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

Question

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

Bunuel · Accepted Answer

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.

Answer: D.

Hope it helps.

ENGRTOMBA2018 · Answer

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 }{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 }{2*n}  =  \frac{ }{2}  = (10+400)/2 = 410/2 = 205.

D is the correct answer.

Hope this helps.

EMPOWERgmatRichC · Answer

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

Final Answer:  D

GMAT assassins aren't born, they're made,
Rich

AMsac123 · Answer

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

AMsac123 · Answer

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

Abhishek009 · Answer

10 (1+2+3...............38+39+40)

Sum of Blue part is  \frac{40*41}{2} = 820

Thus, Product of all multiples of  10  from  10  to  400  inclusive is  820*10

Hence, average of the numbers will be  \frac{820*10}{40} = 205 , Answer will be (D)

luisdicampo · Answer

Deconstructing the Question

The multiples of 10 from 10 to 400 form an arithmetic sequence:

10, 20, 30, \dots, 400

For an arithmetic sequence, the average is:

\frac{	ext{first}+	ext{last}}{2}

Step-by-step

First term:
 10

Last term:
 400

Average:
 \frac{10+400}{2}=\frac{410}{2}=205

Answer: D

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

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