Statement (1) provides the value of y in terms of x, which is not enough to determine the value of x in the list we are given.

Statement (2) gives the arithmetic mean of the list. We can the write the following equation:

However, we cannot find the value of x using the information in Statement (2) only.

Using the information in Statement (1), we can replace y by x-4 in the previous equation:

We need both statements to calculate the value of x.

Both statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient.

The mean class grade is the sum of all average class grades divided by the number of grades:

Using Statement (1):

Therefore Statement (1) is sufficient to calculate the arithmetic mean for these grades.

Using statement (2):

Therefore 

Therefore Statement (2) is sufficient to calculate the arithmetic mean for these grades.

Each Statement ALONE IS SUFFICIENT to answer the question

To find the mean, we find the sum of all of the values, and divide by how many there are:

To find the mean we rearrange the values in ascending numerical order and select the middle value:

The product, then, is 

The arithmetic mean of  and  is equal to .

Statement 1 alone gives us this value directly. 

From Statement 2 alone, the value can be determined by dividing both sides by 4:

The median of three or five numbers (both odd numbers) is the number in the middle when they are arranged in ascending order. Statement 1 alone does not answer the question of which one is the median; both of the following orderings are consistent with that statement:

 - median 

 - median .

For similar reasons, Statement 2 alone does not answer the question.

Now, assume both statements to be true. From Statement 1, exactly one of  and  is less than , and the other is greater. From Statement 2, exactly one of  and  is less than , and the other is greater. Therefore, two of the five values are less than  and two are greater, making  the middle element, or median.

Assume Statement 1 alone. The sequences

and

are both arithmetic, each term being the previous term plus the same number (in the first case, this common difference is 40; in the second, it is 20). The fourth term is 120 in both cases, The second and third terms of the first sequence have arithmetic mean ; the second and third terms of the second sequence have arithmetic mean .  Therefore, the mean of those two terms cannot be determined for certain. A similar argument holds for Statement 2 alone being insufficient.

Now assume both statements. Let  be the common difference of the sequences mentioned in Statement 2. By Statement 2, 0 is the first term, so the sequence will be

By the first statement, the fourth term is 120, so

The second terms is and the third term is , and their arithmetic mean is .

An arithmetic sequence is one in which each term is formed by adding the same number to its preceding term - the common difference.

Let  be the first term, and  be the common difference. The first five terms are

The arithmetic mean of two numbers is half the sum of the numbers. The arithmetic mean of the first and third terms is

,

which is the second term. Statement 2 alone gives this number as 100.

Now assume Statement 1 alone. Consider these two sequences, both of which can be seen to be arithmetic with fifth term 130:

The arithmetic mean of the first and third terms differ, as can be seen by looking at the second terms; in the first sequence, it is 127, and in the second, it is 100. That makes Statement 2 inconclusive.

The median of five numbers (an odd number) is the number in the middle when they are arranged in ascending order. 

These two orderings are both consistent with the ordering given in Statement 1:

 - median 

 - median .

Therefore, Statement 1 alone provides insufficient information to answer the question. For a similar reason, so does Statement 2. 

Assume both statements to be true. Then  is greater than both  and  and less than both  and . That makes  the middle element, and, thus, the median.

The area of a rectangle is the product of its length and width; the area of a triangle is half the product of its height and the length of its base. Therefore, from Statement 1, we get that 

.

From Statement 2, we get that

, or, equivalently,

, or

In other words, the two statements are equivalent, so one of two things happens - either statement alone is sufficient, or both together are insufficient. We show that the latter is the case:

Case 1: 

The mean of the two is .

Case 2: 

The mean of the two is .

Therefore, knowing the area of the rectangle with these dimensions is not helpful to determining their arithmetic mean. This makes Statement 1, and, equivalently, both statements together, unhelpful.

The average or mean is found by taking all of the scores and dividing by the total number of scores. Remember, we must first find the lowest score and not include that in the calculation. Therefore, we get: 

 when rounded.