For each quantity, only count the integers that aren't in the other quantity. Both quantities include the numbers 51 to 98, so those numbers won't affect which is greater. Only Quantity A has 49 and 50 (for a total of 99) and only Quantity B has 99. Since the excluded numbers from both quantities equal 99, you can conclude that the 2 quantities are equal.

The formula here is sum = average value * number of values.  Since this is a consecutive series, the average can be found by averaging only the first and last terms: (1 + 69)/2 = 35.  

sum = average * number of values = 35 * 69 = 2415

The sum of all integers from 1 to 30 can be found using the formula

, where  is 30. In this case, the sum equals 465.

We can represent our numbers as:

 will have to be an odd number since the whole sequence is odd.  However, this will work out when we do the math.  Now, we know that all of these added up will be .  We have  and the sum of the set , the sum of which is .  

Thus, we know:

Solve for :

Therefore, the fourth element will be :

There are two ways to figure out this list of integers.  On the one hand, you might know that the average of a set of consecutive integers is the "middle value" of that set.  So, if the average is  and the size , the list must be:

Another way to figure this out is to represent your integers as:

The average of these values will be all of these numbers added together and then divided by .  This gives us:

Multiply both sides by :

Finish solving:

This means that the largest value is:

The sum of 4 consecutive numbers being 38 can be written as the following equation.

We can simplify this to solve for x.

This tells us that the smallest number is 8 and the largest is (8 + 3) = 11. From this, we can find their mean.

The provision of the bottom-end of the engineering range is the only additional information that provides us a fixed endpoint from which we can build off of by supplementing with the ranges provided in the question, to give us the full range between both engineering and achitecture graduates. See the diagram provided to understand how this can be done.

Even if the mean and medians were provided, these additional values give us no information on the endpoints of the salaries, and the question only asks for the range. 

Let's draw a number line. 

Since a number line is straight and contains the numbers consecutively, we just subtract  from  to get . 

Open circles mean the values are excluded from the set.

The number line shows the set is between  and  exclusive.

The only value in that set would be . 

Because a number line contains both positive and negative integers, we need to consider both possibilities. 

 is  and that value is the same as . Therefore we eliminate the  choice because  will always be greater than those values raised to the  power.

Next  is . We elminate both the positive and negative range of . If we look at the difference between  and , it's over .

Then, we should guess that  will definitely be greater than  so therefore answer is .

Remember, a negative value raised to an even power will always have a positive value.