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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 ## Is Z Between X and Y? tagged by: Brent@GMATPrepNow ##### This topic has 6 expert replies and 2 member replies ## Is Z Between X and Y? If x, y, and z are positive numbers, is z between x and y? (1) x < 2z < y (2) 2x < z < 2y OA: C ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12534 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 bml1105 wrote: If x, y, and z are positive numbers, is z between x and y? (1) x < 2z < y (2) 2x < z < 2y Target question: Is z between x and y? Statement 1: x < 2z < y There are several set values of x, y and z that satisfy this condition. Here are two: Case a: x = 3, y = 10, and z = 2, in which case z is NOT between x and y Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: 2x < z < 2y There are several set values of x, y and z that satisfy this condition. Here are two: Case a: x = 1, y = 2, and z = 3, in which case z is NOT between x and y Case b: x = 1, y = 10, and z = 3, in which case z IS between x and y Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Statements 1 and 2 combined Statement 1: x < 2z < y Statement 2: 2x < z < 2y Since the two inequalities are facing the same direction, we can add them to get: 3x < 3z < 3y Divide all three parts by 3 to get: x < z < y As we can see, z IS definitely between x and y Since we can answer the target question with certainty, the combined statements are SUFFICIENT Answer = C Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15019 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 bml1105 wrote: If x, y, and z are positive numbers, is z between x and y? (1) x < 2z < y (2) 2x < z < 2y Statement 1: x < 2z < y Let x=2 and y=10. In this case: 2 < 2z < 10 1 < z < 5. If z=4, then it is between x=2 and y=10. If z=1.5, then it is not between x=2 and y=10. INSUFFICIENT. Statement 2: 2x < z < 2y Let x=2 and y=10. In this case: 2*2 < z < 2*10 4 < z < 20 If z=5, then it is between x=2 and y=10. If z=19, then it is not between x=2 and y=10. INSUFFICIENT. Statements combined: Inequalities can be ADDED TOGETHER. Adding together x < 2z < y and 2x < z < 2y, we get: (x+2x) < (2z+z) < (y+2y) 3x < 3z < 3y x < z < y. Thus, z is between x and y. SUFFICIENT. The correct answer is C. _________________ 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. Master | Next Rank: 500 Posts Joined 05 Jun 2015 Posted: 360 messages Followed by: 2 members Upvotes: 3 bml1105 wrote: If x, y, and z are positive numbers, is z between x and y? (1) x < 2z < y (2) 2x < z < 2y OA: C Hi GMATGuruNY And Brent@GMATPrepNow, How to quickly choose the numbers to satisfy (1) x < 2z < y (2) 2x < z < 2y I'm Getting Stuck to choose the numbers. Please throw some light Thanks Nandish ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12534 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 NandishSS wrote: bml1105 wrote: If x, y, and z are positive numbers, is z between x and y? (1) x < 2z < y (2) 2x < z < 2y OA: C Hi GMATGuruNY And Brent@GMATPrepNow, How to quickly choose the numbers to satisfy (1) x < 2z < y (2) 2x < z < 2y I'm Getting Stuck to choose the numbers. Please throw some light Thanks Nandish The process of choosing numbers isn't always easy. In most cases, we are looking for numbers that meet the given information AND provide conflicting answers to the target question. So, for example, for statement 1, we have x < 2z < y Notice that this statement is similar to what the target question is asking, yet instead of z, we have 2z. So, we might first make x and y spread out apart enough to allow us to play with the z values. Let's start with x = 3 and y = 10 First value of z is kind of irrelevant (as long as it meets the given information). Let's say z = 4. This value of z meets the condition that x < 2z < y. Also, when x = 3, y = 10, and z = 4, the answer to the target question is "YES, z IS between x and y" At this point, we'll try to find a value of z so that the answer to the target question is "NO, z is NOT between x and y." This is where we need to play around with some z-values. Let's see what happens if we keep x = 3 and y = 10, and work with different z-values. In this case, if we make z small AND close to the x-value, it might be the case that doubling z (aka 2z) will make 2z big enough so that x < 2z < y, HOWEVER z itself will NOT be between x and y. So, how about z = 2. When we double z, we get 2z = 6, so we meet the condition that x < 2z < y, however z itself (z = 2) leads us to a DIFFERENT answer to our target question: "NO, z is NOT between x and y." As I said, choosing numbers isn't always easy. It can take a lot of playing around with numbers. If you're interested, we have a video on choosing numbers to test when answer Data Sufficiency questions: https://www.gmatprepnow.com/module/gmat-data-sufficiency/video/1102 Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our free resources GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 1996 messages Followed by: 237 members Upvotes: 1443 NandishSS wrote: How to quickly choose the numbers to satisfy (1) x < 2z < y (2) 2x < z < 2y I'm Getting Stuck to choose the numbers. Please throw some light Thanks Nandish Here's my general process: go BIG then small! So for each statement, I think "is there an example in which the numbers are HUGE or FAR APART that keeps the statement true?" ex: (1) x < 2z < y x = 0 y = 1,000,000 2z = 100, z = 50 When x and y are far apart, it's easy to think of a number for z where both z and 2z are between x and y. Next, I think: "is there an example in which the numbers are SMALL or very CLOSE TOGETHER that keeps the statement true?" ex: (1) x < 2z < y x = 3 y = 5 2z = 4, z = 2 When x and y are close together, it's possible for 2z to be in between x and y, but for 2z not to be. Then repeat the same thought process of BIG then small (or FAR then CLOSE) for the 2nd statement. _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 1996 messages Followed by: 237 members Upvotes: 1443 _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. Master | Next Rank: 500 Posts Joined 05 Jun 2015 Posted: 360 messages Followed by: 2 members Upvotes: 3 ceilidh.erickson wrote: NandishSS wrote: How to quickly choose the numbers to satisfy (1) x < 2z < y (2) 2x < z < 2y I'm Getting Stuck to choose the numbers. Please throw some light Thanks Nandish Here's my general process: go BIG then small! So for each statement, I think "is there an example in which the numbers are HUGE or FAR APART that keeps the statement true?" ex: (1) x < 2z < y x = 0 y = 1,000,000 2z = 100, z = 50 When x and y are far apart, it's easy to think of a number for z where both z and 2z are between x and y. Next, I think: "is there an example in which the numbers are SMALL or very CLOSE TOGETHER that keeps the statement true?" ex: (1) x < 2z < y x = 3 y = 5 2z = 4, z = 2 When x and y are close together, it's possible for 2z to be in between x and y, but for 2z not to be. Then repeat the same thought process of BIG then small (or FAR then CLOSE) for the 2nd statement. Hi ceilidh, Thanks A lot:-) You People made my day Thanks Nandish ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 1996 messages Followed by: 237 members Upvotes: 1443 NandishSS wrote: Hi ceilidh, Thanks A lot:-) You People made my day Thanks Nandish My pleasure! Very glad to help. _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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