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GRE Prep Club Team Member
Joined: 20 Feb 2017
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Each of the following equations has at least one solution EXCEPT
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04 Jun 2021, 22:27
04 Jun 2021, 22:27
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58% (02:05) wrong based on 67 sessions
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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. \((–2)^{-n} = –2^{-n}\)
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Re: Each of the following equations has at least one solution EXCEPT
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12 Jul 2021, 05:11
12 Jul 2021, 05:11
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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
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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).
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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.
