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.
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