Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 03 Feb 2010
Posts: 56

In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
31 Mar 2010, 11:47
Question Stats:
61% (02:44) correct 39% (02:41) wrong based on 1206 sessions
HideShow timer Statistics
In the infinite sequence A, \(A_n = x^{(n1)} + x^n + x^{(n+1)} + x^{(n+2)} + x^{(n+3)}\) where x is a positive integer constant. For what value of n is the ratio of \(A_n\) to \(x(1+x(1+x(1+x(1+x))))\) equal to x^5? A. 8 B. 7 C. 6 D. 5 E. 4
Official Answer and Stats are available only to registered users. Register/ Login.




Math Expert
Joined: 02 Sep 2009
Posts: 59587

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
31 Mar 2010, 12:33
ksharma12 wrote: 18. In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X^(n+3) where x is a positive integer constant. For what value of n is the ratio of An to x(1+x(1+x(1+x(1+x)))) equal to X^5? (A) 8 (B) 7
(C) 6 (D) 5 (E) 4
note: An= A sub n
Can you explain this in detail? I tried expanding out the bottom equation and solving for X to equal x^5. Didnt really work out... \(x^5=\frac{x^{(n1)}+x^n+x^{(n+1)}+x^{(n+2)}+x^{(n+3)}}{x(1+x(1+x(1+x(1+x))))}\) > \(x^6(1+x(1+x(1+x(1+x))))=x^{(n1)}+x^n+x^{(n+1)}+x^{(n+2)}+x^{(n+3)}\) > take \(x^{(n1)}\) out of the brackets > \(x^6(1+x(1+x(1+x(1+x))))=x^{(n1)}(1+x+x^2+x^3+x^4)\) > \(x^6(1+x(1+x(1+x(1+x))))=x^{(n1)}(1+x(1+x+x^2+x^3))\) > \(x^6(1+x(1+x(1+x(1+x))))=x^{(n1)}(1+x(1+x(1+x+x^2)))\) > \(x^6(1+x(1+x(1+x(1+x))))=x^{(n1)}(1+x(1+x(1+x(1+x))))\) > \(x^6=x^{(n1)}\) > \(n1=6\) > \(n=7\) Answer: B.
_________________




Manager
Joined: 27 Jul 2010
Posts: 132
Location: Prague
Schools: University of Economics Prague

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
02 Feb 2011, 08:32
Its not so hard when you realize how can you solve it, but until that, you spent half of your life.




Manager
Joined: 03 Feb 2010
Posts: 56

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
31 Mar 2010, 13:19
great explanation. Thanks. +1 to you



Manager
Joined: 05 Mar 2010
Posts: 147

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
01 Apr 2010, 11:41
Is it a GMAT level question??????
_________________



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
02 Feb 2011, 21:37
craky wrote: Its not so hard when you realize how can you solve it, but until that, you spent half of your life. Oh no you don't. Work smart! \(An = x^{n1} + x^n + x^{n+1} + x^{n+2} + x^{n+3}\) e.g. \(A2 = x + x^2 + x^3 + x^4 + x^5\) Notice you can only take x common out of all these terms i.e. the smallest term \(x^{n  1}\) If \(\frac{An}{{x(1+x(1+x(1+x(1+x))))}} = x^5\), it means the part: (1+x(1+x(1+x(1+x)))) will get canceled from the num and den. Ignore it. From An, you will be able to take out \(x^6\) common so that \(\frac{x^6}{x}\) gives you \(x^5\) So smallest term must be \(x^6\) i.e. \(x^{n1}\). Therefore, n = 7.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Retired Moderator
Joined: 16 Nov 2010
Posts: 1232
Location: United States (IN)
Concentration: Strategy, Technology

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
04 Feb 2011, 06:00
Hi Karishma What is the meaning of this ? "it means the part: (1+x(1+x(1+x(1+x)))) will get canceled from the num and den." Regards, Subhash
_________________
Formula of Life > Achievement/Potential = k * Happiness (where k is a constant) GMAT Club Premium Membership  big benefits and savings



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
04 Feb 2011, 08:20
subhashghosh wrote: Hi Karishma
What is the meaning of this ?
"it means the part: (1+x(1+x(1+x(1+x)))) will get canceled from the num and den."
Regards, Subhash \(A2 = x + x^2 + x^3 + x^4 + x^5\) \(\frac{An}{{x(1+x(1+x(1+x(1+x))))}} = x^5\) Since the right side of the equation is just x^5, it means the entire expression: (1+x(1+x(1+x(1+x)))) should get canceled out which means we will get the same expression in the numerator as well. You don't need to do it. It is logical since otherwise, you will not get the reduced expression x^5. Also, you can see that you will get something like this in the numerator since the powers are increasing. If you want to see it: \(A2= x( 1 + x + x^2 + x^3 + x^4) = x( 1 + x(1 + x + x^2 + x^3)) = x( 1 + x(1 + x( 1 + x + x^2))) = x( 1 + x(1 + x( 1 + x( 1 + x))))\) Similarly A7 \(= x^6( 1 + x(1 + x( 1 + x( 1 + x))))\) So \(\frac{A7}{{x(1+x(1+x(1+x(1+x))))}} = \frac{x^6( 1 + x(1 + x( 1 + x( 1 + x))))}{x( 1 + x(1 + x( 1 + x( 1 + x))))}= x^5\)
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Retired Moderator
Joined: 20 Dec 2010
Posts: 1546

