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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## For how many integers n is 1^n = n^1? tagged by: M7MBA ##### This topic has 1 expert reply and 0 member replies ### Top Member ## For how many integers n is 1^n = n^1? For how many integers n is 1^n = n^1? A. none B. 1 C. 2 D. 3 E. More than 3 The OA is the option B. How can I show that there is no more than 1 integer? Experts, can you show me this? Thanks.[/spoiler] ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: For how many integers n is 1^n = n^1? A. none B. 1 C. 2 D. 3 E. More than 3 The OA is the option B. How can I show that there is no more than 1 integer? Experts, can you show me this? Thanks.[/spoiler] Hi M7MBA, Let's take a look at your question. We are asked to find, for how many integers, $$1^n=n^1$$ Let's try out some random values. For n = -1 $$1^{(-1)}=(-1)^1$$ $$\frac{1}{1}=-1$$ $$1\ne-1$$ For n = 0 $$1^0=(0)^1$$ $$1\ne0$$ For n = 1 $$1^1=(1)^1$$ $$1=1$$ Therefore, 1^n=n^1 is true for n = 1 Let's check for n = 2, $$1^2=(2)^1$$ $$1\ne2$$ The given equation will only be true for n = 1 Hence, Option B is correct. Hope it helps. I am available if you'd like any follow up. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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