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 3) 66 4) 55 5) 52


Answer : 1) 78

since, it says median of the set is equal to the mean hence , we may assume that it can be in AP series.

lets take the series R1,R2,R3,R4,R5 ; Median is 55 hence the R3=55 either in ascending or the decending order.

R5=3R1+20 ------equation 1

so we can Imply Range=R5-R1 , Where R5 is max value and R1 is the least in the set of 5 numbers.

therefore from equation 1

R5-R1=2R1+20
take the option 1) 78
we can see the
78=2R1+20
R1=29

out of all the given choices , the 78 is the biggest possible range which gives R5=107 and R1=29