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

It is currently 19 Nov 2018, 01:24

INSEAD R1 Results This Week!

First Decision Reported on Decision Tracker  |  Join INSEAD Chat to Calm Your Nerves & Catch the Latest Action


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
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

The nth term of an increasing sequence S is given by Sn = Sn-1 + Sn-2

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

Hide Tags

Manager
Manager
avatar
S
Joined: 14 Sep 2015
Posts: 65
Location: India
GMAT 1: 700 Q45 V40
GPA: 3.41
GMAT ToolKit User
The nth term of an increasing sequence S is given by Sn = Sn-1 + Sn-2  [#permalink]

Show Tags

New post Updated on: 01 Jun 2017, 21:35
1
1
14
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

25% (02:57) correct 75% (03:00) wrong based on 136 sessions

HideShow timer Statistics

The nth term of an increasing sequence S is given by \(S_n = S_{n-1} + S_{n-2}\) for n > 2 and the nth term of a sequence S’ is given by \(S’_n = S’_{n-1} - S’_{n-2}\) for n > 2. If \(S_5 = S’_5\), what is the average (arithmetic mean) of \(S_2\) and \(S’_2\)?

(1) The difference between the fourth term and the second term of sequence S is 14.

(2) The sum of the fourth term and the second term of sequence S’ is 14.

Originally posted by niteshwaghray on 01 Jun 2017, 21:14.
Last edited by Bunuel on 01 Jun 2017, 21:35, edited 1 time in total.
Edited the question.
DS Forum Moderator
avatar
P
Joined: 21 Aug 2013
Posts: 1370
Location: India
Premium Member
Re: The nth term of an increasing sequence S is given by Sn = Sn-1 + Sn-2  [#permalink]

Show Tags

New post 01 Jun 2017, 22:13
2
Let the first 5 terms of sequence S be represented as: S1, S2, S3, S4, S5
Here S3 = S2+S1, S4 = S3+S2, S5 = S4+S3 ..

Let the first 5 terms of sequence S' be represented as: S1', S2', S3', S4', S5'
Here S4' = S3'-S2', S5' = S4'-S3'

Now lets look at the statements: (What I will try to do is write as many terms as possible in terms of either S2 or S2' because our objective is to calculate mean of S2 & S2', which we will get once we have the sum S2+S2')

Statement 1. S4-S2 = 14, Or S4 = 14+S2,
But S4 = S3+S2.. this means S3 = 14
Thus S5 = S4+S3 = 14+S2 + 14 = 28+S2
So S5 can be written in terms of S2 as '28+S2'.

We are given that S5 = S5', so S5' = 28+S2
Now, S5' = S4' - S3' and S4' = (S3'-S2') - S3' = -S2'

See, S5' can be written as (28+S2) and it can also be written as '-S2' . Equating them both:
28+S2 = -S2' Or S2+S2' = -28
We have their sum, so their average = -28/2. Sufficient.

Statement 2. S4' + S2' = 14. Now, S4' = S3'-S2' or S4'+S2' = S3'

But S4' + S2' = 14, So S3'=14.... Thus we can say S4' = S3'-S2' = 14-S2', and S5' will become:
S5' = S4'-S3' = 14-S2' - 14 = -S2'

We are given that S5 = S5' so S5 = -S2' or S4+S3 = -S2'
Replacing S4 with S3+S2, we have S3+S2 + S3 = -S2' or S2+S2' = -2S3

We have their sum in terms of variable S3, so mean cannot be calculated. Insufficient.

Hence A answer
Intern
Intern
avatar
B
Joined: 14 Oct 2016
Posts: 30
Location: India
WE: Sales (Energy and Utilities)
Premium Member
Re: The nth term of an increasing sequence S is given by Sn = Sn-1 + Sn-2  [#permalink]

Show Tags

New post 12 Sep 2017, 12:33
1
S(5)= s4+s3= s3+s2+s2+s1= S2+s1+s2+s2+s1= s2+2(s1+s2)
S'(5)=s'4-s'3=s'3-s'2-s'3= =-s'2

So -s'2= s2+2(s1+s2)
or (s2+s'2)/2= -(s1+s2)

To find : -(s1+s2) or s3.

STMT 1:
s4-s2= s3+s2-s2= s3= 14

We know that s3=s1+s2 and that is required to find

STMT 2:
s'4+s'2=14
s'3-s'2+s'2=14
s'3=14
No use of this value as it does not help us to reach the value of s3 or s1+s2


Hence A
_________________

Abhimanyu

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8819
Premium Member
Re: The nth term of an increasing sequence S is given by Sn = Sn-1 + Sn-2  [#permalink]

Show Tags

New post 23 Sep 2018, 05:20
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

GMAT Club Bot
Re: The nth term of an increasing sequence S is given by Sn = Sn-1 + Sn-2 &nbs [#permalink] 23 Sep 2018, 05:20
Display posts from previous: Sort by

The nth term of an increasing sequence S is given by Sn = Sn-1 + Sn-2

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


cron
Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.