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

It is currently 20 Jun 2018, 00:08
Search
Register
GMAT Club Tests
Decision Tracker
My Rewards
New posts
Unanswered

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.

Go to My Error Log Learn more
Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar
CLICK HERE TO HIDE/SHOW EVENTS

If 6^A = 2, 6^B = 5, and 6^Q = 15, then express Q in terms of A and/or

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
  Sort by Date Sort by Kudos  
Search for:
 
Print view
First unread post
Author Message
TAGS:

Hide Tags
Expert Post
1 KUDOS received
Magoosh GMAT Instructor
User avatar
G
Joined: 28 Dec 2011
Posts: 4668

Top Member of the Month
If 6^A = 2, 6^B = 5, and 6^Q = 15, then express Q in terms of A and/or [#permalink]

Show Tags

New post 05 Nov 2014, 11:17
1
6
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

56% (02:46) correct 44% (01:54) wrong based on 98 sessions

HideShow timer Statistics

If \(6^A = 2\), \(6^B = 5\), and \(6^Q = 15\), then express Q in terms of A and/or B.
(A) 3B
(B) B + 3
(C) 5A + B
(D) \(B^2 - 2B\)
(E) B - A + 1

For the solution to this, as well as for a set of challenging problems on exponents, see:
https://magoosh.com/gmat/2014/challengi ... and-roots/

Mike :-)
Spoiler: OA

_________________

Mike McGarry
Magoosh Test Prep

Image

Image

Education is not the filling of a pail, but the lighting of a fire. — William Butler Yeats (1865 – 1939)

Magoosh Discount CodesJamboree Discount CodesEconomist GMAT Tutor Discount Codes
2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Jun 2013
Posts: 277
Premium Member
Re: If 6^A = 2, 6^B = 5, and 6^Q = 15, then express Q in terms of A and/or [#permalink]

Show Tags

New post 06 Nov 2014, 01:29
2
1
mikemcgarry wrote:
If \(6^A = 2\), \(6^B = 5\), and \(6^Q = 15\), then express Q in terms of A and/or B.
(A) 3B
(B) B + 3
(C) 5A + B
(D) \(B^2 - 2B\)
(E) B - A + 1

For the solution to this, as well as for a set of challenging problems on exponents, see:
https://magoosh.com/gmat/2014/challengi ... and-roots/

Mike :-)



6^A=2 ----------------------1)
6^B=5 -----------------------2)
6^Q= 15 ---------------------3)

multiplying 1,2,3 together, we have
6^(A+B+Q)= 2*5*15
= 2*3*5^2
=6*5^2
from 2, we have 5^2= 6^2B

=6*6^2B
=6^2B+1
thus
A+B+Q=2B+1
Q=B-A+1
4 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1837
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Re: If 6^A = 2, 6^B = 5, and 6^Q = 15, then express Q in terms of A and/or [#permalink]

Show Tags

New post 11 Nov 2014, 02:43
4
1
\(6^q = 15 = \frac{15 * 2}{2} = \frac{30}{2} = \frac{5 * 6}{2}\) .................. (1)

\(6^A = 2, 6^B = 5\)>> Placing these values in (1)

\(6^q = \frac{6^b * 6}{6^a}\)

\(6^q = 6^{(b+1-a)}\)

Bases are same; equating the powers

q = b+1-a

Answer = E
_________________

Kindly press "+1 Kudos" to appreciate :)

Expert Post
Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 5893
Premium Member Reviews Badge
Top Member of the Month
Re: If 6^A = 2, 6^B = 5, and 6^Q = 15, then express Q in terms of A and/or [#permalink]

Show Tags

New post 06 Nov 2017, 11:06
mikemcgarry wrote:
If \(6^A = 2\), \(6^B = 5\), and \(6^Q = 15\), then express Q in terms of A and/or B.
(A) 3B
(B) B + 3
(C) 5A + B
(D) \(B^2 - 2B\)
(E) B - A + 1

For the solution to this, as well as for a set of challenging problems on exponents, see:
https://magoosh.com/gmat/2014/challengi ... and-roots/

Mike :-)



Hi
see if all can be brought to base 6..
now we have 2,5,15 and these can be arranged as \(\frac{15}{5}*2=6\)
substitute corresponding values...
\(\frac{15}{5}*2=\frac{6^Q}{6^B}*6^A=6^{Q+A-B}=6^1........Q+A-B=1........Q=B+1-A\)
E
_________________

Absolute modulus :http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html

GMAT online Tutor

Manager
Manager
avatar
B
Joined: 24 Jun 2017
Posts: 122
Re: If 6^A = 2, 6^B = 5, and 6^Q = 15, then express Q in terms of A and/or [#permalink]

Show Tags

New post 06 Nov 2017, 12:07
6^A=2, 6^B=5, and 6^Q=15
applying log base 6 (log6) to both sides of the equations
log6(6^A) = log6(2)
log6(6^B)=log6(5)
log6(6^Q)=log6(15)
using log properties

A = log6(2)
B = log6(5)
Q = log6(15) and just scrolling the answers down for anyone who knows logs first answer to check is E (as others lead to much greater values of Q)
log6(15) = log6(5) - log6(2) + 1
1 is log6(6) so we can rewrite
log6(15) = log6(5) - log6(2) + log6(6) -> applying another log property
log6(15) = log6 ((5/2)*6) = log6 (15)
Re: If 6^A = 2, 6^B = 5, and 6^Q = 15, then express Q in terms of A and/or   [#permalink] 06 Nov 2017, 12:07
Print view
First unread post
Display posts from previous: Sort by

If 6^A = 2, 6^B = 5, and 6^Q = 15, then express Q in terms of A and/or

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

Moderators: chetan2u, VeritasPrepKarishma, Bunuel, niks18, mikemcgarry, generis

Search for:


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®.

Main navigation

GMAT Resources

Partners

MBA Resources

www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions