AbeNeedsAnswers wrote:If p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers, what is the value of x ?
(1) Twice x is equal to the sum of p, r, and s.
(2) The sum of p, r, and s is zero.
D
Given: p, r, and s are consecutive integers in ascending order and x is the average (arithmetic mean) of the three integers
Since p, r and s are EQUALLY spaced, the mean of the 3 numbers = the median of the 3 numbers.
Since p < r < s, we know that r = the mean = the median.
In other words,
r = x (since we're told x is the mean)
So,
p = x - 1
And
s = x + 1 (since p, r, and s are consecutive integers)
Target question: What is the value of x?
Statement 1: Twice x is equal to the sum of p, r, and s.
We can write:
2x = p + r + s
Replace p with x-1, replace r with x, and replace s with x+1 to get: 2x = (x-1) + x + (x+1)
Simplify: 2x =3x
Solve:
x = 0
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The sum of p, r, and s is zero.
We can write:
p + r + s = 0
Replace p with x-1, replace r with x, and replace s with x+1 to get: (x-1) + x + (x+1) = 0
Simplify: 3x =0
Solve:
x = 0
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer: D
Cheers,
Brent
