BTGModeratorVI wrote: ↑Wed Dec 16, 2020 12:37 pm
The average (arithmetic mean) of the positive integers x, y, and z is 3. If x < y < z, what is the greatest possible value of z ?
A. 5
B. 6
C. 7
D. 8
E. 9
Answer:
B
Source: official guide
The average (arithmetic mean) of the positive integers x, y, and z is 3
We can write: (x+y+z)/3 = 3
Multiply both sides of the equation by [m]3[/m] to get: x + y + z = 9
At this point we need to find the greatest possible value of z
Important: Keep in mind that the three numbers are DIFFERENT POSITIVE INTEGERS
Since we know that x+y+z=9, we can MAXIMIZE the value of z by MINIMIZING the values of x and y
We know that x is the smallest value.
Since x must be a positive integer, the smallest possible value of x is 1
Since y must be different from x, the smallest possible value of y is 2
At this point we have maximized the value of z
If x=1 and y=2, then z=6
Answer: B
Cheers,
Brent
