The average (arithmetic mean) of the multiples of 6

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

28 May 2010, 13:57

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63% (02:13) correct

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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!

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

28 May 2010, 14:16

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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.

Answer: C.
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Intern

Joined: 24 Apr 2010

Posts: 27

Followers: 0

Kudos [?]: 3 [0], given: 6

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

28 May 2010, 14:56

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.

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Posts: 11505

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

28 May 2010, 15:12

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] 28 May 2010, 15:12

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The average (arithmetic mean) of the multiples of 6

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The average (arithmetic mean) of the multiples of 6

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