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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 ax+by=17, 2ax+3by=43, and 3x=2y, tagged by: Vincen This topic has 1 expert reply and 0 member replies Top Member If ax+by=17, 2ax+3by=43, and 3x=2y, If ax+by=17, 2ax+3by=43, and 3x=2y, which of the following is a possible value of a+b if a and b are integers? A. 6 B. 10 C. 14 D. 18 E. 20 The OA is C . How can I solve this PS question? Experts, may you give me an explanation here? Please. GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello Vincen. I will try to explain to you this question in an easy way. $$If\ \ \ ax+by=17\ \rightarrow\ -2ax-2by=-34.$$ Adding this equation to the second given equation we will get $$by=9.$$ Now, replacing this on the first given equation we get $$ax+by=17\ \leftrightarrow\ ax+9=17\ \leftrightarrow\ ax=8.$$ By the other hand, $$if\ \ \ \ 3x=2y\ \rightarrow\ \frac{x}{y}=\frac{2}{3}\ \leftrightarrow\ \frac{8}{9}=\frac{ax}{by}=\frac{2a}{3b}\leftrightarrow\ \frac{a}{b}=\frac{4}{3}.$$ As "a" and "b" are integers, we have the following cases: $$\left(1\right)\ a=3\ and\ b=4.\ Then\ a+b=7.$$ $$\left(2\right)\ a=8\ and\ b=6.\ Then\ a+b=14.$$ $$\left(3\right)\ a=12\ and\ b=9.\ Then\ a+b=21.$$ $$\left(4\right)\ a=16\ and\ b=12.\ Then\ a+b=28.$$ $$\quad\hspace{2cm}\vdots$$ $$\left(k\right)\cdots\ a+b=7\cdot k.$$ If we see the options, we find that the correct answer is C . I hope this explanation may help you. Feel free to ask me if you have any doubt. Cheers. _________________ 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. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for 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 • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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