This is a classic sequencing game.  We know there are six slots and the task is to fit the entities into the correct slot.  The problem gives us slot 3---F goes there.  We can make several deductions here to facilitate quick answering of all the questions.

Because of the rule that C precedes D, we can deduce that C cannot go in slot 6 and D cannot go in slot 1.

Because F is in slot 3 and there is a rule that mandates that A and B be separated by one slot, neither A nor B can be in slot 1.  Thus, we can rule out for slot 1 restaurants A, B, D, and F.  So we know for sure that slot 1 must have either C or E.

Deeper investigation reveals that A cannot go in slot 5.  If we try to put A in slot 5, we see that B cannot fit into a slot that is separated by one slot (slot 3 is occupied and there is no slot 7).  Going even deeper, we see that E cannot go into slot 2, because if that were the case, we could not fit the other restuarants into slots 4, 5, and 6.  In other words, with E in slot 2, C must occupy slot 1.  That leaves A, B, and D for slots 4, 5, and 6.  But notice:  A cannot be next to D, according to the rules.  Since A and B must be separated by one slot, this arrangement would force A to be next to D, which is not permissible. 

Applying these restrictions, we can use process of elimination to arrive at the only viable sequence offered by the answer choices:  C, A, F, B, D, and E.

This is a classic sequencing game.  We know there are six slots and the task is to fit the entities into the correct slot.  The problem gives us slot 3---F goes there.  We can make several deductions here to facilitate quick answering of all the questions.

Because of the rule that C precedes D, we can deduce that C cannot go in slot 6 and D cannot go in slot 1.

Because F is in slot 3 and there is a rule that mandates that A and B be separated by one slot, neither A nor B can be in slot 1.  Thus, we can rule out for slot 1 restaurants A, B, D, and F.  So we know for sure that slot 1 must have either C or E.

Deeper investigation reveals that A cannot go in slot 5.  If we try to put A in slot 5, we see that B cannot fit into a slot that is separated by one slot (slot 3 is occupied and there is no slot 7).  Going even deeper, we see that E cannot go into slot 2, because if that were the case, we could not fit the other restuarants into slots 4, 5, and 6.  In other words, with E in slot 2, C must occupy slot 1.  That leaves A, B, and D for slots 4, 5, and 6.  But notice:  A cannot be next to D, according to the rules.  Since A and B must be separated by one slot, this arrangement would force A to be next to D, which is not permissible. 

From the explicit rules and our deductions, we can quickly eliminate slots 1, 3, and 5 as viable for restaurant A.  So the only issue is whether only slots 2 and 4 are viable, as opposed to slots 2, 4, and 6.  Nothing precludes A from occupying slot 6, so the correct answer is:  Slots 2, 4, 6.

This is a classic sequencing game.  We know there are six slots and the task is to fit the entities into the correct slot.  The problem gives us slot 3---F goes there.  We can make several deductions here to facilitate quick answering of all the questions.

Because of the rule that C precedes D, we can deduce that C cannot go in slot 6 and D cannot go in slot 1.

Because F is in slot 3 and there is a rule that mandates that A and B be separated by one slot, neither A nor B can be in slot 1.  Thus, we can rule out for slot 1 restaurants A, B, D, and F.  So we know for sure that slot 1 must have either C or E.

Deeper investigation reveals that A cannot go in slot 5.  If we try to put A in slot 5, we see that B cannot fit into a slot that is separated by one slot (slot 3 is occupied and there is no slot 7).  Going even deeper, we see that E cannot go into slot 2, because if that were the case, we could not fit the other restuarants into slots 4, 5, and 6.  In other words, with E in slot 2, C must occupy slot 1.  That leaves A, B, and D for slots 4, 5, and 6.  But notice:  A cannot be next to D, according to the rules.  Since A and B must be separated by one slot, this arrangement would force A to be next to D, which is not permissible.

From our deductions, we know that C can occupy slot 1, so that answer choice can be eliminated.  Likewise, A can definitely occupy slot 2---after all, A occupies slot 2 in the earlier question asking us to identify an acceptable sequence. 

