Data Sufficiency

j_shreyans wrote:If S is a finite set of consecutive even numbers, is the median of S an odd number?

(1) The mean of set S is an even number.

(2) The range of set S is divisible by 4.

OAD

NICE RULE : In a set where the numbers are equally spaced, the mean will equal the median.

Target question: Is the median of S an odd number?

Given: S is a finite set of consecutive even numbers

Statement 1: The mean of set S is an even number.
Since the values in S are equally spaced, the above rule applies, which means the median of S must also be even.
In other words, the median of S is NOT an odd number.
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: The range of set S is divisible by 4.
Let's examine some situations where the range (of consecutive EVEN integers) is divisible by 4.
case a: S = {2, 4, 6}. Range = 4. Here the median, 4, is EVEN
case b: S = {6, 8, 10, 12, 14}. Range = 8. Here the median, 10, is EVEN
case c: S = {-8, -6, -4, -2, 0, 2, 4}. Range = 12. Here the median, -2, is EVEN
etc.
Notice that the median is ALWAYS EVEN
In other words, the median of S is NOT an odd number.
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer = D

Cheers,
Brent