Aug 18 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes. Aug 19 08:00 AM PDT  09:00 AM PDT Join a 4day FREE online boot camp to kick off your GMAT preparation and get you into your dream bschool in R1.**Limited for the first 99 registrants. Register today! Aug 20 08:00 PM PDT  09:00 PM PDT EMPOWERgmat is giving away the complete Official GMAT Exam Pack collection worth $100 with the 3 Month Pack ($299) Aug 20 09:00 PM PDT  10:00 PM PDT Take 20% off the plan of your choice, now through midnight on Tuesday, 8/20 Aug 22 09:00 PM PDT  10:00 PM PDT What you'll gain: Strategies and techniques for approaching featured GMAT topics, and much more. Thursday, August 22nd at 9 PM EDT
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
18 Apr 2010, 23:59
Question Stats:
70% (03:08) correct 30% (03:03) wrong based on 228 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
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 57022

Re: average problem
[#permalink]
Show Tags
17 Apr 2012, 01:35
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 163=13. Answer: D. Hope it's clear.
_________________




Manager
Joined: 13 Dec 2009
Posts: 108

Re: average problem
[#permalink]
Show Tags
19 Apr 2010, 00:01
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 please explain Let odd numbers be 2n3, 2n1, 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

Re: average problem
[#permalink]
Show Tags
19 Apr 2010, 00:22
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: 108

Re: average problem
[#permalink]
Show Tags
19 Apr 2010, 00:31
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: 100

Re: average problem
[#permalink]
Show Tags
16 Apr 2012, 21:32
Is there a different approach to this problem? I find the explanations above tough!!
_________________
My First Blog on my GMAT JourneyArise, Awake and Stop not till the goal is reached



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9535
Location: Pune, India

Re: The average of 4 consecutive odd numbers is half that of the
[#permalink]
Show Tags
19 Sep 2016, 03:00
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 Answer (D)
_________________
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 >



VP
Joined: 07 Dec 2014
Posts: 1225

The average of 4 consecutive odd numbers is half that of the
[#permalink]
Show Tags
19 Sep 2016, 15:19
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)➡2xy=2 (x+3)+(y+4)=18➡x+y=11 adding, 3x=9 x=3 y=113=8 8+4*2=16 163=13 D.



Intern
Joined: 13 Mar 2019
Posts: 27

Re: The average of 4 consecutive odd numbers is half that of the
[#permalink]
Show Tags
08 Aug 2019, 10:56
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 163=13




Re: The average of 4 consecutive odd numbers is half that of the
[#permalink]
08 Aug 2019, 10:56






