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# What is the average (arithmetic mean) of all multiples of 10

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What is the average (arithmetic mean) of all multiples of 10 [#permalink]

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13 Oct 2015, 11:10
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What is the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive?

(A) 190

(B) 195

(C) 200

(D) 205

(E) 210
[Reveal] Spoiler: OA

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Re: What is the average (arithmetic mean) of all multiples of 10 [#permalink]

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13 Oct 2015, 11:33
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tuanquang269 wrote:
What is the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive?

(A) 190

(B) 195

(C) 200

(D) 205

(E) 210

This question is straightforward if you realise that the question asks the average of 10,20,30....390,400 . As this is an arithmetic progression, the sum of the series will be = S = $$\frac{n[a+a_n]}{2}$$, where n = number of terms= (400-10)/10+1 = 39+1 = 40, a= 1st term =10 and $$a_n$$ = last term = 400

Also, average = Sum / number of terms = S/n = $$\frac{n[a+a_n]}{2*n}$$ = $$\frac{[a+a_n]}{2}$$ = (10+400)/2 = 410/2 = 205.

Hope this helps.
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Re: What is the average (arithmetic mean) of all multiples of 10 [#permalink]

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13 Oct 2015, 23:19
Hi tuanquang269,

This question can be solved with the Average Formula and 'bunching.'

We're asked for the average of all of the multiples of 10 from 10 to 400, inclusive.

To start, we can figure out the total number of terms rather easily:
1(10) = 10
2(10) = 20
...
40(10) = 400

So we know that there are 40 total numbers.

We can now figure out the SUM of those numbers with 'bunching':

10 + 400 = 410
20 + 390 = 410
30 + 380 = 410
Etc.

Since there are 40 total terms, this pattern will create 20 'pairs' of 410.

Thus, since the average = (Sum of terms)/(Number of terms), we have...

(20)(410)/(40) =
410/2 =
205

[Reveal] Spoiler:
D

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Re: What is the average (arithmetic mean) of all multiples of 10 [#permalink]

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16 Aug 2017, 23:42
Hi Bunuel but can v do it wth ur approach of multiplying with K i.e 10

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Re: What is the average (arithmetic mean) of all multiples of 10 [#permalink]

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16 Aug 2017, 23:58
Asac123 wrote:
What is the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive?

(A) 190

(B) 195

(C) 200

(D) 205

(E) 210

Hi Bunuel but can v do it wth ur approach of multiplying with K i.e 10

Not sure which method you are referring to but probably the easiest way would be to realise that multiples of 10 create an evenly spaced set (aka Arithmetic Progression). For any evenly spaced set the mean is the average of the first and last terms, so it's (10 + 400)/2 = 205.

Hope it helps.
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Re: What is the average (arithmetic mean) of all multiples of 10 [#permalink]

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17 Aug 2017, 08:00
Bunuel wrote:
Asac123 wrote:
What is the average (arithmetic mean) of all multiples of 10 from 10 to 400 inclusive?

(A) 190

(B) 195

(C) 200

(D) 205

(E) 210

Hi Bunuel but can v do it wth ur approach of multiplying with K i.e 10

Not sure which method you are referring to but probably the easiest way would be to realise that multiples of 10 create an evenly spaced set (aka Arithmetic Progression). For any evenly spaced set the mean is the average of the first and last terms, so it's (10 + 400)/2 = 205.

Hope it helps.

If alist gets multiplied by K then mean also gets multiplied by K?

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Re: What is the average (arithmetic mean) of all multiples of 10   [#permalink] 17 Aug 2017, 08:00
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