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

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

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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  Joined: 10 Dec 2015
Posts: 4
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Intern  B
Joined: 05 Jun 2013
Posts: 35
Re: Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

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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 V
Joined: 02 Sep 2009
Posts: 62285
Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

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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 V Joined: 14 Nov 2016 Posts: 1342 Location: Malaysia Math Revolution and GMAT Club Contest! There is a sequence An such [#permalink] ### Show Tags 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 $$5$$?
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Math Expert V
Joined: 02 Sep 2009
Posts: 62285
Re: Math Revolution and GMAT Club Contest! There is a sequence An such  [#permalink]

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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  V Joined: 03 Jun 2019 Posts: 2310 Location: India GMAT 1: 690 Q50 V34 WE: Engineering (Transportation) Re: Math Revolution and GMAT Club Contest! There is a sequence An such [#permalink] ### Show Tags 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 Re: Math Revolution and GMAT Club Contest! There is a sequence An such   [#permalink] 01 Jul 2019, 21:23

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