dchen wrote:Hi,
I'm sure there's a reason for this, but could someone point out an example?

Question in GMATPrep test #2:
Set S consists of 5 consecutive integers and set T consists of 7 consecutive integers. Is the median of the numbers in set S equal to the median of the numbers in Set T?
1. the median of the set of numbers in S is 0
2. the sum of the numbers of Set S is equal to the sum of numbers in Set T

The answer is C. I thought it was B.

My rationale:
If the sum of Set S and Set T are equal, I see no other way (because T has 2 more numbers), and both sets are consecutive, other than the fact that T must have negative or 0 numbers. Since the set it consecutive, there must be a 0 in the set, and there must be at least 1 negative.

I can't think of any examples except where the median of both sets are centered around 0 for which the sum of numbers in Set S are equal to T. So I thought the answer was "B".

What am I missing?

In any set containing n numbers, the average = sum/n. Here we are interested in the sum; the sum = n*average.

Now, in any 'equally spaced' set of n numbers, the median is always equal to the average. Our sets here are 'equally spaced', since they are consecutive integers, so in each set, the sum = n*median.

So if you have a set of five consecutive integers, where m is the median, the sum will always be 5m. Similarly, if M is the median of our set of seven consecutive integers, the sum will be 7M.

So if we know Statement 2 alone, we know that 5m = 7M. It's certainly possible that m=M=0, but it's also possible that, say, m=7 and M=5, in which case you'd have the sets {5,6,7,8,9} and {2,3,4,5,6,7,8}, and there are many other possibilities. So from Statement 2 alone, the medians may or may not be equal.

When we combine the two Statements, we know that m=0, so from the equation 5m=7M, M must also be zero, and the answer is C.