Author 
Message 
TAGS:

Hide Tags

Intern
Joined: 06 Jul 2015
Posts: 22

Re: Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
Show Tags
09 Dec 2015, 21:29
There is a sequence An such that A1=2, A2=5, and An=An−1An−2,when n is an integer greater than 2. What is the value of A149? A1 = 2 A2 = 5 A3 = 5/2 A4= 1/2 A5 = 1/5 A6 = 2/5 A7 = 2 A8 = 5 The numbers are repeating after six steps. The closest multiple of 6 to 149 is 144 . We are 5 five short to 149 . So A149 = A5 Which is 1/5 so the answer is E



Current Student
Joined: 18 Oct 2014
Posts: 797
Location: United States
GPA: 3.98

Re: Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
Show Tags
10 Dec 2015, 13:04
I would go with option 'C' i.e/ 2.5. Please advise if the answer is correct.
_________________
I welcome critical analysis of my post!! That will help me reach 700+



Intern
Joined: 07 Dec 2015
Posts: 1

Re: Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
Show Tags
10 Dec 2015, 23:55
A1=2 A2=5 A3=A2/A1=5/2=2.5 A4=A3/A2=2.5/5=1/2=0.5 A5=A4/A3=0.5/2.5=1/5=0.2 A6=A5/A4=0.2/0.5=2/5=0.4 A7=A6/A5=0.4/0.2=2
A8=A7/A6=2/0.4=5 After every 6 terms the numbers are repeating, so to find A149 divide 149 by 6 & u get a remainder 5.
So A149=A5=1/5



Intern
Joined: 10 Dec 2015
Posts: 4

Re: Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
Show Tags
11 Dec 2015, 04:12
Answer is E, i.e. 1/5



Intern
Joined: 05 Jun 2013
Posts: 35

Re: Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
Show Tags
11 Dec 2015, 11:54
A1=2, A2=5, and An=An−1/An−2
A3=A2/A1 A4=A3/A2=A2/A1*A2 = 1/A1 A5=A4/A3= 1/A2 A6=A5/A4= A1/A2 A7= A6/A5=A1 A8=A7/A6=A2 A9=A8/A7=A2/A1
A3=A9=A2/A1 So the sequence repeats at A3,A9,A15,A21........and goes on till A147 Therefore A147= A2/A1 A148=1/A1 A149= 1/A2
A2=5 and 1/A2= 1/5 Therefore answer is 1/5 and choice E.



Math Expert
Joined: 02 Sep 2009
Posts: 59020

Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
Show Tags
14 Dec 2015, 09:13
Bunuel wrote: Math Revolution and GMAT Club Contest Starts! QUESTION #8:There is a sequence \(A_n\) such that \(A_1=2\), \(A_2=5\), and \(A_n=\frac{A_{n1}}{A_{n2}}\),when n is an integer greater than 2. What is the value of \(A_{149}\)? A. 2 B. 5 C. 2.5 D. 1/2 E. 1/5 Check conditions below: Math Revolution and GMAT Club ContestThe Contest Starts November 28th in Quant Forum We are happy to announce a Math Revolution and GMAT Club Contest For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday). To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize: PS + DS course with 502 videos that is worth $299! All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
Thank you! MATH REVOLUTION OFFICIAL SOLUTION:Generally it is best to substitute in solving sequence questions. The sequence for this question is, \(A_1=2\), \(A_2=5\), \(A_3=\frac{A_2}{A_1}=\frac{5}{2}\), \(A_4=\frac{A_3}{A_2}=(5/2)/5=\frac{1}{2}\), \(A_5=\frac{1}{5}\) and \(A_6=\frac{2}{5}\). This means \(A_{n+6}=A_n\). Then, if we divide \(149=6*24+5\) by 6, the remainder is 5. So, \(A_{149}=A_6*24+5=A_5=\frac{1}{5}\) and E is a correct answer.
_________________



Senior SC Moderator
Joined: 14 Nov 2016
Posts: 1347
Location: Malaysia

Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
Show Tags
18 Feb 2017, 01:50
Bunuel wrote: Bunuel wrote: Math Revolution and GMAT Club Contest Starts! QUESTION #8:There is a sequence \(A_n\) such that \(A_1=2\), \(A_2=5\), and \(A_n=\frac{A_{n1}}{A_{n2}}\),when n is an integer greater than 2. What is the value of \(A_{149}\)? A. 2 B. 5 C. 2.5 D. 1/2 E. 1/5 Check conditions below: Math Revolution and GMAT Club ContestThe Contest Starts November 28th in Quant Forum We are happy to announce a Math Revolution and GMAT Club Contest For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday). To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize: PS + DS course with 502 videos that is worth $299! All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
Thank you! MATH REVOLUTION OFFICIAL SOLUTION:Generally it is best to substitute in solving sequence questions. The sequence for this question is, \(A_1=2\), \(A_2=5\), \(A_3=\frac{A_2}{A_1}=\frac{5}{2}\), \(A_4=\frac{A_3}{A_2}=(5/2)/5=\frac{1}{2}\), \(A_5=\frac{1}{5}\) and \(A_6=\frac{2}{5}\). This means \(A_{n+6}=A_n\). Then, if we divide \(149=6*24+5\) by 6, the remainder is 5. So, \(A_{149}=A_6*24+5=A_5=\frac{1}{5}\) and E is a correct answer. Dear Bunuel, \(A_{149}=A_6*24+5=A_5=\frac{1}{5}\)Does we conclude \(A_{149}=A_{5}\) by obtaining the remainder equal to \(5\)?
_________________
"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: 59020

Re: Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
Show Tags
18 Feb 2017, 01:57
ziyuenlau wrote: Bunuel wrote: Bunuel wrote: Math Revolution and GMAT Club Contest Starts! QUESTION #8:There is a sequence \(A_n\) such that \(A_1=2\), \(A_2=5\), and \(A_n=\frac{A_{n1}}{A_{n2}}\),when n is an integer greater than 2. What is the value of \(A_{149}\)? A. 2 B. 5 C. 2.5 D. 1/2 E. 1/5 Check conditions below: Math Revolution and GMAT Club ContestThe Contest Starts November 28th in Quant Forum We are happy to announce a Math Revolution and GMAT Club Contest For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday). To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize: PS + DS course with 502 videos that is worth $299! All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
Thank you! MATH REVOLUTION OFFICIAL SOLUTION:Generally it is best to substitute in solving sequence questions. The sequence for this question is, \(A_1=2\), \(A_2=5\), \(A_3=\frac{A_2}{A_1}=\frac{5}{2}\), \(A_4=\frac{A_3}{A_2}=(5/2)/5=\frac{1}{2}\), \(A_5=\frac{1}{5}\) and \(A_6=\frac{2}{5}\). This means \(A_{n+6}=A_n\). Then, if we divide \(149=6*24+5\) by 6, the remainder is 5. So, \(A_{149}=A_6*24+5=A_5=\frac{1}{5}\) and E is a correct answer. Dear Bunuel, \(A_{149}=A_6*24+5=A_5=\frac{1}{5}\)Does we conclude \(A_{149}=A_{5}\) by obtaining the remainder equal to \(5\)? The sequence goes in blocks of 6 {2, 5, 5/2, 1/2, 1/5, 2/5} {2, 5, 5/2, 1/2, 1/5, 2/5} {2, 5, 5/2, 1/2, 1/5, 2/5}... 149 is a multiple of 6 (144) plus 5, thus A149 equals to 5th number in the pattern, which is 1/5.
_________________



SVP
Joined: 03 Jun 2019
Posts: 1838
Location: India

Re: Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
Show Tags
01 Jul 2019, 22:23
Bunuel wrote: Math Revolution and GMAT Club Contest Starts! QUESTION #8:There is a sequence \(A_n\) such that \(A_1=2\), \(A_2=5\), and \(A_n=\frac{A_{n1}}{A_{n2}}\),when n is an integer greater than 2. What is the value of \(A_{149}\)? A. 2 B. 5 C. 2.5 D. 1/2 E. 1/5 Check conditions below: Math Revolution and GMAT Club ContestThe Contest Starts November 28th in Quant Forum We are happy to announce a Math Revolution and GMAT Club Contest For the following four (!) weekends we'll be publishing 4 FRESH math questions per weekend (2 on Saturday and 2 on Sunday). To participate, you will have to reply with your best answer/solution to the new questions that will be posted on Saturday and Sunday at 9 AM Pacific. Then a week later, the forum moderator will be selecting 2 winners who provided most correct answers to the questions, along with best solutions. Those winners will get 6months access to GMAT Club Tests. PLUS! Based on the answers and solutions for all the questions published during the project ONE user will be awarded with ONE Grand prize: PS + DS course with 502 videos that is worth $299! All announcements and winnings are final and no whining GMAT Club reserves the rights to modify the terms of this offer at any time. NOTE: Test Prep Experts and Tutors are asked not to participate. We would like to have the members maximize their learning and problem solving process.
Thank you! A1 =2 A2 = 5 A3 =5/2 A4 = 1/2 A5 = 1/5 A6 = 2/5 A7 = 2 A8 = 5 We see that A7 = A1 & A8 = A2, in general A(6+k) = Ak 149 = 6*24 + 5 A149 = A5 = 1/5 IMO E
_________________
"Success is not final; failure is not fatal: It is the courage to continue that counts." Please provide kudos if you like my post. Kudos encourage active discussions. My GMAT Resources:  Efficient LearningAll you need to know about GMAT quantTele: +911140396815 Mobile : +919910661622 Email : kinshook.chaturvedi@gmail.com




Re: Math Revolution and GMAT Club Contest! There is a sequence An such
[#permalink]
01 Jul 2019, 22:23



Go to page
Previous
1 2
[ 29 posts ]



