GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 13 Nov 2019, 20:14

Close

GMAT Club Daily Prep

Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

Close

Request Expert Reply

Confirm Cancel

Math Revolution and GMAT Club Contest! There is a sequence An such

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Intern
Intern
avatar
B
Joined: 06 Jul 2015
Posts: 22
Reviews Badge
Re: Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

Show Tags

New post 09 Dec 2015, 21:29
2
1
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
User avatar
Joined: 18 Oct 2014
Posts: 797
Location: United States
GMAT 1: 660 Q49 V31
GPA: 3.98
GMAT ToolKit User
Re: Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

Show Tags

New post 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
Intern
avatar
Joined: 07 Dec 2015
Posts: 1
Re: Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

Show Tags

New post 10 Dec 2015, 23:55
1
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
Intern
avatar
Joined: 10 Dec 2015
Posts: 4
Re: Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

Show Tags

New post 11 Dec 2015, 04:12
Answer is E, i.e. 1/5
Intern
Intern
avatar
B
Joined: 05 Jun 2013
Posts: 35
Reviews Badge
Re: Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

Show Tags

New post 11 Dec 2015, 11:54
1
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
User avatar
V
Joined: 02 Sep 2009
Posts: 59020
Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

Show Tags

New post 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 \(A_n=\frac{A_{n-1}}{A_{n-2}}\),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 Contest

The 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 6-months 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
User avatar
V
Joined: 14 Nov 2016
Posts: 1347
Location: Malaysia
GMAT ToolKit User
Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

Show Tags

New post 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 \(A_n=\frac{A_{n-1}}{A_{n-2}}\),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 Contest

The 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 6-months 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/advanced-search/
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 59020
Re: Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

Show Tags

New post 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 \(A_n=\frac{A_{n-1}}{A_{n-2}}\),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 Contest

The 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 6-months 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
SVP
User avatar
P
Joined: 03 Jun 2019
Posts: 1838
Location: India
Premium Member Reviews Badge CAT Tests
Re: Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

Show Tags

New post 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 \(A_n=\frac{A_{n-1}}{A_{n-2}}\),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 Contest

The 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 6-months 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 Learning
All you need to know about GMAT quant

Tele: +91-11-40396815
Mobile : +91-9910661622
E-mail : kinshook.chaturvedi@gmail.com
GMAT Club Bot
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 ] 

Display posts from previous: Sort by

Math Revolution and GMAT Club Contest! There is a sequence An such

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  





Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne