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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 ## Let f(x) denotes the sum of... tagged by: BTGmoderatorLU ##### This topic has 1 expert reply and 0 member replies ### Top Member ## Let f(x) denotes the sum of... Let f(x) denotes the sum of the digits of the positive integer x. For example, f(8) =8, f(123) = 1+2+3=6. For how many two-digit values of x is f(f(x))=3? A) 3 B) 4 C) 6 D) 9 E) 10 The OA is E. Can any expert help me with this PS question please? I don't have it clear. Thanks. ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Hello LUANDATO. It is a really interesting question. The idea is that we must find the numbers of two digits such that the sum of their digits is: - 3, that is to say, f(x)=3, so that f(f(x))=f(3)=3. - 12, that is to say, f(x)=12, so that f(f(x))=f(12)=3. The numbers that satisfy this property are: 12, 21, 30, 39, 48, 57, 66, 75, 84 and 93. f(f(12))=f(3)=3 f(f(21))=f(3)=3 f(f(30))=f(3)=3 f(f(39))=f(12)=3 f(f(48))=f(12)=3 f(f(57))=f(12)=3 f(f(66))=f(12)=3 f(f(75))=f(12)=3 f(f(84))=f(12)=3 f(f(93))=f(12)=3 So, the answer is E. Note that f(f(3))=3, but 3 is one-digit number, that is why it is not on the list above. I hope this can help you to understand how to solve this kind of questions. _________________ 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. • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE 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 Study Smarter, Not Harder Available with Beat the GMAT members only code • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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