For the positive integers x, x + 2, x + 4, x + 7, and

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Gmat_mission: Legendary Member; Posts: 1622; Joined: Thu Mar 01, 2018 7:22 amFollowed by: 2 members

by Gmat_mission » Sat Apr 14, 2018 3:24 am

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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.

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Source: Beat The GMAT — Problem Solving | Sat Apr 14, 2018 3:24 am

Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

Answer

by Vincen » Sat Apr 14, 2018 5:52 am

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.

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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

by Brent@GMATPrepNow » Sat Apr 14, 2018 6:43 am

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

MEAN
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

Brent Hanneson - Creator of GMATPrepNow.com

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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sun Apr 15, 2018 3:23 am

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

Let x=1, yielding the following set of values:
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.

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