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Set A consists of the numbers {1, 4, 9, 9, 12}. Set B consists of the

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Set A consists of the numbers {1, 4, 9, 9, 12}. Set B consists of the  [#permalink]

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New post 12 Apr 2018, 10:29
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Set A consists of the numbers {1, 4, 9, 9, 12}. Set B consists of the numbers {1, 6, 8, 12}. If Set C is formed by combining Sets A and B, which of the following expressions give the relationship between the medians of sets A, B, and C?

A. B = C and C > A

B. A < B < C

C. B < A < C

D. B < C < A

E. A = C and C > B

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Re: Set A consists of the numbers {1, 4, 9, 9, 12}. Set B consists of the  [#permalink]

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New post 12 Apr 2018, 10:42
Bunuel wrote:
Set A consists of the numbers {1, 4, 9, 9, 12}. Set B consists of the numbers {1, 6, 8, 12}. If Set C is formed by combining Sets A and B, which of the following expressions give the relationship between the medians of sets A, B, and C?

A. B = C and C > A

B. A < B < C

C. B < A < C

D. B < C < A

E. A = C and C > B


A = {1, 4, 9, 9, 12} Median (A) = 9
B = {1, 6, 8, 12} Median (B) = \(\frac{(6+8)}{2} = 7\)

Combining sets is taking the Union. (All elements of both sets form the new set C)

C = {1, 1, 4, 6, 8, 9, 9, 12} Median (C) = 8

Hence Median of : B < C < A

Option (D) is out answer.

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Gladi
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Re: Set A consists of the numbers {1, 4, 9, 9, 12}. Set B consists of the  [#permalink]

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New post 12 Apr 2018, 12:15
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Hey Gladi, wouldn’t median of group C be 7? (6+8)/2?
Thanks in advance! Cheers.


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Set A consists of the numbers {1, 4, 9, 9, 12}. Set B consists of the  [#permalink]

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New post 12 Apr 2018, 12:25
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jayantbakshi wrote:
Hey Gladi, wouldn’t median of group C be 7? (6+8)/2?
Thanks in advance! Cheers.


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Hey jayantbakshi,

The median of a set with odd number of elements is always the middle element. So median of C will be 8 as it is the middle element.

Also C has two 12s instead of one. Which I forgot to outline in my original answer. So..

C={1,1,4,6,8,9,9,12,12}


Now does it make sense?

Best,
Gladi

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Re: Set A consists of the numbers {1, 4, 9, 9, 12}. Set B consists of the  [#permalink]

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New post 12 Apr 2018, 12:28
Gladiator59 wrote:
jayantbakshi wrote:
Hey Gladi, wouldn’t median of group C be 7? (6+8)/2?
Thanks in advance! Cheers.


Sent from my iPhone using GMAT Club Forum


Hey jayantbakshi,

The median of a set with odd number of elements is always the middle element. So median of C will be 8 as it is the middle element.

Does that make sense?

Best,
Gladi

Posted from my mobile device


Hey Gladi, thanks. I think the set C mentioned in your post had only 8 items - guess the number 12 was written only once - so I got confused.
Thanks so much for the explanation, cheers man!


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Re: Set A consists of the numbers {1, 4, 9, 9, 12}. Set B consists of the  [#permalink]

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New post 12 Apr 2018, 21:35
Set A {1, 4, 9, 9, 12} = Median - 9
Set B {1, 6, 8, 12} = Median - 7
Set C {1,1,4,6,8,9,9,12,12} = Median = 8

We get B < C < A

Answer: D
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