Jun 18 09:00 PM EDT  10:00 PM EDT Strategies and techniques for approaching featured GMAT topics. Tuesday, June 18th at 9 pm ET Jun 18 10:00 PM PDT  11:00 PM PDT Send along your receipt from another course or book to info@empowergmat.com and EMPOWERgmat will give you 50% off the first month of access OR $50 off the 3 Month Plan Only available to new students Ends: June 18th Jun 19 10:00 PM PDT  11:00 PM PDT Join a FREE 1day workshop and learn how to ace the GMAT while keeping your fulltime job. Limited for the first 99 registrants. Jun 22 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jun 23 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.
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 20 Feb 2007
Posts: 245

The sequence a1, a2, a3, ..., an of n integers is such that ak = k if
[#permalink]
Show Tags
Updated on: 11 Jun 2019, 04:29
Question Stats:
64% (01:43) correct 36% (02:08) wrong based on 404 sessions
HideShow timer Statistics
The sequence \(a_1\), \(a_2\), \(a_3\), ... \(a_n\) of \(n\) integers is such that \(a_k=k\) if \(k\) is odd, and \(a_k=a_{k1}\) if \(k\) is even. Is the sum of the terms in the sequence positive? (1) \(n\) is odd. (2) \(a_n\) is positive
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by Summer3 on 18 Mar 2007, 16:41.
Last edited by Bunuel on 11 Jun 2019, 04:29, edited 3 times in total.
Edited the question and added the OA




Math Expert
Joined: 02 Sep 2009
Posts: 55670

The sequence a1, a2, a3, ..., an of n integers is such that
[#permalink]
Show Tags
29 Dec 2012, 04:30
The sequence \(a_1\), \(a_2\), \(a_3\), ... \(a_n\) of \(n\) integers is such that \(a_k=k\) if \(k\) is odd, and \(a_k=a_{k1}\) if \(k\) is even. Is the sum of the terms in the sequence positive?We have following sequence: \(a_1=1\); \(a_2=a_1=1\); \(a_3=3\); \(a_4=a_3=3\); \(a_5=5\); \(a_6=a_5=5\); ... Basically we have a sequence of positive and negative odd integers: 1, 1, 3, 3, 5, 5, 7., 7, 9, 9, ... Notice than if the number of terms in the sequence (n) is odd then the sum of the terms will be positive, for example if \(n=3\) then \(a_1+a_2+a_3=1+(1)+3=3\), but if the number of terms in the sequence (n) is even then the sum of the terms will be zero, for example if \(n=4\) then \(a_1+a_2+a_3+a_4=1+(1)+3+(3)=0\). Also notice that odd terms are positive and even terms are negative. (1) \(n\) is odd > as discussed the sum is positive. Sufficient. (2) \(a_n\) is positive > n is odd, so the same as above. Sufficient. Answer: D. Hope it's clear.
_________________




SVP
Joined: 01 May 2006
Posts: 1722

Re: The sequence a1, a2, a3, ..., an of n integers is such that ak = k if
[#permalink]
Show Tags
18 Mar 2007, 17:00
(D) for me
Let us describe the few first terms to have a better idea of it works:
o a(1) = 1
o a(2) = 1
o a(3) = 3
o a(4) = 3
So,
o If n is even, then the sum of a(k) terms give 0. We always have couples of opposite number in the sequence.
o If n is odd, then the sum will be equal to n. All other numbers are in couple (negative/positive), giving 0 if we add them.
From 1
n is odd. Bingo, the sum is positive.
SUFF.
From 2
a(n) > 0... Then n must be an odd. Bingo, the sum is positive.
SUFF.




