The average (arithmetic mean) of 7 numbers in a certain list is 12. The average of the 4 smallest numbers in this list is 8, while the average of the 4 greatest numbers in this list is 17. How much greater is the sum of the 3 greatest numbers in the list than the sum of the 3 smallest numbers in the list

Step-by-step explanation:

Let the 4 greatest numbers be, A, B, C D

(A + B + C + D) / 4 = 8

Total sum = 4 * 8

= 32

Let the 4 lowest numbers be, D, E F G,

(D + E + F + G) / 4 = 20

Total number = 4 * 20

= 80

Hence, the difference between the sums of the 3 greatest number and the 3 smallest numbers:

A, B, C and E, F, G

= D + (E + F + G) - (A + B + C) - D

= (E + F + G) - (A + B + C)

= 80 - 32

= 48.