Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 01 Sep 2015, 12:41

### 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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by

Author Message
TAGS:
Senior Manager
Joined: 10 Apr 2012
Posts: 281
Location: United States
Concentration: Technology, Other
GPA: 2.44
WE: Project Management (Telecommunications)
Followers: 3

Kudos [?]: 319 [1] , given: 325

A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]  06 Apr 2013, 04:08
1
KUDOS
00:00

Difficulty:

55% (hard)

Question Stats:

65% (02:25) correct 35% (01:37) wrong based on 112 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 .
[Reveal] Spoiler: OA

Attachments

Sequence_1.png [ 12.3 KiB | Viewed 1563 times ]

Last edited by Bunuel on 06 Apr 2013, 04:17, edited 1 time in total.
Renamed the topic and edited the question.
Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50033 [3] , given: 7519

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]  06 Apr 2013, 04:29
3
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.

Hope it's clear.
_________________
Current Student
Joined: 15 Mar 2012
Posts: 60
Location: United States
Concentration: Marketing, Strategy
Followers: 0

Kudos [?]: 12 [0], given: 19

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]  07 Apr 2013, 09:40
Then.. The information for "every k>2" is irrelevant right

Posted from my mobile device
_________________

MV
"Better to fight for something than live for nothing.” ― George S. Patton Jr

Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50033 [0], given: 7519

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 $$a_3$$.
_________________
Current Student
Joined: 15 Mar 2012
Posts: 60
Location: United States
Concentration: Marketing, Strategy
Followers: 0

Kudos [?]: 12 [0], given: 19

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]  09 Apr 2013, 08:15
Bunuel wrote:
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 $$a_3$$.

Oh I get it, thanks!
_________________

MV
"Better to fight for something than live for nothing.” ― George S. Patton Jr

Intern
Joined: 29 Oct 2012
Posts: 1
Schools: ISB '15
GMAT 1: 520 Q42 V20
GMAT 2: 660 Q48 V32
GPA: 2.69
Followers: 0

Kudos [?]: 0 [0], given: 13

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.

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...
Manager
Joined: 04 Dec 2011
Posts: 81
Schools: Smith '16 (I)
Followers: 0

Kudos [?]: 16 [0], given: 13

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]  18 Nov 2013, 10:51
Bunuel wrote:
Now, if $$a_1=a_2=1$$, then ALL 12 terms in the sequence will be positive .

How can we say that because a1 and a2 are positive all terms will be positive?
_________________

Life is very similar to a boxing ring.
Defeat is not final when you fall down…
It is final when you refuse to get up and fight back!

1 Kudos = 1 thanks
Nikhil

Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50033 [0], given: 7519

Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink]  19 Nov 2013, 00:43
Expert's post
nikhil007 wrote:
Bunuel wrote:
Now, if $$a_1=a_2=1$$, then ALL 12 terms in the sequence will be positive .

How can we say that because a1 and a2 are positive all terms will be positive?

$$a_3=(a_2)^2*a_1$$;
$$a_4=(a_3)^2*a_2$$;
...

Now, if a1 and a2 are both positive can a3 be negative? a4? an?
_________________
Manager
Joined: 31 Mar 2013
Posts: 68
Location: United States
Followers: 0

Kudos [?]: 19 [0], given: 109

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?
Math Expert
Joined: 02 Sep 2009
Posts: 29173
Followers: 4736

Kudos [?]: 50033 [0], given: 7519

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] 20 Nov 2013, 00:32
Similar topics Replies Last post
Similar
Topics:
1 If the terms of a sequence are a1, a2, a3, . . . , an, what 2 28 Sep 2013, 10:31
4 Given a sequence: a_1, a_2, a_3, ... a_{14}, a_{15} In the 4 08 Aug 2010, 23:18
7 Given a sequence: a_1, a_2, a_3, ... a_{14}, a_{15} In the 18 12 Jun 2009, 22:24
5 Given a sequence: a_1, a_2, a_3, ... a_{14}, a_{15} In the 7 10 Mar 2008, 10:47
3 Given a sequence: a_1, a_2, a_3, ... a_{14}, a_{15} In the 18 04 Nov 2006, 03:38
Display posts from previous: Sort by