following restrictions:
Each pair must consist of one senior and one junior
Lisa must be paired with William
Nina cannot be paired with Yolanda
William must present in an earlier group than Zoe
Marc can only present first if Oliver presents third
If Marc presents in the first group, what is a complete and accurate list of whom his partners could be?
If Marc presents first, we know that Oliver must present third. Then we must put Lisa and William in the second slot, since William must present before Zoe, and that would not be possible if he and Lisa presented fourth. We are left with placing Xavier, Yolanda and Zoe. Zoe cannot go first, since she must present after William. Therefore the only possible juniors who could be paired with Marc are Xavier and Yolanda.
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A professor is selecting students to work in pairs on four separate parts of a final presentation. There are eight students in the class - Lisa, Marc, Nina and Oliver are seniors; William, Xavier, Yolanda and Zoe are juniors. The pairs will present their sections in a specific order, first through fourth. The assignments of partners and sections must conform to the following restrictions:
Each pair must consist of one senior and one junior
Lisa must be paired with William
Nina cannot be paired with Yolanda
William must present in an earlier group than Zoe
Marc can only present first if Oliver presents third
If Zoe presents in the second group, which of the following CANNOT be true?
If Zoe presents second, we automatically know that William must present first. William must always be paried with Lisa, therefore the senior spot in the first group is filled, and Marc could never present first. *Note - Oliver can still present third even if Marc does not present first. The conditional states that Oliver must be third if Marc is first, but Oliver can still be third even if Marc is not first.
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A professor is selecting students to work in pairs on four separate parts of a final presentation. There are eight students in the class - Lisa, Marc, Nina and Oliver are seniors; William, Xavier, Yolanda and Zoe are juniors. The pairs will present their sections in a specific order, first through fourth. The assignments of partners and sections must conform to the following restrictions:
Each pair must consist of one senior and one junior
Lisa must be paired with William
Nina cannot be paired with Yolanda
William must present in an earlier group than Zoe
Marc can only present first if Oliver presents third
All of the following statements could be true EXCEPT:
If Marc presents first, we automatically put Oliver in the third spot. As previously discussed, Lisa and William fill out the second spot and Nina must go in the fourth. Nina cannot be paired with Yolanda - therefore, if Marc presents first, Yolanda cannot present fourth.
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A baker is making three pizzas, one at a time, each with two toppings. The baker has six available toppings--anchovies, bacon, mushrooms, peppers, sausage, tomatoes. No topping can be put on more than one pizza. The pairings of toppings must conform to the following rules:
Anchovies cannot be paired with peppers
Mushrooms and tomatoes must be on the same pizza
Sausage must be on the second pizza if mushrooms are on the first
Peppers must be on a pizza made after the pizza with sausage
Which of the following is a possible ordering of the pizzas and toppings?
If peppers must be on a pizza made after the sausage pizza, then peppers can never be on the first pizza or the same pizza as sausage. We can also easily eliminate any option in which tomatoes and mushrooms are not paired. Remember, sausage is only required to be on the second pizza if mushrooms are on the first.
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Last week, Sara, Tony, Ulrich, Victor, and Wynne each saw La Traviata once at the opera house. The group divided up five tickets—one for the Thursday performance, one for the Friday performance, two for the Saturday performance, and one for the Sunday matinee—according to the following conditions:
How many total arrangements of tickets to people are there?
The only people who can see the first show are Tony, Sarah, and Victor. Of these initial choices, there is only one arrangement each if Tony or Sarah sees the first show, and two if Victor sees the first show.
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A baker is making three pizzas, one at a time, each with two toppings. The baker has six available toppings--anchovies, bacon, mushrooms, peppers, sausage, tomatoes. No topping can be put on more than one pizza. The pairings of toppings must conform to the following rules:
Anchovies cannot be paired with peppers
Mushrooms and tomatoes must be on the same pizza
Sausage must be on the second pizza if mushrooms are on the first
Peppers must be on a pizza made after the pizza with sausage
If sausage is on the second pizza, which of the following is a complete list of toppings that must be on the third pizza?
Since peppers must be on a pizza made after the pizza with sausage, peppers must be on the third pizza. Now, since the second and third pizzas already have one topping each, and since mushrooms and tomatoes must be on the same pizza, they must be on the first pizza. As a result, anchovies must be on the second pizza because they cannot be on the same pizza as peppers. The only remaining spot for bacon is on the third pizza. Therefore, both bacon and peppers must be on the third pizza.
