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Set D is a new set created by combining all the terms of Set

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Set D is a new set created by combining all the terms of Set [#permalink]

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New post 18 Aug 2013, 13:36
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Set D is a new set created by combining all the terms of Sets A, B, and C. No other terms are added to Set D other than those in Sets A, B, and C. What is the median of Set D?

(1) Sets A, B, and C each have a median of 125.
(2) Sets A, B, and C each have the same number of terms.

[Reveal] Spoiler:
I don't know the answer to this, but I think it's E.

Does anyone either know the answer or can explain to me if I am wrong?

Thank you very much.

Note: I haven't a clue as to how to tag this question but it is from the Veritas Prep: X Statistics and Problem Solving book.
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Mar 2014, 04:53, edited 2 times in total.
Added the OA.
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Re: Set D is a new set created by combining all the terms of... [#permalink]

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New post 18 Aug 2013, 14:13
sophietrophy wrote:
Set D is a new set created by combining all the terms of Sets A, B, and C. No other terms are added to Set D other than those in Sets A, B, and C. What is the median of Set D?

(1) Sets A, B, and C each have a median of 125.
(2) Sets A, B, and C each have the same number of terms.

I don't know the answer to this, but I think it's E.

Does anyone either know the answer or can explain to me if I am wrong?

Thank you very much.

Note: I haven't a clue as to how to tag this question but it is from the Veritas Prep: X Statistics and Problem Solving book.




I think answer is A. Try with different pairs and you will always end up with 125.
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Re: Set D is a new set created by combining all the terms of... [#permalink]

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New post 18 Aug 2013, 14:47
BangOn wrote:
sophietrophy wrote:
Set D is a new set created by combining all the terms of Sets A, B, and C. No other terms are added to Set D other than those in Sets A, B, and C. What is the median of Set D?

(1) Sets A, B, and C each have a median of 125.
(2) Sets A, B, and C each have the same number of terms.

I don't know the answer to this, but I think it's E.

Does anyone either know the answer or can explain to me if I am wrong?

Thank you very much.

Note: I haven't a clue as to how to tag this question but it is from the Veritas Prep: X Statistics and Problem Solving book.




I think answer is A. Try with different pairs and you will always end up with 125.


I don't want to presume that it will hold true in every possible scenario. Is there a rule, by any chance, that will make it true?
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Re: Set D is a new set created by combining all the terms of... [#permalink]

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New post 03 Mar 2014, 04:14
i also find A to be inappropriate
for instance:

A 10 20 25 28 32
B 5 10 20 (25) 30 40 50
C 10 25 40

D 5 10 20 25 28 30 32 40 50
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Re: Set D is a new set created by combining all the terms of... [#permalink]

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New post 03 Mar 2014, 04:15
i also find A to be inappropriate
for instance:

A 10 20 25 28 32 (odd)
B 5 10 20 (25) 30 40 50 (even)
C 10 25 40 (odd)

D 5 10 20 25 28 30 32 40 50 (odd)
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Re: Set D is a new set created by combining all the terms of... [#permalink]

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New post 03 Mar 2014, 04:38
darkwraith wrote:
Set D is a new set created by combining all the terms of Sets A, B, and C. No other terms are added to Set D other than those in Sets A, B, and C. What is the median of Set D?

(1) Sets A, B, and C each have a median of 125.
(2) Sets A, B, and C each have the same number of terms.

i also find A to be inappropriate
for instance:

A 10 20 25 28 32
B 5 10 20 (25) 30 40 50
C 10 25 40

D 5 10 20 25 28 30 32 40 50


Set D in this case is {5, 10, 10, 10, 20, 20, 25, 25, 25, 28, 30, 32, 40, 40, 60} --> median=25.
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Re: Set D is a new set created by combining all the terms of... [#permalink]

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New post 03 Mar 2014, 04:54
Bunuel wrote:
darkwraith wrote:
Set D is a new set created by combining all the terms of Sets A, B, and C. No other terms are added to Set D other than those in Sets A, B, and C. What is the median of Set D?

(1) Sets A, B, and C each have a median of 125.
(2) Sets A, B, and C each have the same number of terms.

i also find A to be inappropriate
for instance:

A 10 20 25 28 32
B 5 10 20 (25) 30 40 50
C 10 25 40

D 5 10 20 25 28 30 32 40 50


Set D in this case is {5, 10, 10, 10, 20, 20, 25, 25, 25, 28, 30, 32, 40, 40, 60} --> median=25.


oh now i get it .... i assumed that the numbers that overlapped were only counted once.... thanks :-D
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Re: Set D is a new set created by combining all the terms of Set [#permalink]

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New post 23 Sep 2014, 07:33
I just kind of imagined this in my head and it worked out:

120 121 122 123 124 125 126 127 128 129 130
10 15 20 125 130 133 135
0 125 250


Here we can see that if we add all of the terms together to form one set, there will still be an equal number of terms on each side of 125, and hence 125 is still the median of the new set.

Therefore option 1) is sufficient.

Answer: A
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Re: Set D is a new set created by combining all the terms of Set [#permalink]

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New post 19 Apr 2016, 18:47
1. median is the same for every set. when arranged, the median of all 3 will be 125. A sufficient.
2. alone not sufficient.
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Re: Set D is a new set created by combining all the terms of Set [#permalink]

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New post 05 Jul 2016, 01:33
Case 1 - Assume all sets have odd number of members
Assume Set A - r numbers , 125 , r numbers
Assume Set B - k numbers , 125 , k numbers
Assume Set C - x numbers , 125 , x numbers

Set D - r + k + x numbers , 125, 125, 125, r + k + x => Median = 125

Case 2 - Even members
Assume Set A - r-1 numbers , 125-a,125+a , r-1 numbers
Assume Set B - k-1 numbers , 125-b,125+b , k-1 numbers
Assume Set C - x-1 numbers , 125-c,125+c , x-1 numbers ( e + f = 125 *2)

Set D - r-1 + k -1 + x-1 numbers , mid numbers , r-1 + k -1 + x-1 numbers
now by property that 125-a and 125 +a and others are equidistant from 125 the mid numbers will always arrange such that mid two numbers would be from one set only

median = (125 -a + 125 +a)/2 = 125 ( or same for b , c)


Case 3 - mix of even and odd sets - would play out the same

Other cases -
Re: Set D is a new set created by combining all the terms of Set   [#permalink] 05 Jul 2016, 01:33
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