Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 25 May 2013
Posts: 26

The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
12 Sep 2013, 06:13
Question Stats:
43% (01:14) correct 57% (01:28) wrong based on 706 sessions
HideShow timer Statistics
The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1? (1) The ninth term in this sequence is 81. (2) The fifth term in this sequence is 1
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 47983

The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
12 Sep 2013, 08:13
The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1?Given that: \(a_2=a_1*k\) \(a_3=a_1*k^2\) \(a_4=a_1*k^3\) ... \(a_n=a_1*k^{n1}\) Also given that k>0 and n=9. (1) The ninth term in this sequence is 81 > \(a_9=a_1*k^8=81\). If \(a_1=1\), then all but \(a_1\) will be greater than 1, but if \(a_1=2\), then all will be greater than 1. Not sufficient. (2) The fifth term in this sequence is 1 > \(a_5=a_1*k^4=1\). Now, if \(a_1<1\), then \(k>1\), and all terms from \(a_5\) (\(a_6\), \(a_7\), \(a_8\), and \(a_9\)), so 4 terms will be greater than 1 AND if \(a_1>1\), then \(k<1\), and all terms till \(a_5\) (\(a_2\), \(a_3\) and \(a_4\)), so again 4 terms will be greater than 1. Sufficient. Answer: B.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics




Math Expert
Joined: 02 Sep 2009
Posts: 47983

The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
12 Sep 2013, 08:20
Bunuel wrote: The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1?
Given that: \(a_2=a_1*k\) \(a_3=a_1*k^2\) \(a_4=a_1*k^3\) ... \(a_n=a_1*k^{n1}\)
Also given that k>0 and n=9.
(1) The ninth term in this sequence is 81 > \(a_9=a_1*k^8=81\). If \(a_1=1\), then all but \(a_1\) will be greater than 1, but if \(a_1=2\), then all will be greater than 1. Not sufficient.
(2) The fifth term in this sequence is 1 > \(a_5=a_1*k^4=1\). Now, if \(a_1<1\), then \(k>1\), and all terms from \(a_5\) (\(a_6\), \(a_7\), \(a_8\), and \(a_9\)), so 4 terms will be greater than 1 AND if \(a_1>1\), then \(k<1\), and all terms till \(a_5\) (\(a_2\), \(a_3\), \(a_4\), and \(a_5\)), so again 4 terms will be greater than 1. Sufficient.
Answer: B. Similar questions to practice: http://gmatclub.com/forum/m1571960.htmlhttp://gmatclub.com/forum/inthesequen ... 26119.htmlhttp://gmatclub.com/forum/ifmisaseq ... 32988.htmlhttp://gmatclub.com/forum/ifa1a2a3a ... 29753.htmlhttp://gmatclub.com/forum/thenumbersa ... 06213.htmlhttp://gmatclub.com/forum/thesequence ... 03947.html
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12192
Location: United States (CA)

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
12 Mar 2015, 17:54
Hi All, This is great 'concept' question. With a bit of 'playing around' you can probably find the patterns involved. This DS question tells us that each term in a sequence is equal to the PREVIOUS term multiplied by a POSITIVE CONSTANT. For example, the sequence 1, 2, 4, 8, 16 would fit this definition (another example would be 16, 8, 4, 2, 1, 1/2, etc.). We don't know any of the terms though and we don't know the constant (it could be either an integer, fraction or mixed number). We DO know that since we're multiplying by a positive constant that the sequence of numbers either "increases" or "decreases." We're asked how many of the first 9 terms are greater than 1? It's interesting that the question asks how many are greater than 1....... Fact 1: The 9th term is 81 Since we don't know what the constant "K" is (it could be a positive fraction or a positive number > 1), we can TEST VALUES. IF... K = 3, then the terms (working backwards from the 9th term....) are: 81, 27, 9, 3, 1, 1/3, 1/9, 1/27, 1/81 Here, the number of terms greater than 1 is 4 IF... K = 1/3, then the terms (working backwards from the 9th terms....) are: 81, 243, 729, then they get bigger and bigger..... Here, the number of terms greater than 1 is 9 Fact 1 is INSUFFICIENT. Fact 2: The fifth term is 1. Since the sequence either increases or decreases, we'd have... 4 numbers less than 1, then the number 1, then 4 numbers greater than 1 OR 4 numbers greater than 1, then the number 1, then 4 numbers less than 1 Regardless of which option, we end up with exactly 4 terms that are greater than 1. Fact 2 is SUFFICIENT Final Answer: GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Intern
Joined: 26 Feb 2015
Posts: 8
GPA: 1.19

