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.

this is another problem about a topic that is one of the darlings of the test authors: namely, sets of consecutive integers, especially as pertaining to the averages of such sets.

here is the fact that you absolutely must know about these sets:
the mean and the median of a set of consecutive integers are the same; both of them are the middle number (for a set with an odd # of numbers in it) or halfway between the two middle numbers (for a set with an even # of numbers in it).

--

remember that average = sum / number of data points. you should be ultra-aware of this relationship; the vast majority of problems about the sum of a set are really concerned with the average - and vice versa. they are tricky, those test writers.

let 'X' stand for the sum of each of the sets.

(1) is clearly insufficient, as we know nothing whatsoever about set t.
still, take the time to interpret it: it says that the middle number of set s is 0, which also means that the sum of the elements in set s is 0 (by the fact above).

(2)
using the fact above, we have that the average (whether mean or median - they're the same) of the numbers in set s is X/5, and the average (again, mean or median) of the numbers in set t is X/7.
it's tempting to say 'sufficient' here, because at first glance X/5 and X/7 appear to be necessarily different, but they aren't: in the singular case X = 0, the two will be identical.
therefore, insufficient.

(together)
this tells us that X = 0, which means that the median of both sets is 0/7 = 0/5 = 0.
sufficient.

hello RON
I have a doubt. I think 2 is sufficient
the sum of these two sets(sets of consecutive integers) will be equal only when the sum is zero.
if there are 5 and 6 elemenmts of consecutive integers then sum will be equal without being zero.
eg 5 consecutive integers 1,2,3,4,5 sum = 15
6 consecutive integers 0,1,2,3,4,5 sum= 15

5 consecutive integers -1, -2, 0, 1, 2
7 consecutive integers -3, -2, -1, 0, 1, 2, 3 else sum can,t be equal

IMO B is the answer. please RON guid me if I m wrong

"the sum of these two sets(sets of consecutive integers) will be equal only when the sum is zero. " is incorrect.
Ex: Set S could be 5,6,7,8 & 9 while Set T could be 2,3,4,5.6.7 & 8 and these sets have equal sums.
There are umpteen other examples.

"the sum of these two sets(sets of consecutive integers) will be equal only when the sum is zero. " is incorrect.
Ex: Set S could be 5,6,7,8 & 9 while Set T could be 2,3,4,5.6.7 & 8 and these sets have equal sums.
There are umpteen other examples.[/quote]

thanx a lot shaji

A) INSUFFICIENT because it mentions nothing about Set T

The median of Set S = S + 2
The median of Set T = T + 3

Does S + 2 = T + 3?
---or---
Does S = T + 1?

B) Says that: 5S + 10 = 7T + 21

5S = 7T + 1

You can put S = 3 T= 2 TEST S= T + 1 YES

You can put S = -4 T=-3 TEST S = T - 1 NO

INSUFFICIENT

RON UR EXPLANATION SEEMS TO BE INCORRECT....?

This is how I viewed this problem:

S = {n-2, n-1, n, n+1, n+2}
T = {m-3, m-2, m-1, m, m+1, m+2, m+3}

Based on this, Median/Mean of S = n, Median/Mean of T = m
From given Statement 2) the sum of each set is the same, hence m = n (because n-2+n-1+n+n+1+n+2 = n and same for m)

Answer is B.

-Raj

whoa there

actually, (n - 2) + (n - 1) + (n) + (n + 1) + (n + 2) = 5n, not just n.
the n's are all like terms, but you actually have to add them up!

same goes for the m's, which will give you 7m (not just m).

you are correct, though, that the numbers (-2, -1, 0, 1, 2) cancel.

Another way of solving this::==>

Let S consist of x,x+1,x+2,x+3 & x+4 integers
& T consist of y,y+1,y+2,y+3, y+4, y+5 & y+6 integers.

Now median for S = x+2
& for T = y+3.

Ques asked is :=> are they equal i.e is x+2 = y+3 ?
in other words is x-y = 1 ??

1.
Now St 1 tells us:
x+2 = 0 or x = -2.
So, nos are -2,-1,0,1 & 2.

But it tells nothing about y. So cant say if x-y = 1.
Hence Insufficient.

2.
Now St 2 says that
5x + 10 = 7y + 21
=> 5x-7y = 11
Hence cant say if x-y = 1.

3.
Now when both the statements are combined we get:
5x + 10 = 7y + 21
=> 5(x+2) = 7(y+3)
but x+2 =0
=> 0 = 7(y+3)
=> y=-3.
So now x-y = -2-(-3) = 1

hence option C is the right one!!

No need to go for such big equation you will definitely make mistake, remember the GMAT pressure :)

What i will say is just remember the basic fundas of mean and median, as Ron already explained, i will just try to say same thing in my own words:

Question says: S & T are sets having consecutive number
we have to say Yes/No whether Median of S = median of T

Choice 1 : Median of S = 0, this does not talk about set T median, so we can straight away say INSUFFICIENT, Now lets validate for whether BC or E

Choice 2: Sum of number of S = Sum of numbers of T, so what comes in your mind (remember consecutive series)

(a) set T may be composed of smaller number but their sum will be equal to set T

(b) both of the set consist of negative or positive number (although thinking this is a little hard while giving exam but just thought about option 1 u will have this thought automatically)

again we can say this option is INSUFFICIENT, now we have to make a choice between C & E

option 1 says, median of set S is 0, something similar is said in option 2 ( X/2 =0 is similar to X = 0 ), now if both the term has same sum then sum of all number of set T is also zero

so we can easily make out that both the options can answer the equation

Answer choice C is correct

well written.

great explanation!

good to see you guys helping each other out.