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Consecutive Integers

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by relic » Wed Apr 08, 2009 5:51 pm
To know if the sets have the same median we need to know enough to determine their medians, or at least a range of the medians.

Statement 1 only mentions Set S's median so it can't possibly be sufficient. Statement 2 mentions both sets, but nothing that will help us find any medians.

When both Statements are used we can determine that the sum of the elements of Set S is zero (the only way for an odd number of consecutive numbers to have a median of zero is if the middle term is zero, hence Set S = {-2,-1,0,1,2}). We are also told that Set T's sum is the same as Set S, so it too is zero.

Again, since Set T consists of seven consecutive numbers whose sum is zero, the numbers must be centered about zero, i.e. Set T = {-3,-2,-1,0,1,2,3} and has a median of zero just like Set S.

Because we needed both Statements to answer the question, the correct answer is C.
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by ML » Wed Apr 08, 2009 6:24 pm
relic wrote:To know if the sets have the same median we need to know enough to determine their medians, or at least a range of the medians.

Statement 1 only mentions Set S's median so it can't possibly be sufficient. Statement 2 mentions both sets, but nothing that will help us find any medians.

When both Statements are used we can determine that the sum of the elements of Set S is zero (the only way for an odd number of consecutive numbers to have a median of zero is if the middle term is zero, hence Set S = {-2,-1,0,1,2}). We are also told that Set T's sum is the same as Set S, so it too is zero.

Again, since Set T consists of seven consecutive numbers whose sum is zero, the numbers must be centered about zero, i.e. Set T = {-3,-2,-1,0,1,2,3} and has a median of zero just like Set S.

Because we needed both Statements to answer the question, the correct answer is C.
Thanks for your response.

Statement 2: provided set S consists of five consecutive integers and set T consists of seven consecutive integers, doesn't statement 2 alone (sum of numbers in both sets equal) lead us to your final conclusion without statement 1? How can the two sets equal without a median of zero?
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by relic » Wed Apr 08, 2009 6:53 pm
I think your question is really insightful--a good sign.

The trick here is to remember that for a series of consecutive integers with an odd number of terms the median and the mean will always be the same. So for Set S, the sum of its terms will be five times its middle term and for Set T the sum of the terms will be seven times its middle term.

It now becomes a common multiple problem; every common multiple of 5 and 7 will be a potential sum of the sets. e.g. Set S= {5,6,7,8,9} Set T = {2,3,4,5,6,7,8}. Each sums to 35 but their medians are different.

Remember, using only Statement 2 we do not know that Set S's median is zero.
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by ML » Wed Apr 08, 2009 6:59 pm
relic wrote:I think your question is really insightful--a good sign.

The trick here is to remember that for a series of consecutive integers with an odd number of terms the median and the mean will always be the same. So for Set S, the sum of its terms will be five times its middle term and for Set T the sum of the terms will be seven times its middle term.

It now becomes a common multiple problem; every common multiple of 5 and 7 will be a potential sum of the sets. e.g. Set S= {5,6,7,8,9} Set T = {2,3,4,5,6,7,8}. Each sums to 35 but their medians are different.

Remember, using only Statement 2 we do not know that Set S's median is zero.
absolutely correct. i think hours of studying today led to such a careless mistake. thank you for the feedback.
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