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

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A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 06 Apr 2013, 04:08
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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
Sequence_1.png [ 12.3 KiB | Viewed 1271 times ]


Last edited by Bunuel on 06 Apr 2013, 04:17, edited 1 time in total.
Renamed the topic and edited the question.
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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 06 Apr 2013, 04:29
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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.
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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 07 Apr 2013, 09:40
Then.. The information for "every k>2" is irrelevant right

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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 07 Apr 2013, 21:33
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marcovg4 wrote:
Then.. The information for "every k>2" is irrelevant right

Posted from my mobile device Image


"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.
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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 09 Apr 2013, 08:15
Bunuel wrote:
marcovg4 wrote:
Then.. The information for "every k>2" is irrelevant right

Posted from my mobile device Image


"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!
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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 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...
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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 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?
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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 19 Nov 2013, 00:43
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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?
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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 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?
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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by [#permalink] New post 20 Nov 2013, 00:32
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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.
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PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: A sequence of terms a1, a2 ,a3, ..., a(m-1), am, is given by   [#permalink] 20 Nov 2013, 00:32
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