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

It is currently 22 Oct 2018, 07:20

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

For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If

  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: 50039
For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If  [#permalink]

Show Tags

New post 04 Apr 2018, 22:10
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

87% (01:26) correct 13% (01:10) wrong based on 66 sessions

HideShow timer Statistics

For the sequence \(a_1\), \(a_2\), \(a_3\) ... \(a_n\), \(an\) is defined by \(a_n = a_{n−1} + 3\). If \(a_1 = 0\), then what is \(a_{15} − a_{12}\)?

A. 3
B. 6
C. 9
D. 12
E. 15

_________________

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
S
Joined: 05 Feb 2016
Posts: 144
Location: India
Concentration: General Management, Marketing
WE: Information Technology (Computer Software)
GMAT ToolKit User CAT Tests
Re: For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If  [#permalink]

Show Tags

New post 04 Apr 2018, 22:25
Bunuel wrote:
For the sequence \(a_1\), \(a_2\), \(a_3\) ... \(a_n\), \(an\) is defined by \(a_n = a_{n−1} + 3\). If \(a_1 = 0\), then what is \(a_{15} − a_{12}\)?

A. 3
B. 6
C. 9
D. 12
E. 15


\(a_{15} = a_{1} + 3*14\)
\(a_{12} = a_{1} + 3*11\)

\(a_{15} − a_{12}=9\)
Senior SC Moderator
avatar
V
Joined: 22 May 2016
Posts: 2040
Premium Member CAT Tests
For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If  [#permalink]

Show Tags

New post 05 Apr 2018, 05:53
Bunuel wrote:
For the sequence \(a_1\), \(a_2\), \(a_3\) ... \(a_n\), \(an\) is defined by \(a_n = a_{n−1} + 3\). If \(a_1 = 0\), then what is \(a_{15} − a_{12}\)?

A. 3
B. 6
C. 9
D. 12
E. 15

The sequence is defined by
\(a_n = a_{n−1} + 3\). If the way to solve is not apparent, list a few terms.

\(a_1 = 0\)
\(a_2 = a_1 + 3 = (0 + 3) = 3\)
\(a_3 = a_2 + 3 = 6\)
\(a_4 = a_3 + 3 = 9\)
\(a_5 = 12\)


There are a lot of ways to handle this pattern.
You can extrapolate, for example, from the number of multiples of 3 between three terms, or rewrite the definition.*

Extrapolate from \(a_1\) to \(a_4\) and \(a_2\) to \(a_5\):
The difference between any three terms is 9
From \(a_{12}\) to \(a_{15}\) there are 3 terms
The difference between those terms is 9

Answer C

Rewrite the definition
Express the values above as [something] + added 3s;[something] is 0 = \(a_1\)

\(a_1 = 0\)
\(a_2 = 3 = (0+3)\)
\(a_3 = 6 = (0+3+3)\)
\(a_4 = 9 = (0)+(3+3+3)\)
\(a_5 = 12 = (0)+(3+3+3+3) =
(a_1 + (4)(3))\)


Each term's multiple of 3 is one fewer than the subscript. Rewritten definition of the AP:
\(a_{n} = a_1 + (n-1)d\)
\(a_{n} = a_1 + (n-1)3\)

\(a_{12} = 0 + (11*3) = 33\)
\(a_{15} = 0 + (14*3) = 42\)
\(a_{15} - a_{12} = (42-33) = 9\)


Answer C

*If the pattern does not strike, list terms \(a_1\) to \(a_{15}\)
\(0,3,6,9,12,15,18,21,24,27,30,\)
\((33 = a_{12}),36,39,(42 = a_{15})\)
\(a_{15} - a_{12} = (42 - 33) = 9\)

_________________

___________________________________________________________________
For what are we born if not to aid one another?
-- Ernest Hemingway

Senior Manager
Senior Manager
User avatar
G
Joined: 31 May 2017
Posts: 322
GMAT ToolKit User Reviews Badge CAT Tests
Re: For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If  [#permalink]

Show Tags

New post 05 Apr 2018, 20:26
1
The numbers are addition of 3 to each numbers from a2 to a15.

a12 = 33
a15 = 42
a15 - a12 = 42-33 = 9

Ans: C

Posted from my mobile device
_________________

Please give kudos if it helps

Resources
Ultimate GMAT Quantitative Megathread | ALL YOU NEED FOR QUANT ! ! ! | SC Blogs by Magoosh | How to improve your verbal score | Things i wish i could've done earlier | Ultimate Q51 Guide

GMAT Club Bot
Re: For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If &nbs [#permalink] 05 Apr 2018, 20:26
Display posts from previous: Sort by

For the sequence a1, a2, a3 ... an, an is defined by an = an−1 + 3. If

  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®.