Each statement alone gives information about only one order, so at the very least, both statements will be necessary.

From Statement 1, it is known that Ralph will pay  for his drinks, since he will only pay for the two espressos. 

From Statement 2, it cannot be determined exactly what Janet will pay. However, she will pay for all three drinks, two of which are cappucinos; the least she will spend is the price of two cappucinos and an Americano, which is .

From both statements together, it is definite that Janet will pay more.

From Statement 1 alone, you know that Patty spent . It is possible, however, that Mickey spent more (for three espressos, for example), just as much (on three Turkish coffees), or less (for three cappucinos, for example). Statement 2 alone gives you even more scant information, since it only tells you one beverage Mickey bought.

Suppose you know both statements. Then you know Patty spent . You do not know how much Mickey spent, but the most he could have spent was  (for an Americano and two esperessos). Therefore, the two statements together are necessary and sufficient to answer the question.

 students voted, so 236 votes were necessary to win a simple majority. 

From Statement 1 alone it can be determined that Crane won at least  votes (his own initial votes plus all of the votes that previously went to Jones), and Trask won at least 98 (his own initial votes).

From Statement 2 alone, it can be determined that Crane won at least  (his own initial votes plus one-third of the votes that previously went to Wells), and Trask won at least  votes (his own initial votes plus two-thirds of the votes that previously went to Wells). 

Neither statement alone will prove a majority vote. From Statement 1 and 2 together, however, it is known that Crane won at least his own initial votes, all of Jones' votes, and one-third of Wells' votes - a minimum of 

 votes. Therefore Crane is the winner, and both statements are needed to prove this.

Statement 1 alone tells us that the population of Renfrow in 1945 was between 13,251 and 15,049, but says nothing about the population in 1955. 

Similarly, Statement 2 alone tells us that the population in 1955 was between 15,049 and 19,415, but says nothing about the population in 1945.

The two statements together, however, tell us that the population rose every year from 1940 to 1960, so the population in 1955 had to have been greater than the population in 1945.

From the two statements together, it can only be surmised that the population in both 1965 and 1975 exceeded the 1970 population. No conclusions can be drawn about the size of the 1965 population relative to the size of the 1975 population.

DO NOT calculate how much Janice and Julie will pay! It's extra work that will slow you down on test day. We don't actually need to determine which of the two women will pay more - we only need to decide if it is possible to figure out who will pay more. Obviously neither statement alone tells us enough. Together, however, the two statements tell us exactly what Janice and Julie ordered. Therefore, using both statements, we have enough information to answer the question.

Candidates A and B are the top two vote-getters, so we must establish which two candidates are A and B.

Statement 1 does just that by identifying them as Rhonda and Sally. It does not identify which one is which, but it is not necessary to know that.

Statement 2 identifies Rhonda as Candidate B, but only Patrick can be eliminated as Candidate A. 

Candidates A and B are the top two vote-getters, so we must establish which two candidates are A and B.

Statement 1 alone establishes that Nora is Candidate B, making her one of the top two vote-getters. Oswald is not one of the top two, since he is Candidate C, but neither Mickey nor Phyllis can be eliminated as Candidate A.

Statement 2 alone established that one boy is Candidate A, one of the top two vote-getters. Since the other boy is Candidate C, then the other one of the top two, Candidate B, is a girl. However, it does not establish the identity of any of them.

Now, assume both statements to be true. By Statement 2, the top two are a boy and a girl. Statement 1 establishes that the girl is Nora. Since Statement 1 also establishes that Oswald is not the boy, the boy is Mickey, and it follows that Mickey and Nora will face each other in the runoff.

Candidates A and B are the top two vote-getters, so we must establish which two candidates are A and B.

Neither statement alone is sufficient to answer the question. 

Assume Statement 1 alone. Barry and Carla could be Candidates A and B, respectively, in which case they would be the runoff candidates; also they could be Candidates B and C, respectively, in which case, Barry and one of the other two would be the runoff candidates. 

Statement 2 alone only knocks Anya out of the runoff election; it leaves the other three as possible candidates.

Assume both statements to be true. Anya is Candidate C. Candidate D, being neither Barry nor Carla, is David. Therefore, Candidates A and B are Barry and Carla; it is unclear which is which, but it is irrelevant; either way, they are the top two vote-getters, and they will participate in the runoff.