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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 integers such that x = 8y + 12, what tagged by: swerve ##### This topic has 3 expert replies and 0 member replies ### Top Member ## If x and y are positive integers such that x = 8y + 12, what ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y? 1) x = 12u, where u is an integer. 2) y = 12z, where z is an integer. The OA is B Source: GMAT Prep ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12995 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 Quote: If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y? (1) x = 12u, where u is an integer (2) y = 12z, where z is an integer Target question: What is the greatest common divisor of x and y? Given: x = 8y + 12 Statement 1: x = 12u, where u is an integer. There are several pairs of values that satisfy the given conditions. Here are two: Case a: x=36 and y=3, in which case the GCD of x and y is 3 Case b: x=60 and y=6, in which case the GCD of x and y is 6 Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: y = 12z, where z is an integer. If y = 12z and x = 8y + 12, then we can replace y with 12z to get: x = 8(12z) + 12, which means x = 96z + 12, which means x = 12(8z + 1) [if we factor] So, what is the GCD of 12z and 12(8z + 1)? Well, we can see that they both share 12 as a common divisor, but what about z and 8z+1? Well, there's a nice rule that says: The GCD of n and kn+1 is always 1 (if n and k are positive integers) So, the GCD of z and 8z+1 is 1, which means the GCD of 12z and 12(8z + 1) is 12. This means that the GCD of x and y is 12 Since we can answer the target question with certainty, statement 2 is SUFFICIENT Answer: B Cheers, Brent _________________ Brent Hanneson â€“ Creator of GMATPrepNow.com Use my video course along with Sign up for free Question of the Day emails And check out all of these 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: 15359 messages Followed by: 1865 members Upvotes: 13060 GMAT Score: 790 swerve wrote: If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y? 1) x = 12u, where u is an integer. 2) y = 12z, where z is an integer. Statement 1: x=12u, where u is an integer and x=8y+12. In other words, x is a multiple of 12. For x to be a multiple of 12, 8y must be a multiple of 12. If y=3, then x = 8*3 + 12 = 36. The GCD of 3 and 36 is 3. If y=6, then x = 8*6 + 12 = 60. The GCD of 6 and 60 is 6. Since the GCD can be different values, INSUFFICIENT. Statement 2: y=12z, where z is an integer and x=8y+12. In other words, y is a multiple of 12. Since we're looking for the GCD, view x in terms of its FACTORS. If y=12, then x = 8(12) + 12 = 12(8+1) = 12*9. The GCD of 12 and 12*9 is 12. If y=24, then x = 8(24) + 12 = 12(8*2 + 1) = 12*17. The GCD of 24 and 12*17 is 12. I'm almost convinced: the GCD is 12. Maybe one more just to be sure: If y=36, then x = 8(36) + 12 = 12(8*3 + 1) = 12*25. The GCD of 36 and 12*25 is 12. SUFFICIENT. 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 swerve wrote: If x and y are positive integers such that x = 8y + 12, what is the greatest common divisor of x and y? 1) x = 12u, where u is an integer. 2) y = 12z, where z is an integer. Source: GMAT Prep $\left\{ \begin{gathered} x,y\,\, \geqslant \,\,1\,\,{\text{ints}} \hfill \\ x - 8y = 12\,\,\,\,\,\left( * \right) \hfill \\ \end{gathered} \right.\,\,\,\,\,\,\,\,\,;\,\,\,\,\,\,\,?\,\, = \,\,GCD\left( {x,y} \right)$ $\left( 1 \right)\,\,\,x = 12u\,\,,\,\,\,u\,\,\operatorname{int} \,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,8y = 12\left( {u - 1} \right)$ $\,\left\{ \begin{gathered} \,{\text{Take}}\,\,u = 3\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,\,y = 3\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {x,y} \right) = \left( {12 \cdot 3\,,\,3} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 3 \hfill \\ \,{\text{Take}}\,\,u = 5\,\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\,\,y = 6\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\left( {x,y} \right) = \left( {12 \cdot 5\,,\,6} \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,? = 6\,\, \hfill \\ \end{gathered} \right.$ $\left( 2 \right)\,\,\,y = 12z\,\,,\,\,\,z\,\,\operatorname{int} \,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,x = 12 + 8 \cdot 12 \cdot z = 12\left( {8z + 1} \right)\,\,\,\,\,\mathop \Rightarrow \limits^{\left( {**} \right)} \,\,\,\,\,\,? = 12$ $\left( {**} \right)\,\,\,GCD\,\,\left( {z\,,\,8z + 1} \right) = \,\,k \geqslant 1\,\,\,{\text{int}}\,\,\,\, \Rightarrow \,\,\,\,\,\left\{ \begin{gathered} \,\frac{z}{k} = {\text{in}}{{\text{t}}_{\text{1}}} \hfill \\ \,\frac{{8z + 1}}{k} = {\operatorname{int} _2}\,\,\,\,\, \hfill \\ \end{gathered} \right. \Rightarrow \,\,\,\,\,\,\,\,\frac{1}{k} = {\operatorname{int} _2} - 8\left( {\frac{z}{k}} \right) = {\operatorname{int} _2} - 8 \cdot {\operatorname{int} _1} = \operatorname{int} \,\,\,\,\,\,\,\mathop \Rightarrow \limits^{k\, \geqslant \,1\,\,\,{\text{int}}} \,\,\,\,\,k = 1$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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