The average of 4 consecutive odd numbers is half that of the : GMAT Problem Solving (PS)
Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 24 Feb 2017, 06:10

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

The average of 4 consecutive odd numbers is half that of the

Author Message
TAGS:

Hide Tags

Intern
Joined: 18 Apr 2010
Posts: 5
Followers: 0

Kudos [?]: 6 [2] , given: 4

The average of 4 consecutive odd numbers is half that of the [#permalink]

Show Tags

18 Apr 2010, 22:59
2
KUDOS
6
This post was
BOOKMARKED
00:00

Difficulty:

45% (medium)

Question Stats:

69% (04:11) correct 31% (02:46) wrong based on 224 sessions

HideShow timer Statistics

The average of 4 consecutive odd numbers is half that of the average of 5 consecutive even numbers. If the sum of these two average is 18, then the difference between the largest and smallest of these numbers is

A. 10
B. 21
C. 7
D. 13
E. 5
[Reveal] Spoiler: OA
Manager
Joined: 13 Dec 2009
Posts: 129
Followers: 6

Kudos [?]: 284 [2] , given: 10

Show Tags

18 Apr 2010, 23:01
2
KUDOS
1
This post was
BOOKMARKED
gmat2012 wrote:
The average of 4 consecutive odd numbers is half that of the average of 5 consecutive even numbers. If the sum of these two average is 18, then the difference between the largest and smallest of these numbers is
a.10
b.21
c.7
d.13
e.5
[Reveal] Spoiler:
OA d

Let odd numbers be 2n-3, 2n-1, 2n + 1, 2n + 3. Average = 2n.
Let even numbers be 2m- 4, 2m - 2, 2m, 2m + 2, 2m + 4. Average = 2m
it is given that 2m = 4n
Also 2n + 2m = 18 => 2n + 4n = 18.
6n = 18, 2n = 6 & 2m = 12. Largest = 16, smallest = 3.
Difference = 16 - 3 = 13.
hope this will help
Intern
Joined: 15 Mar 2010
Posts: 8
Followers: 1

Kudos [?]: 3 [2] , given: 0

Show Tags

18 Apr 2010, 23:22
2
KUDOS
There's a simple solution to this.

To find the average for a set of consecutive numbers, you add the first and last terms and divide by 2. In other words, the average is essentially center/pivot point of the series, whether or not it is a number in the series. (e.g. 1, 3, 5, 7 - the average is 4)

Now we look at the other information given. the average of the odd series is half the average of the even series and they sum up to 18. So let e be the average of the even series. We get 1.5e = 18
=> e = 12

12 will be the middle term of the series and since there are 5, we now know the series look like this: (8, 10, 12, 14, 16)
12/2 = 6, the pivot point of the odd series, since there are 4, we know the series look like this: (3, 5, 7, 9)

16 - 3 = 3.

QED.
Manager
Joined: 13 Dec 2009
Posts: 129
Followers: 6

Kudos [?]: 284 [0], given: 10

Show Tags

18 Apr 2010, 23:31
1
This post was
BOOKMARKED
thanatoz wrote:
There's a simple solution to this.

To find the average for a set of consecutive numbers, you add the first and last terms and divide by 2. In other words, the average is essentially center/pivot point of the series, whether or not it is a number in the series. (e.g. 1, 3, 5, 7 - the average is 4)

Now we look at the other information given. the average of the odd series is half the average of the even series and they sum up to 18. So let e be the average of the even series. We get 1.5e = 18
=> e = 12

12 will be the middle term of the series and since there are 5, we now know the series look like this: (8, 10, 12, 14, 16)
12/2 = 6, the pivot point of the odd series, since there are 4, we know the series look like this: (3, 5, 7, 9)

16 - 3 = 3.

QED.

good thought, i essentially solved using conventional method like assuming even and odd series numbers.. thanks for giving different prospective to the solution.
Manager
Status: And the Prep starts again...
Joined: 03 Aug 2010
Posts: 138
Followers: 2

Kudos [?]: 50 [0], given: 20

Show Tags

16 Apr 2012, 20:32
Is there a different approach to this problem? I find the explanations above tough!!
_________________

My First Blog on my GMAT Journey

Arise, Awake and Stop not till the goal is reached

Math Expert
Joined: 02 Sep 2009
Posts: 37105
Followers: 7252

Kudos [?]: 96496 [4] , given: 10751

Show Tags

17 Apr 2012, 00:35
4
KUDOS
Expert's post
2
This post was
BOOKMARKED
ENAFEX wrote:
Is there a different approach to this problem? I find the explanations above tough!!

The average of 4 consecutive odd numbers is half that of the average of 5 consecutive even numbers. If the sum of these two average is 18, then the difference between the largest and smallest of these numbers is
A. 10
B. 21
C. 7
D. 13
E. 5

Some notes:
The average of evenly spaced set with even number of terms (4 in our case) is the average of two middle terms.
The average of evenly spaced set with odd number of terms (5 i our case) is the middle term.

Say the average of 4 consecutive odd numbers is $$x$$ and the average of 5 consecutive even numbers is $$y$$.

Given: $$x=\frac{y}{2}$$ and $$x+y=18$$ --> solve for $$x$$ and $$y$$: $$x=6$$and $$y=12$$.

So, we have that the average of 4 consecutive odd numbers is 6, which means that those numbers are: {3, 5, 7, 9} (6 is the average of two middle terms);

Similarly we have that the average of 5 consecutive even numbers is 12, which means that those numbers are: {8, 10, 12, 14, 16} (12 is the middle term);

The difference between the largest and smallest of these numbers is 16-3=13.

Hope it's clear.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13953
Followers: 590

Kudos [?]: 167 [0], given: 0

Re: The average of 4 consecutive odd numbers is half that of the [#permalink]

Show Tags

23 Feb 2014, 02:45
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13953
Followers: 590

Kudos [?]: 167 [0], given: 0

Re: The average of 4 consecutive odd numbers is half that of the [#permalink]

Show Tags

14 Apr 2015, 06:04
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 13953
Followers: 590

Kudos [?]: 167 [0], given: 0

Re: The average of 4 consecutive odd numbers is half that of the [#permalink]

Show Tags

18 Sep 2016, 19:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7187
Location: Pune, India
Followers: 2167

Kudos [?]: 14020 [1] , given: 222

Re: The average of 4 consecutive odd numbers is half that of the [#permalink]

Show Tags

19 Sep 2016, 02:00
1
KUDOS
Expert's post
1
This post was
BOOKMARKED
gmat2012 wrote:
The average of 4 consecutive odd numbers is half that of the average of 5 consecutive even numbers. If the sum of these two average is 18, then the difference between the largest and smallest of these numbers is

A. 10
B. 21
C. 7
D. 13
E. 5

Start with what you have been given so that you don't need to take variables. One average is half of the other and the sum of both is 18.
So a + 2a = 18
a = 6

Avg of 4 consecutive odd numbers is 6. The consecutive odd numbers will be 3, 5, 7 and 9. (avg lies in between the middle two numbers)
Avg of 5 consecutive even numbers is 12. The consecutive even numbers will be 8, 10, 12, 14, 16 (avg is the middle number).

Largest - smallest number = 16 - 3 = 13

_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for \$199

Veritas Prep Reviews

Director
Joined: 07 Dec 2014
Posts: 554
Followers: 3

Kudos [?]: 97 [0], given: 3

The average of 4 consecutive odd numbers is half that of the [#permalink]

Show Tags

19 Sep 2016, 14:19
The average of 4 consecutive odd numbers is half that of the average of 5 consecutive even numbers. If the sum of these two average is 18, then the difference between the largest and smallest of these numbers is

A. 10
B. 21
C. 7
D. 13
E. 5

odd average=(4x+12)/4=x+3
even average=(5y+20)/5=y+4
y+4=2(x+3)➡2x-y=-2
(x+3)+(y+4)=18➡x+y=11
x=3
y=11-3=8
8+4*2=16
16-3=13
D.
The average of 4 consecutive odd numbers is half that of the   [#permalink] 19 Sep 2016, 14:19
Similar topics Replies Last post
Similar
Topics:
5 If the average (arithmetic mean) of six consecutive odd 5 15 Feb 2017, 08:08
5 In a series of consecutive odd numbers, 27 is the eighth smallest 5 03 Apr 2015, 13:55
14 If y is the average of x odd consecutive integers and |z - 6/4| = 1/2, 3 08 Mar 2015, 09:01
94 If Q is an odd number and the median of Q consecutive 43 07 Dec 2012, 03:47
143 The sum of four consecutive odd numbers is equal to the sum 23 21 Sep 2011, 10:52
Display posts from previous: Sort by