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Sets of consecutive numbers

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Sets of consecutive numbers [#permalink] New post 04 Dec 2011, 08:29
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Question Stats:

0% (00:00) correct 100% (00:19) wrong based on 2 sessions
Set X consists of seven consecutive integers, and set Y consists
of nine consecutive integers. Is the median of the numbers in
set X equal to the median of the numbers in set Y ?

(1) The sum of the numbers in set X is equal to the sum of
the numbers in set Y.
(2) The median of the numbers in set Y is 0.
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Re: Sets of consecutive numbers [#permalink] New post 04 Dec 2011, 09:05
Statement 2: Does not talk about Set X: Not Sufficient
Statement 1: I see only one possibility for set X and Y
X= {-3,-2,-1,0,1,2,3}
Y={-4,-3,-2,-1,0,1,2,3, 4}
0 being the median for both. Sufficient
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Re: Sets of consecutive numbers [#permalink] New post 04 Dec 2011, 10:07
dreambeliever wrote:
Set X consists of seven consecutive integers, and set Y consists
of nine consecutive integers. Is the median of the numbers in
set X equal to the median of the numbers in set Y ?

(1) The sum of the numbers in set X is equal to the sum of
the numbers in set Y.
(2) The median of the numbers in set Y is 0.


1- Insufficient

There are 7 consecutive integers in X. Lets say the smallest x. The others will be x+1...x+6
There are 9 consecutive integers in Y. Lets say the smallest y. The others will be y+1...y+8

Sum of X = 7x+21= 7.(x+3)
Sum of Y = 9y+36 =9.(y+4)

if Sum of X = Sum of Y then makes 7(x+3)=9(y+4)..................(1)
median of X = x+3
median of Y = y+4

if median of X = median of Y then 7(x+3) must be equal to 9 (x+3) it is possible in only one case that is x=-3.

So we do not infer from this statement that median of x is equal to median of y.

2) we do not know anything about X

getting them together
we see that y+4= 0, so y = -4
and total of them are 0
and if total of X = 0 and X consists of 7 consequtive integers, X must be -3,..0,..3
So medians are equal

D
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Re: Sets of consecutive numbers [#permalink] New post 04 Dec 2011, 10:35
thanks guys!
Ans = b
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Re: Sets of consecutive numbers [#permalink] New post 04 Dec 2011, 11:09
dreambeliever wrote:
thanks guys!
Ans = b


Please recheck and confirm. The answer must be C.

Let set X be (a-3,a-2,......a+3) and set Y be (b-4,b-3,....b+4)
S1:The sum of the numbers in set X is equal to the sum of
the numbers in set Y.

So we have 7a = 9b. Now this is possible if
a=b=0 or if a=9 and b=7. Insufficient. Median may be same or different.

S2: The median of the numbers in set Y is 0. i.e b=0. We do not have any data on the set X. Hence Median may be same or different.

S1 and S2: Sufficient. a=b=0 Median are same sufficient.
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Re: Sets of consecutive numbers [#permalink] New post 04 Dec 2011, 13:03
I think C is the answer

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Re: Sets of consecutive numbers [#permalink] New post 04 Dec 2011, 16:52
My answer is C.
I was freaking out while scrolling down this thread....B, B and than OA was C..I was relieved.

Cheers!
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Re: Sets of consecutive numbers [#permalink] New post 04 Dec 2011, 23:31
Is using Algebra is the best way to deal with SET problem? i was using picking number and had tough to find sets for which the sum is equal (for this problem).
Experts: any specific guidelines for this sort of set problem?
Re: Sets of consecutive numbers   [#permalink] 04 Dec 2011, 23:31
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