Summer is Coming! Join the Game of Timers Competition to Win Epic Prizes. Registration is Open. Game starts Mon July 1st.

It is currently 19 Jul 2019, 16:11

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

Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no

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

Hide Tags

Find Similar Topics 
Manager
Manager
avatar
G
Joined: 02 Jun 2015
Posts: 184
Location: Ghana
Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no  [#permalink]

Show Tags

New post Updated on: 26 Oct 2016, 00:14
1
4
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

47% (01:57) correct 53% (02:13) wrong based on 71 sessions

HideShow timer Statistics


Is the value of 27^a/6^b a prime number? (Source: Bell Curves)

(1) 3a – b = 1
(2) b is a non-zero integer.

_________________
Kindly press kudos if you find my post helpful

Originally posted by duahsolo on 25 Oct 2016, 16:22.
Last edited by duahsolo on 26 Oct 2016, 00:14, edited 1 time in total.
Manager
Manager
avatar
B
Joined: 28 Jun 2016
Posts: 216
Location: Canada
Concentration: Operations, Entrepreneurship
Re: Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no  [#permalink]

Show Tags

New post 25 Oct 2016, 16:54
duahsolo wrote:
Is the value of 27^a/6^b a prime number?

(1) 3a – b = 1
(2) b is a non-zero integer.



Statement 1:

If b=0, then a=1/3 and 27^a/6^b = 3 ---------------Yes

If b=1, Then a=2/3 and 27^a/6^b = 9/6 = 3/2 -----------No

Insufficient

Statement 2:

If b\neq{0} and b is an integer.

Then 27^a/6^b can never be prime number

Sufficient

IMO B
Director
Director
User avatar
D
Joined: 05 Mar 2015
Posts: 995
Re: Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no  [#permalink]

Show Tags

New post 25 Oct 2016, 21:32
duahsolo wrote:
Is the value of 27^a/6^b a prime number?

(1) 3a – b = 1
(2) b is a non-zero integer.


Hi duahsolo

Could u please specify the source of your questions/check OA(last 5-6 posts) :) ???

Per (2) if b>0 then odd/even=non integer---->Not Prime
if b<0 then odd*even=even (2 is only even prime,which is never possible as b is integer)----->Not Prime

suff

Ans B

thanks
Manager
Manager
avatar
S
Joined: 29 May 2016
Posts: 97
Re: Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no  [#permalink]

Show Tags

New post 25 Oct 2016, 21:54
1
answer has to be C.
b = -1 and let a= -1/3
answer can be Prime.
Manager
Manager
avatar
Joined: 29 Aug 2008
Posts: 106
Re: Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no  [#permalink]

Show Tags

New post 25 Oct 2016, 22:16
Given = 27^a/6^b

which can be written as = 3^3a/2^b*3^b

= 3^3a-b/2^b

Statement 1: 3a-b = 1

Which leaves us with 3/2^b

We don't have any info about b so if b = 0, we will be left with 3 which is prime. If b =1 we will be left with 3/2.

So statement 1 is insufficient.

Statement 2: b is a non-zero integer, which in itself in not sufficient as it can have any value from -ve to +ve and we don't have any info on a.

= 3^3a-b/2^b

if we put a = -1/3 and b = -1 this will get solved to 2 which is a prime and there can be scenarios when it will not be prime. So this statement itself isn't sufficient.

Taking statement 1 and 2 together.

3^3a-b/2^b

From st 1 we know 3a-b = 1 and st 2 b is a non zero integer. So we know its not a prime.

So option C IMHO
Director
Director
User avatar
D
Joined: 05 Mar 2015
Posts: 995
Re: Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no  [#permalink]

Show Tags

New post 25 Oct 2016, 23:01
mbaprep2016 wrote:
answer has to be C.
b = -1 and let a= -1/3
answer can be Prime.


Hi mbaprep2016

as per highlighted part if we put b=-1 in statement 1 then a=0 not 1/3 :)

Thanks
Manager
Manager
avatar
G
Joined: 02 Jun 2015
Posts: 184
Location: Ghana
Re: Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no  [#permalink]

Show Tags

New post 26 Oct 2016, 00:17
rohit8865 wrote:
duahsolo wrote:
Is the value of 27^a/6^b a prime number?

