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Math Expert V
Joined: 02 Sep 2009
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7 00:00

Difficulty:   45% (medium)

Question Stats: 58% (01:00) correct 42% (01:00) wrong based on 268 sessions

### HideShow timer Statistics 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

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Math Expert V
Joined: 02 Sep 2009
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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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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?
Math Expert V
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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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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
Math Expert V
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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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What if all the elements of the Set are 0? Then the answer would be E. 0 is a positive number.
Math Expert V
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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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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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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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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.
Math Expert V
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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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+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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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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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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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 Intern  S
Joined: 12 Jun 2017
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Hello,

"Set T was derived from set S when all elements of set S"

I am not able to understand what does "when all the elements are multiplied by 2"?
IIMA, IIMC School Moderator V
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unbroken

Quote:
"Set T was derived from set S when all elements of set S"

I am not able to understand what does "when all the elements are multiplied by 2"?

Set S {1,2,3} or Set S {-2,-1, -4}

Set T {2.4.6} or Set T {-4, -2 , -8} (multiply above set by 2 in both cases)

Q asks: Is median ( middle no) of set T greater than S?

St 1: If all numbers in set S are positive, then when we multiply a positive no by 2 we get larger number. Suff

St 2: Directly gives us that median of Set S is positive, Using same logic as above, Suff

Hope this helps.
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Hi Brunel,

I'm trying to comprehend s2:
Consider S = {-3, -2, 3, 10}; median= 1
T = {-6, -4, 6, 20}, satisfying s2; median is still 1.

Wouldnt this make s2 inconclusive?

Thanks.
Math Expert V
Joined: 02 Sep 2009
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thoomba wrote:
Hi Brunel,

I'm trying to comprehend s2:
Consider S = {-3, -2, 3, 10}; median= 1
T = {-6, -4, 6, 20}, satisfying s2; median is still 1.

Wouldnt this make s2 inconclusive?

Thanks.

The median of S in your example, is (-2 + 3)/2 = 1/2, not 1.
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