Last visit was: 12 Oct 2024, 17:48 It is currently 12 Oct 2024, 17:48
Decision Tracker
My Rewards
Unanswered
Active Topics
New posts
New comers' posts
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10129
Own Kudos [?]: 17491 [13]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   08 Feb 2019, 02:42
13
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

65% (hard)

Question Stats:

64% (03:16) correct 36% (03:10) wrong based on 132 sessions
Hide Show DIFFICULTY AND TIMER STATISTICS
[GMAT math practice question]

a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by \(3\) for \(n ≥ 2\). What is the value of a101 + a102 + a103 + a104 + a105 + a106 + a107 + a108?

A. 0
B. 3
C. 5
D. 7
E. 9
ShowHide Answer
Official Answer
E
User avatar
P
prabsahi
Joined: 09 Jun 2014
Posts: 225
Own Kudos [?]: 285 [0]
Given Kudos: 205
Location: India
Concentration: General Management, Operations
Send PM
Reviews Badge
a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   Updated on: 08 Feb 2019, 04:51
MathRevolution
[GMAT math practice question]

a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by \(3\) for \(n ≥ 2\). What is the value of a101 + a102 + a103 + a104 + a105 + a106 + a107 + a108?

A. 0
B. 3
C. 5
D. 7
E. 9

This is cyclicity question :

The series is as below
A1- 1
A2- 1
A3- 2
A4- 0
A5- 2
A-6 2
A7- 1
A8- 0

So together the sum of first segments gives 9 ..Now picking up any random segments will lead to same set of digits which will sum up to 9

So for even A161+ A162+ ...A168 =sum of digits will be 9 .
or A3 to A11 :)



Hope it helps!!

Originally posted by prabsahi on 08 Feb 2019, 03:52.
Last edited by prabsahi on 08 Feb 2019, 04:51, edited 2 times in total.
User avatar
G
KanishkM
Joined: 09 Mar 2018
Posts: 771
Own Kudos [?]: 465 [1]
Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
Send PM
Re: a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   08 Feb 2019, 04:18
1
Kudos
MathRevolution
[GMAT math practice question]

a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by \(3\) for \(n ≥ 2\). What is the value of a101 + a102 + a103 + a104 + a105 + a106 + a107 + a108?

A. 0
B. 3
C. 5
D. 7
E. 9

The trick was to find a pattern.
Keyword = Remainder when divided by 3
an is the remainder when an-1 + an-2 is divided by \(3\)

a_0 = 0
a_1 = 1
a_2 = 1 (1+0)/3
a_3 = 2 (1+1)/3
a_4 = 0 (2+1)/3
a_5 = 2 (0+2)/3
a_6 = 2 (0+2)/3
a_7 = 1 (2+2)/3
a_8 = 0(2+1)/3

If you go forward you will notice the same series.

So now the series starts from 101 ...... 108
1+1+2+0+2+2+1+0
9

E
User avatar
P
prabsahi
Joined: 09 Jun 2014
Posts: 225
Own Kudos [?]: 285 [0]
Given Kudos: 205
Location: India
Concentration: General Management, Operations
Send PM
Reviews Badge
Re: a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   08 Feb 2019, 04:32
KanishkM
MathRevolution
[GMAT math practice question]

a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by \(3\) for \(n ≥ 2\). What is the value of a101 + a102 + a103 + a104 + a105 + a106 + a107 + a108?

A. 0
B. 3
C. 5
D. 7
E. 9

The trick was to find a pattern.
Keyword = Remainder when divided by 3
an is the remainder when an-1 + an-2 is divided by \(3\)

a_0 = 0
a_1 = 1
a_2 = 1 (1+0)/3
a_3 = 2 (1+1)/3
a_4 = 0 (2+1)/3
a_5 = 2 (0+2)/3
a_6 = 2 (0+2)/3
a_7 = 1 (2+2)/3
a_8 = 0(2+1)/3

If you go forward you will notice the same series.

So now the series starts from 101 ...... 108
1+1+2+0+2+2+1+0
9

E


I see .I made a mistake :)

Thanks
User avatar
G
KanishkM
Joined: 09 Mar 2018
Posts: 771
Own Kudos [?]: 465 [0]
Given Kudos: 123
Location: India
Schools: DeGroote'21 Desautels '21 NUS '21
Send PM
Re: a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   08 Feb 2019, 04:38
prabsahi

I see .I made a mistake :)

Thanks

prabsahi, your approach was right. :thumbup:

But i still feel that is not the easiest way to solve it. :)
User avatar
P
prabsahi
Joined: 09 Jun 2014
Posts: 225
Own Kudos [?]: 285 [0]
Given Kudos: 205
Location: India
Concentration: General Management, Operations
Send PM
Reviews Badge
Re: a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   08 Feb 2019, 04:44
KanishkM
prabsahi

I see .I made a mistake :)

Thanks

prabsahi, your approach was right. :thumbup:

But i still feel that is not the easiest way to solve it. :)

yes..You are right KanishkM..Will update it :)

Thanks
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8084
Own Kudos [?]: 4380 [0]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy)
Send PM
GMAT ToolKit User CAT Tests
Re: a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   08 Feb 2019, 05:11
MathRevolution
[GMAT math practice question]

a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by \(3\) for \(n ≥ 2\). What is the value of a101 + a102 + a103 + a104 + a105 + a106 + a107 + a108?

