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A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If

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udaymathapati
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A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink] New post   23 Sep 2010, 11:45
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A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x?

A. 16
B. 15
C. 14
D. 13
E. 12

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Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink] New post   23 Sep 2010, 11:56
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A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x?

A. 16
B. 15
C. 14
D. 13
E. 12

{4, 5, 6, 8, 10, x}

Median would be the average of two middle terms --> \(median=\frac{6+8}{2}=7\);
\(mean=\frac{4+5+6+8+10+x}{6}=\frac{33+x}{6}\);

Given: \(median=\frac{6}{7}*mean\) --> \(7=\frac{6}{7}*\frac{33+x}{6}\) --> \(x=16\).

Answer: A.
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A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink] New post   23 Jul 2016, 00:53
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udaymathapati wrote:
A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x?

A. 16
B. 15
C. 14
D. 13
E. 12

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Image1.JPG


Median of a set with even # of terms = Average of the middle two terms = \(\frac{(6+8)}{2} --->\frac{14}{2} ---> 7\)
Median is 7 ; Mean = \(\frac{(4+5+6+8+10+x)}{6}\)

Given that Median = \(\frac{6}{7}\) of Mean

Median =\(\frac{6}{7}* \frac{(4+5+6+8+10+x)}{6}\)

\(7 = \frac{6}{7}* \frac{(4+5+6+8+10+x)}{6}\)

\(7=\frac{6}{7} * \frac{(33+x)}{6}\)

\(49=33+x\)

\(x=49-33\)\(x=16\)

ANSWER IS A
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Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink] New post   24 Sep 2010, 00:20
4, 5, 6, 8, 10 and x => median is : (6+8)/2 = 7
mean is = (4+5+6+8+10+x)/6 = (33+x)/6
since the median is 6/7 times of mean ==> 7= 6/7(33+x)/6 ==> 16
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Re: A list of measurements in increasing order is 4,5,6,8,10,x. If the med [#permalink] New post   20 Jul 2016, 01:49
bimalr9 wrote:
A list of measurements in increasing order is 4,5,6,8,10,x. If the median of these measurements is 6/7 times their arithmetic mean, What is the value of x?

A.16
B.15
C.14
D.13
E.12

This question was locked.


Given a list of measurements in increasing order is 4,5,6,8,10,x and then x is the greatest number in the list.

Median = (6+8)/2 ( since is even number of series)

AM = mean=(4+5+6+8+10+x)/6 = (33+x)/6

{(33+x) /6 }*6/7 =7

x=49-33=16.

Correction option is A.
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Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink] New post   26 Sep 2017, 16:34
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udaymathapati wrote:
A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If the median of these measurements is 6/7 times their arithmetic mean, what is the value of x?

A. 16
B. 15
C. 14
D. 13
E. 12


We are given the following measurements in increasing order:

4, 5, 6, 8, 10, x

Let’s first calculate the mean:

average = sum/quantity

avg = (4 + 5 + 6 + 8 + 10 + x)/6

avg = (33 + x)/6

We also know that the median of the set is (6 + 8)/2 = 14/2 = 7

Since the the median of these measurements is 6/7 times the arithmetic mean, we can create the following equation:

(6/7)*[(33 + x)/6] = 7

6*(33 + x)/6 = 49

33 + x = 49

x = 16

Answer: A
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Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink] New post   20 Jun 2021, 17:42
Median you can figure out right away (remember, the values given are sorted).
So the median is 7.
We are told that median = (6/7) * mean
7 = (6/7) * mean
mean = 49/6

We also know that (4 + 5 + 6 + 8 +10 + x)/6 = mean
So, (33 + x) / 6 = 49/6
33 + x = 49
and finally, x = 49 - 33 = 16
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Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink] New post   03 Jul 2023, 06:25
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Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If [#permalink]
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