(1) 3a – b = 1
(2) b is a non-zero integer.


Hi duahsolo

Could u please specify the source of your questions/check OA(last 5-6 posts) :) ???

Per (2) if b>0 then odd/even=non integer---->Not Prime
if b<0 then odd*even=even (2 is only even prime,which is never possible as b is integer)----->Not Prime

suff

Ans B

thanks


Hi rohit8865,

The source of the question has been added. Thanks for reminding me.

Cheers!
_________________
Kindly press kudos if you find my post helpful
GMATH Teacher
User avatar
P
Status: GMATH founder
Joined: 12 Oct 2010
Posts: 937
Re: Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no  [#permalink]

Show Tags

New post 26 Sep 2018, 15:10
1
duahsolo wrote:
Is the value of 27^a/6^b a prime number? (Source: Bell Curves)

(1) 3a – b = 1
(2) b is a non-zero integer.

Beautiful problem duahsolo. (Kudos!)
\(\frac{{{{27}^a}}}{{{6^b}}} = \frac{{{3^{3a - b}}}}{{{2^b}}}\,\,\mathop = \limits^? \,\,{\text{prime}}\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ \begin{gathered}
\,b = 0\,\,\,{\text{and}}\,\,\,3a - b = 1 \hfill \\
\,{\text{OR}} \hfill \\
b = - 1\,\,{\text{and}}\,\,3a - b = 0 \hfill \\
\end{gathered} \right.\,\,\,\,\,\,\,\,\, \Leftrightarrow \,\,\,\,\,\,\,\left\{ \begin{gathered}
\,\left( {a\,;\,b} \right)\,\,\mathop = \limits^? \,\,\,\left( {\frac{1}{3};0} \right) \hfill \\
\,{\text{OR}} \hfill \\
\,\left( {a\,;\,b} \right)\,\,\mathop = \limits^? \,\,\,\left( { - \frac{1}{3}; - 1} \right) \hfill \\
\end{gathered} \right.\)

\(\left( 1 \right)\,\,\,3a - b = 1\,\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {a\,;\,b} \right)\,\, = \,\,\left( {\frac{1}{3};0} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \,\, \hfill \\
\,{\text{Take}}\,\,\left( {a\,;\,b} \right)\,\, = \,\,\left( {1;2} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\
\end{gathered} \right.\)


\(\left( 2 \right)\,\,\,b \ne 0\,\,\,\operatorname{int} \,\,\,\,\,\,\left\{ \begin{gathered}
\,{\text{Take}}\,\,\left( {a\,;\,b} \right)\,\, = \,\,\left( {1;2} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{NO}}} \right\rangle \,\, \hfill \\
\,{\text{Take}}\,\,\left( {a\,;\,b} \right)\,\, = \,\,\left( { - \frac{1}{3}; - 1} \right)\,\,\,\,\, \Rightarrow \,\,\,\left\langle {{\text{YES}}} \right\rangle \hfill \\
\end{gathered} \right.\,\,\)


\(\left( {1 + 2} \right)\,\,\,\left\{ \begin{gathered}
\,\left( {a\,;\,b} \right)\,\, = \,\,\left( {\frac{1}{3};0} \right)\,\,\,\,{\text{contradicts}}\,\,\left( 2 \right)\,\, \hfill \\
\,\,\left( {a\,;\,b} \right)\,\, = \,\,\left( { - \frac{1}{3}; - 1} \right)\,\,\,\,{\text{contradicts}}\,\,\left( 1 \right)\,\, \hfill \\
\end{gathered} \right.\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{NO}}} \right\rangle\)


The correct answer is (C), indeed.


This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.
_________________
Fabio Skilnik :: GMATH method creator (Math for the GMAT)
Our high-level "quant" preparation starts here: https://gmath.net
GMAT Club Bot
Re: Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no   [#permalink] 26 Sep 2018, 15:10
Display posts from previous: Sort by

Is the value of 27^a/6^b a prime number? (1) 3a – b = 1 (2) b is a no

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





cron

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne