'manpreet singh wrote:Is the average of n consecutive integers equal to 1?
(1) n is even.
(2) If S is the sum of the n consecutive integers, then 0 <S <n.
Here's a slightly different approach.
Target question:
Is the average of n consecutive integers equal to 1?
Statement 1: n is even.
IMPORTANT: In a set of consecutive integers, the mean and the median will be equal.
So, let's see if we have enough information to find the
median of this set.
When we have an even number of integers, the median will equal the mean (average) of the two middlemost values.
Now notice that the mean of two consecutive numbers can never be an integer.
For example, the mean of 3 and 4 is 3.5, the mean of 0 and 1 is 0.5, and the mean of -5 and -4 is -4.5
So, from statement 1, we can conclude that
the average of the n consecutive integers cannot equal 1
Since we can answer the
target question with certainty, statement 1 is SUFFICIENT
Statement 2: If S is the sum of the n consecutive integers, then 0 <S <n.
This tells us that the average of the n values must equal S/n
Can S/n = 1?
No. If S<n, then S/n cannot equal 1.
In other words,
the average of the n consecutive integers cannot equal 1
Since we can answer the
target question with certainty, statement 2 is SUFFICIENT
Answer =
D
Cheers,
Brent
