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

It is currently 19 Oct 2018, 07:18

Fuqua EA Calls Expected Soon:

Join us in the chat | track the decision tracker | See forum posts/summary


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

The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for

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

Hide Tags

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 30 Jan 2014, 01:50
2
7
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

91% (01:18) correct 9% (01:39) wrong based on 898 sessions

HideShow timer Statistics

The Official Guide For GMAT® Quantitative Review, 2ND Edition

The sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21

Problem Solving
Question: 67
Category: Algebra Sequences
Page: 70
Difficulty: 600


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 30 Jan 2014, 01:50
SOLUTION

The sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21

\(a_5 = 31\);
\(a_4 =31-5=26\);
\(a_3 =26-5=21\);
\(a_2 =21-5=16\);
\(a_1 =16-5=11\).

Answer: C.
_________________

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

Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 692
Location: India
GPA: 3.21
WE: Business Development (Other)
Premium Member Reviews Badge
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 30 Jan 2014, 03:10
1
1
The sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21


Sol: Given a5=31....and also a5=a4+5 ---> a4=26-----> a3=21----->a2=16 ---->a1=11.
Ans C

600 level is okay
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

Manager
Manager
avatar
Joined: 20 Dec 2013
Posts: 238
Location: India
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 30 Jan 2014, 03:31
1
Ans.C
This is nothing but an AP with common diff=5
a5=31,
a4=26
a3=21,
a2=16,
a1=11

a5=a1+4d
31=a1+4*5
31-20=a1=11
Manager
Manager
avatar
Joined: 18 Oct 2013
Posts: 74
Location: India
Concentration: Technology, Finance
GMAT 1: 580 Q48 V21
GMAT 2: 530 Q49 V13
GMAT 3: 590 Q49 V21
WE: Information Technology (Computer Software)
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 30 Jan 2014, 10:42
2
1
This answer can be easily be solve by A.P.
The sequence is an A.P. with each term at an increment of 5 from the previous term.
So a5 is nothing but a1+20.

a5=a1+20=31
=> a1=11.

Answer is C
Manager
Manager
avatar
Joined: 04 Oct 2013
Posts: 154
Location: India
GMAT Date: 05-23-2015
GPA: 3.45
GMAT ToolKit User Premium Member Reviews Badge
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 31 Jan 2014, 06:13
1
2
The sequence \(a_1, a_2, a_3, a_4, a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21


Given sequence is A.P. with common difference of 5.
Last Term - First Term = (Number of terms -1)* common difference

\(a_5-a_1 = (5-1)*\) \(common\) \(difference\)

Or, \(31-a_1=(5-1)*5\)

Or, \(a_1=31-20=11\)

Answer: (C)
Intern
Intern
avatar
Joined: 21 Oct 2012
Posts: 34
Location: United States
Concentration: Marketing, Operations
GMAT 1: 650 Q44 V35
GMAT 2: 600 Q47 V26
GMAT 3: 660 Q43 V38
GPA: 3.6
WE: Information Technology (Computer Software)
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 18 Mar 2014, 23:12
Bunuel wrote:
SOLUTION

The sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21

\(a_5 = 31\);
\(a_4 =31-5=26\);
\(a_3 =26-5=21\);
\(a_2 =21-5=16\);
\(a_1 =16-5=1\).

Answer: C.



But 2<= n <= 5 so how is this applicable to a1 i.e. n=1?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50002
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 19 Mar 2014, 01:59
havoc7860 wrote:
Bunuel wrote:
SOLUTION

The sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21

\(a_5 = 31\);
\(a_4 =31-5=26\);
\(a_3 =26-5=21\);
\(a_2 =21-5=16\);
\(a_1 =16-5=1\).

Answer: C.



But 2<= n <= 5 so how is this applicable to a1 i.e. n=1?


\(a_n= a_{n-1} + 5\) --> for n=2, we get: \(a_2= a_{1} + 5\).

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

Director
Director
User avatar
Joined: 10 Mar 2013
Posts: 518
Location: Germany
Concentration: Finance, Entrepreneurship
GMAT 1: 580 Q46 V24
GPA: 3.88
WE: Information Technology (Consulting)
GMAT ToolKit User
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 14 May 2015, 15:25
-5 is constant here so --> a5 - 4*5 = 11 (4*5 because we have 4 numbers between a5 and a1 ... a4,3,2,1 )
_________________

When you’re up, your friends know who you are. When you’re down, you know who your friends are.

Share some Kudos, if my posts help you. Thank you !

800Score ONLY QUANT CAT1 51, CAT2 50, CAT3 50
GMAT PREP 670
MGMAT CAT 630
KAPLAN CAT 660

Director
Director
User avatar
G
Joined: 24 Nov 2015
Posts: 522
Location: United States (LA)
Reviews Badge
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 04 May 2016, 03:40
a5 = 31
a4 = 31-5 = 26
a3 = 26 - 5 = 21
a2 = 21 - 5 = 16
a1 = 16 - 5 = 11
correct answer - C
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for  [#permalink]

Show Tags

New post 26 Mar 2018, 17:34
Quote:

The sequence \(a_1\), \(a_2\), \(a_3\), \(a_4\), \(a_5\) is such that \(a_n= a_{n-1} + 5\) for \(2\leq n \leq 5\). If \(a_5 = 31\), what is the value of \(a_1\) ?

(A) 1
(B) 6
(C) 11
(D) 16
(E) 21


a(5) = 31, so:

a(5) = a(4) + 5

31 = a(4) + 5

26 = a(4)

The pattern is to subtract 5 to obtain the value of the previous term in this recursively-defined sequence.

Thus, a(3) = 21, a(2) =16, and a(1) = 11.

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

GMAT Club Bot
Re: The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for &nbs [#permalink] 26 Mar 2018, 17:34
Display posts from previous: Sort by

The sequence a1, a2, a3, a4, a5 is such that an=a(n-1)+5 for

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


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®.