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M19-23

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Bunuel
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M19-23 [#permalink] New post   16 Sep 2014, 01:06
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If set \(T\) is obtained by multiplying every elements of set \(S\) 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.
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Bunuel
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Re M19-23 [#permalink] New post   16 Sep 2014, 01:06
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If set \(T\) is obtained by multiplying every element of set \(S\) by 2, is the median of set \(T\) greater than that of set \(S\) ?

The median of a set is either the middle term or the average of two middle terms of the set, when the terms are arranged in ascending or descending order. This implies that when all elements of a set are multiplied by 2, its median is also multiplied by 2.

Consider three cases:

• If the median of \(S\) is negative, the media of \(T\) will be less than that of \(S\). For example, if the median of \(S\) is -10, the median of \(T\) will be -20, and hence less than that of \(S\).

• If the median of \(S\) is 0, the media of \(T\) will also be 0, and the medians will be equal.

• If the median of \(S\) is positive, the media of \(T\) will be greater than that of \(S\). For example, if the median of \(S\) is 10, the median of \(T\) will be 20, and hence greater than that of \(S\).

(1) All elements of set \(S\) are positive. This implies that the median of set \(S\) is positive. Therefore, the median of \(T\) is greater than that of \(S\). Sufficient.

(2) The median of set \(S\) is positive. As discussed earlier, this means that the median of \(T\) is greater than that of \(S\). Sufficient.


Answer: D
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Re: M19-23 [#permalink] New post   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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Re: M19-23 [#permalink] New post   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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Re: M19-23 [#permalink] New post   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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Re: M19-23 [#permalink] New post   02 Nov 2016, 10:55
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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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Re: M19-23 [#permalink] New post   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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Bunuel
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Re: M19-23 [#permalink] New post   09 Dec 2016, 02:24
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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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Re: M19-23 [#permalink] New post   23 Aug 2017, 06:51
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.
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Bunuel
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Re: M19-23 [#permalink] New post   23 Aug 2017, 07:04
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adil123 wrote:
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}.
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Re: M19-23 [#permalink] New post   08 Jun 2020, 04:21
I think this is a high-quality question and I agree with explanation.
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Bunuel
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Re: M19-23 [#permalink] New post   26 Feb 2023, 13:13
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I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.
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Re: M19-23 [#permalink]
26 Feb 2023, 13:13
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