Bunuel wrote:
What is the average (arithmetic mean) of 5 consecutive integers?
(1) The average (arithmetic mean) of the largest and the smallest of the integers is 18.
(2) The average (arithmetic mean) of the 5 integers is 2 more than the smallest of the integers.
Useful property: In a set of consecutive integers, the mean = medianLet x - 2 = the smallest integer
So, x - 1 = the next integer
x = the next integer
x + 1 = the next integer
x + 2 = the biggest integer
As we can see, x = the median = the mean Target question: What is the value of x? Statement 1: The average (arithmetic mean) of the largest and the smallest of the integers is 18. We can write: \(\frac{(x+2) + (x - 2)}{2} = 18\)
Simplify the numerator: \(\frac{2x}{2} = 18\)
Simplify again:
\(x = 18\)Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: The average (arithmetic mean) of the 5 integers is 2 more than the smallest of the integers. We can write: mean - (smallest integer) = 2
Substitute to get: \(x - (x - 2) = 2\)
Simplify: \(2 = 2\)
This tells us nothing about the value of x.
In fact, in a set of 5 consecutive integers, the mean will always be 2 greater than the smallest integer.
Since we can’t answer the
target question with certainty, statement 2 is NOT SUFFICIENT
Answer: A
Cheers,
Brent