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median and consecutive integers

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by abhasjha » Thu Nov 21, 2013 8:30 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
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Source: — Data Sufficiency |
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by Uva@90 » Thu Nov 21, 2013 9:14 am
abhasjha 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
Hi Abhasjha,
Statement 1: The median of the numbers in Set S is 0.
Nothing is said about set T. Hence Insufficient.

Statement2: The sum of the numbers in set S is equal to the sum of the numbers in set T

set S have 5 Numbers and
set set T have 7 numbers

Let S = {5,6,7,8,9} :: Sum = 35 => Median is 7
and T = {2,3,4,5,6,7,8} :: Sum = 35 => Median is 5
Hence Insufficient.

Combine 1 and 2:
Median of set S is 0
it should be of S = {-2,-1,0,1,2}
since sum in both set should be same
T = {-3,-2,-1,0,1,2,3}
Now Both set has same median = 0
Hence Sufficient.

Answer is C

Regards,
Uva.
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by GMATGuruNY » Thu Nov 21, 2013 11:09 am
abhasjha 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
For any set of consecutive integers:
Sum = (number of integers)(median).

Let s = the median of Set S and t = the median of set T.
Then:
Sum of the 5 integers in Set S = 5s.
Sum of the 7 integers in Set T = 7t.

Statement 1:
No information about t.
INSUFFICIENT.

Statement 2:
5s = 7t.
It's possible that s=t=0, in which case the medians are equal.
It's possible that s=7 and t=5, in which case the medians are NOT equal.
INSUFFICIENT.

Statements combined:
Since 5s=7t and s=0, we know that s=t=0.
SUFFICIENT.

The correct answer is C.
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by Mathsbuddy » Fri Nov 22, 2013 7:32 am
Once the rock has all dissolved and the mountain is reduced to sand, there will be no slope for a flowing river to exist. So in the river's ultimate victory, both have lost and a draw will prevail (if you ignore the rock called planet Earth, which would otherwise win by its brute magnitude!)
Last edited by Mathsbuddy on Fri Nov 22, 2013 7:45 am, edited 1 time in total.
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by Mathsbuddy » Fri Nov 22, 2013 7:45 am
S = A,B,C,D,E -> median = C
T = F,G,H,I,J,K,L -> median = I

If C = I = 0, then:

F=-3
A=G=-2
B=H=-1
C=I=0
D=J=1
E=K=2
L=3

Sum of S = 0
Sum of T = 0

Therefore it is possible.

Not only that, but S=T=0 has only one solution, therefore YES, the medians are the same.
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