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If the average (arithmetic mean) of x,(x+6),(x−4),(x+3), and (x+10) is

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If the average (arithmetic mean) of x,(x+6),(x−4),(x+3), and (x+10) is [#permalink]

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New post 09 Apr 2018, 01:51
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If the average (arithmetic mean) of x, (x+6), (x−4), (x+3), and (x+10) is 21, what is the median of those five numbers?

A. 17
B. 18
C. 19
D. 20
E. 21
[Reveal] Spoiler: OA

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If the average (arithmetic mean) of x,(x+6),(x−4),(x+3), and (x+10) is [#permalink]

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New post 09 Apr 2018, 03:27
Bunuel wrote:
If the average (arithmetic mean) of x, (x+6), (x−4), (x+3), and (x+10) is 21, what is the median of those five numbers?

A. 17
B. 18
C. 19
D. 20
E. 21


The sum of the five numbers is 21*5 = 105.
Therefore x, + (x+6), + (x−4), + (x+3), + (x+10) = 5x +15 = 105.
5x= 105-15 = 90
x= 18.
Therefore the five numbers are:
18, 24, 14, 21, 28. The numbers arranged in ascending order are 14, 18, 21, 24 and 28.
Hence the median and answer is 21 or option E.
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Re: If the average (arithmetic mean) of x,(x+6),(x−4),(x+3), and (x+10) is [#permalink]

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New post 09 Apr 2018, 03:42
Ans is E

(x + (x+6) + (x−4) + (x+3) + (x+10))/5 = 21 * 5
5X + 15 = 105,

Solving the equation
X = 18

So the series becomes the following after sorting
14, 18, 21, 24 & 31 respectively.

Hence 21 is the median. Ans E.

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Re: If the average (arithmetic mean) of x,(x+6),(x−4),(x+3), and (x+10) is [#permalink]

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New post 10 Apr 2018, 17:10
Bunuel wrote:
If the average (arithmetic mean) of x, (x+6), (x−4), (x+3), and (x+10) is 21, what is the median of those five numbers?

A. 17
B. 18
C. 19
D. 20
E. 21


Notice that we can arrange the expressions in ascending order of their values as:

x - 4, x, x + 3, x + 6, x + 10

Thus, the median is x + 3. So if we know the value of x, then we can determine the value of median.

To solve for x, we can create the equation:

(x + x + 6 + x - 4 + x + 3 + x + 10)/5 = 21

5x + 15 = 105

5x = 90

x = 18

Thus the median is 18 + 3 = 21.

Answer: E
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Re: If the average (arithmetic mean) of x,(x+6),(x−4),(x+3), and (x+10) is   [#permalink] 10 Apr 2018, 17:10
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