Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 16 Jul 2019, 20:21

Close

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
Your Progress

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

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

If m is the average (arithmetic mean) of the first 10

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

Hide Tags

Find Similar Topics 
Intern
Intern
User avatar
Joined: 20 Feb 2012
Posts: 28
If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 27 Feb 2012, 14:40
4
18
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

86% (01:24) correct 14% (01:55) wrong based on 964 sessions

HideShow timer Statistics


If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M – m ?

(A) –5
(B) 0
(C) 5
(D) 25
(E) 27.5
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56244
Re: If m is the average  [#permalink]

Show Tags

New post 27 Feb 2012, 14:43
13
1
6
BANON wrote:
If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M – m ?

(A) –5
(B) 0
(C) 5
(D) 25
(E) 27.5


10 sec approach:

The first 10 positive multiples of 5 is an evenly spaced set. One of the most important properties of evenly spaced set (aka arithmetic progression) is: in any evenly spaced set the arithmetic mean (average) is equal to the median.

Hence M=m --> M-m=0.

Answer: B.

For more on this issue check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps.
_________________
General Discussion
Intern
Intern
User avatar
Joined: 20 Feb 2012
Posts: 28
Re: If m is the average  [#permalink]

Show Tags

New post 27 Feb 2012, 15:08
1st 10 multiples of 5: 5,10,15,20,25,30,35,40,45,50

mean = 275/10 = 27.5 = m


median = (25+30)/2 = 22.5 = M

M-m= -5

where i am doing wrong???
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56244
Re: If m is the average  [#permalink]

Show Tags

New post 27 Feb 2012, 15:13
2
Intern
Intern
User avatar
Joined: 20 Feb 2012
Posts: 28
Re: If m is the average  [#permalink]

Show Tags

New post 27 Feb 2012, 15:15
1
right now i am banging my head to the wall. :oops:
Intern
Intern
avatar
Joined: 03 Dec 2012
Posts: 4
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 20 Jun 2013, 23:00
1
2
As it is a Evenly spaced set, the MEAN and MEDIAN will be same for the set.

So, the MEAN or MEDIAN for such sets will be -> Avg. of First term and last term.
i.e, (5+50)/2 in this case.
Blindly we can say answer is zero, because the Q asks the difference between MEAN and MEDIAN for Evenly spaced set(Basic Thumb rule)... :-D
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9433
Location: Pune, India
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 24 Jun 2013, 21:30
1
BANON wrote:
If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M – m ?

(A) –5
(B) 0
(C) 5
(D) 25
(E) 27.5



Responding to a pm:

m = mean = (5 + 10 + 15 + ....+ 50)/10 = 27.5

M = median
Median of 10 numbers will be the average of the middle two numbers i.e. 5th and the 6th numbers. 5th number = 25, 6th number = 30. Median = (25+30)/2 = 27.5

m - M = 0

This solution is the simplest I could think of which uses nothing but the definition of mean and median.
Notice that actually, you will do far less to arrive at the answer.

Mean of an arithmetic progression is the middle value in case there are odd number of terms and average of middle 2 values if there are even number of terms.
Median of an arithmetic progression is the middle term in case there are odd number of terms and average of middle 2 values if there are even number of terms.
So basically, they are both same in case of an arithmetic progression.

I would suggest you to check out the following posts. They discuss these concepts in detail:

http://www.veritasprep.com/blog/2012/04 ... etic-mean/
http://www.veritasprep.com/blog/2012/05 ... eviations/
http://www.veritasprep.com/blog/2012/05 ... on-median/
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
avatar
Joined: 15 Apr 2013
Posts: 68
Location: India
Concentration: Finance, General Management
Schools: ISB '15
WE: Account Management (Other)
GMAT ToolKit User
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 25 Jun 2013, 13:52
Just out of curiosity, Why are we not taking 0 as the first multiple of 5. After all, 0 should be the first multiple of any number :)
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 56244
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 25 Jun 2013, 14:04
3
1
Manager
Manager
avatar
Joined: 07 Apr 2014
Posts: 104
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 11 Sep 2014, 01:45
BANON wrote:
If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M – m ?

(A) –5
(B) 0
(C) 5
(D) 25
(E) 27.5



for the evenly spaced set

, Mean = median
Current Student
User avatar
D
Joined: 12 Aug 2015
Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154
GMAT ToolKit User
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 15 Dec 2016, 05:18
The first 10 multiples of 5 would be an AP series with D=5

Rule => For any Ap series => Mean = Median = Average of the first and the last term.
Hence we don't need to calculate the mean or the median as they would be equal=> m=M

Hence M-m= Zero
Hence B

_________________
GMAT Tutor
avatar
B
Joined: 01 Oct 2016
Posts: 10
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 05 Jan 2017, 15:15
The first 10 positive multiples of 5 will form an evenly spaced set (0 is not included as it's not positive), and with any evenly spaced set, the median equals the mean, so their difference will be zero.
_________________
Dan the GMAT Man
Offering tutoring and admissions consulting in the NYC area and online
danthegmatman.squarespace.com
danthegmatman@gmail.com
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2823
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 09 Jan 2017, 10:42
BANON wrote:
If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M – m ?

