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.
GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2508
Given Kudos: 1053
GPA: 3.39
Each of the following equations has at least one solution EXCEPT
[#permalink]
04 Jun 2021, 22:27
04 Jun 2021, 22:27
1
Expert Reply
16
Bookmarks
00:00
Question Stats:
42% (02:04) correct
57% (02:04) wrong based on 66 sessions
Hide Show timer Statistics
Each of the following equations has at least one solution EXCEPT
A. \(–2^n = (–2)^{-n}\)
B. \(2^{-n} = (–2)^n\)
C. \(2^n = (–2)^{-n}\)
D. \((–2)^n = –2^n\)
E. \((–2)^{-n} = –2^{-n}\)
A. \(–2^n = (–2)^{-n}\)
B. \(2^{-n} = (–2)^n\)
C. \(2^n = (–2)^{-n}\)
D. \((–2)^n = –2^n\)
E. \((–2)^{-n} = –2^{-n}\)
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Each of the following equations has at least one solution EXCEPT
[#permalink]
12 Jul 2021, 05:11
12 Jul 2021, 05:11
6
1
Bookmarks
GeminiHeat wrote:
Each of the following equations has at least one solution EXCEPT
A. \(–2^n = (–2)^{-n}\)
B. \(2^{-n} = (–2)^n\)
C. \(2^n = (–2)^{-n}\)
D. \((–2)^n = –2^n\)
E. \((–2)^{-n} = –2^{-n}\)
A. \(–2^n = (–2)^{-n}\)
B. \(2^{-n} = (–2)^n\)
C. \(2^n = (–2)^{-n}\)
D. \((–2)^n = –2^n\)
E. \((–2)^{-n} = –2^{-n}\)
Rather than trying to solve each individual equation, it will be much faster to recognize that some POSSIBLE solutions include n = 0, n = 1 and n = -1
We should be able to quickly eliminate answer choices by testing possible solutions.
Let's start with n = 0
We get:
A. \(–2^0 = (–2)^{-0}\) becomes \(-1 = 1\). Doesn't work. Keep answer choice A for now.
B. \(2^{-0} = (–2)^0\) becomes \(1 = 1\). Works!. Eliminate B.
C. \(2^0 = (–2)^{-0}\) becomes \(1 = 1\). Works!. Eliminate C.
D. \((–2)^0 = –2^0\) becomes \(1 = -1\). Doesn't work. Keep answer choice D for now
E. \((–2)^{-0} = –2^{-0}\) becomes \(1 = -1\). Doesn't work. Keep answer choice E for now
Now let's try n = 1 with the remaining three answer choices
We get:
A. \(–2^1 = (–2)^{-1}\) becomes \(-2 = -\frac{1}{2}\). Doesn't work. Keep answer choice A for now.
D. \((–2)^1 = –2^1\) becomes \(-2 = -2\). Works!. Eliminate D.
E. \((–2)^{-1} = –2^{-1}\) becomes \(-\frac{1}{2} = -\frac{1}{2}\). Works!. Eliminate E
By the process of elimination, the correct answer is A
General Discussion
Re: Each of the following equations has at least one solution EXCEPT
[#permalink]
19 Aug 2024, 09:05
19 Aug 2024, 09:05
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.
