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
This topic has expert replies
- chacha0212
- Junior | Next Rank: 30 Posts
- Posts: 16
- Joined: Tue Sep 09, 2014 1:05 pm
- Followed by:1 members
- MartyMurray
- Legendary Member
- Posts: 2131
- Joined: Mon Feb 03, 2014 9:26 am
- Location: https://martymurraycoaching.com/
- Thanked: 955 times
- Followed by:140 members
- GMAT Score:800
There is an even number of elements in the set. So the median of the set is the mean of the two middle elements.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
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.
GMAT/MBA Expert
- [email protected]
- Elite Legendary Member
- Posts: 10392
- Joined: Sun Jun 23, 2013 6:38 pm
- Location: Palo Alto, CA
- Thanked: 2867 times
- Followed by:511 members
- GMAT Score:800
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
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
- MartyMurray
- Legendary Member
- Posts: 2131
- Joined: Mon Feb 03, 2014 9:26 am
- Location: https://martymurraycoaching.com/
- Thanked: 955 times
- Followed by:140 members
- GMAT Score:800
Indeed, attention to detail is so important.[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
I edited it so future readers will not be led astray.
GMAT/MBA Expert
- Scott@TargetTestPrep
- GMAT Instructor
- Posts: 7249
- Joined: Sat Apr 25, 2015 10:56 am
- Location: Los Angeles, CA
- Thanked: 43 times
- Followed by:29 members
We are given the following measurements in increasing order: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
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
-
- Senior | Next Rank: 100 Posts
- Posts: 94
- Joined: Tue Dec 16, 2014 9:50 am
- Location: London, UK
- Thanked: 2 times
- Followed by:4 members
- GMAT Score:770
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.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
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