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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 (1+x)y=y, which of the following must be true? ##### This topic has 5 expert replies and 3 member replies ## If (1+x)y=y, which of the following must be true? If (1+x)y=y, which of the following must be true? A. x=-1 or y=0 B. x=0 or y=0 C. x=1 or y=1 D. x=-1 or y=-1 E. x=0 or y=1 OA is B How to approach this question ? My working:- y + xy - y = 0 xy = 0 Now, here I am little confused. While taking answer choices should I put both values of x and y or should I work with the values of x and y independently or one at a time i.e For (A) case 1 : x = -1 --> -1 * y = 0 (might be true) case 2: y = 0 --> x * 0 = 0 (TRUE) So, A is not the answer ### GMAT/MBA Expert Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 497 members Upvotes: 2867 GMAT Score: 800 Top Reply Hi vinni.k, We're told that (1+X)(Y) = (Y). We're asked which of the following MUST be true - meaning that one of these answers is ALWAYS true no matter how many different examples we come up with. The answer choices provide us with a limited number of possibilities, so we can use them 'against' the prompt and TEST THE ANSWERS. Mathematically-speaking, it would likely be easiest to TEST one of the '0' values first, so let's see what happens IF Y = 0.... (1+X)(Y) = (Y) (1+X)(0) = (0) 0 = 0 This is clearly a possible solution to the given equation. If Y=0, then X could be any value. Thus, we need an answer that includes Y=0 and we need an "or" (since the value of X doesn't matter in this scenario). Eliminate Answers C, D and E. Of the remaining 2 Answers, let's TEST X = 0 next... (1+X)(Y) = (Y) (1+0)(Y) = (Y) (1)(Y) = Y Y = Y This is also clearly a possible solution to the given equation. If X=0, then Y could be any value. We now have the answer to the question. Final Answer: B GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15386 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 Top Reply vinni.k wrote: If (1+x)y=y, which of the following must be true? A. x=-1 or y=0 B. x=0 or y=0 C. x=1 or y=1 D. x=-1 or y=-1 E. x=0 or y=1 OA is B How to approach this question ? My working:- y + xy - y = 0 xy = 0 Now, here I am little confused. While taking answer choices should I put both values of x and y or should I work with the values of x and y independently or one at a time i.e For (A) case 1 : x = -1 --> -1 * y = 0 (might be true) case 2: y = 0 --> x * 0 = 0 (TRUE) So, A is not the answer Once you have determined that xy=0, consider each solution separately. One solution for xy=0 is x=0. A: x=-1 or y=0 If x=0, then it does not have to be true that x=-1 or y=0. Eliminate A. C: x=1 or y=1 If x=0, then it does not have to be true that x=1 or y=1. Eliminate C. D: x=-1 or y=-1 If x=0, then it does not have to be true that x=-1 or y=-1. Eliminate D. Another solution for xy=0 is y=0. E: x=0 or y=1 If y=0, then it does not have to be true that x=0 or y=1. Eliminate E. 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 Last edited by GMATGuruNY on Tue Feb 06, 2018 11:11 am; edited 1 time in total 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 (1+x)y=y, which of the following must be true? A. x=-1 or y=0 B. x=0 or y=0 C. x=1 or y=1 D. x=-1 or y=-1 E. x=0 or y=1 OA is B How to approach this question ? My working:- y + xy - y = 0 xy = 0 Now, here I am little confused. While taking answer choices should I put both values of x and y or should I work with the values of x and y independently or one at a time i.e For (A) case 1 : x = -1 --> -1 * y = 0 (might be true) case 2: y = 0 --> x * 0 = 0 (TRUE) So, A is not the answer Hi vinni.k, Let's take a look at your question. $$\left(1+x\right)y=y$$ $$\left(1+x\right)=\frac{y}{y}$$ $$\left(1+x\right)=1$$ $$x=1-1=0$$ To find y let's evaluate the equation: $$\left(1+x\right)y=y$$ $$y+xy=y$$ $$xy=y-y$$ $$xy=0$$ $$y=0$$ Therefore, Option B is correct. I 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. Master | Next Rank: 500 Posts Joined 17 Apr 2011 Posted: 421 messages Followed by: 2 members Upvotes: 6 Test Date: 2016 Target GMAT Score: 700+ GMAT Score: 620 Thanks Economist for your explanation. I understood your explanation, but i can still stuck when i am putting value of x = 0 back to the equation while evaluating for y. I can plug in x = 0 here (1+x)y=y (1 + 0)y = y (1)y = y y = y Now, it can create a problem, but after understanding your approach, i think if i play around with the equation, then i can land with y = 0. However, i still want to understand how can i use the answer choices as i have explained my doubt in the first post. Master | Next Rank: 500 Posts Joined 17 Apr 2011 Posted: 421 messages Followed by: 2 members Upvotes: 6 Test Date: 2016 Target GMAT Score: 700+ GMAT Score: 620 Hi, Can anyone please let me know how to approach this question through answer options. I have explained my doubt in the first post. Though i have understood what Economist has explained, but i still think that i can get stuck somewhere. Thanks ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 vinni.k wrote: If (1+x)y=y, which of the following must be true? A. x=-1 or y=0 B. x=0 or y=0 C. x=1 or y=1 D. x=-1 or y=-1 E. x=0 or y=1 Letâ€™s simplify the given equation: (1 + x)y = y y + xy = y xy = 0 We see that either x or y must be zero. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews Master | Next Rank: 500 Posts Joined 17 Apr 2011 Posted: 421 messages Followed by: 2 members Upvotes: 6 Test Date: 2016 Target GMAT Score: 700+ GMAT Score: 620 Thanks for your different approaches on this question. Finally doubt cleared. Really appreciate it Regards ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 vinni.k wrote: Thanks Economist for your explanation. I understood your explanation, but i can still stuck when i am putting value of x = 0 back to the equation while evaluating for y. I can plug in x = 0 here (1+x)y=y (1 + 0)y = y (1)y = y y = y Now, it can create a problem, but after understanding your approach, i think if i play around with the equation, then i can land with y = 0. However, i still want to understand how can i use the answer choices as i have explained my doubt in the first post. Hi vinni.k, xy=0 itself indicates that one of the variables either x or y or both should be zero, only then this equation will be true. So we can say that either x = 0 or y = 0. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. 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