Asmakan wrote:
A list consists of three different positive integers whose sum is 10.
Which of the following statements individually provide(s) sufficient additional information to determine the value of the greatest integer in the list?
Indicate all such statements.
I. The median of the integers in the list is 3.
II. The range of the integers in the list is 5.
III. The sum of the greatest integer and the least integer in the list is 7.
Source : ETSmentor
The key thing to notice here is that both I. and II. lead to the same conclusion: that y = 3 , x = 1 or 2, and z = 6 or 5. As we must select at least on of the three possibilities, this guarantees that
II. is the correct answer. A more detailed explanation is included below:
x < y < z
x + y + z = 10
I. The median of the integers in the list is 3 -----> y = 3 ====> x + z = 7
x < 3 and is a positive integer -----> x = 1 or 2
z > 3 and is a positive integer -----> z = 6 or 5
Not enough information to determine the value of z.II. The range of the integers in the list is 5.
z - x = 5 ----- substitution----> x + y + (x + 5) = 10 ------> 2x + y = 5
As x < y, and both are integers x
must be 1 and y
must be 3 -----> 1 + 3 + z = 10 ====>
z = 6 III. The sum of the greatest integer and the least integer in the list is 7.
x + z = 7 -----> y = 3 =====> x = 1 or 2 and z = 6 or 5
Not enough information to determine the value of z.Thus, only
II. provides sufficient additional information to determine the value of the greatest integer in the list.
04 Dec 2022, 07:48 
36% (02:18) correct
