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

It is currently 17 Oct 2018, 09:54

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

If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?

  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: 49968
If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?  [#permalink]

Show Tags

New post 12 Sep 2017, 05:30
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

68% (01:39) correct 32% (01:33) wrong based on 98 sessions

HideShow timer Statistics

Senior PS Moderator
User avatar
V
Joined: 26 Feb 2016
Posts: 3182
Location: India
GPA: 3.12
Premium Member CAT Tests
Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?  [#permalink]

Show Tags

New post 12 Sep 2017, 05:39
1
Given \(3^a – 3^{(a – 2)} = 8(3^{27})\), we have been asked to find the value of 2a.

\(8(3^{27}) = (3^2 - 1)(3^27) = 3^{2+27} - 3{27}\)

Therefore we know that \(3^a – 3^{(a – 2)} = 3^{29} - 3{27} = 3^{29} - 3{(29 - 2)}\)

Therefore, a = 29 and 2a = 58(Option E)

_________________

You've got what it takes, but it will take everything you've got

Director
Director
User avatar
P
Joined: 09 Mar 2017
Posts: 529
Location: India
Concentration: Marketing, Organizational Behavior
WE: Information Technology (Computer Software)
CAT Tests
Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?  [#permalink]

Show Tags

New post 12 Sep 2017, 07:39
Bunuel wrote:
If \(3^a – 3^{(a – 2)} = 8(3^{27})\), what is the value of 2a ?

A. 20
B. 25
C. 27
D. 29
E. 58


3^a - 3^(a-2) = 8(3^27)
3^a -(3^a/3^2) = 8(3^27)
take lcm = 3^2 and then cross multiply the denominator
(3^a)(3^2) - (3^a) = (3^2)(8)(3^27)
take (3^a) common on LHS
(3^a)[9-1] = (3^29)(8)
cancel 8 on both sides
(3^a) = (3^29)
a= 29
2a = 58
option E
_________________

------------------------------
"Trust the timing of your life"
Hit Kudus if this has helped you get closer to your goal, and also to assist others save time. Tq :)

PS Forum Moderator
avatar
D
Joined: 25 Feb 2013
Posts: 1217
Location: India
GPA: 3.82
GMAT ToolKit User Premium Member Reviews Badge
Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?  [#permalink]

Show Tags

New post 12 Sep 2017, 08:29
Bunuel wrote:
If \(3^a – 3^{(a – 2)} = 8(3^{27})\), what is the value of 2a ?

A. 20
B. 25
C. 27
D. 29
E. 58


LHS: \(3^a-\frac{3^a}{3^2}\) \(= 3^a(1-\frac{1}{3^2})\) = \(3^a*\frac{8}{9}\)
or, \(3^{a-2}*8\) \(= 8*3^{27}\)
Hence \(a-2=27\) or \(a=29\). Therefore \(2a = 58\)

Option E
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3009
Location: Canada
Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?  [#permalink]

Show Tags

New post 12 Sep 2017, 10:03
Top Contributor
Bunuel wrote:
If \(3^a – 3^{(a – 2)} = 8(3^{27})\), what is the value of 2a ?

A. 20
B. 25
C. 27
D. 29
E. 58


Given: \(3^a – 3^{(a – 2)} = 8(3^{27})\)

Factor \(3^{(a – 2)}\) from the left side to get: \(3^{(a – 2)}(3^2 – 1) = 8(3^{27})\)

Evaluate the part in the brackets: \(3^{(a – 2)}(8) = 8(3^{27})\)

Divide both sides by 8 to get: \(3^{(a – 2)} = 3^{27}\)

This means: \(a - 2 = 27\)

Solve: a = 29
So, 2a = (2)(29) = 58

Answer:

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2830
Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?  [#permalink]

Show Tags

New post 15 Sep 2017, 10:07
Bunuel wrote:
If \(3^a – 3^{(a – 2)} = 8(3^{27})\), what is the value of 2a ?

A. 20
B. 25
C. 27
D. 29
E. 58


We can simplify the given equation:

3^a - (3^a)(3^-2) = 8(3^27)

Factor 3^a from the left side:

3^a(1 - 1/9) = 8(3^27)

3^a(8/9) = 8(3^27)

3^a = 8(3^27) x 9/8

3^a = 3^27 x 3^2

3^a = 2^29

a = 29

So, 2a = 58.

Alternate Solution:

Observe that 3^a = 3^(a - 2 + 2) = (3^(a - 2))(3^2). Then:

(3^(a - 2))(3^2) - (3^(a - 2)) = 8(3^27)

Let’s factor the common 3^(a - 2) from the left side:

3^(a - 2)(3^2 - 1) = 8(3^27)

3^(a - 2)(8) = 8(3^27)

3^(a - 2) = 3^27

a - 2 = 27

a = 29

2a = 58

Answer: E
_________________

Jeffery Miller
Head of GMAT Instruction

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

Manager
Manager
avatar
B
Joined: 04 May 2014
Posts: 161
Location: India
WE: Sales (Mutual Funds and Brokerage)
If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?  [#permalink]

Show Tags

New post Updated on: 24 Sep 2017, 06:30
RHS
8 can be written as (9-1) or (3²-1)
8(3²⁷)=(3²-1)X(3²⁷)
=3²⁹-3²⁷
check answer choices.
Start with easy one.
let 2a=10 or a=5
plugin into LHS and check
3⁵-3³-Not correct
let 2a=58
a=29
Plugin to LHS of the equation
3²⁹-3²⁷=LHS=correct=E

Originally posted by gps5441 on 24 Sep 2017, 06:27.
Last edited by gps5441 on 24 Sep 2017, 06:30, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 04 May 2014
Posts: 161
Location: India
WE: Sales (Mutual Funds and Brokerage)
Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?  [#permalink]

Show Tags

New post 24 Sep 2017, 06:29
RHS
8(3²⁷)=(3²-1)X(3²⁷)
=3²⁹-3²⁷
check answer choices.
Start with easy one.
let 2a=10 or a=5
plugin into LHS and check
3⁵-3³-Not correct
let 2a=58
a=29
Plugin to LHS of the equation
3²⁹-3²⁷=LHS=correct=E
Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4094
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?  [#permalink]

Show Tags

New post 24 Sep 2017, 07:14
Bunuel wrote:
If \(3^a – 3^{(a – 2)} = 8(3^{27})\), what is the value of 2a ?

A. 20
B. 25
C. 27
D. 29
E. 58


Or, \(3^a – 3^{(a – 2)} = 8(3^{27})\)

Or, \(3^a – \frac{3^a}{3^2} = (3^2 - 1)(3^{27})\)

Or, \(3^a*3^2 – 3^a = 3^2(3^2 - 1)(3^{27})\)

Or, \(3^a(3^2 – 1) = 3^2(3^2 - 1)(3^{27})\)

Or, \(3^a = 3^2(3^{27})\)

Or, \(3^a = 3^{29}\)

Or, \(a = 29\)

So, 2a = 58 , answer will be (E)

_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

GMAT Club Bot
Re: If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ? &nbs [#permalink] 24 Sep 2017, 07:14
Display posts from previous: Sort by

If 3^a – 3^(a – 2) = 8(3^27), what is the value of 2a ?

  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®.