Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 13 Oct 2011
Posts: 15

The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
08 Mar 2012, 22:14
2
This post received KUDOS
14
This post was BOOKMARKED
Question Stats:
58% (03:14) correct
42% (02:01) wrong based on 215 sessions
HideShow timer Statistics
The sequence \(a_n\) is defined so that, for all \(n\) is greater than or equal to 3, \(a_n\) is the greater of \(a_{n2} +1\) and \(a_{n1}\). (If the two quantities are the same, then \(a_n\) is equal to either of them.) Which of the following values of \(a_1\) and \(a_2\) will produce a sequence in which no value is repeated? A. \(a_1=1\), \(a_2=1.5\) B. \(a_1=1\), \(a_2=1\) C. \(a_1=1\), \(a_2=1\) D. \(a_1=1\), \(a_2=1.5\) E. \(a_1=1.5\), \(a_2=1\) I am having trouble understanding what the question is asking and also solving it
Official Answer and Stats are available only to registered users. Register/ Login.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: The Sequence a(n) is... [#permalink]
Show Tags
09 Mar 2012, 00:29
shawndx wrote: The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n2) +1) and (an1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?
a) a1=1, a2=1.5 b) a1=1, a2=1 c) a1=1, a2=1 d) a1=1, a2=1.5 e) a1=1.5, a2=1
I am having trouble understanding what the question is asking and also solving it Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally. Given: \(a_n\) = Greater of \((a_{n2} + 1, a_{n1})\) (n is 3 or greater) This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term) If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term' So what can you deduce about \(a_1\) and \(a_2\)? 1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B) 2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\) Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= 0.5)\) so reject it. Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it. Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it. Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\). OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D)
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 13 Oct 2011
Posts: 15

Re: The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
09 Mar 2012, 08:56
1
This post received KUDOS
thank you so much



Intern
Joined: 13 Oct 2011
Posts: 15

Re: The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
09 Mar 2012, 15:05
I do not understand the rule though... so if we were to just substitute values, how would one do that... if n were 3 or 4



Intern
Joined: 03 Sep 2010
Posts: 16

Re: The Sequence a(n) is... [#permalink]
Show Tags
10 Mar 2012, 01:38
VeritasPrepKarishma wrote: shawndx wrote: The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n2) +1) and (an1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?
a) a1=1, a2=1.5 b) a1=1, a2=1 c) a1=1, a2=1 d) a1=1, a2=1.5 e) a1=1.5, a2=1
I am having trouble understanding what the question is asking and also solving it Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally. Given: \(a_n\) = Greater of \((a_{n2} + 1, a_{n1})\) (n is 3 or greater) This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term) If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term' So what can you deduce about \(a_1\) and \(a_2\)? 1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B) 2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\) Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= 0.5)\) so reject it. Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it. Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it. Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\). OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D) @karishma To be honest what is probability of such questions landing up on your gmat and on what level ... I think, I would just flip the computer table and walk out rather than solve such types



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
11 Mar 2012, 02:17
shawndx wrote: I do not understand the rule though... so if we were to just substitute values, how would one do that... if n were 3 or 4 \(a_3\) depends on \(a_1\) and \(a_2\). Given the values of \(a_1\) and \(a_2\), you can find the values of all other terms. Say if \(a_1 = 1\) and \(a_2 = 1.5\), then \(a_3 = Greater (1 + 1, 1.5) = 2\) \(a_4 = Greater (1.5+ 1, 2) = 2.5\) etc On the other hand, if \(a_1 = 1\) \(a_2 = 1.8\), then \(a_3 = Greater (1 + 1, 1.8) = 2\) \(a_4 = Greater (1.8+ 1, 2) = 2.8\) etc
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: The Sequence a(n) is... [#permalink]
Show Tags
11 Mar 2012, 02:21
utkarshlavania wrote: @karishma To be honest what is probability of such questions landing up on your gmat and on what level ... I think, I would just flip the computer table and walk out rather than solve such types
The question is not tough Utkarsh. I would suggest you to go one step at a time and try to figure it out. Such questions can be a part of actual GMAT and it's just a 700+, not exceptionally over the top. It looks complicated but most of the steps would be kind of intuitive after some practice. GMAT excels at testing simple concepts wrapped in a twisted package.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Intern
Joined: 01 Jun 2012
Posts: 21
Location: United States
Concentration: Nonprofit
GPA: 3.83

