BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course

Redeem
TTP OnDemand GMAT Video Course
Featured Course

Target Test Prep GMAT OnDemand

Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.

  • 715+ score guarantee — highest in the industry (99th percentile)
  • 52 chapters · 1,500+ lessons · 4,000+ practice questions
  • 400 hours of video · 1,500+ instructor-led HD smartboard lessons
  • 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
  • 24/7 live support + weekly Zoom office hours with GMAT instructors
  • TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
  • 1,200+ flashcards + AI-powered study assistant & daily calendar
  • OnDemand, LiveTeach & GMAT Bootcamp formats available
  • Also: GRE, SAT Math & Executive Assessment courses
  • MBA Admissions Consulting now available
  • 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
  • 200,000+ students served
  • 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★ 5.0 (559 reviews)
130-pt guarantee
$0 to start then $127/mo
Start Free 5-Day Trial Read 559 Reviews →

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

Expert replies
Post new topic Post Reply
Previous Topic Next Topic

GMAT/MBA Expert

User avatar
GMAT Instructor
Posts: 768
Joined: Wed Dec 28, 2011 4:18 pmFollowed by: 140 members
Location: Berkeley, CA
Thanked: 387 times
by Mike@Magoosh » Wed Nov 05, 2014 10:21 am
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 OA & OE of this particular problem, as well as a full set of challenging problems on exponents, see:
https://magoosh.com/gmat/2014/challengi ... and-roots/

Mike :-)
Magoosh GMAT Instructor
https://gmat.magoosh.com/
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Source: — Problem Solving |
User avatar
Legendary Member
Posts: 1100
Joined: Sat May 10, 2014 11:34 pmFollowed by: 24 members
Location: New Delhi, India
Thanked: 205 times

by GMATinsight » Wed Nov 05, 2014 10:54 am
Mike@Magoosh 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 OA & OE of this particular problem, as well as a full set of challenging problems on exponents, see:
https://magoosh.com/gmat/2014/challengi ... and-roots/

Mike :-)
Answer: Option E
Attachments
Untitled.jpg
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member
Thanked: 25 times

by Mathsbuddy » Mon Nov 10, 2014 11:41 am
As GMat problems require a straight forward answer, you can solve this quickly as follows:

The given integers are 2, 5, 6 and 15.
Now, by inspection, find a common multiplicative relationship between them:

5/2 = 15/6 (= 2.5)

So, 6^B/6^A = 6^Q/6^1
Index laws give us:
6^(B-A) = 6^(Q-1)
By equivalence of exponents:
B-A = Q-1
Therefore Q = B - A + 1 (JOB DONE!)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member
Thanked: 25 times

by Mathsbuddy » Mon Nov 10, 2014 11:44 am
Even quicker:

Using 15 = 6 x 5/2
gives
6^Q = 6^1 x 6^B/6^A
Index laws give us:
6^Q = 6^(1 + B - A)
Therefore Q = B - A + 1
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
GMAT Instructor
Posts: 2630
Joined: Wed Sep 12, 2012 3:32 pmFollowed by: 119 members
Location: East Bay all the way
Thanked: 625 times
GMAT Score:780

by Matt@VeritasPrep » Mon Nov 10, 2014 11:59 am
How about an easier way with less jargon? (Note: for whatever reason 'q' is not in the ASCII superscript alphabet, so I'm using 6á´½ to mean 6^q.)

6á´½ = 15 = 30/2 = (6*5)/2

Since we know 2 and 5 in terms of powers of 6, let's replace 2 and 5 with those powers.

6á´½ = (6*6á´®)/6á´¬
6ᴽ = (6ᴮ�¹)/6ᴬ
6ᴽ = 6ᴮ�¹�ᴬ

So Q = B + 1 - A, or B - A + 1.

This is neat, but I don't know if the GMAT would ask a question that's so trivial for students who already know their logarithms and so challenging for students who don't. (The GMAT tends to avoid questions that are easily solved with methods from trig and calculus, but hey, you never know!)
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Master | Next Rank: 500 Posts
Posts: 447
Joined: Fri Nov 08, 2013 7:25 amFollowed by: 1 member
Thanked: 25 times

by Mathsbuddy » Tue Nov 11, 2014 4:42 am
Alternatively for those who like logarithms:

Using log x = log x (base 6):

B = log 5
A = log 2
1 = log 6

Q = log 15 = log(5/2 * 6)
Using logarithm laws, this becomes:
Q = log5 - log 2 + log 6 = B - A + 1
Top
Join the discussion
Log in to postLogin with Googleuse password
QUOTE IN REPLY
Post new topic Post Reply
• Page 1 of 1