BTGmoderatorDC 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.

OA D

Source: Manhattan Prep

Since S is a finite set of consecutive even numbers, its numbers are evenly spaced.

Let's take each statement one by one.

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

For an evenly spaced set of numbers, mean = median. Thus, the answer to the question, "is the median of S an odd number" is no. Sufficient.

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

Case 1: Say Set S has x, (x + 2), and (x + 4) elements. Thus, its range = (x + 4) - x = 4, divisible by 4. We see that (x + 2), an even number is the median. Thus, the answer to the question, "is the median of S an odd number" is no.

Case 2: Say Set S has x, (x + 2), (x + 4) and (x + 6) elements. Thus, its range = (x + 6) - x = 6, not divisible by 4. Thus, this is not a possible case.

Case 3: Say Set S has x, (x + 2), (x + 4) , (x + 6) and (x + 8) elements. Thus, its range = (x + 8) - x = 8, divisible by 4. We see that (x + 4), an even number is the median. Thus, the answer to the question, "is the median of S an odd number" is no.

From above we conclude that for the range to be divisible by 4, the largest number must be greater than the smallest by a number that is a multiple of 4. In this scenario, the median is even number. Thus, the answer to the question, "is the median of S an odd number" is no. Sufficient.

The correct answer: D

Hope this helps!

-Jay
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