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,

\(\displaystyle y-y_1=m(x-x_1)\).

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 \(\displaystyle x\).

Statement 1 tells us the absolute value of \(\displaystyle x\), indeed, it is \(\displaystyle 5\).

Statement 2 also tells us that the absolute value of \(\displaystyle x\) is 5, since \(\displaystyle \sqrt{x^{2}}=\left | x\right |=\sqrt{25}=5\).

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

To be able to answer the question, we must have a definitive value for \(\displaystyle x\). 

Statement 1 tells us that \(\displaystyle \left | x\right |\) is \(\displaystyle 4\), in other words \(\displaystyle x\) could be two values \(\displaystyle -4\) or \(\displaystyle 4\). This statement gives us two possibilities for \(\displaystyle x\) and is therefore insufficient.

Statement 2 tells us that the cube of \(\displaystyle x\) is \(\displaystyle 64\), therefore \(\displaystyle x\) must be \(\displaystyle 4\). This statement gives a single possible value for \(\displaystyle x\) and therefore is, alone, sufficient.

To answer the question, we should be able to find a single value for \(\displaystyle x\). 

Statement 1 gives us two possible values for \(\displaystyle x\). Indeed, \(\displaystyle x=\sqrt{3}\) or \(\displaystyle x=-\sqrt{3}\). 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 \(\displaystyle \left | x\right |\), which is not sufficient.

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

To begin with, we should see that information about unknowns \(\displaystyle A\) or \(\displaystyle x\) 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 \(\displaystyle x\). However, \(\displaystyle x\) can still be an infinity of values, therefore this statement alone is insufficient.

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

Taking these statements together we get that \(\displaystyle 2< x< 4\). Since \(\displaystyle x\) is an integer, \(\displaystyle x\) can only be \(\displaystyle 3\). Both statements together are sufficient.

Firstly, we should try to simplify the equation, to see solutions for \(\displaystyle x\). We get \(\displaystyle (x-3)(x-2)\). The best west way to simplify quadratic equations is to find the possible factors for the last term \(\displaystyle c\) in the general quadratic equation \(\displaystyle ax^{2}+bx+c\) and those two factors must add up to \(\displaystyle b\). Here for example, \(\displaystyle -2\) and \(\displaystyle -3\) add up to \(\displaystyle -5\) and their products is \(\displaystyle 6\).

So we have to solutions for the equation and we need to know what \(\displaystyle x\) we are looking for.

Statement 1 tells us that \(\displaystyle x\) is positive, however, the two possible solutions are positive and therefore, statement 1 doesn't help us find the correct solution for \(\displaystyle x\).

Statement 2 tells us that \(\displaystyle x\) is smaller than 3. Only one of our solutions is smaller than 3. Therefore statement 2 alone is sufficient.

First, we should try to simplify the quadratic equation, and we get \(\displaystyle (x+3)(x-1)=0\). This allows to see the two solutions for our equation.

Statement 1 tells us that \(\displaystyle x\) is between \(\displaystyle -4\) and \(\displaystyle 2\). But both possible solutions are in this interval. Therefore statement 1 alone is not sufficient.

Statement 2 tells us that \(\displaystyle x\) is an integer, which we already knew by reducing the equation. Therefore, this statements doesn't help us find a single value for \(\displaystyle x\)

Statements 1 and 2 together are still insufficient, since none can help us find a single value for \(\displaystyle x\).

Firstly, we should try to find a simplified equation to better see the possible values for \(\displaystyle x\). We get \(\displaystyle (x-1)(x-5)\). We can see that \(\displaystyle x\) can either be \(\displaystyle 1\) or \(\displaystyle 5\).

Statement 1 tells us that the square of \(\displaystyle x\) is \(\displaystyle 25\). It follows that \(\displaystyle x\) must be \(\displaystyle 5\), therefore, this statement is sufficient.

Statement 2 tells us that the absolute value of \(\displaystyle x\) is \(\displaystyle 5\), therefore \(\displaystyle x\) must be \(\displaystyle 5\) and therefore the statement is also sufficient alone.

Note that it is possible to answer with either statement only because \(\displaystyle x\) can either be \(\displaystyle 5\) or \(\displaystyle 1\). If \(\displaystyle x\) could have been \(\displaystyle -5\) or \(\displaystyle 5\) than statements 1 and 2 would have been insufficient.