Set X consists of seven consecutive integers, and Set Y consists of

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.

In retaltion to the clue (1), I have the following doubt:
Algebraicaly, we can express the question in this way:
\(X = {x, x+1, x+2,...x+6}\)
\(Y = {y, y+1, y+2,...., y+8}\)
Being x and y integers.

Based on the clue (1) that the sum of the numbers in set X is equal to the sum of the numbers in set Y, we can say:

\(7x + 21 = 9y + 36\)
\(7x - 9y = 15\)

Picking numbers I have found two possible combinations:
x = -3 and y = -4, which means YES to the question.
x = -12 and y = -11, which means NO to the question.

Is there a faster way to solve it?

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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.

Quite tricky question.
In such questions i try to answer YES or NO precisely by using the info from one of the statements. Lets try YES - two medians are equal, considering that both sets consists of consequtive integers, this to happen all number of set X should be within the set Y and then the mid number will be the same. Since there are no restrictions lets take numbers from 1 to 7 for set X and 1 to 9 for set Y - mid muber is 5.

Statement 1) from the first glance this condition does not fit into our sets from 1 to 9 and 1 to 7. So this statemnt seems sufficient, and i am about to say that possible answer for this question is either A or D. But then i am looking at the statement 2.

Statement 2) sometimes it helps to look at both statements before making any kind of conclusion because in real GMAT questions both statements never contradict each other, and by knowing more information it is easier to make final conclusion. In this qestion i forgot to consider that negative numbers also could be within the sets. This statement tells us about set y only, no info about set X - not sufficient.

Combining both statements: from st.1 we see that sum of set Y is 0, by st.1 we see that the sum of the set X also should be 0. This is only possible if the middle number of the set X is 0.

Answer is C

we can get the answer:

the first number of set x is x, then the the median is x+4

the first number of set y is y, then the median is y+5

so when x-y=1, the medians are equal

the question is asking: is x-y=1?

(1) the sum of set x is 7(x+3) and of set y is 9(y+4)

so 7x-9y=15

insufficient, because

you can solve the equation:

7x-9y=15
x-y=1

then you get:

when x=-3, y=-4, the medians are equal, otherwise not

(2) y=-5

nothing to do with x, insufficient

(1)(2)

from one we know when y=-4, the medians equal, so

sufficient

My way of solving

X = a, a+1, a+2...a+6
Y = p, p+1, .........p+9

To find Med X = Med Y ?

S-1) a+21 = p+36, So a = p+15.
a = -10 then p =-25
a = -1 then p =14. Many such scenarios leads to nothing. Not sufficient

S-2) -4,-3,-2,-1,0,1,2,3,4. Median = 0 and Sum = 0. Not sufficient as no info for X.

S-T) Since from S-1 sum X = sum Y means X = -3,-2,-1,0, 1,2,3. Yes Median will be same as Sum = Median = 0

let's A is the media of X, and B is the median of Y => 7A= 9B => A > B or A=B= 0

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.

Okay so I have a better approach
If sum in set X=sum in set Y
therefore mean of X cannot be equal to mean of Y as total number of elements are different EXCEPT IF THE SUM ITSELF IS 0!
so we dont know that : insufficient
b-> median of Y is zero therefore mean of Y is zero therefore sum of Y is zero and well thats it still not sufficient

A+B
Aaaha so if i know sum of Y is zero and its equal to X
I can be sure as hell that median = mean = 0 and hence they are equal and C is OA

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