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# M19-23

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Math Expert
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16 Sep 2014, 01:06
Expert's post
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Difficulty:

55% (hard)

Question Stats:

55% (00:59) correct 45% (00:53) wrong based on 159 sessions

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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 $$S$$?

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

(2) The median of set $$S$$ is positive
[Reveal] Spoiler: OA

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16 Sep 2014, 01:06
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Official Solution:

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 $$S$$.

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02 Nov 2016, 10:31
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?

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02 Nov 2016, 10:42
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ocolmenares wrote:
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.
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02 Nov 2016, 10:49
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

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02 Nov 2016, 10:55
ocolmenares wrote:
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.

2/3 > 1/3.
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08 Dec 2016, 21:51
What if all the elements of the Set are 0? Then the answer would be E. 0 is a positive number.

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09 Dec 2016, 02:24
dhaariniv wrote:
What if all the elements of the Set are 0? Then the answer would be E. 0 is a positive number.

0 is neither positive nor negative even integer.
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01 Apr 2017, 01:46
Bunuel wrote:
Official Solution:

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 $$S$$.

Hi Bunnel
I didn't get the solution. Could you please elaborate by taking examples
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27 Jul 2017, 20:28
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
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23 Aug 2017, 06:51
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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.

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23 Aug 2017, 07:04
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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}.
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23 Aug 2017, 09:38
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+1 for D.

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.
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28 Aug 2017, 00:11
Bunuel wrote:
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?

Eshwar Nag Lanka

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28 Aug 2017, 02:20
leshwarnag wrote:
Bunuel wrote:
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?

Eshwar Nag Lanka

Set T was derived from set S when ALL elements of set S were multiplied by 2.
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28 Aug 2017, 03:26
Bunuel wrote:
leshwarnag wrote:
Bunuel wrote:
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?

Eshwar Nag Lanka

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

Ohkay... Got it Thanks

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Re: M19-23   [#permalink] 28 Aug 2017, 03:26
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