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This problem trains for: SAT-I, AMC-8, GMAT.

The average of four numbers is 55. If the largest number is 100 and the range of the set is 110, what is the value of the median?

Since the average is 55 the sum of all the numbers must be:

equation

Let us assume that a is the largest number and d is the smallest, then the range is:

equation

Solving for d we obtain:

equation

If we arrange the numbers in increasing or decreasing order, the median is the average of the two numbers in the middle (because there is an even number of numbers):

equation

equation

The median is equal to 65.