The simplest way to do this problem is visually. From looking at the graph, the greatest difference between Beetleton and Caterpilly is 2 billion US, and this difference is also observed where those points for Beetleton and Caterpilly are closest to the x-axis: 2008.

Of course, the percent differences can also be calculated using the formula:

and for each year, the percent differences are as follows:

Of course this method is much more time consuming.

Percent growth is given by the formula:

So the percent grown for Caterpilly from 2010 to 2011 is:

Conversely, if percent growth is known, a new value can be found as follows:

The GDP for 2014 is  ( in billions US dollars), so the projected GDP in billions of US dollars for 2015 is:

For this problem, note that for the  students elected from the  running for either president, vice president, and hall monitor, position matters, and so this is dealing with a permution, with the following number of potential outcomes:

However, for the second election, in which  students are competing for  positions, since all the secretarial offices are equal, position does not matter, and so we are dealing with a combination:

The total potential outcomes is given by the product of these two values:

This problem merely requires careful working out of each part. Begin by simplifying the first fraction:

The numerator will be:

The denominator will be:

Thus, we have the following fraction:

Remember that you must multiply the numerator by the reciprocal of the denominator:

Now, work on the second fraction:

This fraction is much easier. After simplifying the numerator, you get:

This is the same as:

Thus, we come to our original expression! It is:

The common denominator of these fractions is . Thus, you have:

As it is, quantities A and B have different denominators, so making a comparison can be tricky. Making a common denominator will allow for comparison of just the numerators, so that would make a good first step:

Quantity A:

Quantity B:

Disregarding equal denominators, since they'll always have a positive value, compare the numerators. If  is subtracted from quantity A and from quantity B, we're left with  for the former and  for the latter.

Quantity A is greater.

One way to approach this question is to try to reduce the complexity of each quantity. By subtracting the value of Quantity A,  from both A and B, we can make a new comparison:

Quantity A': 

Quantity B': 

Now, it's easy to see that for different values of  Quantity B may be greater, lesser, or equal to Quantity A.

Since  is not restricted in its possible values, the relationship cannot be determined.

To find out how many rhododendrons Rita will need to prune in an hour, we must first find out how many she needs to prune.

If Rhoda can prune  rhododendrons in  hours, then she can prune  in  hours, and if Rhonda can prune  in  hours, she can prune  in  hours.

If this is not readily apparent, it can be found by finding out how many each prunes in one hour, then multiplying by .

Rhoda:

Rhonda: 

Between Rhoda and Rhonda,  of the  rhododendrons can be pruned, leaving  for Rita.

Since she has  hours for the task, her rate of pruning can be found to be: