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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 N is a positive two-digit integer, is N+1 prime? tagged by: fskilnik@GMATH ##### This topic has 4 expert replies and 0 member replies ### GMAT/MBA Expert ## If N is a positive two-digit integer, is N+1 prime? ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 16) If N is a positive two-digit integer, is N+1 prime? (1) The sum of the digits of N is equal to 11. (2) N-1 is divisible by 7. Answer: _____(A)__ _________________ 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 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) If N is a positive two-digit integer, is N+1 prime? (1) The sum of the digits of N is equal to 11. (2) N-1 is divisible by 7. Statement 1: Any integer whose digits sum to a multiple of 3 must itself be a multiple of 3. Since N has a digit sum of 11, N+1 must have a digit sum of 12. One exception: If N=29, then N+1 = 30, which has a digit sum of 3. Since the digit sum of N+1 must be a multiple of 3 -- either 12 or 3 -- N+1 itself must be a 2-digit multiple of 3 and thus cannot be prime. Since N+1 is not prime, the answer to the question stem is NO. SUFFICIENT. Statement 2: N-1 = 14, 21, 28... N = 15, 22, 29... N+1 = 16, 23, 30... If N+1 = 16, the answer to the question stem is NO. If N+1 = 23, the answer to the question stem is YES. INSUFFICIENT. The correct answer is A. _________________ 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 Last edited by GMATGuruNY on Thu Mar 14, 2019 9:07 am; edited 2 times in total 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 02 Jun 2008 Posted: 2475 messages Followed by: 351 members Upvotes: 1090 GMAT Score: 780 GMATGuruNY wrote: Since N has a digit sum of 11, N+1 must have a digit sum of 12. The logic of your answer is perfect, but this is not quite true - when you add 1 to a number, when that number ends in 9, the digit sum drops by 8 (the tens digit goes up by 1, the units digit falls by 8) rather than increases by 1. So here, when N = 29, after adding 1 we don't get a digit sum of 12, but instead of 3. That's still divisible by 3 of course. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 Ian Stewart wrote: The logic of your answer is perfect, but this is not quite true - when you add 1 to a number, when that number ends in 9, the digit sum drops by 8 (the tens digit goes up by 1, the units digit falls by 8) rather than increases by 1. So here, when N = 29, after adding 1 we don't get a digit sum of 12, but instead of 3. That's still divisible by 3 of course. Good catch. In my solution, the lone exception (N=29) is now noted. _________________ 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) If N is a positive two-digit integer, is N+1 prime? (1) The sum of the digits of N is equal to 11. (2) N-1 is divisible by 7. Thank you both (Mitch and Ian) for your nice contributions! $$N = \left\langle {AB} \right\rangle$$ $$N + 1\,\,\mathop = \limits^? \,\,{\rm{prime}}$$ $$\left( 1 \right)\,\,A + B = 11\,\,\,\,\left\{ \matrix{ \,B\,\,{\rm{odd}}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\left[ {N + 1\,\,{\rm{even}}\,\, > 2\,\,} \right] \hfill \cr \,B\,\,{\rm{even}}\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\,\,\,\,\,\left[ {N + 1\,\, \in \left\{ {92 + 1,74 + 1,56 + 1,38 + 1} \right\}\,\,\, \Rightarrow \,\,\,{\rm{multiple}}\,\,{\rm{of}}\,\,3\,\,\, > 3} \right]\,\, \hfill \cr} \right.$$ $$\left( 2 \right)\,\,{{N - 1} \over 7} = {\mathop{\rm int}} \,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,N = 15\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{NO}}} \right\rangle \,\, \hfill \cr \,{\rm{Take}}\,\,N = 22\,\,\,\, \Rightarrow \,\,\,\left\langle {{\rm{YES}}} \right\rangle \,\, \hfill \cr} \right.$$ The correct answer is (A). We follow the notations and rationale taught in the GMATH method. Regards, Fabio. P.S. (to the careful reader): there is at least one number N that satisfies the question stem (pre-statements) and both statements together (92). This is expected to avoid "internal contradictions". _________________ 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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