With Ellen occupying the Wednesday slot, Flavio must occupy the Thursday slot.  That means Alfred takes Tuesday for his day to play (since he can only play on Tuesday or Thursday, and Thursday is already taken).  Daniel cannot play on Sunday or Monday because there are not enough slots to fit Claire and Beatrice, who must play back-to-back.  That forces Daniel into the Friday slot.  (Saturday is out because Gwen must follow Daniel.)

The new conditions imposed by this question compel Alfred to play on Thursday.  He could not play on Tuesday because the new rules have Beatrice and Flavio playing before Alfred, which also means that Claire must also play before Alfred (Beatrice must play on the day after Claire plays).  So there aren't enough slots to fit those three violinists if Alfred plays on Tuesday.  Furthermore, all this tells us is that Beatrice, Claire, and Flavio must play before Thursday, and all three of them potentially could play on Tuesday.  Of those three, the answer choices only specify Beatrice as a Tuesday player.  So that is the credited response.

This problem requires you to eliminate those who cannot be in the Wednesday slot.  With Claire in the Monday slot, Beatrice takes Tuesday, thus leaving Thursday for Alfred.  With Alfred in the Thursday slot, Ellen cannot play Wednesday, since the rules require that if she did, Flavio would have to play on Thursday (but Thursday is already taken by Alfred). So that eliminates five soloists as viable violinists for Wednesday, leaving only Daniel and Gwen.

The added conditions imposed by this question create a block of three:  Ellen--Claire--Beatrice.  It also creates a block with Flavio and Alfred.  Since Alfred can only play on Tuesday or Thursday, we must consider whether either of those days are precluded---and indeed we find that Alfred cannot play on Thursday because that would force Flavio into a Wednesday slot, which the rules don't permit.  So with Alfred in the Tuesday slot, Flavio must take the Monday slot to satisfy the new condition imposed by this particular question.  Now we can deduce that Ellen, Claire and Beatrice must occupy the last three slots because they are a block of three and that is the only place they can fit.  We're left with Daniel and Gwen.  Daniel cannot play on Sunday, because if he did, the rules require Claire to play on Monday, but Monday is already taken by Flavio.  So Daniel can only play on Wednesday.

Each incorrect answer violates one or more of the conditions.  Carefully apply the rules to eliminate the incorrect answer choices.

You can eliminate wrong answers by checking each rule against the possible answers.

From the fourth global rule, the lion must be on the fourth shelf, allowing you to eliminate the sequence that lists the lion third.

From the third global rule, the penguin must be on the first or seventh shelf, allowing you to eliminate the sequence that lists the penguin fifth.

From the first global rule, the frog must come before the dog, allowing you to eliminate the sequence that lists the dog just before the frog.

From the second global rule, the monkey must be exactly before the bear, allowing you to eliminate the sequence that puts the cat and lion between them.

This leaves you with the correct answer, which conforms to all rules: frog, cat, dog, lion, monkey, bear, penguin.

Here you are looking for the answer choice that is always necessarily true.

Based on the global rule, the monkey must always immediately precede the bear. This question adds that the bear must immediately precede the frog, creating a monkey-bear-frog sequence. This sequence must also come before the dog, as the first global rule states the frog must come before the dog.

With the lion starting on shelf 4, the monkey-bear-frog sequence must take up shelves 1-2-3 so that the dog can go after it. This also means the penguin must go on shelf 7, since it cannot go on shelf 1:

monkey, bear, frog, lion, __, __, penguin

For the empty shelves 6 and 7, either shelf can hold the dog or the cat.

The bear will never be on shelf 5, so you can eliminate that answer. The monkey will never be on shelf 6, so you can eliminate that answer. The penguin will never be on shelf 1, so you can eliminate that answer.

The cat can sometimes be on shelf 5, but it can also be on shelf 6, so you can eliminate that answer - it is not always true.

The frog will always be on shelf 3, so that is your correct answer.

Here we are looking for an outcome that could possibly happen. If you find an option that leads to an allowable outcome, that is the correct answer.

If the monkey is on shelf 1, that means the bear is on shelf 2, since it must immediately follow. The lion is always on shelf 4. The penguin must go on shelf 7, since shelf 1 is taken:

monkey, bear, __, lion, __, __, penguin

You have the frog, dog, and cat remaining. There are a couple of possible arrangements; you must remember that the frog must always go somewhere before the dog.

The cat can never go one lower than the bear, because the monkey is already one lower than the bear, so you can eliminate that answer.

The bear can never go one lower than the dog, because this would keep the frog from going before the dog, so you can eliminate that answer.

The frog can never go one lower the cat, because this would have to happen on shelves 5-6, leaving no way for the frog to stay ahead of the dog, so you can eliminate that answer.

The frog can never go one lower than the penguin, because this would keep the frog from staying ahead of the dog, so you can eliminate that answer.

The bear can go one lower than the cat, by completing the sequence as such:

monkey, bear, cat, lion, frog, dog, penguin

This, then, is your correct answer: The bear is placed on a shelf numbered one lower than the shelf on which the cat is placed.

The incorrect answers all violate at least one of the stated conditions:

(I, J, G, E, F, K, H): E must be a higher payer than G.

(E, G, I, J, F, H, K): J must be a higher payer than G.

(E, G, F, I, J, H, K): G must be a lower payer than J.

(F, H, E, I, K, J, G): K cannot be in prime time.

The correct answer satisfies all of the stated conditions.

Using the fourth condition that changes F's position as a basis, we can make two scenarios:

       H
      /
    F --- E
             \
              G
             /
    I --- J

As K cannot be in prime time, it must be in either the sixth or seventh slots and either directly before or after G or H.

          E
           \
            G -- F -- H
           /
   I --- J

For the same reasons as above, K must be immediately before or after H.

H can be last in either scenario and all the statements can occur in one of the scenario except the statement that I is aired fifth, which is impossible.