In order to find the range for a set of data, take the largest number and subtract the smallest number. 

In this case, the largest number is  and the smallest number is . 

Remember that when we subtract a negative, we are actually adding the absolute value of the numbers: 

Therefore:

 is the same as  

To find the range, we will find the smallest number and the largest number.  Then, we will find the difference of those two numbers.  

So, given the set

we can see the smallest number is 2 and the largest number is 10.  Now, we will find the difference.  We get

Therefore, the range of the data set is 8.

A range is simply the highest score minus the lowest score.

The highest score was , and the lowest score was . 

 is the union of  and  - that is, it is the set of all elements in one set or the other. 

A set is a subset of  if and only if every one of its elements is in . Three of the listed sets do not meet this criterion:

,   , and , but none of those three elements are in . All of the elements in  do appear in , however, so it is the subset.

 is the intersection of  and  - the set of all elements appearing in both sets. Thus, an element can be eliminated from  by demonstrating either that it is not an element of or that it is not an element of .

 is the set of positive integers ending in "5". 513 and 657 are not in , so they are not in .

 is the set of muliples of 9. We test the three remaining numbers easily by seeing if 9 divides their digit sum:

425 and 565 are not multiples of 9; neither is in , so neither is in .

 and , so   . This is the correct choice.

The set is composed of consecutive squares.

We can see that will b equal to

Therefore, 36 is the correct answer. 

The elements of the set  - that is, the intersection of  and  - are exactly those in both sets. We can test each of the six elements in  for inclusion in set  by dividing each by 7 and noting which divisions yield no remainder:

 and  have no elements in common, so  has zero elements. This is not one of the choices.

For a set to be a subset of , all of its elements must be elements of  - that is, all of its elements must be multiples of 3. A set can therefore be proved to not be a subset of  by identifying one element not a multiple of 3.

We can do that with four choices:

: 

: 

: 

: 

However, the remaining set, , can be demonstrated to include only multiples of 3:

 is the correct choice.

The elements of the set  - that is, the intersection of  and  - are exactly those in both sets. We can test each of the six elements in  for inclusion in set  by testing for divisibility by 5 - but this can be accomplished by looking at the last digit. Only 345, 600, and 855 have last digit 5 or 0 so only these three elements are divisible by 5. This makes three the correct answer.

We show that none of the four listed sets can be a subset of the primes by identifying one composite number in each - that is, by proving that there is at least one factor not equal to 1 or itself:

, so 25 has 5 as a factor, and 25 is not prime.

, so 9 has 3 as a factor, and 9 is not prime.

, so 21 has 3 and 7 as factors, and 21 is not prime.

, so 21 has 3 and 9 as factors, and 27 is not prime.

Since each set has at least one element that is not a prime, each has at least one element not in , and none of the sets are subsets of .