If m is the average (arithmetic mean) of the first 10 positi

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BTGmoderatorAT: Moderator; Posts: 426; Joined: Tue Aug 22, 2017 8:48 pmFollowed by: 1 member

by BTGmoderatorAT » Sat Feb 24, 2018 5:14 am

If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M - m ?

(A) -5
(B) 0
(C) 5
(D) 25
(E) 27.5

I'm confused how to set up the formulas here. Can any experts help?

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Source: Beat The GMAT — Problem Solving | Sat Feb 24, 2018 5:14 am

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 » Sat Feb 24, 2018 5:33 am

ardz24 wrote:If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M - m ?

(A) -5
(B) 0
(C) 5
(D) 25
(E) 27.5

For any EVENLY SPACED SET, mean = median.
The first 10 positive multiples of 5 constitute an evenly spaced set.
Thus, mean = median, implying that M=m and that M-m = 0.

The correct answer is B.

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8152; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

by Scott@TargetTestPrep » Fri Jun 14, 2019 2:45 pm

BTGmoderatorAT wrote:If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M - m ?

(A) -5
(B) 0
(C) 5
(D) 25
(E) 27.5

To answer this question we can use the following rule:

When we have an evenly spaced set of numbers, the mean and the median are equal. Recall that in an evenly spaced set of numbers there is a common difference between consecutive terms in the set. For example, consecutive integers, consecutive odd integers, consecutive even integers, and consecutive multiples of any given number are all examples of evenly spaced sets.

Thus the answer is 0.

Answer: B

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