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Manager  Joined: 02 Dec 2012
Posts: 173
If the median of the numbers in list I above is equal to the  [#permalink]

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3
1
6 00:00

Difficulty:   5% (low)

Question Stats: 92% (00:39) correct 8% (01:10) wrong based on 954 sessions

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List I: 3, 6, 8, 19
List II: x, 3, 6, 8, 19

If the median of the numbers in list I above is equal to the median of the numbers in list II above, what is the value of x?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10
Math Expert V
Joined: 02 Sep 2009
Posts: 60555
Re: If the median of the numbers in list I above is equal to the  [#permalink]

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2
1
List I: 3, 6, 8, 19
List II: x, 3, 6, 8, 19

If the median of the numbers in list I above is equal to the median of the numbers in list II above, what is the value of x?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

List I has even number of terms, thus its median is the average of two middle terms (when arranged in ascending/descending order), so median=(6+8)/2=7.

List II has odd number of terms, thus its median is the middle term (when arranged in ascending/descending order). As no other number in the list equal to 7, then x=7.

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Manager  Joined: 07 Apr 2014
Posts: 98
Re: If the median of the numbers in list I above is equal to the  [#permalink]

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List I: 3, 6, 8, 19
List II: x, 3, 6, 8, 19

If the median of the numbers in list I above is equal to the median of the numbers in list II above, what is the value of x?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

median of first set = 6+8 = 14/2 =7

since 2nd set has 5 values, middle value should be median. so x should be 7
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If the median of the numbers in list I above is equal to the  [#permalink]

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2
Median of List I = 7

List II I exactly list I with the addition of "x"

Median of List I = Median of List II

So, x = 7

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Re: If the median of the numbers in list I above is equal to the  [#permalink]

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Attached is a visual that should help
Attachments Screen Shot 2016-05-25 at 9.41.48 PM.png [ 96.51 KiB | Viewed 11652 times ]

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Re: If the median of the numbers in list I above is equal to the  [#permalink]

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List I: 3, 6, 8, 19
List II: x, 3, 6, 8, 19

If the median of the numbers in list I above is equal to the median of the numbers in list II above, what is the value of x?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

We start by calculating the median of the numbers of list I: 3, 6, 8, 19. We see that the numbers in the list are in order already and, since we have an even number of numbers, the median is the average of the two middle numbers.

median = (6 + 8)/2

median = 14/2

median = 7

The median of list I is 7.

Looking at list II: x, 3, 6, 8, 19, we see that we have an odd number of terms. Thus, when the list is ordered from least to greatest the median must be the middle term. Since the medians of the two lists must be equal, we know that the median of list II must be 7 and therefore x is 7.

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Director  G
Joined: 02 Sep 2016
Posts: 638
Re: If the median of the numbers in list I above is equal to the  [#permalink]

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List I: 3, 6, 8, 19
List II: x, 3, 6, 8, 19

If the median of the numbers in list I above is equal to the median of the numbers in list II above, what is the value of x?

(A) 6
(B) 7
(C) 8
(D) 9
(E) 10

Median of list I is: (6+8)/2= 7

In list II, there is no 7. Therefore x=7.
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Joined: 14 May 2016
Posts: 17
Re: If the median of the numbers in list I above is equal to the  [#permalink]

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List I [3,6,8,19]
List II [x,3,6,8,19]

the median from list I: since list I only contains 4 numbers then you need to sum the two numbers in the middle and divided by 2. Therefore (6+8)/2=7. OK, now that you have list I median then the questions is saying median from list I = median list II. Let's check list II, the middle number in list II is 6 ---> since there are 5 numbers in list II and the middle number is 6. It's time to put it together since question is saying 7 = 6, but you have an "x" in list II, then you need to add the "x" to the 6. Then we have 7 = 6 + x and solving this equation we have x = 7 - 6 or x = 1. Now you substitute the value of x in the equation 7 = 6 + 1 which you are left with 7 = 7. Hence answer is "B"
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Re: If the median of the numbers in list I above is equal to the  [#permalink]

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Hi All,

We're told that the MEDIAN of both lists is the same, so we have to find the exact value of X that will make the median of List II equal the median of List I.

Since List I has 4 values, the median is equal to the average of the two "middle terms"; here, that is (6+8)/2 = 7.
In List II, the median will be the 3rd value (from least to greatest); that means that X must equal 7.

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Re: If the median of the numbers in list I above is equal to the  [#permalink]

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