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Problem Solving — algebra and arithmetic
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by chacha0212 » Thu Dec 04, 2014 5:19 pm
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
d. 12
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by MartyMurray » Thu Dec 04, 2014 5:52 pm
chacha0212 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
d. 12
There is an even number of elements in the set. So the median of the set is the mean of the two middle elements.

The two middle elements are 6 and 8. So the median is (6+8)/2 = 7

Since there are six elements, the mean, m, of the set is 1/6 of the total of all the elements, t.

m = t/6 and 6m = t

From the prompt we already know that the median, 7, is 6/7 of the mean. So 7 = (6/7)m = 6m/7

Substitute t for 6m and we get 7 = t/7

Multiply both sides by 7 to get 49 = t

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

33 + x = 49

x = 16

Choose A.
Last edited by MartyMurray on Thu Dec 04, 2014 6:05 pm, edited 3 times in total.
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by [email protected] » Thu Dec 04, 2014 5:59 pm
Hi chacha0212,

Marty Murray's math is correct except for the last step:

33 + X = 49

X = 16 (not 12)

This goes to show how important attention-to-detail can be, even in the last steps of a question.

Final Answer: A

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by MartyMurray » Thu Dec 04, 2014 6:10 pm
[email protected] wrote:Hi chacha0212,

Marty Murray's math is correct except for the last step:

33 + X = 49

X = 16 (not 12)

This goes to show how important attention-to-detail can be, even in the last steps of a question.

Final Answer: A
Indeed, attention to detail is so important. :o

I edited it so future readers will not be led astray.
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by Scott@TargetTestPrep » Fri Jan 05, 2018 6:24 am
chacha0212 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
d. 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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by mbawisdom » Thu Mar 01, 2018 7:38 am
chacha0212 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
d. 12
Set has 6 elements and since they are in increasing order the median is the average of the third and fourth element. Median = (6+8)/2 = 7.

From the information in the question:
Median = (6/7)*Mean
7 = (6/7)*Mean
Mean = 49/6

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

From above: 49/6 = (33+x)/6
49 = 33+x
x = 16

Answer is (A) 16
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