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please explain gmat prep question

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by yvonne12 » Sun Apr 01, 2007 3:35 pm

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a list of measurements in increasing order is 4,5,6,8,10, x if the medium of these measurements is 6/7 times their arithmetic mean . what is x?

ans 16

please explain
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by 800GMAT » Sun Apr 01, 2007 3:55 pm
I remember this question. The answer choices, i think, were all greater than 10.

Hence x cannot be the median.

Hence the median is ( 6+8 )/2 = 7

Now, 7 = 6/7 [(4+5+6+8+10+x)/6]

Solving the above equation, you get x = 16
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by Cybermusings » Mon Apr 02, 2007 4:56 am
median of the list = 6+8/2 = 7

Median = 6/7 times the arithmetic mean

7 = 6/7 * Mean

Thus Mean = 7*7/6 = 49/6

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

x = 49 - 33 = 16
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by Jeff@TargetTestPrep » Sun Jun 24, 2018 5:02 pm
yvonne12 wrote:a list of measurements in increasing order is 4,5,6,8,10, x if the medium of these measurements is 6/7 times their arithmetic mean . what is x?
We see that the median is (6 + 8)/2 = 7. Thus we have:

(6/7)(4 + 5 + 6 + 8 + 10 + x)/6 = 7

(4 + 5 + 6 + 8 + 10 + x)/7 = 7

33 + x = 49

x = 16

Answer: 16

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