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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 ## How many positive two-digit numbers are odd, not divisible b tagged by: fskilnik@GMATH ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## How many positive two-digit numbers are odd, not divisible b ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 16) How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits? (A) 28 (B) 27 (C) 26 (D) 25 (E) 24 Answer: ____(B)__ _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13001 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 16) How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits? (A) 28 (B) 27 (C) 26 (D) 25 (E) 24 Answer: ____(B)__ After about 30 seconds, I recognized that I couldn't see a nice straightforward solution (one that doesn't involve considering multiple cases), so I had 3 options: 1) Keep searching for a nice straightforward solution 2) Guess and move on 3) List the possible outcomes Since the answer choices are reasonably small, I can quickly list the outcomes and be finished in under 2 minutes (total) So, let's do that. We get: 17, 19, 23, 25, 29, 31, 35, 37, 41, 43, 47, 49, 53, 55, 59, 61, 65, 67, 71, 73, 79, 83, 85, 89, 91, 95, 97 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: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 fskilnik@GMATH wrote: [size=17]GMATH practice exercise (Quant Class 16) How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits? (A) 28 (B) 27 (C) 26 (D) 25 (E) 24 For any set of consecutive integers: count = biggest - smallest + 1 Thus: Number of two-digit integers between 10 and 99, inclusive = 99-10+1 = 90. Of these 90 consecutive integers, 1 of every 3 will be a multiple of 3, implying that 2/3 will NOT be divisible by 3: (2/3)(90) = 60. Of these 60 remaining integers, exactly 1/2 will be ODD: (1/2)(60) = 30. Of these 30 remaining integers that are not divisible by 3 but are odd, three -- 11, 55 and 77 -- have repeated digits and thus must be subtracted from the total: 30-3 = 27. 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 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 16) How many positive two-digit numbers are odd, not divisible by 3, and have distinct digits? (A) 28 (B) 27 (C) 26 (D) 25 (E) 24 $$?\,\,\,\,:\,\,\,\# N\,,\,\,N \in \left[ {10,99} \right]\,\,,\,\,{\rm{odd}}\,\,{\rm{,}}\,\,{\rm{not}}\,\,{\rm{divisible}}\,\,{\rm{by}}\,\,{\rm{3}}\,,\,\,\,{\rm{not}}\,\,{\rm{divisible}}\,\,{\rm{by}}\,\,11$$ $${\rm{I}}{\rm{.}}\,\,\,\,{\rm{odd}} \in \left[ {10,99} \right]\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,{1 \over 2}\left( {99 - 10 + 1} \right) = 45\,\,{\rm{numbers}}$$ $${\rm{I}}{\rm{.}}\,\, \cap \,\,\left( {{\rm{div}}\,\,{\rm{by}}\,\,3} \right)\,\,\,:\,\,\,\left\{ \matrix{ \,15 = 3 \cdot 5 + 0 \cdot 6 \hfill \cr \,21 = 3 \cdot 5 + 1 \cdot 6 \hfill \cr \,\,\, \ldots \hfill \cr \,99 = 3 \cdot 5 + 14 \cdot 6 \hfill \cr} \right.\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,14 + 1 = 15\,\,{\rm{numbers}}$$ $${\rm{I}}{\rm{.}}\,\, \cap \,\,\left( {\underline {{\rm{not}}} \,\,{\rm{div}}\,\,{\rm{by}}\,\,3} \right)\,\,\,:\,\,\,45 - 15 = 30\,\,{\rm{numbers}}$$ $${\rm{I}}{\rm{.}}\,\, \cap \,\,\left( {\underline {{\rm{not}}} \,\,{\rm{div}}\,\,{\rm{by}}\,\,3} \right) \cap \,\,\left( {{\rm{div}}\,\,{\rm{by}}\,\,11} \right)\,\,\,:\,\,\,\left\{ {11,33,55,77,99} \right\} - \left\{ {33,99} \right\}\,\,\,\,\, \Rightarrow \,\,\,\,\,3\,\,{\rm{numbers}}$$ $$?\,\, = \,\,{\rm{I}}{\rm{.}}\,\, \cap \,\,\left( {\underline {{\rm{not}}} \,\,{\rm{div}}\,\,{\rm{by}}\,\,3} \right) \cap \,\,\left( {\underline {{\rm{not}}} \,\,{\rm{div}}\,\,{\rm{by}}\,\,11} \right) = \,\,30 - 3 = 27\,\,{\rm{numbers}}$$ The correct answer is (B). We follow 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 • Award-winning private GMAT tutoring Register now and save up to$200

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