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

It is currently 19 Jul 2018, 04:56

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

What is the smallest integer a for which 27^a>3^24?

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

Hide Tags

Expert Post
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 47109
What is the smallest integer a for which 27^a>3^24? [#permalink]

Show Tags

New post 29 Feb 2016, 11:06
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

83% (00:25) correct 17% (00:22) wrong based on 148 sessions

HideShow timer Statistics

Intern
Intern
avatar
Joined: 23 Jan 2015
Posts: 42
Location: India
Concentration: Operations
WE: Information Technology (Computer Software)
Re: What is the smallest integer a for which 27^a>3^24? [#permalink]

Show Tags

New post 29 Feb 2016, 11:43
Bunuel wrote:
What is the smallest integer a for which 27^a > 3^24?

A. 7
B. 8
C. 9
D. 10
E. 12



27= 3^3
hence, (3^3)^a
Option C would make it 3^27 > 3^24
Expert Post
Senior Manager
Senior Manager
User avatar
Joined: 20 Aug 2015
Posts: 392
Location: India
GMAT 1: 760 Q50 V44
Re: What is the smallest integer a for which 27^a>3^24? [#permalink]

Show Tags

New post 03 Mar 2016, 03:12
Bunuel wrote:
What is the smallest integer a for which 27^a > 3^24?

A. 7
B. 8
C. 9
D. 10
E. 12


27^a > 3^24
Converting into the same bases:
27^a > 27^8
Therefore for the equation to hold true, a > 8 or a = 9
Option C
Senior Manager
Senior Manager
avatar
Joined: 15 Sep 2011
Posts: 344
Location: United States
WE: Corporate Finance (Manufacturing)
GMAT ToolKit User
What is the smallest integer a for which 27^a>3^24? [#permalink]

Show Tags

New post 03 Mar 2016, 18:10
Simply and how else is there to do so then:
\(3^{3a} > 3^{24}\)
\(3a > 24\)
\(a > 8\)

Therefore, the smallest integer is 9.

C.
BSchool Forum Moderator
User avatar
D
Joined: 12 Aug 2015
Posts: 2647
GRE 1: Q169 V154
GMAT ToolKit User Premium Member
Re: What is the smallest integer a for which 27^a>3^24? [#permalink]

Show Tags

New post 09 Mar 2016, 23:43
VP
VP
User avatar
D
Status: It's near - I can see.
Joined: 13 Apr 2013
Posts: 1135
Location: India
Concentration: International Business, Operations
GMAT 1: 480 Q38 V22
GPA: 3.01
WE: Engineering (Consulting)
Premium Member Reviews Badge CAT Tests
Re: What is the smallest integer a for which 27^a>3^24? [#permalink]

Show Tags

New post 21 Mar 2018, 03:21
Bunuel wrote:
What is the smallest integer a for which 27^a > 3^24?

A. 7
B. 8
C. 9
D. 10
E. 12


\(27^a > 3^{24}\)

or, \(3^{3a} > 3^{24}\)

when "a" = 9

\(3^{3*9} > 3^{24}\)

\(3^{27} > 3^{24}\)

Hence (B)
_________________

"Do not watch clock; Do what it does. KEEP GOING."

Expert Post
Target Test Prep Representative
User avatar
G
Status: Head GMAT Instructor
Affiliations: Target Test Prep
Joined: 04 Mar 2011
Posts: 2679
Re: What is the smallest integer a for which 27^a>3^24? [#permalink]

Show Tags

New post 22 Mar 2018, 15:44
Bunuel wrote:
What is the smallest integer a for which 27^a > 3^24?

A. 7
B. 8
C. 9
D. 10
E. 12


Re-expressing 27 as 3^3, we have:

3^3a > 3^24

When bases are equal, we can deal with just the exponents, as follows:

3a > 24

a > 8

Answer: C
_________________

Jeffery Miller
Head of GMAT Instruction

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

Expert Post
e-GMAT Representative
User avatar
G
Joined: 04 Jan 2015
Posts: 1771
Re: What is the smallest integer a for which 27^a>3^24? [#permalink]

Show Tags

New post 26 Mar 2018, 10:52

Solution:



Given:

    • a is an integer.

    • \(27^a > 3^{24}\).

Working out:

We need to find the smallest value of the integer “a”.

The given inequality is \(27^a >3^{24}\)

\(27^a\) can be written as \((3^3)^a\)

So, our inequality now becomes: \(3^3a > 3^{24}\)

    • Since the bases are same, we can equate the exponents.

    • Thus, \(3a> 24\)

    • Or, \(a>8\)

The smallest integer greater than 8 is 9, and hence \(a =9\)

Answer: Option C
_________________







Ace GMAT quant
Articles and Question to reach Q51 | Question of the week

Must Read Articles
Number Properties – Even Odd | LCM GCD
Word Problems – Percentage 1 | Percentage 2 | Time and Work 1 | Time and Work 2 | Time, Speed and Distance 1 | Time, Speed and Distance 2
Advanced Topics- Permutation and Combination 1 | Permutation and Combination 2 | Permutation and Combination 3 | Probability
Geometry- Triangles 1 | Triangles 2 | Triangles 3 | Common Mistakes in Geometry
Algebra- Wavy line

Practice Questions
Number Properties 1 | Number Properties 2 | Algebra 1 | Geometry | Prime Numbers | Absolute value equations | Sets



| '4 out of Top 5' Instructors on gmatclub | 70 point improvement guarantee | www.e-gmat.com

Re: What is the smallest integer a for which 27^a>3^24?   [#permalink] 26 Mar 2018, 10:52
Display posts from previous: Sort by

What is the smallest integer a for which 27^a>3^24?

  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®.