It is currently 19 Apr 2018, 12:38

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Set K contains every multiple of 6 from 18 to 306 inclusive. If w is

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44566
Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 17 Sep 2015, 00:57
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

88% (01:15) correct 12% (03:04) wrong based on 156 sessions

HideShow timer Statistics

Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?

A) -6
B) -3
C) 0
D) 3
E) 6

Kudos for a correct solution.
[Reveal] Spoiler: OA

_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Current Student
avatar
Joined: 03 Sep 2012
Posts: 40
GMAT 1: 710 Q50 V36
GPA: 3.9
Reviews Badge
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 17 Sep 2015, 01:44
1
This post received
KUDOS
2
This post was
BOOKMARKED
I would solve this problem in a calculative way, but with less chances of errors !
First find median of the Set K.

Set K ={18,24,30,....306}
Let the no. of terms be n.

so we know the AP formulae to calculate the the tn term:

tn= a+(n-1)*d where d = common difference of the terms.

306= 18 +(n-1)*6
n=49.
So the set K consist of n terms.
The median of the set having odd nos of elements is (n+1)/2., which in this case is 25.

Let's find the 25th term using the same formulae again:
t25= 18+(25-1)*6
t25= 162

So , the median of the set K is 162 i.e. w=162.

Now. lets find the average (arithmetic mean) of the set. For that we need to find the sum of all the elements first, lets call it S.
Since, set k is nothing but a Arithmetic Progression series having first element(a) as 18, common difference (d) as 6 and no. of terms(n) as 49.

Using the formulae to calculate sum of an AP series, which is

S= n/2[2a + (n-1)*d], we will calculate the sum.

so, S= 49/2 [2*18 + (49-1)*6]
This gives us S= 7938.

Now Arithmetic mean of Set K = 7938/no. of terms= 7938/49= 162.

So x= 162.
Now, (w-x) = (162-162)= 0.

Therefore Correct Answer = C
_________________

My GMAT Debrief | ISB Interview 2015 ! | ISB Interview 2016

Expert Post
1 KUDOS received
Math Revolution GMAT Instructor
User avatar
D
Joined: 16 Aug 2015
Posts: 5245
GMAT 1: 800 Q59 V59
GPA: 3.82
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 17 Sep 2015, 02:50
1
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?

A) -6
B) -3
C) 0
D) 3
E) 6




Since 18/6 =3, 306/6=51, K= {6*3(=18), 6*4, ...., 6*50, 6*51(=306)}. The number of elements of K is, therefore, 49(=51-3+1). Since is arithmetic progress and the number of elements is odd, the average of sequence is equal to the median of the sequence. So w-x=0. The answer is C.

Well, if you insist a tedious computations :
The sum of all elements --> 6*(3+4+....+51)= 6*(54*49)/2 = 3*2*27*49=6*27*49
The average of the set ---> 6*27*49/49= 6*27=162

Since the number of elements is 49(odd), the median is the 25th element(=6*27=162).

As a result x=162, w=162, so w-x=o, as we predicted.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only $79 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

1 KUDOS received
Manager
Manager
avatar
Joined: 29 Jul 2015
Posts: 159
GMAT ToolKit User
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 17 Sep 2015, 16:03
1
This post received
KUDOS
1
This post was
BOOKMARKED
Bunuel wrote:
Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?

A) -6
B) -3
C) 0
D) 3
E) 6

Kudos for a correct solution.


According to the properties of evenly spaced sets,
Mean = Median = (first+last)/2

Set K is evenly spaced as all the elements are multiples of 6
Since, mean = median
their difference w-x = 0

Answer:- C
1 KUDOS received
Manager
Manager
avatar
S
Joined: 13 Mar 2013
Posts: 174
Location: United States
Concentration: Leadership, Technology
GPA: 3.5
WE: Engineering (Telecommunications)
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 17 Sep 2015, 21:56
1
This post received
KUDOS
Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?

A) -6
B) -3
C) 0
D) 3
E) 6

Kudos for a correct solution.

15 sec only need to answer or the time need to read the question .

Note that the question clearly says it a consecutive multiple of 6 from 6 to 306 inclusive .
so avg = median
so its 0 C ans .

Property of consecutive integer property ---- avg = median
_________________

Regards ,

1 KUDOS received
Current Student
avatar
B
Joined: 31 Oct 2011
Posts: 52
Location: India
GMAT 1: 660 Q48 V32
GPA: 3.56
WE: Programming (Computer Software)
Reviews Badge
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 19 Sep 2015, 23:44
1
This post received
KUDOS
1
This post was
BOOKMARKED
In any set of numbers having the same common difference ie., consecutive multiples of a number,

Mean = Median = \(\frac{(First Term + Last Term)}{2}\)

Since we know mean = median, we don't even have to bother to calculate either of them as we only want the difference between the two, which will always be 0.
Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5769
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 20 Sep 2015, 00:04
Expert's post
1
This post was
BOOKMARKED
MathRevolution wrote:
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?

A) -6
B) -3
C) 0
D) 3
E) 6




Since 18/6 =3, 306/6=51, K= {6*3(=18), 6*4, ...., 6*50, 6*51(=306)}. The number of elements of K is, therefore, 49(=51-3+1). Since is arithmetic progress and the number of elements is odd, the average of sequence is equal to the median of the sequence. So w-x=0. The answer is C.

