We know that Sandra has more shoes than either Ellen or Joan and that Ellen has more shoes than Kerri. We do not know, however, how many shoes Ellen has compared to Joan. This is the key to determining whether Kerri has more shoes than Joan. Therefore, the third sentence is uncertain.

If Daniel is faster than Sean, but Sean is the fastest swimmer on his team, Daniel cannot swim on the same team as Sean.

The only two facts that we know for certain are:

1) Sarah gets better grades in math than Luis; and

2) Luis gets better grades in science than Sarah.

These are both quantifiable statements. This means that we can put an absolute number to each statement. Although we don't know what the actual grades are, we know that Sarah's grades are better in math and Luis' grades are better in science. 

The third sentence, "Luis is a better student than Sarah" has many unknown variables.  We don't know what grades either student receives in any other class. We don't know how much better Sarah is in math than Luis, or how much better Luis is in science than Sarah. Finally, the phrase "better student" is not defined. This could mean higher grades in classes, or it could mean higher grades on standardized tests. "Better student" could even mean the student that studies the hardest or pays the best attention in class. For these reasons, the truthfulness of the third sentence is uncertain.

Both Owen and Andrea purchase five items at the same restaurant and spend exactly the same amount of money.  If we look at the problem mathematically, the equation would be:

h=hamburger; d=drinks (Owen is on the left-hand side of the equation and Andrea is on the right-hand side of the equation.)

For comparison, we need to isolate each variable on its own side.  First, subtract  from each side.  This results in:

Next, subtract  from each side.  This results in:

This proves, logically, that one drink costs the same amount of money as one hamburger.

The accuracy of the third sentence is uncertain because the speed of a squirrel is not compared to either a peregrine falcon or a cheetah in the first two sentences. Therefore, there is not enough information to form an accurate conclusion.

(In case you're wondering: all three statements are accurate.)

We know that Brice is older than Pat and that Pat is younger than Jim. We do not have any information regarding Brice and Jim's relationship. Therefore, the third sentence may be true, or it may be false.

Let's put the information we have on a spectrum. The animal that the zoo has the most of will be placed on the left and the animal the zoo has the least of will be placed on the right. Sentence 1 tell us that the zoo has more wolves than tigers.

Wolves -- tigers

Sentence 2 tells us that the zoo has more tigers than leopards.

Wolves -- tigers -- leopards

Sentence 3 must be true. If the zoo has more wolves than tigers, and they have more tigers than leopards, then they must have more wolves than leopards.

The first two sentences compare sales of cameras and computers to TVs. There is no reference point in relating cameras sales to computer sales. Therefore, we do not have enough information to determine whether the store sold the same number of cameras as computers. The answer must be uncertain.

Let's look at each sentence numerically. 

This means that Grade 1 MUST be larger than Grade 2. Sentence 3 states that there are more 2nd graders than 1st graders at Lincoln Elementary. This statement must be false.

Let's put the information we know on a spectrum, with the person that owns the most animals on the extreme left and the person that owns the fewest animals on the extreme right. Sentence 1 tells us that Andrew owns fewer animals than Jason. This means that Jason owns MORE animals than Andrew. 

MOST                 FEWEST

Jason     --         Andrew

Sentence 2 tells us that Dennis owns fewer animals than Andrew. Therefore, Dennis should be placed to the right of Andrew.

MOST                       FEWEST

Jason   -- Andrew  -- Dennis

Sentence 3 says that Jason owns more animals than Dennis. Looking at the spectrum above, this statement is true.