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
04 Feb 2011, 08:26
\(A_n=x^{(n1)}(1+x+x^2+x^3+x^4)\) \(x(1+x(1+x(1+x(1+x))))=x(1+x+x^2+x^3+x^4)\)
\(\frac{x^{(n1)}(1+x+x^2+x^3+x^4)}{x(1+x+x^2+x^3+x^4)}=x^5\)
\(x^{(n1)}=x^6\) \(n1=6\) \(n=7\)
Ans: "B"



Intern
Joined: 30 Mar 2011
Posts: 46
Schools: Virginia Tech

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
13 Apr 2011, 13:25
I hope this is a 700+ level question...



Manager
Joined: 14 Feb 2011
Posts: 60

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
27 Dec 2011, 13:03
aznboi986 wrote: I hope this is a 700+ level question... this is 800+ level question You definitely do not see any question like this one on real exam. GC problems usually too difficult.



Intern
Joined: 28 Jan 2012
Posts: 2

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
05 Jun 2012, 09:42
i) x(1 + x(1 + x(1 + x(1 + x)))) = x + x^2 + x^3 + x^4 + x^5 ii) An = x^(n2) (x + x^2 + x^3 + x^4 + x^5)
Divide ii by i = x^(n2) We want ratio = x^5. So, n2 = 5 => n = 7. (B)



Manager
Status: Prevent and prepare. Not repent and repair!!
Joined: 13 Feb 2010
Posts: 172
Location: India
Concentration: Technology, General Management
GPA: 3.75
WE: Sales (Telecommunications)

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
24 Jul 2012, 19:27
omg.. by the time u read and digest the question its 1 minut e



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
24 Jul 2012, 21:36
rajathpanta wrote: omg.. by the time u read and digest the question its 1 minut e It certainly takes you a minute or even more to get through the question and digest it but after that, it takes you less than a minute to solve it. This is true for most GMAT questions. If you understand the question well, it takes you very little time to actually solve it. If you don't understand the question well, you could end up spending 20 mins on it.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Retired Moderator
Joined: 23 Oct 2011
Posts: 196

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
30 Jul 2012, 22:28
Is this a typical 700 level GMAT question? or just an off topic question? experts pls advice.



Director
Joined: 22 Mar 2011
Posts: 584
WE: Science (Education)

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
31 Jul 2012, 01:49
mohankumarbd wrote: Is this a typical 700 level GMAT question? or just an off topic question? experts pls advice. Who can tell you? If you ask all those who took the test if they ever saw such a question on a real test, you might get the real picture... IMO, the chance is slim that such a question will appear on a real test. It is too technical, too lengthy to be done with plugging in numbers... Until now, I didn't get the feeling that GMAT wants to test just algebraic abilities. Not that this question needs some really advanced techniques, but it's above basics...
_________________
PhD in Applied Mathematics Love GMAT Quant questions and running.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
31 Jul 2012, 08:36
mohankumarbd wrote: Is this a typical 700 level GMAT question? or just an off topic question? experts pls advice. It is an algebra question that looks tricky but can be easily reasoned out. It will take you some time to understand the question but once you do, you can solve it quickly  pretty much like high level GMAT questions.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >



Intern
Joined: 03 Sep 2012
Posts: 3

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
05 Sep 2012, 09:02
I did it like it : as you can see x(1+x(1+x(1+x(1+x)))) X comes 5 times, therefore the max term will be X^5, in the question you see that you want to arrive at X^5 so it means that in the sum of X^n1...x^n+3 the max term must be X^10 so that it can be x^5(x^5) therefore 10 = 3+n, n=7, timer indicate me 1min 53.
But definitely i had the answer, but i was unable to demonstrate it in that time, it would take more like 5 to 10 minutes.



Intern
Joined: 17 Sep 2013
Posts: 24
Location: United States
Concentration: Economics, Statistics
GPA: 3.36
WE: Analyst (Health Care)

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
19 Sep 2013, 13:34
Could someone please explain to me how that's an infinite sequence? That's what really threw me off.



Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9850
Location: Pune, India

Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
Show Tags
19 Sep 2013, 21:48
mfabros wrote: Could someone please explain to me how that's an infinite sequence? That's what really threw me off. The information that it is an infinite sequence doesn't have much to do with the question. You are given this only to tell you that n can take any positive integer value. An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X^(n+3) tells you that the nth term is given by plugging in the value of n in this expression. A is not a sequence of 2 or 4 terms but infinite so n can take any value. We found out that the required relation holds when n is 7. We could have just as well got n = 10298 and that would have been fine too since A has infinite terms so any value for n is alright.
_________________
Karishma Veritas Prep GMAT Instructor
Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >




Re: In the infinite sequence A, An = X^(n1) + X^n + X^(n+1) + X^(n+2) + X
[#permalink]
19 Sep 2013, 21:48



Go to page
1 2
Next
[ 30 posts ]



