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chacha0212: Junior | Next Rank: 30 Posts; Posts: 16; Joined: Tue Sep 09, 2014 1:05 pmFollowed by: 1 member

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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Source: Beat The GMAT — Quantitative Reasoning | Thu Dec 04, 2014 5:19 pm

MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

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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[email protected]: Elite Legendary Member; Posts: 10392; Joined: Sun Jun 23, 2013 6:38 pmFollowed by: 511 members; Location: Palo Alto, CA; Thanked: 2867 times; GMAT Score:800

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

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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MartyMurray: Legendary Member; Posts: 2135; Joined: Mon Feb 03, 2014 9:26 amFollowed by: 140 members; Location: https://martymurraycoaching.com/; Thanked: 955 times; GMAT Score:800

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.

I edited it so future readers will not be led astray.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8142; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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

Scott Woodbury-Stewart
Founder and CEO
[email protected]

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

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mbawisdom: Senior | Next Rank: 100 Posts; Posts: 94; Joined: Tue Dec 16, 2014 9:50 amFollowed by: 4 members; Location: London, UK; Thanked: 2 times; GMAT Score:770

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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