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.

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.

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

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.

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.

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.

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.

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.

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.

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.