(A) –5
(B) 0
(C) 5
(D) 25
(E) 27.5


To answer this question we can use the following rule:

When we have an evenly spaced set of numbers, the mean and the median are equal. Recall that in an evenly spaced set of numbers there is a common difference between consecutive terms in the set. For example, consecutive integers, consecutive odd integers, consecutive even integers, and consecutive multiples of any given number are all examples of evenly spaced sets.

Thus the answer is 0.

Answer: B
_________________

Jeffrey Miller

Head of GMAT Instruction

Jeff@TargetTestPrep.com
TTP - Target Test Prep Logo
122 Reviews

5-star rated online GMAT quant
self study course

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button.

Director
Director
avatar
G
Joined: 02 Sep 2016
Posts: 657
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 01 Apr 2017, 09:17
BANON wrote:
If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median of the first 10 positive multiples of 5, what is the value of M – m ?

(A) –5
(B) 0
(C) 5
(D) 25
(E) 27.5


m=(5+10+15+20+25+30+.......+50)/10= 275/10=27.5 (Formula to find sum: nth term=a+(n-1)d) (where a=first term and d=difference)
M=(Sum of 5th and 6th term)/2
M=(25+30)/2= 27.5


Therefore M-m= 27.5-27.5=0
Intern
Intern
avatar
Joined: 23 Mar 2017
Posts: 1
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 11 Jun 2017, 06:58
Bunuel wrote:
pavan2185 wrote:
Just out of curiosity, Why are we not taking 0 as the first multiple of 5. After all, 0 should be the first multiple of any number :)


Yes, 0 is a multiple of every integer, except 0 itself. But the question talks about positive integers and 0 is neither positive nor negative.

Hope it's clear.

Thank you!

Sent from my Moto G (4) using GMAT Club Forum mobile app
IIMA, IIMC School Moderator
User avatar
V
Joined: 04 Sep 2016
Posts: 1360
Location: India
WE: Engineering (Other)
CAT Tests
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 26 Sep 2017, 17:25
VeritasPrepKarishma Bunuel

Quote:
Mean of an arithmetic progression is the middle value in case there are odd number of terms and average of middle 2 values if there are even number of terms.


I hope arithmetic mean and average are the same.

For no is arithmetic progression, does not average = (first term + last term) / 2

I got to same answer using this approach.
Veritas Prep GMAT Instructor
User avatar
D
Joined: 16 Oct 2010
Posts: 9433
Location: Pune, India
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 27 Sep 2017, 02:57
adkikani wrote:
VeritasPrepKarishma Bunuel

Quote:
Mean of an arithmetic progression is the middle value in case there are odd number of terms and average of middle 2 values if there are even number of terms.


I hope arithmetic mean and average are the same.

For no is arithmetic progression, does not average = (first term + last term) / 2

I got to same answer using this approach.


Yes, arithmetic mean and average are the same.

Average = Sum/Number of elements

For an arithmetic prog,
Average = (first term + last term) / 2
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Manager
avatar
B
Joined: 30 Oct 2016
Posts: 67
Location: United States
Schools: HBS '20, Kellogg '20
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 21 Dec 2017, 17:57
BANON wrote:
1st 10 multiples of 5: 5,10,15,20,25,30,35,40,45,50

mean = 275/10 = 27.5 = m


median = (25+30)/2 = 22.5 = M

M-m= -5

where i am doing wrong???


Not directly relateed by when a questsion asks for the first __ multiples, wouldn't that exclude the number itself so in this case.... it would start at 10? 10,15,20.....
IIMA, IIMC School Moderator
User avatar
V
Joined: 04 Sep 2016
Posts: 1360
Location: India
WE: Engineering (Other)
CAT Tests
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 21 Dec 2017, 18:16
arcticTO
Quote:
1st 10 multiples of 5: 5,10,15,20,25,30,35,40,45,50


Quote:
Not directly relateed by when a questsion asks for the first __ multiples, wouldn't that exclude the number itself so in this case.... it would start at 10? 10,15,20....


I am not an expert, but here are my two cents.
The SHORT ans to your query is NO, we can not exclude the no itself since the smallest (first) multiple of that no will
be when the no is multiplied by 1.

Say first multiple of 10 is always 10* 1 = 10
Next ones will !0 *2 = 20 ...

Hope this helps!
_________________
It's the journey that brings us happiness not the destination.

Feeling stressed, you are not alone!!
VP
VP
User avatar
D
Joined: 09 Mar 2016
Posts: 1273
Re: If m is the average (arithmetic mean) of the first 10  [#permalink]

Show Tags

New post 24 Feb 2018, 05:03
VeritasPrepKarishma wrote:
adkikani wrote:
VeritasPrepKarishma Bunuel

Quote:
Mean of an arithmetic progression is the middle value in case there are odd number of terms and average of middle 2 values if there are even number of terms.


I hope arithmetic mean and average are the same.

For no is arithmetic progression, does not average = (first term + last term) / 2

I got to same answer using this approach.


Yes, arithmetic mean and average are the same.

Average = Sum/Number of elements

For an arithmetic prog,
Average = (first term + last term) / 2



Hi VeritasPrepKarishma hope my questions finds you well :)

what is difference between this formula For an arithmetic prog, Average = (first term + last term)/2 and this one \(x_n = a + d(n−1)\) ?

happy weekend :)
GMAT Club Bot
Re: If m is the average (arithmetic mean) of the first 10   [#permalink] 24 Feb 2018, 05:03

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

If m is the average (arithmetic mean) of the first 10

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





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne