GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 25 May 2020, 06:51 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # The average of 4 consecutive odd numbers is half that of the

Author Message
TAGS:

### Hide Tags

Intern  Joined: 18 Apr 2010
Posts: 4
The average of 4 consecutive odd numbers is half that of the  [#permalink]

### Show Tags

2
9 00:00

Difficulty:   55% (hard)

Question Stats: 69% (03:08) correct 31% (03:03) wrong based on 236 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
Math Expert V
Joined: 02 Sep 2009
Posts: 64101

### Show Tags

8
4
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.
_________________
##### General Discussion
Manager  Joined: 13 Dec 2009
Posts: 95

### Show Tags

2
1
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
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: 7

### Show Tags

2
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: 95

### Show Tags

1
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: 95

### Show Tags

Is there a different approach to this problem? I find the explanations above tough!! Veritas Prep GMAT Instructor V
Joined: 16 Oct 2010
Posts: 10442
Location: Pune, India
Re: The average of 4 consecutive odd numbers is half that of the  [#permalink]

### Show Tags

2
4
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

VP  D
Joined: 07 Dec 2014
Posts: 1252
The average of 4 consecutive odd numbers is half that of the  [#permalink]

### Show Tags

1
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.
Intern  B
Joined: 13 Mar 2019
Posts: 27
Re: The average of 4 consecutive odd numbers is half that of the  [#permalink]

### Show Tags

1
Clearly there are two equations possible.
And by the averages' property -
1.x=y/2 and x+y=18 Solving- x=6x=6and y=12.
Now the highest and lowest - 16 and 3.
So 16-3=13 Re: The average of 4 consecutive odd numbers is half that of the   [#permalink] 08 Aug 2019, 09:56

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