GRE Prep 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
Track
Your Progress
Practice
Pays
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
If 4^a*4^b=2(8^3), what is the value of a+b?
[#permalink]
21 Feb 2021, 10:51
21 Feb 2021, 10:51
Expert Reply
00:00
Question Stats:
88% (00:55) correct
11% (00:43) wrong based on 43 sessions
Hide Show timer Statistics
If \(4^a*4^b=2(8^3)\), what is the value of a+b?
A. 4
B. 5
C. 6
D. 7
E. 8
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
A. 4
B. 5
C. 6
D. 7
E. 8
Kudos for the right answer and explanation
Question part of the project GRE Quantitative Reasoning Daily Challenge - (2021) EDITION
GRE - Math Book
If 4^a*4^b=2(8^3), what is the value of a+b?
[#permalink]
21 Feb 2021, 11:14
21 Feb 2021, 11:14
Solution:
\(4^a*4^b=2^2^a*2^2^b\)
\(2(8^3)=2(2^3^*^3)=2(2^9)=2^1^0\)
\(2^2^a*2^2^b=2^1^0\)
2a+2b=10
Dividing throughout by 2
a+b=5
IMO B
Hope this helps!
\(4^a*4^b=2^2^a*2^2^b\)
\(2(8^3)=2(2^3^*^3)=2(2^9)=2^1^0\)
\(2^2^a*2^2^b=2^1^0\)
2a+2b=10
Dividing throughout by 2
a+b=5
IMO B
Hope this helps!
Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
If 4^a*4^b=2(8^3), what is the value of a+b?
[#permalink]
21 Feb 2021, 11:50
21 Feb 2021, 11:50
Carcass wrote:
If \(4^a*4^b=2(8^3)\), what is the value of a+b?
A. 4
B. 5
C. 6
D. 7
E. 8
A. 4
B. 5
C. 6
D. 7
E. 8
\(4^a*4^b = 2*(8^3)\)
\(2^{2a}*2^{2b} = 2*(2^3)^3\)
\(2^{2a+2b} = 2^{10}\)
When the bases are equal, the powers are equal
\(2a + 2b = 10\)
\(a + b = 5\)
Hence, option B
