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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If

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Manager  Joined: 06 Apr 2010
Posts: 102
A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 78% (01:54) correct 22% (02:34) wrong based on 323 sessions

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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

Attachment: Image1.JPG [ 8.42 KiB | Viewed 10307 times ]
Math Expert V
Joined: 02 Sep 2009
Posts: 59588
Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If  [#permalink]

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

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Manager  Joined: 25 Aug 2010
Posts: 54
Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If  [#permalink]

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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
Retired Moderator G
Joined: 26 Nov 2012
Posts: 554
Re: A list of measurements in increasing order is 4,5,6,8,10,x. If the med  [#permalink]

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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.
Director  B
Joined: 04 Jun 2016
Posts: 547
GMAT 1: 750 Q49 V43 A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If  [#permalink]

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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

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

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

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

$$49=33+x$$

$$x=49-33$$$$x=16$$

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Target Test Prep Representative G
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2809
Re: A list of measurements in increasing order is 4, 5, 6, 8, 10 and x. If  [#permalink]

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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

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Re: A list of measurements in increasing order is 4,5,6,8,10 and  [#permalink]

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_________________ Re: A list of measurements in increasing order is 4,5,6,8,10 and   [#permalink] 08 Oct 2019, 04:35
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