For the positive integers x, x + 2, x + 4, x + 7, and x + 12, the mean is how much greater than the median?
A. 0
B. 1
C. 2
D. 4
E. 7
[spoiler]OA=B[/spoiler].
How can I calculate this difference without knowing the value of x? What is the way to solve it? Thanks in advanced.
For the positive integers x, x + 2, x + 4, x + 7, and
This topic has expert replies
-
- Legendary Member
- Posts: 1622
- Joined: Thu Mar 01, 2018 7:22 am
- Followed by:2 members
Timer
00:00
Your Answer
A
B
C
D
E
Global Stats
-
- Legendary Member
- Posts: 2898
- Joined: Thu Sep 07, 2017 2:49 pm
- Thanked: 6 times
- Followed by:5 members
Hello Gmat_mission.
It's not necessary to know the value of x.
- The median of a set with an odd number of elements is the middle element, hence the median of the given set is x+4.
- Now the mean is $$\frac{x+\left(x+2\right)+\left(x+4\right)+\left(x+7\right)+\left(x+12\right)}{5}=\frac{5x+25}{5}=x+5.$$ Now, the difference between the average and the median is $$x+5-\left(x+4\right)=1.$$ And this is how we can calculate the difference without knowing the value of x. The OA is B.
I hope this answer can help you.
It's not necessary to know the value of x.
- The median of a set with an odd number of elements is the middle element, hence the median of the given set is x+4.
- Now the mean is $$\frac{x+\left(x+2\right)+\left(x+4\right)+\left(x+7\right)+\left(x+12\right)}{5}=\frac{5x+25}{5}=x+5.$$ Now, the difference between the average and the median is $$x+5-\left(x+4\right)=1.$$ And this is how we can calculate the difference without knowing the value of x. The OA is B.
I hope this answer can help you.
GMAT/MBA Expert
- Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
MEANGmat_mission wrote:For the positive integers x, x + 2, x + 4, x + 7, and x + 12, the mean is how much greater than the median?
A. 0
B. 1
C. 2
D. 4
E. 7
mean = [(x) + (x + 2) + (x + 4) + (x + 7) + (x + 12)/5
= (5x + 25)/5
= x + 5
MEDIAN
The 5 values are already arranged in ASCENDING order {x, x + 2, x + 4, x + 7, x + 12}
So, the median = the middle value = x + 4
The mean is how much greater than the median?
In other words x + 5 is how much greater than the x + 4?
Answer = (x + 5) - (x + 4)
= 1
Answer: B
Cheers
Brent
- GMATGuruNY
- GMAT Instructor
- Posts: 15539
- Joined: Tue May 25, 2010 12:04 pm
- Location: New York, NY
- Thanked: 13060 times
- Followed by:1906 members
- GMAT Score:790
Let x=1, yielding the following set of values:Gmat_mission wrote:For the positive integers x, x + 2, x + 4, x + 7, and x + 12, the mean is how much greater than the median?
A. 0
B. 1
C. 2
D. 4
E. 7
x = 1
x+2 = 3
x+4 = 5
x+7 = 8
x+12 = 13.
Mean = (1+3+5+8+13)/5 = 30/5 = 6.
Median = 5.
Mean - median = 6-5 = 1.
The correct answer is B.
Since only one answer choice can be correct, there is no need to test any other values for x.
Private tutor exclusively for the GMAT and GRE, with over 20 years of experience.
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3
Followed here and elsewhere by over 1900 test-takers.
I have worked with students based in the US, Australia, Taiwan, China, Tajikistan, Kuwait, Saudi Arabia -- a long list of countries.
My students have been admitted to HBS, CBS, Tuck, Yale, Stern, Fuqua -- a long list of top programs.
As a tutor, I don't simply teach you how I would approach problems.
I unlock the best way for YOU to solve problems.
For more information, please email me (Mitch Hunt) at [email protected].
Student Review #1
Student Review #2
Student Review #3