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If set \(T\) was derived from set \(S\) when all elements of set \(S\) were multiplied by 2, is the median of set \(T\) greater than that of set \(S\)?

The median of a set is either an element from the set or the average of two elements from the set. This means that if all elements of the set are multiplied by 2, its median will also be multiplied by 2.

Statement (1) by itself is sufficient. The median of set \(S\) is positive. Thus, the median of set \(T\) is greater than that of set \(S\).

Statement (2) by itself is sufficient. The median of set \(S\) is positive. Thus, the median of set \(T\) is greater than that of set \(S\).

What if the elements are Fractions? the statement does not say that the numbers are integers, for example if Set S is (1/4, 1/3 and 1/2) then if you multiply all elements by 2 then the new set would be (1/8, 1/6 and 1/4) thus the median would not be greater in any of the 2 statements. hat am I not seeing?

What if the elements are Fractions? the statement does not say that the numbers are integers, for example if Set S is (1/4, 1/3 and 1/2) then if you multiply all elements by 2 then the new set would be (1/8, 1/6 and 1/4) thus the median would not be greater in any of the 2 statements. hat am I not seeing?

Even your example gives the same YES answer: the median of set T is greater than that of set S.
_________________

In my example Median of SET S is 1/3 and after multiplying by 2 then the median of SET T is 1/6 which is less than 1/3. Sorry for insisting maybe there is still something I am not seeing

In my example Median of SET S is 1/3 and after multiplying by 2 then the median of SET T is 1/6 which is less than 1/3. Sorry for insisting maybe there is still something I am not seeing

No.

The median of S = {1/4, 1/3, 1/2} is 1/3. The median of T = {1/2, 2/3, 1} is 2/3.

The median of a set is either an element from the set or the average of two elements from the set. This means that if all elements of the set are multiplied by 2, its median will also be multiplied by 2.

Statement (1) by itself is sufficient. The median of set \(S\) is positive. Thus, the median of set \(T\) is greater than that of set \(S\).

Statement (2) by itself is sufficient. The median of set \(S\) is positive. Thus, the median of set \(T\) is greater than that of set \(S\).

Answer: D

Hi Bunnel I didn't get the solution. Could you please elaborate by taking examples
_________________

You have to have the darkness for the dawn to come.

1. says all elements of set S are positive, So if S = {1, 2, 3, 4, 5.....} then T ={2,4, 6, 8, 10....} here median S<median T (same goes for decimals, and zero is not part of the set. 2 Says median of S is positive so S= {-a,-b, -c, 1, a,b,c} so T becomes {-2a, -2b, -2c, 2, 2a, 2b, 2c} so median of S, median of T
_________________

Sometimes you have to burn yourself to the ground before you can rise like a phoenix from the ashes.

please help bunuel if i take S= 1,2,3,4,5,6,7,8,9 so median of s here is 5 . Now we take T= 1,2,3 so median of t is 2 . so your logic fails here . The answer is D because now we can calibrate which one is greater either S or T, We don't know yet but with D we can calculate that is why I opted for D . I can't get your logic of , the median of set TT is greater than that of set SS. Hope my doubt is clear. Regards.

please help bunuel if i take S= 1,2,3,4,5,6,7,8,9 so median of s here is 5 . Now we take T= 1,2,3 so median of t is 2 . so your logic fails here . The answer is D because now we can calibrate which one is greater either S or T, We don't know yet but with D we can calculate that is why I opted for D . I can't get your logic of , the median of set TT is greater than that of set SS. Hope my doubt is clear. Regards.

Set T was derived from set S when all elements of set S were multiplied by 2. So, if S = {1, 2, 3, 4, 5, 6, 7, 8, 9}, then T = {2, 4, 6, 8, 10, 12, 14, 16, 19}.
_________________

Statement 1 gives us a definite answer. If all entries are positive, an entity multiplied by two will also be positive. Hence statement 1 is sufficient.

Statement 2 : Sufficient. If median of S is positive, median of T will also be positive and greater than that of S. Hence positive.

Both 1 & 2 are sufficient. Hence option D.
_________________

If set \(T\) was derived from set \(S\) when all elements of set \(S\) were multiplied by 2, is the median of set \(T\) greater than that of set \(S\)?

(1) All elements of set \(S\) are positive

(2) The median of set \(S\) is positive

Hi Bunuel, I understand the why Statement 1 is sufficient. But for statement 2 consider the following

S = {-1,-2,1,2,3} and T is derived from S so suppose T = {-4} or {-2} (As 2 X S = {-2,-4,2,4,6}) Then statement 2 is not satisfied. Please let me know if i am missing something?

If set \(T\) was derived from set \(S\) when all elements of set \(S\) were multiplied by 2, is the median of set \(T\) greater than that of set \(S\)?

(1) All elements of set \(S\) are positive

(2) The median of set \(S\) is positive

Hi Bunuel, I understand the why Statement 1 is sufficient. But for statement 2 consider the following

S = {-1,-2,1,2,3} and T is derived from S so suppose T = {-4} or {-2} (As 2 X S = {-2,-4,2,4,6}) Then statement 2 is not satisfied. Please let me know if i am missing something?

Thanks in Advance, Eshwar Nag Lanka

Set T was derived from set S when ALL elements of set S were multiplied by 2.
_________________

If set \(T\) was derived from set \(S\) when all elements of set \(S\) were multiplied by 2, is the median of set \(T\) greater than that of set \(S\)?

(1) All elements of set \(S\) are positive

(2) The median of set \(S\) is positive

Hi Bunuel, I understand the why Statement 1 is sufficient. But for statement 2 consider the following

S = {-1,-2,1,2,3} and T is derived from S so suppose T = {-4} or {-2} (As 2 X S = {-2,-4,2,4,6}) Then statement 2 is not satisfied. Please let me know if i am missing something?

Thanks in Advance, Eshwar Nag Lanka

Set T was derived from set S when ALL elements of set S were multiplied by 2.