GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 18 Apr 2019, 11:37

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Retired Moderator
Status: Flying over the cloud!
Joined: 17 Aug 2011
Posts: 550
Location: Viet Nam
Concentration: International Business, Marketing
GMAT Date: 06-06-2014
GPA: 3.07
What is the average (arithmetic mean) of all multiples of 10  [#permalink]

### Show Tags

13 Oct 2015, 11:10
1
1
00:00

Difficulty:

25% (medium)

Question Stats:

76% (01:21) correct 24% (01:31) wrong based on 158 sessions

### HideShow timer Statistics

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

_________________
CEO
Joined: 20 Mar 2014
Posts: 2624
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: What is the average (arithmetic mean) of all multiples of 10  [#permalink]

### Show Tags

13 Oct 2015, 11:33
1
1
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.

D is the correct answer.

Hope this helps.
EMPOWERgmat Instructor
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 13950
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: Q170 V170
Re: What is the average (arithmetic mean) of all multiples of 10  [#permalink]

### Show Tags

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

GMAT assassins aren't born, they're made,
Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels
Contact Rich at: Rich.C@empowergmat.com

*****Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!*****

# Rich Cohen

Co-Founder & GMAT Assassin

Special Offer: Save \$75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee
www.empowergmat.com/
Manager
Joined: 08 Jun 2017
Posts: 56
Re: What is the average (arithmetic mean) of all multiples of 10  [#permalink]

### Show Tags

16 Aug 2017, 23:42
Hi Bunuel but can v do it wth ur approach of multiplying with K i.e 10
Math Expert
Joined: 02 Sep 2009
Posts: 54369
Re: What is the average (arithmetic mean) of all multiples of 10  [#permalink]

### Show Tags

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.
_________________
Manager
Joined: 08 Jun 2017
Posts: 56
Re: What is the average (arithmetic mean) of all multiples of 10  [#permalink]

### Show Tags

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?
Re: What is the average (arithmetic mean) of all multiples of 10   [#permalink] 17 Aug 2017, 08:00
Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.