Bunuel
If the average (arithmetic mean) of four different positive integers is greater than 3 and less than 4, what is the range of the four numbers?
(1) One number is greater than 7
(2) The median of the four numbers is 2.5
Project DS Butler Data Sufficiency (DS3)
For DS butler Questions Click Herelet’s assume 4 numbers as A, B, C, and D
given that all of these are different positive integers
also given that 3 < (A+B+C+D)/4 < 4 ----- leads us to 12 < A+B+C+D < 16
now since these are integers their sum can only be an integer
hence A + B + C + D = 13 or 14 or 15
Statement 1:
Given that one number is > 7
Lets say that D > 7 ---- D = 8, 9 etc.
The least value of A(=1) + B(=2) + C(=3) = 6
A + B + C + D => 1+ 2+ 3+ 8 = 14 ----- range = 8-1 = 7
A+ B +C + D => 1+2+3+9 = 15 -------- range = 9-1 = 8
NOT SUFFICIENT
Statement 2:
The median of the four numbers is 2.5
C + D = 5 ------ the only possibility is C = 2 and D = 3 -------- hence A = 1
Now A + B + C + D => 1+2+3+8 = 14 ---- range = 8-1 = 7
And A + B + C + D => 1+2+3+9 = 15 ------ range = 9-1 = 8
NOT SUFFICIENT
Upon combination you will still be left with D = 8 or D = 9 which will not give a conclusive range
NOT SUFFICIENT
Answer – E