Since you know Nancy learns flute, the first global rule tells you Max must also play flute.

With a couple of deductions, you can also determine that no one can learn violin. You know Trig cannot because the the third global rule tells you he must learn cello or flute. You know that Pete cannot because the fourth global rule tells you if Pete learns violin then Max must learn violin, which cannot happen here. You finally know that Raina cannot becuase the fifth global rule tells you no one can learn an instrument alone.

This allows you to eliminate the three answer choices involving the violin.

The second global rule tells you Pete and Raina must learn different instruments. Since we've crossed out the violin, one of them must learn the cello and the other must learn the flute. Either of these two possibilities is valid.

Whichever instrument they choose, that means Trig must learn cello, so that the other person learning cello does not learn the instrument alone.

This allows you to eliminate the answer choice of Trig learning to play flute, since he must learn to play cello.

Your correct answer is Pete learns to play flute because this is a possible outcome.

Since the painting slot is now full (remember that Olivia must be assigned to painting), Rachel can't be assigned to photography because that would push Nan into painting. Therefore, Rachel must be assigned to sculpture. According to the rules, Pete can't be paired up with Rachel, which means he must be assigned to photography.

There is consequently an open slot for Savan in either sculpture or photography, which means Savan can be paired with either Pete or Rachel. 

The rules tell us that Olivia must be assigned to painting. If Olivia and Pete are filling up the painting slot, then Rachel cannot fit in the photography group; the rules tell us that if Rachel is in photography Nan must be in painting, but with Olivia and Pete occupying those slots already, there would be no space for Nan. Therefore, we know the answer is "Rachel is assigned to photography."

This is an orientation question. The best approach to answering this question is to go through the rules one by one, and then eliminate the choices that violate any of the rules. The choice that remains is the correct one.

Master Diagram (s is for swimming pool, c is for central air, and p is for patio:

A              B                C                    D               E                   F

s/c/p        s p (only)     s c (only)        s c p           p (only)       c + s or p (only)

Explanation of the plug-ins:

rule 1 allows us to plug s and p into the diagram under B

rule 2 allows us to plug s and c into the diagram under C

rule 3 establishes that E must have p because it cannot have s and c; rule 3 further establishes that C only has s and c (if it were otherwise, then C and E would have features in common, which rule 3 disallows)

rule 4 establishes that, since C only has two features, D must have all three features

rule 5 establishes that B and F have exactly one feature in common, so that means s or p could be attached to F; but we know that F cannot have all three features because that would violate rule 5; likewise, B cannot have all three features;

furthermore, we know that F must have two features because rule 6 says A has fewer features than F (thus, F cannot have only one feature); consequently, F must have c as a feature, with either s or p attached to it.

The diagram firmly establishes that B, C, D, and E are definitely set in terms of their features.  So the answer is FOUR.

The question establishes that F has at least one feature in common with the other models except Model A. F already has central air conditioning in common with C and D. To share a feature with E, F must have a patio, and that would also allow F to have the patio in common with B. A, therefore, must have a swimming pool in order to avoid having anything in common with F.

A must have central air conditioning (F already has central air, and B,C, D, and E are all set). F must have a swimming pool. So all the features are set, and therefore we need only check the choices to see that it is false to say that C and F have exactly one feature in common. The false statement is the correct answer on this problem.

Even with the rule change, C is still limited to having a pool and central air (because of rule 3). So D must have a pool and central air. The only question is whether D has a patio as well. Consequently, it is false to say D and F have no features in common because, in fact, they have central air in common, at the very least.

Master Diagram (s is for swimming pool, c is for central air, and p is for patio:

A              B                C                    D               E                   F

s/c/p        s p (only)     s c (only)        s c p           p (only)       c + s or p (only)

Explanation of the plug-ins:

rule 1 allows us to plug s and p into the diagram under B

rule 2 allows us to plug s and c into the diagram under C

rule 3 establishes that E must have p because it cannot have s and c; rule 3 further establishes that C only has s and c (if it were otherwise, then C and E would have features in common, which rule 3 disallows)

rule 4 establishes that, since C only has two features, D must have all three features

rule 5 establishes that B and F have exactly one feature in common, so that means s or p could be attached to F; but we know that F cannot have all three features because that would violate rule 5; likewise, B cannot have all three features;

furthermore, we know that F must have two features because rule 6 says A has fewer features than F (thus, F cannot have only one feature); consequently, F must have c as a feature, with either s or p attached to it.

The diagram set forth shows that two of the six models (B and E) are precluded from having central air conditioning. That means a maximum of four models can have that feature.

Master Diagram (s is for swimming pool, c is for central air, and p is for patio:

A              B                C                    D               E                   F

s/c/p        s p (only)     s c (only)        s c p           p (only)       c + s or p (only)

Explanation of the plug-ins:

rule 1 allows us to plug s and p into the diagram under B

rule 2 allows us to plug s and c into the diagram under C

rule 3 establishes that E must have p because it cannot have s and c; rule 3 further establishes that C only has s and c (if it were otherwise, then C and E would have features in common, which rule 3 disallows)

rule 4 establishes that, since C only has two features, D must have all three features

rule 5 establishes that B and F have exactly one feature in common, so that means s or p could be attached to F; but we know that F cannot have all three features because that would violate rule 5; likewise, B cannot have all three features;

furthermore, we know that F must have two features because rule 6 says A has fewer features than F (thus, F cannot have only one feature); consequently, F must have c as a feature, with either s or p attached to it.

The diagram set forth establishes that F must have central air conditioning and either a swimming pool or a patio, but not both. The question requires that central air conditioning exist in tandem with a swimming pool. Therefore, F cannot have a patio.