Re: The Sequence a(n) is... [#permalink]
Show Tags
04 Nov 2012, 15:53
VeritasPrepKarishma wrote: shawndx wrote: The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n2) +1) and (an1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?
a) a1=1, a2=1.5 b) a1=1, a2=1 c) a1=1, a2=1 d) a1=1, a2=1.5 e) a1=1.5, a2=1
I am having trouble understanding what the question is asking and also solving it Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally. Given: \(a_n\) = Greater of \((a_{n2} + 1, a_{n1})\) (n is 3 or greater) This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term) If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term' So what can you deduce about \(a_1\) and \(a_2\)? 1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B) 2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\) Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= 0.5)\) so reject it. Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it. Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it. Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\). OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D) Hi Karishma, Thanks for your blog...I have been trying to solve every problem without using a pen per your advice and I am getting better at the quant section as a result. Here is where I am confused about the above problem: "If we want that every term in the sequence should be unique, \(n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'" I'm reading the rule as \(A(n)\) is greater than \(A(n2) + 1\). Above, you say they must be equal (at least that is how I'm reading it). Overall, the wording of this problem is awkward to me. I've never seen the phrase "...is the greater of". That just means it is great than, right?



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: The Sequence a(n) is... [#permalink]
Show Tags
04 Nov 2012, 21:29
egiles wrote: "If we want that every term in the sequence should be unique, \(n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term'"
I'm reading the rule as \(A(n)\) is greater than \(A(n2) + 1\). Above, you say they must be equal (at least that is how I'm reading it). Overall, the wording of this problem is awkward to me. I've never seen the phrase "...is the greater of". That just means it is great than, right? There are 2 diff things: 1. 'Is greater than' x is greater than 4 and 5. This means x is a number greater than 5. 2. 'Is greater of' x is greater of 4 and 5. This means x = 5. Look at it this way: x = Greater of (4, 5) First you find that which number is greater out of 4 and 5. x will be equal to that number. x = Greater of (Last to last term + 1, Last term) means find which is greater 'Last to last term + 1' or 'Last term'. X will be equal to that.
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15933

Re: The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
21 Feb 2014, 12:35
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources



Intern
Joined: 20 May 2014
Posts: 39

Re: The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
03 Jul 2014, 09:41
VeritasPrepKarishma wrote: shawndx wrote: The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n2) +1) and (an1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?
a) a1=1, a2=1.5 b) a1=1, a2=1 c) a1=1, a2=1 d) a1=1, a2=1.5 e) a1=1.5, a2=1
I am having trouble understanding what the question is asking and also solving it Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally. Given: \(a_n\) = Greater of \((a_{n2} + 1, a_{n1})\) (n is 3 or greater) This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term) If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term' So what can you deduce about \(a_1\) and \(a_2\)? 1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B) 2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\) Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= 0.5)\) so reject it. Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it. Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it. Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\). OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D) KARISHMA (SORRY FOR CAPS JUST TRYING TO HIGHLIGHT WHERE MY QUESTION IS): WHEN YOU SAY N IS 3 OR GREATER TOWARDS THE BEGINNING OF YOUR ANSWER HOW EXACTLY DID YOU DEDUCE THAT? SECONDLY WHEN YOU ARE TESTING ANSWER CHOICES HOW EXACTLY DO YOU GET THE VALUE OF A3? FOR EXAMPLE WHEN YOU TEST CHOICE C HOW DID YOU GET A3 = 2? THANKS



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

Re: The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
03 Jul 2014, 19:38
sagnik2422 wrote: KARISHMA (SORRY FOR CAPS JUST TRYING TO HIGHLIGHT WHERE MY QUESTION IS): WHEN YOU SAY N IS 3 OR GREATER TOWARDS THE BEGINNING OF YOUR ANSWER HOW EXACTLY DID YOU DEDUCE THAT? SECONDLY WHEN YOU ARE TESTING ANSWER CHOICES HOW EXACTLY DO YOU GET THE VALUE OF A3? FOR EXAMPLE WHEN YOU TEST CHOICE C HOW DID YOU GET A3 = 2? THANKS Since all previous quotes have a lighter background, it is easy to see where your question is so don't worry about that. WHEN YOU SAY N IS 3 OR GREATER TOWARDS THE BEGINNING OF YOUR ANSWER HOW EXACTLY DID YOU DEDUCE THAT? It is given in the question: "The sequence a(n) is defined so that, for all n is greater than or equal to 3". SECONDLY WHEN YOU ARE TESTING ANSWER CHOICES HOW EXACTLY DO YOU GET THE VALUE OF A3? FOR EXAMPLE WHEN YOU TEST CHOICE C HOW DID YOU GET A3 = 2? We know that An is greater of A(n2) + 1 and A(n1). This means An will be either (A(n2)+ 1) or A(n1), whichever is greater! Now use options: a) a1=1, a2=1.5 A3 = Greater of (A(1)+1, A(2)) A3 = Greater of (1+1, 1.5) A3 = Greater of (0, 1.5) A3 = 0 c) a1=1, a2=1 A3 = Greater of (A(1)+1, A(2)) A3 = Greater of (1+1, 1) A3 = Greater of (2, 1) A3 = 2 and so on...
_________________
Karishma Veritas Prep  GMAT Instructor My Blog
Get started with Veritas Prep GMAT On Demand for $199
Veritas Prep Reviews



Senior Manager
Joined: 01 Nov 2013
Posts: 345
WE: General Management (Energy and Utilities)

Re: The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
16 Mar 2015, 02:02
shawndx wrote: The sequence \(a_n\) is defined so that, for all \(n\) is greater than or equal to 3, \(a_n\) is the greater of \(a_{n2} +1\) and \(a_{n1}\). (If the two quantities are the same, then \(a_n\) is equal to either of them.) Which of the following values of \(a_1\) and \(a_2\) will produce a sequence in which no value is repeated?
A. \(a_1=1\), \(a_2=1.5\) B. \(a_1=1\), \(a_2=1\) C. \(a_1=1\), \(a_2=1\) D. \(a_1=1\), \(a_2=1.5\) E. \(a_1=1.5\), \(a_2=1\)
I am having trouble understanding what the question is asking and also solving it I solved the first option to get a hang of what kind of series comes out... Quickly figured out that only in D it is possible \(a_{n2} +1\) is always greater than \(a_{n1}\) bcoz both entities are positive and \(a_2=1.5\) > \(a_1=1\)
_________________
Our greatest weakness lies in giving up. The most certain way to succeed is always to try just one more time.
I hated every minute of training, but I said, 'Don't quit. Suffer now and live the rest of your life as a champion.Mohammad Ali



Director
Joined: 07 Aug 2011
Posts: 579
Concentration: International Business, Technology

Re: The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
21 Mar 2015, 08:22
VeritasPrepKarishma wrote: shawndx wrote: The sequence a(n) is defined so that, for all n is greater than or equal to 3, a(n) is the greater of (a(n2) +1) and (an1). (If the two quantities are the same, then an is equal to either of them.) Which of the following values of a1 and a2 will produce a sequence in which no value is repeated?
a) a1=1, a2=1.5 b) a1=1, a2=1 c) a1=1, a2=1 d) a1=1, a2=1.5 e) a1=1.5, a2=1
I am having trouble understanding what the question is asking and also solving it Take one line of the question at a time and try to make sense of it. Sequence questions seem daunting due to all the subscripts but they are pretty straight forward, generally. Given: \(a_n\) = Greater of \((a_{n2} + 1, a_{n1})\) (n is 3 or greater) This means that starting from the third term, every term is the greater of (one more than previous to previous term, the previous term) If we want that every term in the sequence should be unique, \(a_n\) should not be equal to the previous term. It should be equal to 'one more than previous to previous term' So what can you deduce about \(a_1\) and \(a_2\)? 1. \(a_1 + 1\) should be greater than \(a_2\) so that \(a_3 \neq a_2\). Reject option (B) 2. To ensure that \(a_4 \neq a_3\), \(a_4 = a_2 + 1\). Therefore, \(a_2 + 1 > a_3\) Option (A) \(a_3\) = 0 which is greater than \(a_2 + 1 (= 0.5)\) so reject it. Option (C) \(a_3\) = 2 which is greater than \(a_2 + 1 (= 0)\) so reject it. Option (E) \(a_3\) = 2.5 which is greater than \(a_2 + 1 (= 2)\) so reject it. Answer must be option (D). \(a_3\) = 2 which is less than \(a_2 + 1\). OR if you want to think the logical way, realize that the first term must be smaller than the second term but the difference between them should be less than 1 (so that when 1 is added, it becomes more than the second term). If you understand this, then you can quickly jump to option (D) I have noticed that manahattan gmat questions are very time intensive. i would rather build the series for each of the given options AE , atleast 2 elements .
_________________
Thanks, Lucky
_______________________________________________________ Kindly press the to appreciate my post !!



GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15933

Re: The sequence a(n) is defined so that, for all n is greater [#permalink]
Show Tags
18 May 2016, 19:52
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.
_________________
GMAT Books  GMAT Club Tests  Best Prices on GMAT Courses  GMAT Mobile App  Math Resources  Verbal Resources




Re: The sequence a(n) is defined so that, for all n is greater
[#permalink]
18 May 2016, 19:52