Well, if you insist a tedious computations :
The sum of all elements --> 6*(3+4+....+51)= 6*(54*49)/2 = 3*2*27*49=6*27*49
The average of the set ---> 6*27*49/49= 6*27=162

Since the number of elements is 49(odd), the median is the 25th element(=6*27=162).

As a result x=162, w=162, so w-x=o, as we predicted.


Hi,
even if the numbers are even but in arithmetic progression, the median and average should be the same.....
so its not important that the number of elements is odd...
only difference in odd and even elements will be that the median will be a part of the set in odd numbers
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


GMAT online Tutor

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5769
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 20 Sep 2015, 00:06
Bunuel wrote:
Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?

A) -6
B) -3
C) 0
D) 3
E) 6

Kudos for a correct solution.


median and mean are the same in sets having numbers evenly spaced out or in arithmetic progression..
so the answer is 0
C
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html


GMAT online Tutor

Expert Post
2 KUDOS received
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 44566
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 27 Sep 2015, 11:32
2
This post received
KUDOS
Expert's post
2
This post was
BOOKMARKED
Bunuel wrote:
Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?

A) -6
B) -3
C) 0
D) 3
E) 6

Kudos for a correct solution.


Gmatprepnow Official Solution:

If set K contains every multiple of 6 from 18 to 306, then set K looks like this: {18, 24, 30, 36, 42, . . ., 294, 300, 306}. Since the numbers in set K are equally spaced, the median (w) and mean (x) of this set will be equal.

Do we need to calculate the median and mean of set K?

No. We can answer the question without making any calculations whatsoever.

If w and x are equal, then w-x = 0, so the answer to the question is C.

So, when it comes to statistics questions on then GMAT, be sure to watch out for equally spaced numbers in a set. If they’re equally spaced, you may be able to save yourself a lot of time.
_________________

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?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
B
Joined: 05 Jan 2017
Posts: 427
Location: India
Premium Member
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 28 Feb 2017, 03:43
To find the total number of numbers in the set, we can say that
306 = 18 + (n-1)6 or n = 49.
Median term (w) will be 25th term which will be equal to 18 +(25-1)6 = 162
Average (x) = {n/2( first term +last term)}/n
= (first term +last term)/2
= (306+18)/2 = 162.
Therefore w - x = 162-162 = 0. Option C
Senior Manager
Senior Manager
User avatar
S
Joined: 24 Oct 2016
Posts: 305
Location: India
Concentration: Finance, International Business
Schools: IIMB
GMAT 1: 550 Q42 V28
GPA: 3.96
WE: Human Resources (Retail Banking)
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 02 Mar 2017, 04:51
answer should be c
don't need to do much calculation as we can clearly see that its an A.P. so median and average will always be the same
so w-x=0
hence answer is C
Board of Directors
User avatar
G
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 3385
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 02 Mar 2017, 07:49
Bunuel wrote:
Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?

A) -6
B) -3
C) 0
D) 3
E) 6

Kudos for a correct solution.


The set of numbers is = 18, 24, 30 ....... 300 , 306

Or, we may write the set as 6 ( 3 , 4 , 5 ..... 50 , 51 )

There will be 51 - 3 + 1 = 49 numbers

Median will be 49+1/2 = 25th term which will be 27*6 = 162

Mean will be 1323/49 = 27 , so the value of mean will be 27*6 = 162

Thus , Mean - Median = 162 - 162 => 0

Hence, correct answer must be (C) 0
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Expert Post
1 KUDOS received
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2248
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 02 Mar 2017, 18:12
1
This post received
KUDOS
Expert's post
Bunuel wrote:
Set K contains every multiple of 6 from 18 to 306 inclusive. If w is the median of set K, and x is the average (arithmetic mean) of set K, what is the value of w-x?

A) -6
B) -3
C) 0
D) 3
E) 6


Since we have a set of evenly spaced integers, we know the median is equal to the mean. Thus, the difference between the median and the mean is zero.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Manager
Manager
User avatar
S
Joined: 05 Dec 2016
Posts: 59
Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is [#permalink]

Show Tags

New post 31 Mar 2018, 07:06
we have an evenly spaced set so mean and median are always equal so C is correct

with algebra:
Set K contains every multiple of 6 from 18 to 306 inclusive so we have an evenly spaced set with increment=6 so \(n=\frac{(last-first)}{increment}+1\) both 18 and 306 are multiples of 6 (both divided by 2 and 3) so \(n=\frac{(306-18)}{(6)}+1=49\). To find the mean since its odd we can do this : \(\frac{n+1}{2}=25\) so the 25th number must be \((25-1+3)6=27*6=162\) since its an evenly spaced set \(\frac{first+last}{2}=Avg=\frac{18+306}{2}=162\) so \(mean-median=0\).
_________________

lets all unite to reach our target together
Kudos if you like the post!

Re: Set K contains every multiple of 6 from 18 to 306 inclusive. If w is   [#permalink] 31 Mar 2018, 07:06
Display posts from previous: Sort by

Set K contains every multiple of 6 from 18 to 306 inclusive. If w is

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

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®.