We can affirmatively deduce the correct answer choice.  E cannot go into slot 2, because if that were the case, we could not fit the other restuarants into slots 4, 5, and 6.  In other words, with E in slot 2, C must occupy slot 1.  That leaves A, B, and D for slots 4, 5, and 6.  But notice:  A cannot be next to D, according to the rules.  Since A and B must be separated by one slot, this arrangement would force A to be next to D, which is not permissible. 

We know that A must be first, that B or C must be second, and that D or G must be seventh, based upon all of our deductions:

A . . . B/C (this sequence, combined with the other two, establishes that B or C must be second)

A . . . C . . . F/G

B . . . E . . . D/F (this sequence establishes that A must be the highest vote-getter, and this sequence combined with the other two establishes that D or G must be seventh)

Because F must have four players in front of him, and because the last rule precludes F from being seventh, we can deduce that F must be in either slot 5 or 6.

With these deductions, we can eliminate all the incorrect answer options.

D comes after E, and E comes after B, and B comes after A. So we know that three players received more votes than D. So D cannot be third.

Because B gets more votes than C, we can establish that B is in slot 2. Thus, D cannot receive more votes than C, so that answer is eliminated.

Because G gets more votes than E, we know that G cannot be in slot 7, which means D must be in slot 7. So that eliminates any answer choices involving D getting more votes than another player.

Because F receives less votes than E (under the original rules), and because the new rule states that G gets more votes than E, F cannot get more votes than G, so that answer is eliminated.

The only viable option is that B receives more votes than G.

Because E received more votes than C, we know that slot 2 is occupied by B (because only B or C can occupy slot 2).

Because E received more votes than C, we also know that E must be in slot three, because four players must have received less votes than E. G and F received less votes than C, so that means C must be in slot 4 or 5.

D becomes a floater, which means that D could receive more votes than C (i.e., D could occupy slot 4).

Therefore, it is not required that C is the fourth vote-getter, and that is our answer (it is false to say that it must be true that C received the fourth most votes).

With D in the fourth slot, we know that G must be in slot 7 (since D and G are the only ones who can occupy slot 7).

Because slot 5 is taken up by E, slot 6 must be taken by F (F can only occupy either slot 5 or 6, based on all of our initial deductions).

So it must be true that F received the least amount of votes, except for G.

Note:  B and C occupy either of slots 2 and 3, but we cannot specify for certain which one occupies which.

You can reach the correct answer here by using the global rules to eliminate wrong answers.

The first global rule tells you that if Sue gives her speech first, Mort must give his speech last. That allows you to eliminate two possibilities. You can eliminate "Sue, Mort, Othello, Paul, Quinn" and "Sue, Othello, Paul, Mort, Quinn."

The second global rule tells you if Mort gives his speech second, Quinn gives her speech first. This just reinforces that you can eliminate the first of the two choices you eliminated above.

The third global rule tells you that Mort cannot give his speech first. This allows you to eliminate "Mort, Othello, Paul, Sue, Quinn."

The fourth global rule tells you that Paul must give his speech immediately after Othello gives his speech. This allows you to eliminate "Othello, Sue, Paul, Quinn, Mort."

This leaves you with the correct answer: Quinn, Mort, Sue, Othello, Paul which follows all global rules.

If Paul gives his speech third, the fourth global rule tells you that Othello must give his speech second:

___, Othello, Paul, ___, ___

You know from the third global rule that Mort cannot give his speech first, so he must give his speech either fourth or fifth. This allows you to eliminate the answer choice of Mort giving his speech second.

You also can eliminate the answer choice of Mort giving his speech before Paul. The only way to do that is for Mort to give his speech first, which cannot happen.

If Mort gives his speech before Quinn gives her speech, that would require Mort going fourth and Quinn going fifth. However, this cannot work because this would require Sue to give her speech first, and the first global rule tells you that if Sue gives her speech first, then Mort must give his speech last. This allows you to eliminate two answers: Mort giving his speech before Quinn AND Quinn giving her speech last.

The correct answer is Mort gives his speech before Sue gives her speech. This can work with the following possible outcome:

Quinn, Othello, Paul, Mort, Sue