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Medians!

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by gmat_for_life » Sun Feb 28, 2016 8:18 am
Set S consists of five consecutive integers, and set T consists of seven 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 numbers in set S is 0.
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T.

Statement 1 is clearly insufficient. However my approach for statement 2 is as below:
If S={n,n+1,n+2,n+3,n+4} and T=(x,x+1,x+2,x+3,x+4,x+5,x+6}
then essentially, the question is whether n+2=x+3

Now, 5n+10=7x+21

this implies, x=(5n-11)/7

Therefore x+3 becomes (5n-11)/7+ (3)=5/7(n+2) which is clearly less than n+2.

What's wrong with my approach here? OA is
C.
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by DavidG@VeritasPrep » Sun Feb 28, 2016 8:38 am
gmat_for_life wrote:Set S consists of five consecutive integers, and set T consists of seven 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 numbers in set S is 0.
(2) The sum of the numbers in set S is equal to the sum of the numbers in set T.

Statement 1 is clearly insufficient. However my approach for statement 2 is as below:
If S={n,n+1,n+2,n+3,n+4} and T=(x,x+1,x+2,x+3,x+4,x+5,x+6}
then essentially, the question is whether n+2=x+3

Now, 5n+10=7x+21

this implies, x=(5n-11)/7

Therefore x+3 becomes (5n-11)/7+ (3)=5/7(n+2) which is clearly less than n+2.

What's wrong with my approach here? OA is
C.
(5/7) * (n + 2) doesn't have to be less than n + 2. If n = -2, for example, the two are equal. (5/7) * 0 = 0. (If n had to be positive, your analysis would be correct.)
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by ceilidh.erickson » Sun Feb 28, 2016 5:38 pm
You're doing FAR more math here than you need to!

Since we're looking at consecutive sets, the median = average. So, we could rephrase the question: is the average of set S equal to the average of set T? I'll use the variables s = average of set S, and t = average of set T. So, s = t ?

As you noted, statement 1 is clearly insufficient, as it tells us nothing about set T.

When looking at statement 2, don't make it so complicated. You could turn it into a complicated equation, but why not just use the formula sum = (average)(# of terms) ?

(2) Sum of S = Sum of T
This implies:
5(average of S) = 7(average of T)
5s = 7t

If this is true, the two averages will only be equal if both s and t equal 0, but we have no further information about whether our terms are positive, negative, etc. Insufficient.

If we put the two statements together, then s = 0, so 5(0) = 7t. The average of set T must also be equal to 0. Sufficient.

The answer is C.
Ceilidh Erickson
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Harvard Graduate School of Education
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by gmat_for_life » Sun Feb 28, 2016 10:19 pm
David and Ceilidh,

Thank you very much for your explainations.The crux I believe is to have an idea about the various rules pertaining to medians.

Could you please do me a favor and list out some important concepts related to median that are frequently tested on data sufficiency questions?

Regards,
Amit
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by DavidG@VeritasPrep » Mon Feb 29, 2016 5:56 am
gmat_for_life wrote:David and Ceilidh,

Thank you very much for your explainations.The crux I believe is to have an idea about the various rules pertaining to medians.

Could you please do me a favor and list out some important concepts related to median that are frequently tested on data sufficiency questions?

Regards,
Amit
There isn't too much you need to memorize when it comes to stat-questions on the GMAT. Ceilidh hit on two important ideas in her explanation.

In evenly spaced sets: Mean = Median= (High + Low/2)
And for all sets: Mean * # of Elements = Sum

Of course, you should know the definitions of mode, range, and standard deviation.

But I find that on DS questions, I'm often constructing simple sets. If a statement tells me that the range of a set is 10, for example, I'll make the following sets: {0, 10} or {0, 1, 2, 3,...10} etc. Just remember that logic and flexibility are among the most useful tools in our toolbox.
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by ceilidh.erickson » Mon Feb 29, 2016 6:02 am
Yup, those are the two big ones. The other one I'd add: don't assume that the median = mean unless you're given enough information to know that it's a consecutive / evenly spaced set.
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