Set R contains five numbers that have an average value of 55. If the median of the set is equal to the mean, and the largest number in the set is equal to 20 more than three times the smallest number, what is the largest possible range for the numbers in the set?

1) 78

2) 77 1/5

3) 66 1/7

4) 55 1/7

5) 52

Answer is

option (1) = 78

My question is: Mean is equal to median only when we have a set of consecutive no.s (difference between any two consecutive no.s is the same). So in this case the largest no. in the set is fixed. How can we manipulate the no.s when we know that the difference between 2 no.s is the same. I think the question is slightly flawed. If we were to manipulate other no.s to find largest no. in the set, then we should not be given the fact that mean = median.

Pls some instructor help me with this.

Jigar