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.
It appears that you are browsing the GMAT Club forum unregistered!
Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club
Registration gives you:
Tests
Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.
Applicant Stats
View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more
Books/Downloads
Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!
Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:
A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]
06 Apr 2013, 04:08
1
This post received KUDOS
1
This post was BOOKMARKED
00:00
A
B
C
D
E
Difficulty:
65% (hard)
Question Stats:
64% (02:27) correct
36% (01:39) wrong based on 155 sessions
A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?
(1) \(a_3\) is positive (2) \(a_4\) is positive
My apologies . I could not find a way to type the sequence here , so I am attaching the DS question .
Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]
06 Apr 2013, 04:29
4
This post received KUDOS
Expert's post
A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?
From above: \(a_3=(a_2)^2*a_1\); \(a_4=(a_3)^2*a_2\); ...
(1) \(a_3\) is positive --> \(a_3=(a_2)^2*a_1=positive\) --> \(a_1=positive\). Now, if \(a_1=a_2=1\), then ALL 12 terms in the sequence will be positive but if \(a_1=1\), and \(a_2=-1\) (\(a_3=(a_2)^2*a_1=(-1)^2*1=1=positive\)), then not all the terms in the sequence will be positive. Not sufficient.
(2) \(a_4\) is positive --> \(a_4=(a_3)^2*a_2=positive\) --> \(a_2=positive\). The same here: if \(a_1=a_2=1\), then ALL 12 terms in the sequence will be positive but if \(a_1=-1\), and \(a_2=1\) (\(a_3=(a_2)^2*a_1=(1)^2*(-1)=-1\) and \(a_4=(a_3)^2*a_2=(-1)^2*1=1=positive\)), then not all the terms in the sequence will be positive. Not sufficient.
(1)+(2) From above we have that \(a_1=positive\) and \(a_2=positive\). Therefore, all 12 terms of the sequence are positive. Sufficient.
Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]
07 Apr 2013, 21:33
Expert's post
marcovg4 wrote:
Then.. The information for "every k>2" is irrelevant right
Posted from my mobile device
"A sequence ... is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2" means that the given formula applies for the terms starting \(a_3\). _________________
Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]
06 Sep 2013, 11:12
Bunuel wrote:
A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?
From above: \(a_3=(a_2)^2*a_1\); \(a_4=(a_3)^2*a_2\); ...
(1) \(a_3\) is positive --> \(a_3=(a_2)^2*a_1=positive\) --> \(a_1=positive\). Now, if \(a_1=a_2=1\), then ALL 12 terms in the sequence will be positive but if \(a_1=1\), and \(a_2=-1\) (\(a_3=(a_2)^2*a_1=(-1)^2*1=1=positive\)), then not all the terms in the sequence will be positive. Not sufficient.
(2) \(a_4\) is positive --> \(a_4=(a_3)^2*a_2=positive\) --> \(a_2=positive\). The same here: if \(a_1=a_2=1\), then ALL 12 terms in the sequence will be positive but if \(a_1=-1\), and \(a_2=1\) (\(a_3=(a_2)^2*a_1=(1)^2*(-1)=-1\) and \(a_4=(a_3)^2*a_2=(-1)^2*1=1=positive\)), then not all the terms in the sequence will be positive. Not sufficient.
(1)+(2) From above we have that \(a_1=positive\) and \(a_2=positive\). Therefore, all 12 terms of the sequence are positive. Sufficient.
Answer: C.
Hope it's clear.
Although the Answer is correct..but as I see the question Posted and the question in the image are different. Considering the question in the image a1 = +ve, a2=-ve, a3=+ve, a4=-ve and so on...Therefore, there will be 6 +ve terms in the sequence...
Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]
19 Nov 2013, 22:58
guerrero25 wrote:
A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?
(1) \(a_3\) is positive (2) \(a_4\) is positive
My apologies . I could not find a way to type the sequence here , so I am attaching the DS question .
Statement 2 in the question and in the screenshot are different! is \(a_4\) positive or negative?
Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]
20 Nov 2013, 00:32
Expert's post
emailmkarthik wrote:
guerrero25 wrote:
A sequence of non-zero terms \(a_1\), \(a_2\), \(a_3\), ..., \(a_{m-1}\), \(a_m\), is given by \(a_k=(a_{k-1})^2(a_{k-2})\) for every k>2. If m=12, then how many terms in the given sequence are positive?
(1) \(a_3\) is positive (2) \(a_4\) is positive
My apologies . I could not find a way to type the sequence here , so I am attaching the DS question .
Statement 2 in the question and in the screenshot are different! is \(a_4\) positive or negative?
The discussion is on the question which says that \(a_4\) is positive. _________________
Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]
10 Sep 2015, 00:22
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. _________________
As I’m halfway through my second year now, graduation is now rapidly approaching. I’ve neglected this blog in the last year, mainly because I felt I didn’...
Perhaps known best for its men’s basketball team – winners of five national championships, including last year’s – Duke University is also home to an elite full-time MBA...
Hilary Term has only started and we can feel the heat already. The two weeks have been packed with activities and submissions, giving a peek into what will follow...