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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 x and y are positive , is 4x>3y? ##### This topic has 5 expert replies and 3 member replies ## if x and y are positive , is 4x>3y? I need help! If x and y are positive, is 4x>3y? 1. x>y-x 2. x/y<1 I get how the two statements alone are not sufficient but how about together?? this is what i did so far: 1. x>y-x becomes 2x>y some values that satisfy this are x=1, y=1....x=2, y=3.... x=3, y =5 putting these values in 4x>3y gives true/false statements....2>1 yes......8>9...no..12>15..no so insufficient 2. since x, >0 x/y <1 becomes x values of x,y that satisfy this are...4,2...6,1...3,4 putting these in 4x>3y we get Y/N statements agn.....16>6 yes.....24>3 yes.....12>12...no so insufficient BUT together...i'm not sure how to combine the two statements: 2x>y & x 3y What do i do??? It would take me forever to find values to satisfy both stat 1 & 2 and then to check if any of the values give a consistent answer for 4x>3y. Is there a shortcut that i'm missing????? Also another issue related to this i have is that i never know which "trial" values to pick. I tend to start with small positive no.s then i try higher positive no.s then if the question allows i'll plug in negative values or fractions. my question is how do i speed up this process? any tips on plug-in values would be greatly appreciated! thanks ### GMAT/MBA Expert GMAT Instructor Joined 25 Aug 2009 Posted: 147 messages Followed by: 17 members Upvotes: 76 GMAT Score: 770 >>> _________________ Rich Zwelling GMAT Instructor, Veritas Prep Last edited by Rich@VeritasPrep on Sat Jun 12, 2010 9:33 am; edited 1 time in total Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! Master | Next Rank: 500 Posts Joined 19 May 2010 Posted: 124 messages Upvotes: 3 Test Date: 09/2010 Target GMAT Score: 650+ GMAT Score: 1100 raz1024 wrote: Hey Mitz (?), Nice job in getting everything down to 2x>y & x Combining those two statements, you can form a single inequality: x Now, you're interested in 3y, according to the prompt, so multiply everything by 3: 3x<3y<4x. ! shouldnt this be 6x ? You know from this inequality that 3y is less than 4x, and thus 4x>3y. SUFFICIENT. As for plugging in values, it looks like you did just fine. Your strategy of starting with smaller numbers is exactly what should be done, because it keeps everything simple. You could also think about it strictly in terms of the algebra: (1) tells you that 2x>y, which means 4x>2y. Does that mean 4x>3y? Not necessarily. (2) tells you x3y? Not necessarily. Thanks Raz1024! Ok, so you're saying... given 2x>y & x we get x since we want to know the answer in relation 3y, multiply all by 3 so we get 3x<3y<6x so since 6x>3y ....4x must be greater than 3y... correct? BUT ! there's an issue. the answer provided is E not C. So maybe there's a flaw in there somewhere...?! Junior | Next Rank: 30 Posts Joined 22 Jul 2009 Posted: 11 messages Upvotes: 1 Target GMAT Score: 700 GMAT Score: 640 The answer should be E -1 ) 2x > y --4x >2y -2) x4x<4y Combining both 2y<4x<4y Even both statements do not tell us that 4x >3y. Hope that clarifies. Hence E. ### GMAT/MBA Expert GMAT Instructor Joined 25 Aug 2009 Posted: 147 messages Followed by: 17 members Upvotes: 76 GMAT Score: 770 The answer is indeed E...why? Because sometimes even instructors make silly mistakes Nice job catching the error from yours truly! So, the lesson here? Be careful with your calculations. Although at this point, my saying that is like the pot and the kettle. Do as I say, not as I do _________________ Rich Zwelling GMAT Instructor, Veritas Prep Enroll in a Veritas Prep GMAT class completely for FREE. Wondering if a GMAT course is right for you? Attend the first class session of an actual GMAT course, either in-person or live online, and see for yourself why so many students choose to work with Veritas Prep. Find a class now! ### GMAT/MBA Expert GMAT Instructor Joined 21 Jan 2009 Posted: 3650 messages Followed by: 82 members Upvotes: 267 GMAT Score: 760 raz1024 wrote: The answer is indeed E...why? Because sometimes even instructors make silly mistakes Nice job catching the error from yours truly! So, the lesson here? Be careful with your calculations. Although at this point, my saying that is like the pot and the kettle. Do as I say, not as I do This famous saying must have been invented by a GMAT instructor only, very entertaining. _________________ The mind is everything. What you think you become. â€“Lord Buddha Sanjeev K Saxena Quantitative Instructor The Princeton Review - Manya Abroad Lucknow-226001 www.manyagroup.com 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 12 Sep 2010 Posted: 905 messages Followed by: 122 members Upvotes: 378 GMAT Score: 760 mitzwillrockgmat wrote: I need help! 2x>y & x 3y What do i do??? It would take me forever to find values to satisfy both stat 1 & 2 and then to check if any of the values give a consistent answer for 4x>3y. Is there a shortcut that i'm missing????? Also another issue related to this i have is that i never know which "trial" values to pick. I tend to start with small positive no.s then i try higher positive no.s then if the question allows i'll plug in negative values or fractions. my question is how do i speed up this process? any tips on plug-in values would be greatly appreciated! thanks It won't take forever if you think about the concepts behind the plug ins. At this point, you are trying to show that 4x can be both greater and smaller than 3y, while satisfying both statements. You know that 2x is greater than y, but y is greater than x. So let's first try with an x and y that are very close to each other: x=1 and y=1.1, so that 2x=2 is greater than y=1.1. in this case, 4x=4 is greater than 3y=3.3, so we have a yes. Now think: Can we have a "no", preferably without reinventing the wheel altogether? Keep x as 1, so that 4x is still 4. All we need is a y that is great enough to pass 3y>4: y=1.5 would work, and still satisfy the requirement of 2x>y. Take home messages: 1) plug in with direction, not blindly: plug in one set, see what answer you get, then think about which plug in will get you the opposite answer. 2) When plugging in a second time for more than one value, keep one and play with the other. _________________ Geva Senior Instructor Master GMAT 1-888-780-GMAT https://www.mastergmat.com 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. Newbie | Next Rank: 10 Posts Joined 10 Nov 2010 Posted: 8 messages You can also solve this question graphically as I have discussed on the Veritas blog here: https://www.veritasprep.com/blog/2011/01/quarter-wit-quarter-wisdom-bagging-the-graphs-part-iii/ mitzwillrockgmat wrote: I need help! If x and y are positive, is 4x>3y? 1. x>y-x 2. x/y<1 I get how the two statements alone are not sufficient but how about together?? this is what i did so far: 1. x>y-x becomes 2x>y some values that satisfy this are x=1, y=1....x=2, y=3.... x=3, y =5 putting these values in 4x>3y gives true/false statements....2>1 yes......8>9...no..12>15..no so insufficient 2. since x, >0 x/y <1 becomes x values of x,y that satisfy this are...4,2...6,1...3,4 putting these in 4x>3y we get Y/N statements agn.....16>6 yes.....24>3 yes.....12>12...no so insufficient BUT together...i'm not sure how to combine the two statements: 2x>y & x 3y What do i do??? It would take me forever to find values to satisfy both stat 1 & 2 and then to check if any of the values give a consistent answer for 4x>3y. Is there a shortcut that i'm missing????? Also another issue related to this i have is that i never know which "trial" values to pick. I tend to start with small positive no.s then i try higher positive no.s then if the question allows i'll plug in negative values or fractions. my question is how do i speed up this process? any tips on plug-in values would be greatly appreciated! thanks _________________ Karishma Private Tutor for GMAT Contact: bansal.karishma@gmail.com ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15385 messages Followed by: 1872 members Upvotes: 13060 GMAT Score: 790 mitzwillrockgmat wrote: I need help! If x and y are positive, is 4x>3y? 1. x>y-x 2. x/y<1 Since y is POSITIVE, the inequalities can safely be divided by y. 4x > 3y x > (3/4)y x/y > 3/4 Question stem, rephrased: Is x/y > 3/4? Statement 1: x > y-x 2x > y 2(x/y) > 1 x/y > 1/2 Case 1: x/y = 2/3 In this case, x/y < 3/4, so the answer to the rephrased question stem is NO. Case 2: x/y = 9/10 In this case, x/y > 3/4, so the answer to the rephrased question stem is YES. Since the answer is NO in Case 1 but YES in Case 2, INSUFFICIENT. Cases 1 and 2 satisfy BOTH statements. Since the answer is NO in Case 1 but YES in Case 2, the two statements combined are INSUFFICIENT. The correct answer is E. _________________ 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. • FREE GMAT Exam Know how you'd score today for$0

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