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 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value o
[#permalink]
16 Apr 2020, 09:06
16 Apr 2020, 09:06
Expert Reply
1
Bookmarks
00:00
Question Stats:
60% (01:50) correct
40% (01:54) wrong based on 10 sessions
Hide Show timer Statistics
If \(2^k + 2^{k-2} - 2^{k-3} = 2^{2k}*3^m\), what is the value of k+m?
A. -1
B. 0
C. 1
D. 2
E. 3
A. -1
B. 0
C. 1
D. 2
E. 3
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value o
[#permalink]
16 Apr 2020, 09:49
16 Apr 2020, 09:49
Carcass wrote:
If \(2^k + 2^{k-2} - 2^{k-3} = 2^{2k}*3^m\), what is the value of k+m?
A. -1
B. 0
C. 1
D. 2
E. 3
A. -1
B. 0
C. 1
D. 2
E. 3
Given: \(2^k + 2^{k-2} - 2^{k-3} = 2^{2k}*3^m\)
Factor to get: \(2^{k-3}(2^3 + 2^1 - 1) = 2^{2k}*3^m\)
Evaluate: \(2^{k-3}(9) = 2^{2k}*3^m\)
Rewrite \(9\) as a power of \(3\) to get: \(2^{k-3}(3^2) = 2^{2k}*3^m\)
We can now conclude two things: \(2^{k-3}= 2^{2k}\) and \(3^2 = 3^m\)
If \(2^{k-3}= 2^{2k}\), then \(k-3= 2k\), which means \(k = -3\)
If \(3^2 = 3^m\), then \(m = 2\)
So, \(k+m = (-3) + 2 = -1\)
Answer: A
Cheers,
Brent
Re: If 2^k + 2^(k-2) + 2^(k-3) = 2^(2k)*3^m, what is the value o
[#permalink]
24 Sep 2022, 09:20
24 Sep 2022, 09:20
Hello from the GRE Prep Club BumpBot!
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
Thanks to another GRE Prep Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).
Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