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
04 Jul 2016, 07:33
What if the first term is 1 ? should not c be the answer?



Math Expert
Joined: 02 Sep 2009
Posts: 47983

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
04 Jul 2016, 07:44



Manager
Joined: 22 Feb 2016
Posts: 97
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47 GMAT 2: 710 Q47 V39
GPA: 3.57

The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
03 Dec 2016, 20:06
Bunuel wrote: The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1?
Given that: \(a_2=a_1*k\) \(a_3=a_1*k^2\) \(a_4=a_1*k^3\) ... \(a_n=a_1*k^{n1}\)
Also given that k>0 and n=9.
(1) The ninth term in this sequence is 81 > \(a_9=a_1*k^8=81\). If \(a_1=1\), then all but \(a_1\) will be greater than 1, but if \(a_1=2\), then all will be greater than 1. Not sufficient.
(2) The fifth term in this sequence is 1 > \(a_5=a_1*k^4=1\). Now, if \(a_1<1\), then \(k>1\), and all terms from \(a_5\) (\(a_6\), \(a_7\), \(a_8\), and \(a_9\)), so 4 terms will be greater than 1 AND if \(a_1>1\), then \(k<1\), and all terms till \(a_5\) (\(a_2\), \(a_3\), \(a_4\), and \(a_5\)), so again 4 terms will be greater than 1. Sufficient.
Answer: B. Just wondering, can K take any positive fractional value or does it need to be an interger. It does not explicitly mentions that K has to be an integer. I agree the answer will be the same in both the cases however just want to clarify in case we face a similar situation during the main exam.



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12192
Location: United States (CA)

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
04 Dec 2016, 13:22
Hi AmritaSarkar89, In my solution (above), I discuss this exact issue. GMAT questions are very carefully worded, so you have to pay attention to the details (what those details state and DON'T state). Here, we're told that K is a POSITIVE CONSTANT. That's does not mean that K is necessarily an integer (in the same way that stating N > 0 does not mean that N is necessarily an integer). Be mindful of these details when working through GMAT questions and make sure to write everything on the pad when you're working (so that you don't forget anything). GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Manager
Joined: 22 Feb 2016
Posts: 97
Location: India
Concentration: Economics, Healthcare
GMAT 1: 690 Q42 V47 GMAT 2: 710 Q47 V39
GPA: 3.57

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
04 Dec 2016, 22:11
EMPOWERgmatRichC wrote: Hi AmritaSarkar89,
In my solution (above), I discuss this exact issue. GMAT questions are very carefully worded, so you have to pay attention to the details (what those details state and DON'T state). Here, we're told that K is a POSITIVE CONSTANT. That's does not mean that K is necessarily an integer (in the same way that stating N > 0 does not mean that N is necessarily an integer). Be mindful of these details when working through GMAT questions and make sure to write everything on the pad when you're working (so that you don't forget anything).
GMAT assassins aren't born, they're made, Rich Thanks a lot for the detailed reply Will surely keep in mind



Intern
Joined: 24 Nov 2016
Posts: 1

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
05 Dec 2016, 04:10
But what if a1=1 and K=2? or a1=0?



EMPOWERgmat Instructor
Status: GMAT Assassin/CoFounder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 12192
Location: United States (CA)

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
05 Dec 2016, 12:06
Hi ldelcerro, While it's certainly beneficial to think about all the possibilities (including negatives and 0), neither of those options 'fits' the given information in the two Facts. If the 9th term is 81, then the first term cannot be negative and it cannot be 0 (since repeatedly multiplying either of those options by a positive constant will NEVER lead to +81). The same issue occurs if the 5th term is 1. Thus, that initial term MUST be a positive. GMAT assassins aren't born, they're made, Rich
_________________
760+: Learn What GMAT Assassins Do to Score at the Highest Levels Contact Rich at: Rich.C@empowergmat.com
Rich Cohen
CoFounder & GMAT Assassin
Special Offer: Save $75 + GMAT Club Tests Free
Official GMAT Exam Packs + 70 Pt. Improvement Guarantee www.empowergmat.com/
***********************Select EMPOWERgmat Courses now include ALL 6 Official GMAC CATs!***********************



Director
Joined: 12 Nov 2016
Posts: 771
Location: United States
GPA: 2.66

The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
19 Apr 2017, 18:51
What I don't understand about this question is for statement 1 why can we not have a sequence such as k=1/2 and
A[16, 8, 4, 2 , 1, 1/2 , 1/4, 1/8, 1/16] ?
Actually nvm in that instance the number of integers greater than 1 would still be the same if we kept K and made all the values positive.



Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1322
Location: Malaysia

The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
04 Jun 2017, 02:04
Bunuel wrote: The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1?
Given that: \(a_2=a_1*k\) \(a_3=a_1*k^2\) \(a_4=a_1*k^3\) ... \(a_n=a_1*k^{n1}\)
Also given that k>0 and n=9.
(1) The ninth term in this sequence is 81 > \(a_9=a_1*k^8=81\). If \(a_1=1\), then all but \(a_1\) will be greater than 1, but if \(a_1=2\), then all will be greater than 1. Not sufficient.
(2) The fifth term in this sequence is 1 > \(a_5=a_1*k^4=1\). Now, if \(a_1<1\), then \(k>1\), and all terms from \(a_5\) (\(a_6\), \(a_7\), \(a_8\), and \(a_9\)), so 4 terms will be greater than 1 AND if \(a_1>1\), then \(k<1\), and all terms till \(a_5\) (\(a_2\), \(a_3\), \(a_4\), and \(a_5\)), so again 4 terms will be greater than 1. Sufficient.
Answer: B. Hi Bunuel, Could you help to elaborate the highlighted part by giving an example to illustrate?
_________________
"Be challenged at EVERY MOMENT."
“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”
"Each stage of the journey is crucial to attaining new heights of knowledge."
Rules for posting in verbal forum  Please DO NOT post short answer in your post!
Advanced Search : https://gmatclub.com/forum/advancedsearch/



Math Expert
Joined: 02 Sep 2009
Posts: 47983

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
04 Jun 2017, 06:07
hazelnut wrote: Bunuel wrote: The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1?
Given that: \(a_2=a_1*k\) \(a_3=a_1*k^2\) \(a_4=a_1*k^3\) ... \(a_n=a_1*k^{n1}\)
Also given that k>0 and n=9.
(1) The ninth term in this sequence is 81 > \(a_9=a_1*k^8=81\). If \(a_1=1\), then all but \(a_1\) will be greater than 1, but if \(a_1=2\), then all will be greater than 1. Not sufficient.
(2) The fifth term in this sequence is 1 > \(a_5=a_1*k^4=1\). Now, if \(a_1<1\), then \(k>1\), and all terms from \(a_5\) (\(a_6\), \(a_7\), \(a_8\), and \(a_9\)), so 4 terms will be greater than 1 AND if \(a_1>1\), then \(k<1\), and all terms till \(a_5\) (\(a_2\), \(a_3\), \(a_4\), and \(a_5\)), so again 4 terms will be greater than 1. Sufficient.
Answer: B. Hi Bunuel, Could you help to elaborate the highlighted part by giving an example to illustrate? If \(a_1=1\), then from \(a_9=a_1*k^8=81\) > \(1*k^8=81\) > \(k=\sqrt{3}\) > \(a_2=a_1*k=\sqrt{3}>1\) and so on. If \(a_1=2\), then from \(a_9=a_1*k^8=81\) > \(2*k^8=81\) > \(k \approx 1.6\) > \(a_2=a_1*k \approx 3.3 > 1\) and so on.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1322
Location: Malaysia

