Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 20 Feb 2012
Posts: 41

If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
27 Feb 2012, 14:40
Question Stats:
86% (01:01) correct 14% (01:22) wrong based on 1150 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
Official Answer and Stats are available only to registered users. Register/ Login.



Math Expert
Joined: 02 Sep 2009
Posts: 46284

Re: If m is the average [#permalink]
Show Tags
27 Feb 2012, 14:43



Intern
Joined: 20 Feb 2012
Posts: 41

Re: If m is the average [#permalink]
Show Tags
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
Mm= 5
where i am doing wrong???



Math Expert
Joined: 02 Sep 2009
Posts: 46284

Re: If m is the average [#permalink]
Show Tags
27 Feb 2012, 15:13
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
Mm= 5
where i am doing wrong??? Arithmetic: (25+30)/2 = 55/2 = 27.5.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
Collection of Questions: PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Intern
Joined: 20 Feb 2012
Posts: 41

Re: If m is the average [#permalink]
Show Tags
27 Feb 2012, 15:15
right now i am banging my head to the wall.



Intern
Joined: 03 Dec 2012
Posts: 4

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
20 Jun 2013, 23:00
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)...



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
24 Jun 2013, 21:30
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 ... eticmean/http://www.veritasprep.com/blog/2012/05 ... eviations/http://www.veritasprep.com/blog/2012/05 ... onmedian/
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 15 Apr 2013
Posts: 74
Location: India
Concentration: Finance, General Management
WE: Account Management (Other)

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
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
Joined: 02 Sep 2009
Posts: 46284

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
25 Jun 2013, 14:04



Manager
Joined: 07 Apr 2014
Posts: 119

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
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



BSchool Forum Moderator
Joined: 12 Aug 2015
Posts: 2642
GRE 1: 323 Q169 V154

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
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 Mm= Zero Hence B
_________________
MBA Financing: INDIAN PUBLIC BANKS vs PRODIGY FINANCE! Getting into HOLLYWOOD with an MBA! The MOST AFFORDABLE MBA programs!STONECOLD's BRUTAL Mock Tests for GMATQuant(700+)AVERAGE GRE Scores At The Top Business Schools!



GMAT Tutor
Joined: 01 Oct 2016
Posts: 10

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
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
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2570

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
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
_________________
Jeffery Miller
Head of GMAT Instruction
GMAT Quant SelfStudy Course
500+ lessons 3000+ practice problems 800+ HD solutions



Director
Joined: 02 Sep 2016
Posts: 744

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
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+(n1)d) (where a=first term and d=difference) M=(Sum of 5th and 6th term)/2 M=(25+30)/2= 27.5 Therefore Mm= 27.527.5=0



Intern
Joined: 23 Mar 2017
Posts: 1

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
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



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1016
Location: India
WE: Engineering (Other)

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
26 Sep 2017, 17:25
VeritasPrepKarishma BunuelQuote: 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
Joined: 16 Oct 2010
Posts: 8102
Location: Pune, India

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
27 Sep 2017, 02:57
adkikani wrote: VeritasPrepKarishma BunuelQuote: 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 My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Manager
Joined: 30 Oct 2016
Posts: 68
Location: United States

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
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
Mm= 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.....



Study Buddy Forum Moderator
Joined: 04 Sep 2016
Posts: 1016
Location: India
WE: Engineering (Other)

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
21 Dec 2017, 18:16
arcticTOQuote: 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.



Director
Joined: 09 Mar 2016
Posts: 608

Re: If m is the average (arithmetic mean) of the first 10 [#permalink]
Show Tags
24 Feb 2018, 05:03
VeritasPrepKarishma wrote: adkikani wrote: VeritasPrepKarishma BunuelQuote: 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




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



Go to page
1 2
Next
[ 21 posts ]