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A baker is making three pizzas, one at a time, each with two toppings. The baker has six available toppings--anchovies, bacon, mushrooms, peppers, sausage, tomatoes. No topping can be put on more than one pizza. The pairings of toppings must conform to the following rules:
Anchovies cannot be paired with peppers
Mushrooms and tomatoes must be on the same pizza
Sausage must be on the second pizza if mushrooms are on the first
Peppers must be on a pizza made after the pizza with sausage
If mushrooms and tomatoes can be on different pizzas, but all other conditions remain the same, which of the following could be true when peppers are on the second pizza?
The important thing to note here is that, under the new conditions, mushrooms cannot be on the first pizza but tomatoes could be. If mushrooms are on the first pizza, sausage must be on the second, but peppers and sausage may not be on the same pizza.
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A baker is making three pizzas, one at a time, each with two toppings. The baker has six available toppings--anchovies, bacon, mushrooms, peppers, sausage, tomatoes. No topping can be put on more than one pizza. The pairings of toppings must conform to the following rules:
Anchovies cannot be paired with peppers
Mushrooms and tomatoes must be on the same pizza
Sausage must be on the second pizza if mushrooms are on the first
Peppers must be on a pizza made after the pizza with sausage
Instead of three pizzas, the baker makes four. Anchovies and bacon are each used on two separate pizzas. All other conditions are the same. If anchovies are on the second and fourth pizzas, each of the following could be true EXCEPT
In this scenario, we actually know the toppings on all four pizzas.
Since anchovies are on the second and fourth pizzas, we know that peppers cannot be on the second and fourth pizzas based on our first condition. Also, peppers have to come after sausage, based on the fourth condition, which means they cannot be first. Thus, peppers MUST be on the third pizza.
The second condition states that mushrooms and tomatoes MUST be on the same pizza. At this point, since anchovies are on two pizzas, and peppers on another, the only possible pizza for both mushrooms and tomatoes is the first pizza. The first pizza is now fully topped.
The third condition states that sausage must be on the second pizza if mushrooms are on the first pizza. Therefore, sausage must be the second topping on the second pizza. The second pizza is fully topped.
There are only two spots available, so bacon becomes the second topping on both the third and the fourth pizzas. So our order must be:
MT, AS, PB, AB
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A college advisor is scheduling students for six time slots, consecutively. The students she must schedule are Larissa, Melinda, Nick, Oscar, Patricia, and Quinn. Two of them are seniors and the rest are juniors. The scheduling must conform to the following conditions:
A senior must be immediately preceeded by a junior
Larissa's meeting must be before Melinda's meeting
Nick's meeting must be before Quinn's meeting
Patricia is a junior, and she must be schedued either first or last
The third meeting scheduled is with a junior
Oscar cannot be scheduled first unless Nick is scheduled third
Which of the following is a complete and accurate possible schedule for the advisor's meetings?
This is a typical "grab a rule" type question; we can eliminate each wrong answer choice by going through each of the rules. Any answer in which Patricia is not first or last can be eliminated. Then any answer that does not feature Larissa before Melinda and Nick before Quinn can be eliminated. Finally an answer that breaks the conditional and has Oscar in the first slot without Nick in the third slot is eliminated, leaving only the correct answer.
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A college advisor is scheduling students for six time slots, consecutively. The students she must schedule are Larissa, Melinda, Nick, Oscar, Patricia, and Quinn. Two of them are seniors and the rest are juniors. The scheduling must conform to the following conditions:
A senior must be immediately preceeded by a junior
Larissa's meeting must be before Melinda's meeting
Nick's meeting must be before Quinn's meeting
Patricia is a junior, and she must be schedued either first or last
The third meeting scheduled is with a junior
Oscar cannot be scheduled first unless Nick is scheduled third
If Oscar is scheduled for the first meeting, all of the following could be true EXCEPT?
This question gives us specific new information, so we can go ahead and diagram all possibilities to see which of the answers could be true, and which one cannot. If Oscar is first, we immediately put Nick third because of the conditional. Since Oscar is in the first spot Patricia must be sixth. We know now that Patricia and Nick are juniors, due to the rules. We also know that Oscar is a junior - since every senior must be preceeded by a junior, the first spot cannot be a senior. Since Nick and Larissa have to come before Quinn and Melinda respectively, We have to put Larissa in the second spot. Melinda and Quinn can rotate between the fourth and fifth spots. We still need to assign the two seniors and one more junior. In order to abide by the rules, there are only two ways this can pan out. The first is : Junior, Senior, Junior, Senior, Junior, Junior. The second is: Junior, Senior, Junior, Junior, Senior, Junior. Therefore the only spots that are undetermined as far as whether they are a junior or a senior are the fourth and fifth spots. Therefore, the only possibility here that could never work is that Larissa is in the second spot and is a junior, since we know that spot must be a senior.
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A college advisor is scheduling students for six time slots, consecutively. The students she must schedule are Larissa, Melinda, Nick, Oscar, Patricia, and Quinn. Two of them are seniors and the rest are juniors. The scheduling must conform to the following conditions:
A senior must be immediately preceeded by a junior
Larissa's meeting must be before Melinda's meeting
Nick's meeting must be before Quinn's meeting
Patricia is a junior, and she must be schedued either first or last
The third meeting scheduled is with a junior
Oscar cannot be scheduled first unless Nick is scheduled third
If Larissa and Nick are juniors scheduled third and fourth respectively, which of the following could be true?
When we set this question up, placing Larissa and Nick in the third and fourth spots respectively, we can automatically make a couple of judgements. Oscar cannot be first, since Nick is not third. We also know that Melinda and Quinn must follow Larissa and Nick, respectively. Therefore, we must fill out the last two spots with those two though they can go in either order. Since Patricia cannot be last, she must go first. Oscar will fill the only spot left, which is the second spot. Patricia is always a junior, so we can label the first spot a junior, as well as the third spot which is always occupied by a junior. We are also given the information that Nick is a junior, so we can label the fourth spot as a junior as well. With this set up, we now move to placing our seniors. Knowing that seniors must be preceeded by juniors, we can fill in the last two spots with either "junior, senior" or "senior, junior". Either way, the second spot must be reserved for the other senior.
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A college advisor is scheduling students for six time slots, consecutively. The students she must schedule are Larissa, Melinda, Nick, Oscar, Patricia, and Quinn. Two of them are seniors and the rest are juniors. The scheduling must conform to the following conditions:
A senior must be immediately preceeded by a junior
Larissa's meeting must be before Melinda's meeting
Nick's meeting must be before Quinn's meeting
Patricia is a junior, and she must be schedued either first or last
The third meeting scheduled is with a junior
Oscar cannot be scheduled first unless Nick is scheduled third
Which of the following must be true?
This is an inference we could have made just from the initial set up of this game. Since seniors must always be preceeded by juniors, the first spot must always be a junior. All of the other scenarios are possible and most have been seen in other set ups for other questions.
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A creative writing professor is creating a set list for a poetry reading. She must chose five poems from those written by eight students - Alan, Belle, Charlie, Dorian, Ernest, Xue, Yardley, and Zack. The poems chosen and the order in which they are presented must conform to the following restrictions:
If Alan is chosen, Belle is also chosen
If Charlie is chosen, Dorian is not chosen
Ernest is chosen if and only if Xue is chosen
If Belle and Yardley are both chosen, Belle must read before Yardley
If Zack is chosen he must read first
If Charlie and Alan are both chosen, Charlie must read before Alan
Which of the following is a complete and accurate possible set list?
This question can be answered by eliminating incorrect answers based on rule violations. Any answer in which Zack appears anywhere but first is elminated. Any answer that includes Alan without Belle is eliminated. Any answer that features Yardley performing before Belle is eliminated. Any answer that includes Xue without Ernest (or vice versa) is eliminated, leaving only the correct answer.
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A creative writing professor is creating a set list for a poetry reading. She is choosing five poems from those written by eight students - Alan, Belle, Charlie, Dorian, Ernest, Xue, Yardley, and Zack. The poem's chosen and the order in which they are presented must conform to the following restrictions:
If Alan is chosen, Belle is also chosen
If Charlie is chosen, Dorian is not chosen
Ernest is chosen if and only if Xue is chosen
If Belle and Yardley are both chosen, Belle must read before Yardley
If Zack is chosen he must read first
If Charlie and Alan are both chosen, Charlie must read before Alan
If Dorian and Xue are NOT chosen, each of the following must be true EXCEPT:
If Xue is not chosen, Ernest also must not be chosen. This means our group consists of Zack, Charlie, Alan, Belle and Yardley. If Zack is in a group, he must be first. If Charlie and Alan are both chosen, Charlie must come before Alan. In this case the first available spot is second, so Alan cannot go second. Similarly, because of the rule about Belle and Yardley, Yardley cannot go second either. Since Yardley has to come after Belle, Belle cannot go last. The only possibility within these answers is Alan reading third. The order in this case would be: Zack, Charlie, Alan, Belle, Yardley.
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A creative writing professor is creating a set list for a poetry reading. She is choosing five poems from those written by eight students - Alan, Belle, Charlie, Dorian, Ernest, Xue, Yardley, and Zack. The poem's chosen and the order in which they are presented must conform to the following restrictions:
If Alan is chosen, Belle is also chosen
If Charlie is chosen, Dorian is not chosen
Ernest is chosen if and only if Xue is chosen
If Belle and Yardley are both chosen, Belle must read before Yardley
If Zack is chosen he must read first
If Charlie and Alan are both chosen, Charlie must read before Alan
If Zack is reading first and Dorian is reading last, which of the following could be a list of the students reading second, third and fourth, respectively?
If Dorian is reading we know Charlie cannot read, so any answer that includes him can be eliminated. Any answer that includes either Ernest or Xue without the other can also be eliminated. Any answer that includes Alan and not Belle is also eliminated. Any answer that includes Belle and Yardley and does not have Belle reading first is also eliminated, leaving only the correct answer.
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A creative writing professor is creating a set list for a poetry reading. She is choosing five poems from those written by eight students - Alan, Belle, Charlie, Dorian, Ernest, Xue, Yardley, and Zack. The poem's chosen and the order in which they are presented must conform to the following restrictions:
If Alan is chosen, Belle is also chosen
If Charlie is chosen, Dorian is not chosen
Ernest is chosen if and only if Xue is chosen
If Belle and Yardley are both chosen, Belle must read before Yardley
If Zack is chosen he must read first
If Charlie and Alan are both chosen, Charlie must read before Alan
Which of the following must be false?
If Yardley reads first, Belle cannot be in the game because she cannot read before Yardley. If Belle is not in the game, Alan is not in the game either. And if Yardley is in the first spot, Zack cannot be in the game at all. This leaves only Charlie, Dorian, Ernest and Xue to fill the remaining four spots. Since Charlie and Dorian can never read together, this scenario can never happen.
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Chef Henri has six dinner specialties, A, B, C, D, E, and F. One dinner specialty, and only one dinner specialty, is presented on the menu for each evening the restaurant is open, which is Monday through Saturday (closed Sunday).
The following conditions must hold:
Free wine is served with C or D, but not for both, and free wine is served only on Tuesday or Wednesday.
A must be served earlier in the week than B or C.
If B is served on Thursday, then B is served earlier in the week than E and F.
If B is not served on Thursday, then B is served later in the week than E and F.
Either D or E is served on Friday.
If D is the dinner specialty served with free wine, then which one of the following must be true?
Dinner E must be served on Friday because only Dinners D or E can be served on Friday and the stipulation in the question requires D to be served on either Tuesday or Wednesday. That leaves dinner E as the only option for Friday.
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A school has seven sports teams---baseball, football, golf, hockey, karate, swimming, and track. The new school gymnasium has three floors. Each floor can allow for a maximum of four sports teams to do indoor practicing or working out. No sports team can practice or work out on more than one floor. Assignment of the sports teams to the appropriate floor of the gym is subject to the following conditions:
Karate and track must conduct their practices or workouts on the same floor.
Football must conduct practices or workouts on the floor immediately above golf.
Hockey must conduct practices or workouts on its own floor without any other sports team.
Which one of the following CANNOT be the assignment of sports teams to floors of the gymnasium?
Karate and track must be with either football or golf, by virtue of rules one and two. The correct answer violates this necessity.
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Chef Henri has six dinner specialties, A, B, C, D, E, and F. One dinner specialty, and only one dinner specialty, is presented on the menu for each evening the restaurant is open, which is Monday through Saturday (closed Sunday).
The following conditions must hold:
Free wine is served with C or D, but not for both, and free wine is served only on Tuesday or Wednesday.
A must be served earlier in the week than B or C.
If B is served on Thursday, then B is served earlier in the week than E and F.
If B is not served on Thursday, then B is served later in the week than E and F.
Either D or E is served on Friday.
Which one of the following must be true?
C must be served earlier in the week than B. A key insight in this problem is that B can only be served on Thursday or Saturday. This follows from the fact that if B is not served on Thursday, E and F must precede B. But this particular condition precludes B from being served on Monday, Tuesday, or Wednesday because there are insufficient slots to accommodate E, F, and the free-wine meal (C or D). These latter dinners must precede B if B is served on a day other than Thursday. Therefore, the only non-Thursday slot available for B is Saturday (Friday is reserved strictly for D or E). All this leads to the conclusion that C must be served earlier in the week than B.
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