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If set T was derived from set S when all elements of set S w

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dennis14
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If set T was derived from set S when all elements of set S w [#permalink] New post   Updated on: 26 Feb 2023, 13:15
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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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D

Originally posted by dennis14 on 18 Mar 2014, 03:30.
Last edited by Bunuel on 26 Feb 2023, 13:15, edited 2 times in total.
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   18 Mar 2014, 03:32
What i would like to know in this question is that why cant we assume the set to be with only 1 element == { 0 } ??
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   18 Mar 2014, 05:22
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dennis14 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

What i would like to know in this question is that why cant we assume the set to be with only 1 element == { 0 } ??


Because 0 is not a positive number, it's neither positive nor negative.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rule 3. Thank you.
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   18 Jun 2016, 05:02
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Hi Bunuel,

My doubt here is the word derived. Does it mean the number of elements in both the sets are equal.

I have solved the questions as below: Combining A + B

1st case
S = { 1 2 3 8 9 11 19} Median = 8
T = { 2 4 } Median = 3
M(T) < M(S)

2nd case
S = { 1, 2, 3, 8, 9, 11, 19} Median = 8
T = { 2, 4, 9, 64, 81,121,361} Median = 64
M(T) > M(S)

Both the cases are possible - Hence E
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   19 Jun 2016, 09:26
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divyaverma wrote:
Hi Bunuel,

My doubt here is the word derived. Does it mean the number of elements in both the sets are equal.

I have solved the questions as below: Combining A + B

1st case
S = { 1 2 3 8 9 11 19} Median = 8
T = { 2 4 } Median = 3
M(T) < M(S)

2nd case
S = { 1, 2, 3, 8, 9, 11, 19} Median = 8
T = { 2, 4, 9, 64, 81,121,361} Median = 64
M(T) > M(S)

Both the cases are possible - Hence E


Set T was derived from set S when all elements of set S were multiplied by 2, so the number of elements in T and S are the same.
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   23 Aug 2016, 03:16
Here is my approach on this one =>let Median of set S be s and Median of set T be t
We need to see whether t>s or not
Statement one => all elements of set S are positive hence the elements of T set are also positive ans are twice as elements of set S
So the median would e twice hence => t=2s or t>s
=> suff

Statement 2=> Median of set S is positive so the median of set T would be just the twice and positive too=>t=2s=> suff
hence suff
SMASH that D
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   02 Feb 2018, 06:30
FieryLeo wrote:
Hi Bunuel,

My doubt here is the word derived. Does it mean the number of elements in both the sets are equal.

I have solved the questions as below: Combining A + B

1st case
S = { 1 2 3 8 9 11 19} Median = 8
T = { 2 4 } Median = 3
M(T) < M(S)

2nd case
S = { 1, 2, 3, 8, 9, 11, 19} Median = 8
T = { 2, 4, 9, 64, 81,121,361} Median = 64
M(T) > M(S)

Both the cases are possible - Hence E


I fell in the same trap as you. When a set is derived from another set, I thought the new set need not have the same number of elements as the original set. I too got E.
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   02 Feb 2018, 07:12
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Verb (used without object), derived, deriving = to come from a source or origin; originate (often followed by from).
How can I know that the elements in set T are in the same number of set S?

S = [4,6,8,10]
T = [1,8,5,12,16,20]

I think that for the question to be without flaws this difference should be pointed out :-)
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   02 Feb 2018, 10:56
MvArrow wrote:
Verb (used without object), derived, deriving = to come from a source or origin; originate (often followed by from).
How can I know that the elements in set T are in the same number of set S?

S = [4,6,8,10]
T = [1,8,5,12,16,20]

I think that for the question to be without flaws this difference should be pointed out :-)


Hi

I think when it says 'Set T was derived from set S when all elements of set S were multiplied by 2', isn't it perfectly clear that we just have to double every element of set S to form set T, and not to do anything else?
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   03 Feb 2018, 03:38
dennis14 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

M19-23



Let Set S = {1,2,3,4,500,1000,2000}

Now Set T can only be derived when set S is multiplied by 2

so , Set S will be {2,4,6,8,1000,2000,4000} [BUT THIS IS NOT ACTUAL SET S]

and
LET Set T can be

1) {2,4,6}

Hence here Median of set T < Median of set S

2) LET set T can be

{4,2000,4000}

Hence here Median of set T > Median of set S


Its not certain that if Median of T > or < than that of S....


Is the question flawed?
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   03 Feb 2018, 05:01
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rocko911 wrote:
dennis14 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

M19-23



Let Set S = {1,2,3,4,500,1000,2000}

Now Set T can only be derived when set S is multiplied by 2

so , Set S will be {2,4,6,8,1000,2000,4000} [BUT THIS IS NOT ACTUAL SET S]

and
LET Set T can be

1) {2,4,6}

Hence here Median of set T < Median of set S

2) LET set T can be

{4,2000,4000}

Hence here Median of set T > Median of set S


Its not certain that if Median of T > or < than that of S....


Is the question flawed?


Set S and set T contain equal number of elements. To get set T you multiply EACH element in S by 2.
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Re: If set T was derived from set S when all elements of set S w [#permalink] New post   26 Feb 2023, 13:15
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dennis14 wrote:
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.


Official Solution:


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: If set T was derived from set S when all elements of set S w [#permalink]
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