In order to solve an equation set, one requires a number of equations equal to the number of variables. Therefore, three equations are needed and both statements are required to solve the problem.

Let:

t: the number of trucks sold last week

d: the number of dolls sold last week - d is the value we are looking to find

To evaluate the statements, we translate the word problems into equations

(1):  or 

(2): 

Each statement provides a single equation with two unknowns which is unsolvable, so each statement alone is not enough.

The two statements taken together give us a system of two equations with two unknowns, which we can solve.

Therefore the right answer is C.

Statement 1 gives us the time and the speed so we can derive the distance:

 .

Therefore,

Statement 2 tells us that the gas station is halfway betweent the two houses so:

distance between Barry's house and gas station = distance between Harry's house and gas station = 0.5 distance between the two houses

Furthermore, we learn that the distance between the gas station and Harry's house is 20 miles.

Therefore:

distance between Harry's house and gas station = 20 miles = 0.5 distance between the two houses

So the distance = 2 x 20 = 40 miles

So the correct answer is D; each statement alone is sufficient.

We are given a point and two clues.

Both I and II give us the slope of f(x). It must be 4 because we are told so in II. This holds true from statement I since it must be parallel to g(x), which has a slope of four.

With a slope and a point we can find the equation of f(x) using the point slope form,

.

Therefore either statement alone is enough. 

To find b, we need a point on k(t). 

I) Gives us that point.

II) Gives us some details about a parallel line, which is cool and all, but it doesn't help us find b.

So statement I alone is sufficient to answer the question.

To find m, we need a point on the line.

Both I and II give us points, so we can use either of them to solve for m.

To answer the question we must know the absolute value of .

Statement 1 tells us the absolute value of , indeed, it is .

Statement 2 also tells us that the absolute value of  is 5, since .

Therefore, the final answer is each statement alone is sufficient.

To be able to answer the question, we must have a definitive value for . 

Statement 1 tells us that  is , in other words  could be two values  or . This statement gives us two possibilities for  and is therefore insufficient.

Statement 2 tells us that the cube of  is , therefore  must be . This statement gives a single possible value for  and therefore is, alone, sufficient.

To answer the question, we should be able to find a single value for . 

Statement 1 gives us two possible values for . Indeed,  or . Hence, the information provided doesn't allow us to find the answer to the problem.

Statement 2 although a complicated equation to calculate, won't prove useful because the power is an even number and therefore, the equation will also have two solutions. 

Both statements together are not sufficient because they both give us the value of , which is not sufficient.

Hence, statements 1 and 2 taken together are not sufficient.

To begin with, we should see that information about unknowns  or  would be useful to answer the problem. We already know that both these unknowns are integers.

Statement 1 gives us information about the upper bound for . However,  can still be an infinity of values, therefore this statement alone is insufficient.

Statement 2 gives us information about the lower bound for , just as statement 1, this statement alone doesn't allow us to find a single value for .

Taking these statements together we get that . Since  is an integer,  can only be . Both statements together are sufficient.