Last visit was: 23 Jul 2024, 11:26 It is currently 23 Jul 2024, 11:26
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
SORT BY:
Date
Tags:
Show Tags
Hide Tags
Math Expert
Joined: 02 Sep 2009
Posts: 94592
Own Kudos [?]: 643320 [2]
Given Kudos: 86728
Send PM
Most Helpful Reply
Director
Director
Joined: 25 Jul 2018
Posts: 663
Own Kudos [?]: 1150 [0]
Given Kudos: 69
Send PM
General Discussion
Senior Manager
Senior Manager
Joined: 29 Jun 2019
Posts: 356
Own Kudos [?]: 218 [0]
Given Kudos: 16
Send PM
IIM School Moderator
Joined: 05 Jan 2015
Status:So far only Dreams i have!!
Posts: 385
Own Kudos [?]: 365 [0]
Given Kudos: 214
WE:Consulting (Computer Software)
Send PM
Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink]
Approach:

Simplify the given equation:

\(\frac{8^r}{4^s} =2^t --> 2^3 ^r=2^t*2^2 ^s\)

\(3r = t + 2s\)

\(r = \frac{2s+t}{3}\)

IMO Option C it is!
Intern
Intern
Joined: 07 Jan 2019
Posts: 2
Own Kudos [?]: 3 [0]
Given Kudos: 44
Send PM
Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink]
Q: 8^r/4^s=2^t

8^r=2^3r and 4^s=2^2s

so we have: 2^3r/2^2s=2^t

for the rules of the exponents--->x^y/x^z=x^(y-z) this means 2^3r/2^2s=2^(3r-2s)

2^(3r-2s)=2^t---->3r-2s=t---->r=(t+2s)/3

hope this helps.
Target Test Prep Representative
Joined: 14 Oct 2015
Status:Founder & CEO
Affiliations: Target Test Prep
Posts: 19185
Own Kudos [?]: 22702 [0]
Given Kudos: 286
Location: United States (CA)
Send PM
Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink]
Expert Reply
Bunuel wrote:
If \(\frac{8^r}{4^s}=2^t\), then what is r in terms of s and t ?


A. \(s + t + 1\)

B. \(s + t + 5\)

C. \(\frac{2s+t}{3}\)

D. \(\frac{2st}{3}\)

E. \(\frac{s}{2}+\frac{t}{4}\)



Simplifying the equation, we have:

2^(3r)/2^(2s) = 2^t

2^(3r-2s) = 2^t

3r - 2s = t

3r = 2s + t

r = (2s + t)/3

Answer: C
GMAT Club Legend
GMAT Club Legend
Joined: 03 Jun 2019
Posts: 5312
Own Kudos [?]: 4245 [0]
Given Kudos: 161
Location: India
GMAT 1: 690 Q50 V34
WE:Engineering (Transportation)
Send PM
Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink]
Bunuel wrote:
If \(\frac{8^r}{4^s}=2^t\), then what is r in terms of s and t ?


A. \(s + t + 1\)

B. \(s + t + 5\)

C. \(\frac{2s+t}{3}\)

D. \(\frac{2st}{3}\)

E. \(\frac{s}{2}+\frac{t}{4}\)


If \(\frac{8^r}{4^s}=2^t\), then what is r in terms of s and t ?

\(2^{3r-2s} = 2^t\)
3r -2s = t
\(r = \frac{2s + t}{3}\)

IMO C
VP
VP
Joined: 18 Dec 2017
Posts: 1161
Own Kudos [?]: 1047 [0]
Given Kudos: 421
Location: United States (KS)
GMAT 1: 600 Q46 V27
Send PM
Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink]
Bunuel wrote:
If \(\frac{8^r}{4^s}=2^t\), then what is r in terms of s and t ?


A. \(s + t + 1\)

B. \(s + t + 5\)

C. \(\frac{2s+t}{3}\)

D. \(\frac{2st}{3}\)

E. \(\frac{s}{2}+\frac{t}{4}\)


Just take 8/4=2 which makes r=s=t=1

Only Option C works.
GMAT Club Bot
Re: If 8^r/4^s =2^t, then what is r in terms of s and t ? [#permalink]
Moderator:
Math Expert
94592 posts