A. 0
B. 3
C. 5
D. 7
E. 9


the pattern here followed is of divisibility of a no with 3 ; which is always for consective no is series of 0,1,2,0,1,2
0,1,2 is our pattern
so the 99th term would be 2 and 101st would be 1
so sum = 1+2+0+1+2+0+1+2; 9
IMO E
User avatar
P
prabsahi
Joined: 09 Jun 2014
Posts: 225
Own Kudos [?]: 285 [0]
Given Kudos: 205
Location: India
Concentration: General Management, Operations
Send PM
Reviews Badge
a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   08 Feb 2019, 05:14
Archit3110
MathRevolution
[GMAT math practice question]

a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by \(3\) for \(n ≥ 2\). What is the value of a101 + a102 + a103 + a104 + a105 + a106 + a107 + a108?

A. 0
B. 3
C. 5
D. 7
E. 9


the pattern here followed is of divisibility of a no with 3 ; which is always for consective no is series of 0,1,2,0,1,2
0,1,2 is our pattern
so the 99th term would be 2 and 101st would be 1
so sum = 1+2+0+1+2+0+1+2; 9
IMO E


Hi Archit,

I guess you made a similar mistake like I did.

Please check the pattern mentioned in my previous post or KanishkM's.I have corrected it.

Its 0 1 1 2 0 2 2 1 0

Hope it helps !!
User avatar
L
MathRevolution
Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 10129
Own Kudos [?]: 17491 [0]
Given Kudos: 4
GMAT 1: 760 Q51 V42
GPA: 3.82
Send PM
Re: a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   10 Feb 2019, 18:14
Expert Reply
=>

a0 = 0
a1 = 1
a2 = a1 + a0 = 1 + 0 = 1
a3 = a2 + a1 = 1 + 1 = 2
a4 = 0 since a3 + a2 = 2 + 1 = 3 = 3(1)+0, and the remainder when a3 + a2 is divided by 3 is zero.
a5 = a4 + a3 = 0 + 2 = 2
a6 = a5 + a4 = 2 + 0 = 2
a7 = 1 since a6 + a5 = 2 + 2 = 4= 3(1)+1, and the remainder when a6 + a5 is divided by 3 is 1.
a8 = 0 since a7 + a6 = 1 + 2 = 3= 3(1)+0, the remainder is 0, when a7 + a6 is divided by 3.
a9 = a8 + a7 = 0 + 1 = 1
Thus, the sequence is periodic, with period 8.
a101 + a102 + a103 + a104 + a105 + a106 + a107 + a108
= a5 + a6 + a7 + a0 + a1 + a2 + a3 + a4
\(= 2 + 2 + 1 + 0 + 1 + 1 + 2 + 0 = 9\)
Therefore, the answer is E.
Answer: E
avatar
B
SWAPNILP
Joined: 13 Mar 2018
Posts: 12
Own Kudos [?]: 2 [0]
Given Kudos: 183
Send PM
Re: a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   13 Feb 2019, 07:51
KanishkM
MathRevolution
[GMAT math practice question]

a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by \(3\) for \(n ≥ 2\). What is the value of a101 + a102 + a103 + a104 + a105 + a106 + a107 + a108?

A. 0
B. 3
C. 5
D. 7
E. 9

The trick was to find a pattern.
Keyword = Remainder when divided by 3
an is the remainder when an-1 + an-2 is divided by \(3\)

a_0 = 0
a_1 = 1
a_2 = 1 (1+0)/3
a_3 = 2 (1+1)/3
a_4 = 0 (2+1)/3
a_5 = 2 (0+2)/3
a_6 = 2 (0+2)/3
a_7 = 1 (2+2)/3
a_8 = 0(2+1)/3

If you go forward you will notice the same series.

So now the series starts from 101 ...... 108
1+1+2+0+2+2+1+0
9

E
I dont understand what quotient to take here. Please explain.
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 35208
Own Kudos [?]: 891 [0]
Given Kudos: 0
Send PM
Re: a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink] a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f   16 Aug 2024, 23:47
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 Club Bot
gmatclubot
Re: a0 = 0, a1 = 1. an is the remainder when an-1 + an-2 is divided by 3 f [#permalink]
16 Aug 2024, 23:47
Moderator:
Bunuel
Math Expert
96080 posts