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# What is the solution of the equation (x-1)/(1-x) = 0?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 8011
GMAT 1: 760 Q51 V42
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What is the solution of the equation (x-1)/(1-x) = 0?  [#permalink]

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11 Oct 2018, 01:39
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Difficulty:

35% (medium)

Question Stats:

50% (00:41) correct 50% (00:50) wrong based on 91 sessions

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[Math Revolution GMAT math practice question]

What is the solution of the equation $$\frac{(x-1)}{(1-x)} = 0?$$

$$A. -1$$
$$B. 0$$
$$C. 1$$
$$D. 0$$ or $$1$$
E. The equation has no solution.

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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" GMATH Teacher Status: GMATH founder Joined: 12 Oct 2010 Posts: 935 Re: What is the solution of the equation (x-1)/(1-x) = 0? [#permalink] ### Show Tags 11 Oct 2018, 07:45 1 MathRevolution wrote: [Math Revolution GMAT math practice question] What is the solution of the equation $$\frac{(x-1)}{(1-x)} = 0?$$ $$A. -1$$ $$B. 0$$ $$C. 1$$ $$D. 0$$ or $$1$$ E. The equation has no solution. Important conceptual question. Congrats, Max! BEFORE any manipulation/calculation is done, the "mathematical entity" (in this case, the fraction) must EXIST. Hence we must impose the denominator different from zero, i.e., x different from 1. We know that any fraction given (if it exists) is zero if, and only if, its numerator is zero. Only x=1 satisfies that (x-1 = 0 implies x=1). From the fact that x=1 is not allowed, the equation given has no solutions! This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator (Math for the GMAT) Our high-level "quant" preparation starts here: https://gmath.net Board of Directors Status: QA & VA Forum Moderator Joined: 11 Jun 2011 Posts: 4782 Location: India GPA: 3.5 WE: Business Development (Commercial Banking) Re: What is the solution of the equation (x-1)/(1-x) = 0? [#permalink] ### Show Tags 11 Oct 2018, 09:00 MathRevolution wrote: [Math Revolution GMAT math practice question] What is the solution of the equation $$\frac{(x-1)}{(1-x)} = 0?$$ $$A. -1$$ $$B. 0$$ $$C. 1$$ $$D. 0$$ or $$1$$ E. The equation has no solution. $$\frac{(x-1)}{(1-x)} = 0$$ Or, $$x - 1 = 0$$ So, $$x = 1$$ If $$x = 1$$ ; $$\frac{(x-1)}{(1-x)} = \frac{1 - 1}{1 - 1}$$ Now, here denominator can not be 0 as anything divided by 0 is Undefined... Lets try with $$x = 0$$ ; $$\frac{(x-1)}{(1-x)} = \frac{0 - 1}{1 - 0} = -1 ≠ 0$$ Lets try with $$x = -1$$ ; $$\frac{(x-1)}{(1-x)} = \frac{-1 - 1}{1 + 1} = -1 ≠ 0$$ Thus, the equation has no solution, the answer must be (E) The equation has no solution. _________________ Thanks and Regards Abhishek.... PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only ) Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8011 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: What is the solution of the equation (x-1)/(1-x) = 0? [#permalink] ### Show Tags 14 Oct 2018, 18:51 => In order for a fraction to be zero, its numerator must be $$0$$. This occurs when $$x = 1$$. However, if $$x = 1$$, then the denominator of this fraction is $$0$$. Thus, $$0$$ is an erroneous solution, and the equation has no solution. Therefore, the answer is E. Answer: E _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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Re: What is the solution of the equation (x-1)/(1-x) = 0?   [#permalink] 14 Oct 2018, 18:51
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