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

It is currently 18 Sep 2018, 12:42

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 a certain series, each term (except for the first term) is one grea

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

Hide Tags

Retired Moderator
avatar
Joined: 29 Apr 2015
Posts: 854
Location: Switzerland
Concentration: Economics, Finance
Schools: LBS MIF '19
WE: Asset Management (Investment Banking)
GMAT ToolKit User Premium Member
In a certain series, each term (except for the first term) is one grea  [#permalink]

Show Tags

New post 14 Jun 2015, 05:09
2
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

83% (01:40) correct 18% (01:51) wrong based on 120 sessions

HideShow timer Statistics

In a certain series, each term (except for the first term) is one greater than twice the previous term. If the fifth term is equal to the third term, then the first term is which of the following?

A. −2
B. −1
C. 0
D. 1
E. 2

_________________

Saving was yesterday, heat up the gmatclub.forum's sentiment by spending KUDOS!

PS Please send me PM if I do not respond to your question within 24 hours.

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 49206
Re: In a certain series, each term (except for the first term) is one grea  [#permalink]

Show Tags

New post 14 Jun 2015, 11:58
reto wrote:
In a certain series, each term (except for the first term) is one greater than twice the previous term. If the fifth term is equal to the third term, then the first term is which of the following?

A. −2
B. −1
C. 0
D. 1
E. 2


Each term (except for the first term) is one greater than twice the previous term: \(a_n=2*a_{n-1}+1\), for n>1.

The fifth term is equal to the third term: \(a_5=a_3\);

\(a_5=2*a_4+1=2*(2*a_3+1)+1\), hence \(2*(2*a_3+1)+1=a_3\) --> \(a_3=-1\).

\(a_3=2*a_2+1=2*(2*a_1+1)+1=-1\) --> \(a_1=-1\).

Answer: B.
_________________

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

Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 1973
Premium Member CAT Tests
In a certain series, each term (except for the first term) is one grea  [#permalink]

Show Tags

New post 08 Oct 2017, 12:40
reto wrote:
In a certain series, each term (except for the first term) is one greater than twice the previous term. If the fifth term is equal to the third term, then the first term is which of the following?

A. −2
B. −1
C. 0
D. 1
E. 2

Working from answer choices is fast.

For n > 1, \(A_{n} = 2(A_{n-1}) + 1\)

\(A_1 = ??\)
\(A_2 = 2(A_1) + 1\)
\(A_3 = 2(A_2) + 1\) . .

I didn't write all that out; just the rule.

There are a couple of ways to conclude that the first term can't be 0, 1, or 2.

One way is testing. Start with (C) where
\(A_1 = 0\)
\(A_2 = 1\)
\(A_3 = 3\). Stop.

The sequence's values are increasing. Nothing in the rule will reverse that. Doubling and adding 1 means more successive increase. If 0 as a first term leads to successive increase, first terms of 1 and 2 make the growth worse.

OR: Logically, eliminate C, D, and E. This rule's operation includes doubling and adding +1. Both operations = successive increase of positive integers.

\(A_5\) will be greater than, not equal to, \(A_3\).

If not sure about this growth pattern, test just 0, as above.

Answers A and B are left. Try (B) -1:

\(A_1 = -1\)
\(A_2 = -1\)
\(A_3 = -1\)

There is the pattern we need. If first term = -1, this rule always produces a result of -1.\(A_5\), too, will = -1.

Answer B
_________________

In the depths of winter, I finally learned
that within me there lay an invincible summer.

-- Albert Camus, "Return to Tipasa"

In a certain series, each term (except for the first term) is one grea &nbs [#permalink] 08 Oct 2017, 12:40
Display posts from previous: Sort by

In a certain series, each term (except for the first term) is one grea

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

Events & Promotions

PREV
NEXT


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®.