NEW HERE? LEARN MORE
closeclose
Last visit was: 29 Apr 2024, 01:21 It is currently 29 Apr 2024, 01:21
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

if z1,z2,z3, ... zn is a series of consequtive positive

User avatar
MA
Director
Director
Joined: 25 Nov 2004
Posts: 707
Own Kudos [?]: 449 [0]
Given Kudos: 0
Send PM
if z1,z2,z3, ... zn is a series of consequtive positive [#permalink] New post   27 Jan 2005, 00:18
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Hide Show timer Statistics
ok guys, we are having short of problems. let us post some problems.......

if z1,z2,z3, ..................zn is a series of consequtive positive integers, is the sum of all the integers in this series odd?

(i) (z1+z2+z3+ ..................+zn)/n is an odd integer.
(ii) n is an odd integer.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
avatar
HongHu
Director
Director
Joined: 03 Jan 2005
Posts: 971
Own Kudos [?]: 769 [0]
Given Kudos: 0
Send PM
Re: if z1,z2,z3, ... zn is a series of consequtive positive [#permalink] New post   27 Jan 2005, 00:48
MA wrote:
ok guys, we are having short of problems. let us post some problems.......

if z1,z2,z3, ..................zn is a series of consequtive positive integers, is the sum of all the integers in this series odd?

(i) (z1+z2+z3+ ..................+zn)/n is an odd integer.
(ii) n is an odd integer.


If n is even, then there's always even numbers of odd numbers and thus the sum would be even
If n is odd, however, depends on if the starting number is odd or even.
(i)S/n is odd
S=S/n*n if n is even, S is even; if n is odd, S is odd.
Insufficient
(II) n is odd
insufficient as it depends on the starting number

Combine together, we can determine that S is odd. Sufficient

(C)
User avatar
mdf2
Intern
Intern
Joined: 11 Jan 2005
Posts: 48
Own Kudos [?]: 3 [0]
Given Kudos: 0
Send PM
Re: if z1,z2,z3, ... zn is a series of consequtive positive [#permalink] New post   27 Jan 2005, 01:20
per definition

odd/odd = odd
even/odd = even

odd + even = odd
odd + odd = even
finally odd + even + odd = even
as such

i. no sufficient
ii. no sufficient, we know only that n is odd

both : sufficient
as we know that the division by n (as odd) is odd
so the sum is odd
User avatar
ssumitsh
Intern
Intern
Joined: 06 Sep 2004
Posts: 26
Own Kudos [?]: 1 [0]
Given Kudos: 0
Send PM
Re: if z1,z2,z3, ... zn is a series of consequtive positive [#permalink] New post   27 Jan 2005, 06:19
(i) (z1+z2+z3+ ..................+zn)/n is an odd integer.
(ii) n is an odd integer

I will go with A.

(i) is sufficient to prove that the sum of consecutive integers z1 to zn is odd.
avatar
HongHu
Director
Director
Joined: 03 Jan 2005
Posts: 971
Own Kudos [?]: 769 [0]
Given Kudos: 0
Send PM
Re: if z1,z2,z3, ... zn is a series of consequtive positive [#permalink] New post   27 Jan 2005, 09:08
Oh my, I just realized.

S=n(n+1)/2
S/n=(n+1)/2 if it is an odd integer, meaning n+1 is even
In other words n is odd and S is odd
It is sufficient!!!

Yes (A) is right.
User avatar
ian7777
CIO
CIO
Joined: 09 Mar 2003
Posts: 230
Own Kudos [?]: 171 [0]
Given Kudos: 0
Send PM
Re: if z1,z2,z3, ... zn is a series of consequtive positive [#permalink] New post   27 Jan 2005, 10:00
I go for A, too. If the list had an even number of numbers, then the average would be a .5 (as in, if the list was 4,5,6,7, the average would be 5.5)

If it has an odd number of numbers, then the average is an integer, and if that integer is an odd number, then the sum must have been odd, too.
User avatar
banerjeea_98
Director
Director
Joined: 18 Nov 2004
Posts: 679
Own Kudos [?]: 198 [0]
Given Kudos: 0
Send PM
Re: if z1,z2,z3, ... zn is a series of consequtive positive [#permalink] New post   27 Jan 2005, 10:13
ian7777 wrote:
I go for A, too. If the list had an even number of numbers, then the average would be a .5 (as in, if the list was 4,5,6,7, the average would be 5.5)

If it has an odd number of numbers, then the average is an integer, and if that integer is an odd number, then the sum must have been odd, too.



That's a good way to figure this one. Avg of even number of +ve consecutive integers is not an integer (rather .5) and for odd number of +ve consecutive integers it is an integer.



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Data Sufficiency (DS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: if z1,z2,z3, ... zn is a series of consequtive positive [#permalink]
27 Jan 2005, 10:13
Moderators:
Bunuel
Math Expert
92979 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts
GMATBusters
GMAT Tutor
1905 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions