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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 ## If 6-9/x = x, then x has how many... tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 1 member reply ### Top Member ## If 6-9/x = x, then x has how many... If $$6-\frac{9}{x}=x$$ then x has how many possible values? (A) None (B) One (C) Two (D) A finite number greater than two (E) Three The OA is B. Can anye expert explain this PS question please? Thanks. Newbie | Next Rank: 10 Posts Joined 02 Nov 2014 Posted: 1 messages Upvotes: 1 Target GMAT Score: 750 GMAT Score: 660 6-9/x = x When x=1 --> 6-9 = -3 When x=2 --> 6-4.5 = 1.5 When x=3 --> 6-3 = 3 When x=4 --> 6-9/4 not equal to 4 and same is the case for any other value for x henceforth So x has only one possible value 3. Other way to solve: Algebrically, this will be of form (x-a)(x-b) = x$$^2$$ -ax -bx +ab From the question, ab = 9. Since 3*3 = 9. a=b=3. Hence the solution is (x-3)$$^2$$ and x value will be 3 --> only one possible value. _________________ Regards, Sathish Life begins at the end of your comfort zone ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15387 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 LUANDATO wrote: If $$6-\frac{9}{x}=x$$ then x has how many possible values? (A) None (B) One (C) Two (D) A finite number greater than two (E) Three Multiplying both sides by x, we get: 6x - 9 = xÂ² 0 = xÂ² - 6x + 9 0 = (x-3)(x-3). Thus, x=3. The correct answer is B. _________________ Mitch Hunt Private Tutor for the GMAT and GRE GMATGuruNY@gmail.com If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Student Review #1 Student Review #2 Student Review #3 Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Quote: If $$6-\frac{9}{x}=x$$ then x has how many possible values? (A) None (B) One (C) Two (D) A finite number greater than two (E) Three Hi LUANDATO, Let's take a look at your question. $$6-\frac{9}{x}=x$$ $$6=x+\frac{9}{x}$$ Simplify right hand side by adding up like terms. $$6=\frac{x^2+9}{x}$$ $$6x=x^2+9$$ $$x^2-6x+9=0$$ Let's factorize the left hand side by grouping, $$x^2-3x-3x+9=0$$ $$x(x-3)-3(x-3)=0$$ $$(x-3)(x-3)=0$$ $$Either (x-3)=0 or (x-3)=0$$ It gives us: $$x = 3$$ It means x has only one value. Therefore, Option B is correct. Hope this 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. • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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