The average (arithmetic mean) of the multiples of 6 : GMAT Problem Solving (PS)
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# The average (arithmetic mean) of the multiples of 6

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Intern
Joined: 24 Apr 2010
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Kudos [?]: 67 [1] , given: 6

The average (arithmetic mean) of the multiples of 6 [#permalink]

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28 May 2010, 12:57
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74% (02:12) correct 26% (01:35) wrong based on 131 sessions

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The average (arithmetic mean) of the multiples of 6 that are greater than 0 and less than 1,000 is

A. 499
B. 500
C. 501
D. 502
E. 503
[Reveal] Spoiler: OA
Math Expert
Joined: 02 Sep 2009
Posts: 36582
Followers: 7086

Kudos [?]: 93266 [2] , given: 10555

Re: The average (arithmetic mean) of the multiples of 6 [#permalink]

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28 May 2010, 13:16
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perseverant wrote:
The average (arithmetic mean) of the multiples of 6 that are greater than 0 and less than 1,000 is

499
500
501
502
503

Could someone explain what the quickest way to solve this is?
Thanks!

Multiples of 6 represent arithmetic progression (aka evenly spaced set). In any evenly spaced set the arithmetic mean (average) is equal to the median and can be calculated by the formula $$mean=median=\frac{a_1+a_n}{2}$$, where $$a_1$$ is the first term and $$a_n$$ is the last term.

First term is 6 and last term is 996 (the last even multiple of 3 below 1000). So $$mean=\frac{6+996}{2}=501$$.

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Re: The average (arithmetic mean) of the multiples of 6 [#permalink]

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28 May 2010, 13:56
Thank you! this is very helpful!

First term is 6 and last term is 996 (the last even multiple of 3 below 1000). So $$mean=\frac{6+996}{2}=501$$.
I assume you meant multiple of 6 instead of 3.
Math Expert
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Posts: 36582
Followers: 7086

Kudos [?]: 93266 [0], given: 10555

Re: The average (arithmetic mean) of the multiples of 6 [#permalink]

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28 May 2010, 14:12
perseverant wrote:
Thank you! this is very helpful!

First term is 6 and last term is 996 (the last even multiple of 3 below 1000). So $$mean=\frac{6+996}{2}=501$$.
I assume you meant multiple of 6 instead of 3.

No. This is how I found the last multiple of 6 below 1000: it would be the last EVEN multiple of 3 (thus multiple of 6) below 1000 .
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Re: The average (arithmetic mean) of the multiples of 6 [#permalink]

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09 Nov 2014, 02:58
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Re: The average (arithmetic mean) of the multiples of 6 [#permalink]

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29 Sep 2016, 02:12
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: The average (arithmetic mean) of the multiples of 6   [#permalink] 29 Sep 2016, 02:12
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