Both  and  can be calculated using the definition of  for the case of exactly one of  and  being odd and one being even:

.

Add: 

A prime number has exactly two factors, 1 and the number itself.

Neither 6 nor 1 is a prime number; 1 has only one factor and is not considered to be prime, and 6 has more than two factors - 1, 2, 3, and 6. Therefore,  can be evaluated using the defintion of  for two numbers whose absolute values are not prime:

2 and 3 are prime numbers, since each has exactly two factors, 1 and the number itself. Therefore,  can be evaluated using the defintion of  for two numbers whose absolute values are prime:

The product is 

2 is a prime number, since 2 has only two factors, 1 and 2 itself. 50 is not a prime number, since 50 has other factors, such as 2.  can be evaluated using the definition of  for exactly one of  and  prime:

Neither 4 nor 25 are prime, since each has factors other than 1 and itself; for example,  and .  can be evaluated using the definition of  for neither  nor  prime:

The difference:

If  is the additive inverse of , then 

, or, equivalently,

By way of substitution and the identity property of addition,

17 and 13 are both prime numbers, since each has exactly two factors - 1 and the number itself. Therefore, we first evaluate  using the definition of  for  and  both prime:

Therefore, . 7 is also prime, since its only two factors are 1 and 7 itself. 30, however, is not prime, since 30 has factors other than 1 and itself - for example, . Therefore,  is evaluated using the definition of  for exactly one of  and  prime:

, the correct response.

Of the integers shown in the five choices, the following are primes, since they have exactly two factors, 1 and the number itself:  2, 5.

1 is not consdered to be a prime, having exactly one factor (1). Also, 4, 10, 20, 25, 50, and 100 are not primes, since each has at least one factor other than 1 and itself.

  and can both be evaluated using the definition of for exactly one of and prime - that is, by multiplying the numbers:

Each of , , and  can be evaluated using the definition of for neither of and prime - that is, by adding the numbers:

The greatest of the five expressions is .

The range is the difference between the maximum and minimum value.

The range is the highest value number minus the lowest value number in a sorted data set:

We need to sort the data set:

The range is the difference between the highest and lowest number.

First sort the set:

The range of a data set is the difference of the highest and lowest scores,

The numbers in the "stem" of this display represent tens digits of the test scores, and the numbers in the "leaves" represent the units digits. The highest and lowest scores represented are 87 and 42, so the range is their difference: .