Intern
Joined: 26 Oct 2010
Posts: 19

Re: The sequence a1, a2, a3, ..., an of n integers is such that ak = k if
[#permalink]
Show Tags
29 May 2011, 12:24
I'll take a shot at explaining ...
If k is odd we know all the values are +ve and are equal to k (e.g. 1,3,5,7...) If k is even we know all the values are ve and are equal to the value of the prior term (e.g. a2 = 1,a4=3... so the values will be, 1,3,5,7 ....)
1, 1, 3, 3, 5, 5 .....
So as you can see at this point we know that for every value of k (when odd) we have a ve value from when K is even, unless N (total terms) is odd in which case we will have one extra +ve term that will not cancel out. So if we have even number terms we know the result will be 0 (which is not positive). Therefore to get a positive sum we need one extra odd term.
Try it out,
N=5 1, 1, 3, 3, 5 (if add them, everything cancels out except 5, which is positive).
N=6 1, 1, 3, 3, 5, 5 (if add them, everything cancels out, result is not positive).
So, before looking at the statements we are able to rephrase the question to: "Is the number terms in the sequence odd?"
Statement 1: Gives us exactly that, therefore sufficient. Statement 2: Well, it gives the same thing but instead of saying the number of terms is odd, it says the last term is +ve, which means the same thing as per our sequence above, there sufficient.
Answer D.
I hope this helps and makes sense.



Intern
Joined: 31 Oct 2012
Posts: 22

Re: The sequence a1, a2, a3, ..., an of n integers is such that
[#permalink]
Show Tags
14 Feb 2013, 05:55
Now this is what i dont understand. They just mention "k" (i guess constant) but k can take any value 1,3 or +2. SHouldnt the answer be B then because the statement 2 specifically says that an is positive.



Math Expert
Joined: 02 Sep 2009
Posts: 55670

Re: The sequence a1, a2, a3, ..., an of n integers is such that
[#permalink]
Show Tags
14 Feb 2013, 06:05
maddyboiler wrote: Now this is what i dont understand. They just mention "k" (i guess constant) but k can take any value 1,3 or +2. SHouldnt the answer be B then because the statement 2 specifically says that an is positive. \(k\) in \(a_k\) is a subscript, meaning that \(a_k\) is \(k_{th}\) term in the given sequence which starts from \(a_1\), thus k must be some positive integer. Complete solution is here: thesequencea1a2a3anofnintegersissuchthat76926.html#p1162192Hope it helps.
_________________



MBA Section Director
Affiliations: GMAT Club
Joined: 22 Feb 2012
Posts: 6269
City: Pune

Re: The sequence a1, a2, a3, ..., an of n integers is such that
[#permalink]
Show Tags
14 Feb 2013, 10:17
maddyboiler wrote: Now this is what i dont understand. They just mention "k" (i guess constant) but k can take any value 1,3 or +2. SHouldnt the answer be B then because the statement 2 specifically says that an is positive. dont go into complex things. Just visualize the sequence It can be 2 way 1,1, 3,3, 5,5, 7,7 ending in negative term The sum will be zero in this case 1,1, 3,3, 5,5, 7 ending in positive term The sum will be the last term of sequence we have asked is the sum positive ? > is the sequence as per 2nd case ? > is the a(n) odd ? or is the a(n) positive ? both the statements answer these questions so both are sufficient
_________________
2020 MBA Applicants: Introduce Yourself Here! MBA Video Series  Video answers to specific components and questions about MBA applications.



Director
Joined: 26 Oct 2016
Posts: 627
Location: United States
Concentration: Marketing, International Business
GPA: 4
WE: Education (Education)

Re: The sequence a1, a2, a3, ..., an of n integers is such that ak = k if
[#permalink]
Show Tags
29 Jan 2017, 03:47
(1) n is odd If n is 5, for instance, then a5=5, a4=3, a3=3, a2=1, a1=1 (I used each of the equations listed above to get these numbers I just followed the pattern) When added together [5+(3)+(3)+(1)+(1)] the result is +ve5 You could also plugin 7 for n to make sure and you would still get a +ve resultfollow the same pattern. This statement alone is sufficient. (2) an is +ve/ means the result must be +ve not zero or ve If n=5 (you get the same result as in statement 1) However, if you let n=4/ following the same procedure as above (statement 1) you will see that the result is 0; therefore, one can conclude that n must be an odd number to get a +ve result. n cannot be even. This statement alone is also sufficient. The answer is D.
_________________
Thanks & Regards, Anaira Mitch



NonHuman User
Joined: 09 Sep 2013
Posts: 11393

Re: The sequence a1,a2,a3....an of n integers is such that ak =
[#permalink]
Show Tags
11 Jun 2019, 04:25
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.
_________________




Re: The sequence a1,a2,a3....an of n integers is such that ak =
[#permalink]
11 Jun 2019, 04:25






