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

It is currently 24 Sep 2018, 00:43

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

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the

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

Hide Tags

Manager
Manager
avatar
Joined: 16 Apr 2006
Posts: 225
In the sequence 1, 2, 4, 8, 16, 32, …, each term after the  [#permalink]

Show Tags

New post 03 Nov 2010, 02:51
1
3
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

65% (01:15) correct 35% (01:32) wrong based on 295 sessions

HideShow timer Statistics

In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?

(1) t3 = 1/4
(2) t1 - t5 = 15/16

_________________

Trying hard to achieve something unachievable now....

Most Helpful Expert Reply
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8288
Location: Pune, India
Re: GWD set 4-Q15 concept question.  [#permalink]

Show Tags

New post 30 Jan 2014, 21:33
4
1
sehosayho wrote:
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

I sloved this question, but I heard antoher theory that can solve this question.
The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1
And I don't understand how this works.
Can some explain how this concept work??


This is the concept of a geometric progression (GP). In a GP, every term is related to the previous term by a fixed ratio r.
So \(t_2 = t_1*r\)
\(t_3 = t_2*r = t_1*r*r\) (substituting from above)
\(t_4 = t_3*r = t_1*r*r*r\)
I hope you understand this.

Here, you are given that \(t_{n+1} = t_n *(\frac{1}{2})\)
So r = 1/2
\(t_2 = t_1 * (1/2)\)
\(t_3 = t_1*(1/2)*(1/2)\)
\(t_4 = t_1 *(1/2)^3\)
\(t_5 = t_1 * (1/2)^4\)

Statement 1 gives you \(t_1\) so you get \(t_5\) easily.
Statement 2 gives you \(t_1 - t_5\). You can substitute \(t_5\) from above and get \(t_1\) and then \(t_5\).

Check out this post on GPs: http://www.veritasprep.com/blog/2012/04 ... gressions/
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

General Discussion
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49364
In the sequence 1, 2, 4, 8, 16, 32, …, each term after the  [#permalink]

Show Tags

New post 03 Nov 2010, 03:14
2
2
dkverma wrote:
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers
n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16


Given: \(t_{n+1}=\frac{t_n}{2}\). So \(t_2=\frac{t_1}{2}\), \(t_3=\frac{t_2}{2}=\frac{t_1}{4}\), \(t_4=\frac{t_3}{2}=\frac{t_1}{8}\), ...

Basically we have geometric progression with common ratio \(\frac{1}{2}\): \(t_1\), \(\frac{t_1}{2}\), \(\frac{t_1}{4}\), \(\frac{t_1}{8}\), ... --> \(t_n=\frac{t_1}{2^{n-1}}\).

Question: \(t_5=\frac{t_1}{2^4}=?\)

(1) \(t_3=\frac{1}{4}\) --> we can get \(t_1\) --> we can get \(t_5\). Sufficient.
(2) \(t_1-t_5=2^4*t_5-t_5=\frac{15}{16}\) --> we can get \(t_5\). Sufficient.

Answer: D.

Generally for arithmetic (or geometric) progression if you know:

- any particular two terms,
- any particular term and common difference (common ratio),
- the sum of the sequence and either any term or common difference (common ratio),

then you will be able to calculate any missing value of given sequence.

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Manager
Manager
avatar
Joined: 16 Apr 2006
Posts: 225
Re: Sequence of Non-Zero  [#permalink]

Show Tags

New post 03 Nov 2010, 03:19
Thanks Bunuel for the detailed explanation.
_________________

Trying hard to achieve something unachievable now....

Intern
Intern
avatar
Joined: 26 Aug 2013
Posts: 11
GWD set 4-Q15 concept question.  [#permalink]

Show Tags

New post 30 Jan 2014, 19:38
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

I sloved this question, but I heard antoher theory that can solve this question.
The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1
And I don't understand how this works.
Can some explain how this concept work??
Manager
Manager
avatar
Joined: 19 Apr 2013
Posts: 74
Concentration: Entrepreneurship, Finance
GMAT Date: 06-05-2015
GPA: 3.88
WE: Programming (Computer Software)
GMAT ToolKit User
Re: GWD set 4-Q15 concept question.  [#permalink]

Show Tags

New post 30 Jan 2014, 20:27
1
sehosayho wrote:
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

I sloved this question, but I heard antoher theory that can solve this question.
The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1
And I don't understand how this works.
Can some explain how this concept work??


Hi, it is very simple.

The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1. In this theory they just generalize it.

Given -- tn+1 = tn/2

Putting n = n- 1

tn= t(n-1) *1/ 2 ----- consider this first equation.
while

t(n-1) = t(n-2)*1/2 ----- consider this 2nd equation.

if you put t(n-1) in first equation

tn = t(n-2) * 1/ 2^2

so when we need t1 on the right hand side.

tn=t1*(1/2)^n-1

Easy way to understand is ---

t2 = t1/2

t3 = t2 / 2

t3 = t1* 1/2^2

So on generalization

tn = t1* 1/ 2^(n-1)

Hope I make it clear.
_________________

Thanks,
AB

+1 Kudos if you like and understand.

Intern
Intern
avatar
Joined: 26 Aug 2013
Posts: 11
Re: GWD set 4-Q15 concept question.  [#permalink]

Show Tags

New post 30 Jan 2014, 20:58
bhatiamanu05 wrote:
sehosayho wrote:
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

I sloved this question, but I heard antoher theory that can solve this question.
The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1
And I don't understand how this works.
Can some explain how this concept work??


Hi, it is very simple.

The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1. In this theory they just generalize it.

Given -- tn+1 = tn/2

Putting n = n- 1

tn= t(n-1) *1/ 2 ----- consider this first equation.
while

t(n-1) = t(n-2)*1/2 ----- consider this 2nd equation.

if you put t(n-1) in first equation

tn = t(n-2) * 1/ 2^2

so when we need t1 on the right hand side.

tn=t1*(1/2)^n-1

Easy way to understand is ---

t2 = t1/2

t3 = t2 / 2

t3 = t1* 1/2^2

So on generalization

tn = t1* 1/ 2^(n-1)

Hope I make it clear.





Thanks! I considered your explanation and got the idea.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49364
Re: GWD set 4-Q15 concept question.  [#permalink]

Show Tags

New post 30 Jan 2014, 22:36
sehosayho wrote:
In the sequence of nonzero numbers t1, t2, t3, …, tn, …, tn+1 = tn / 2 for all positive integers n. What is the value of t5?
(1) t3 = 1/4
(2) t1 - t5 = 15/16

I sloved this question, but I heard antoher theory that can solve this question.
The theory is that tn+1 = tn / 2 equals tn=t1*(1/2)^n-1
And I don't understand how this works.
Can some explain how this concept work??


Merging similar topics. Please refer to the solutions above.

Also, please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html Pay attention to rules 1 and 3. Thank you.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 8162
Premium Member
Re: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the  [#permalink]

Show Tags

New post 21 Feb 2017, 14:04
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: In the sequence 1, 2, 4, 8, 16, 32, …, each term after the &nbs [#permalink] 21 Feb 2017, 14:04
Display posts from previous: Sort by

In the sequence 1, 2, 4, 8, 16, 32, …, each term after the

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

Events & Promotions

PREV
NEXT


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®.