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.

Suppose we only know that 200 ml of the 40% solution is used. Then we can call  the amount of 25% solution used, and the total amount made is  . The solution equation becomes, 

So 100 ml of the 25% solution is used.

Similarly, if we only know that 100 ml of the 25% solution is used, then we can call  the amount of 40% solution used, and the total amount made is   . The solution equation becomes, 

So 200 ml of the 10% solution is used.

Either way, we get that

and 300 ml of solution is created.

The answer is that either statement is sufficient to answer the question.

Using statement 1, we can find that he has 10 green boxes and 10 brown. We solve mixture problems using 2 equations. If we let  be the number of green boxes, and  be the number of brown boxes. We can set the equations

1)  and

2)

Solving equation 1) for , we get .

Subsituting for  into equation 2) results in

 Simplifying we get  or

Therefore, this answer would be 10 green boxes and 10 brown.

The second statement is irrelevant in finding our answer. 

Assume both statements are true.

Let  be the amount of Chocolate Explosion and  be the amount of Cherry Cherry Delight. Then the price of the Chocolate and Cherry coffees will be  dollars and  dollars, respectively. The total price of the beans is , so we can set up the equation:

However, there is no further information we can use to set up a second equation, so there is insufficient information to answer the question.

Let  be the number of pounds of Vanilla Heaven coffee beans in the mixture.

If we assume Statement 1 alone, then the total price of the Vanilla Dream coffee beans is $10 per pound times  pounds, or . Similarly, the total price of the Mountain Goodness beans is , and the overall price of the beans in the mixture is . Add these together to get the equation

.

If we assume Statement 2 alone, the price of the Vanilla Dream beans is again . However, the price of the Mountain Goodness beans is  and the overall price of the beans is , so we can set up this equation:

From either equation we can solve for  and get the answer to the question. 

Using Statement (1), we can set up the following equation:

The amount of acid in the original solution (40% multiplied by 15 liters) should equal the amount of acid in the final diluted solution (remember there is no acid in water!!!)

Therefore knowing the value of x, we are able to calculate y. We can now find the amount of water used to dilute the solution by subtracting x from y.

Using Statement (2), we set up the following equation:

We can also calculate the amount of water used since we can calculate x from knowing y.

Each Statement ALONE is sufficient to answer the question.

(1) A pound of almonds is twice as expensive as a pound of walnuts.

Let x be the price per pound of walnuts and y the price per pound of almonds.

We don't know the respective amounts of almonds and walnuts and the prices of any of the nuts aren't clearly stated.

Statement(1) Alone is not sufficient.

(2) The mixture contains 0.7 pounds of walnuts and 0.3 pounds of almonds.

Statement (2) alone is not sufficient, it indicates the quantities of almonds and walnuts in a pound of mixture. However the price per pound of each type of nuts is unknown.

Combining both statements, we can write the price of one pound of the mixture as:

We do not know x, the price per pound of walnuts, therefore both statements together are not sufficient.

(1) A mixture of half almonds and half walnuts sells for $14 per pound.

Let x be the price per pound of walnuts and y the price per pound of almonds.

Since we do not know the price per pound of walnuts or the price per pound of almonds, statement(1) is not sufficient.

(2) A pound of almonds is twice as expensive as the pound of walnuts.

Let x be the price per pound of walnuts and y the price per pound of almonds.

Statement (2) alone is not sufficient.

Combining both statements:

The price per pound of almonds is: