Min Max GMAT, GRE Question

Positive integers a, b, c, d and e are such that a < b < c < d < e. If the average (arithmetic mean) of the five numbers is 6 and d - b = 3, then what is the greatest possible range of the five numbers?

A. 12
B. 17
C. 18
D. 19
E. 20






maximize (ba+cb +dc+ed) 
= (ba+3+ed)
a + b + c + d + e = 30

a + (a+ba) + (a+ba+cb) + (a+ba+3) + (a+ba+3+ed) = 30

ba+3+ed = 30 - {5a + 3ba + cb +3}

Min (5a + 3ba + cb +3) = 5+3+1+3 = 12 

Max Range = 30-12 = 18