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Mean Median

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Source: — Problem Solving |

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by Mike@Magoosh » Sun Sep 30, 2012 7:21 pm
avada wrote:From OG practice

A list of measurements in increasing order is 4 5 6 8 10 and x. if the median of these measurements is 6/7 of the mean what is the value of x?
16
15
14
13
12
OG: 16
Hi, there. I'm happy to help with this. :-)

Determining the median would be difficult if we knew nothing about x. Fortunately, all of the answer choices are more than 10, so whatever the value of x, it must be the highest value in the set. The set in order is: 4, 5, 6, 8, 10, x.

The median is the average of the middle two numbers ---- median = 7

This median, 7, is, is 6/7 of the mean.
median = (6/7)*(mean)
7 = (6/7)*(mean)
mean = (7/6)*7 = 49/6

If the mean is 49/6, and there are six numbers, this means the sum of the numbers must be 49.

4 + 5 + 6 + 8 + 10 + x = 49

4 + 5 + 6 + 8 + x = 39

5 + 8 + x = 29

5 + x = 21

x = 16

Answer = A

You may find this blog post helpful.
https://magoosh.com/gmat/2012/gmat-avera ... -formulas/

Does all this make sense? Let me know if you have any further questions.

Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
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by GMATGuruNY » Sun Sep 30, 2012 7:24 pm
avada wrote:From OG practice

A list of measurements in increasing order is 4 5 6 8 10 and x. if the median of these measurements is 6/7 of the mean what is the value of x?
16
15
14
13
12

OG: 16
Mean = sum/number.
Thus, the mean = (4+5+6+8+10+x)/6 = (33+x)/6.

The median = the average of the 2 middle numbers = (6+8)/2 = 7.

Since the median is equal to 6/7 of the mean, we get:
7 = (6/7) * (33+x)/6
7 = (33+x)/7
49 = 33+x
x = 16.

The correct answer is A.
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