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

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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.


OA D

Source: Manhattan Prep

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BTGmoderatorDC wrote:
Sat Jun 25, 2022 6:41 pm
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.


OA D

Source: Manhattan Prep
We need to recall the following for this problem:
- "If the number of terms in a set of consecutive even integers is even, then the median is odd"
- "If the number of terms in a set of consecutive even integers is odd, then the median is even"

We can try this with the following sets:
\(2, 4, 6, 8\) (Median \(= 5\))
\(2, 4, 6, 8, 10\) (Median \(= 6\))

As we know, mean and median are equal in evenly spaced sets.

Statement 1: Sufficient \(\Large{\color{green}\checkmark}\)
If the mean is even, then the median is even.

Statement 2: Sufficient \(\Large{\color{green}\checkmark}\)
You can try different scenarios and you'll always yield the right answer. However, I wouldn't know how to explain the algebraic approach.

Therefore, D

Hope this helps.