The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
04 Jun 2017, 17:37
Bunuel wrote: The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1?
Given that: \(a_2=a_1*k\) \(a_3=a_1*k^2\) \(a_4=a_1*k^3\) ... \(a_n=a_1*k^{n1}\)
Also given that k>0 and n=9.
(1) The ninth term in this sequence is 81 > \(a_9=a_1*k^8=81\). If \(a_1=1\), then all but \(a_1\) will be greater than 1, but if \(a_1=2\), then all will be greater than 1. Not sufficient.
(2) The fifth term in this sequence is 1 > \(a_5=a_1*k^4=1\). Now, if \(a_1<1\), then \(k>1\), and all terms from \(a_5\) (\(a_6\), \(a_7\), \(a_8\), and \(a_9\)), so 4 terms will be greater than 1 AND if \(a_1>1\), then \(k<1\), and all terms till \(a_5\) (\(a_2\), \(a_3\), \(a_4\), and \(a_5\)), so again 4 terms will be greater than 1. Sufficient.
Answer: B. Hi Bunuel, I think \(a_5\) should not count in the term as in highlighted part since \(a_5=1\). If \(a_1>1\), \(a_5=1\), then (\(a_1\), \(a_2\), \(a_3\), \(a_4\)) will be > 1. Quote: If \(a_1=2\), then from \(a_9=a_1*k^8=81\) > \(2*k^8=81\) > \(k \approx 1.6\) > \(a_2=a_1*k \approx 3.3 > 1\) and so on. How could we calculate the value of k without using the calculator? \(2*k^8=81\) > \(k^8=40.5\) > \(k \approx 1.6\)
_________________
"Be challenged at EVERY MOMENT."
“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.”
"Each stage of the journey is crucial to attaining new heights of knowledge."
Rules for posting in verbal forum  Please DO NOT post short answer in your post!
Advanced Search : https://gmatclub.com/forum/advancedsearch/



Math Expert
Joined: 02 Sep 2009
Posts: 47983

The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
04 Jun 2017, 23:04



Manager
Joined: 06 Nov 2016
Posts: 105
Location: India
GPA: 2.8

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
05 Jun 2017, 04:29
Bunuel wrote: The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1?
Given that: \(a_2=a_1*k\) \(a_3=a_1*k^2\) \(a_4=a_1*k^3\) ... \(a_n=a_1*k^{n1}\)
Also given that k>0 and n=9.
(1) The ninth term in this sequence is 81 > \(a_9=a_1*k^8=81\). If \(a_1=1\), then all but \(a_1\) will be greater than 1, but if \(a_1=2\), then all will be greater than 1. Not sufficient.
(2) The fifth term in this sequence is 1 > \(a_5=a_1*k^4=1\). Now, if \(a_1<1\), then \(k>1\), and all terms from \(a_5\) (\(a_6\), \(a_7\), \(a_8\), and \(a_9\)), so 4 terms will be greater than 1 AND if \(a_1>1\), then \(k<1\), and all terms till \(a_5\) (\(a_2\), \(a_3\) and \(a_4\)), so again 4 terms will be greater than 1. Sufficient.
Answer: B. How do we know that k is an integer. if k is a fraction then statement 2 does not become insufficient? Bunuel please respond.



Math Expert
Joined: 02 Sep 2009
Posts: 47983

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
05 Jun 2017, 07:01
sonikavadhera wrote: Bunuel wrote: The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1?
Given that: \(a_2=a_1*k\) \(a_3=a_1*k^2\) \(a_4=a_1*k^3\) ... \(a_n=a_1*k^{n1}\)
Also given that k>0 and n=9.
(1) The ninth term in this sequence is 81 > \(a_9=a_1*k^8=81\). If \(a_1=1\), then all but \(a_1\) will be greater than 1, but if \(a_1=2\), then all will be greater than 1. Not sufficient.
(2) The fifth term in this sequence is 1 > \(a_5=a_1*k^4=1\). Now, if \(a_1<1\), then \(k>1\), and all terms from \(a_5\) (\(a_6\), \(a_7\), \(a_8\), and \(a_9\)), so 4 terms will be greater than 1 AND if \(a_1>1\), then \(k<1\), and all terms till \(a_5\) (\(a_2\), \(a_3\) and \(a_4\)), so again 4 terms will be greater than 1. Sufficient.
Answer: B. How do we know that k is an integer. if k is a fraction then statement 2 does not become insufficient? Bunuel please respond. Your question is not clear. First of all, we do not assume that k is an integer. Next, (2) IS sufficient. Please reread the solution.
_________________
New to the Math Forum? Please read this: Ultimate GMAT Quantitative Megathread  All You Need for Quant  PLEASE READ AND FOLLOW: 12 Rules for Posting!!! Resources: GMAT Math Book  Triangles  Polygons  Coordinate Geometry  Factorials  Circles  Number Theory  Remainders; 8. Overlapping Sets  PDF of Math Book; 10. Remainders  GMAT Prep Software Analysis  SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS)  Tricky questions from previous years.
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.
What are GMAT Club Tests? Extrahard Quant Tests with Brilliant Analytics



Manager
Joined: 06 Nov 2016
Posts: 105
Location: India
GPA: 2.8

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
05 Jun 2017, 11:39
Bunuel wrote: sonikavadhera wrote: Bunuel wrote: The next number in a certain sequence is defined by multiplying the previous term by some positive constant k, where k ≠ 1. How many of the first nine terms in this sequence are greater than 1?
Given that: \(a_2=a_1*k\) \(a_3=a_1*k^2\) \(a_4=a_1*k^3\) ... \(a_n=a_1*k^{n1}\)
Also given that k>0 and n=9.
(1) The ninth term in this sequence is 81 > \(a_9=a_1*k^8=81\). If \(a_1=1\), then all but \(a_1\) will be greater than 1, but if \(a_1=2\), then all will be greater than 1. Not sufficient.
(2) The fifth term in this sequence is 1 > \(a_5=a_1*k^4=1\). Now, if \(a_1<1\), then \(k>1\), and all terms from \(a_5\) (\(a_6\), \(a_7\), \(a_8\), and \(a_9\)), so 4 terms will be greater than 1 AND if \(a_1>1\), then \(k<1\), and all terms till \(a_5\) (\(a_2\), \(a_3\) and \(a_4\)), so again 4 terms will be greater than 1. Sufficient.
Answer: B. How do we know that k is an integer. if k is a fraction then statement 2 does not become insufficient? Bunuel please respond. Your question is not clear. First of all, we do not assume that k is an integer. Next, (2) IS sufficient. Please reread the solution. I am not sure how statement 2 is sufficient if k is a fraction.?



Intern
Joined: 23 Feb 2017
Posts: 37

Re: The next number in a certain sequence is defined by multiply
[#permalink]
Show Tags
05 Jun 2017, 19:37
Hi banuel, I tried this problem in different way.. 1. given 9th term is 81 .. lets find factors of 81 > 3*3*3*3, so it could be 27*3 or 9*9 lets start with k as 3, then a5 term is 1 means we have 4 terms above 1 lets take k as 9, then a7 is 1, we have 2 terms above 1.. so 1 is NS
2. a5 is 1, a9 = a5*3*3*3*3 = 81, means k is 3, and B is sufficient
ans B




Re: The next number in a certain sequence is defined by multiply &nbs
[#permalink]
05 Jun 2017, 19:37



Go to page
1 2
Next
[ 28 posts ]



