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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 ## When positive integer N is divided by positive integer J, ##### This topic has 4 expert replies and 1 member reply ### Top Member ## When positive integer N is divided by positive integer J, ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J? A. 22 B. 56 C. 78 D. 112 E. 175 OA E Source: Magoosh ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 Top Reply BTGmoderatorDC wrote: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J? A. 22 B. 56 C. 78 D. 112 E. 175 Source: Magoosh $N,J \geqslant 1\,\,\,{\text{ints}}$ LetÂ´s consider what the Division Algorithm say! $$N = QJ + 14\,\,,\,\,\,\left\{ \matrix{ \,Q\,\,{\mathop{\rm int}} \hfill \cr \,J \ge 15\,\,\,\,\,,\,\,\,\,\,\,? = J\,\, \hfill \cr} \right.\,\,\,\,\,\,\,\,\,\left( * \right)$$ $$134.08 = {N \over J} = Q + {{14} \over J}\,\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{\left( * \right)} \,\,\,\,\,\,\left\{ \matrix{ \,Q = 134 \hfill \cr \,{{14} \over J} = 0.08 = {8 \over {100}}\,\,\,\,\, \Rightarrow \,\,\,\,\,? = J = {{14 \cdot 100} \over 8} = 7 \cdot 25 = 175 \hfill \cr} \right.\,\,\,\,$$ 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 ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12999 messages Followed by: 1250 members Upvotes: 5254 GMAT Score: 770 Top Reply BTGmoderatorDC wrote: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J? A. 22 B. 56 C. 78 D. 112 E. 175 ASIDE: 7/2 = 3 1/2 = 3 + 0.5 = 3.5 Notice that 1 is the remainder when we divide 7 by 2. 23/5 = 4 3/5 = 4 + 0.6 = 4.6 Notice that 3 is the remainder when we divide 23 by 5. 31/4 = 7 3/4 = 7 + 0.75 = 7.75 Notice that 3 is the remainder when we divide 31 by 4. GIVEN: N/J = 134.08 This means 14/J = 0.08 So, J = 14/0.08 = 175 Answer: E 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 Elite Legendary Member Joined 23 Jun 2013 Posted: 10197 messages Followed by: 496 members Upvotes: 2867 GMAT Score: 800 Hi All, This question is a 'lift' of an Official Guide question: OG2018 and OG2019 pg. 170, question #154 We're told that P and J are positive INTEGERS, when P is divided by J, the REMAINDER is 14 and N/J = 134.08. We're asked for the value of J. This question has a great 'math shortcut' built into it that can help you to avoid a calculation-heavy approach, but you have to pay careful attention to the answer choices. Since N and J are INTEGERS and N/J = 134.08, we know that N = 134.08(J). Thus, whatever J is, when we multiply that number by 134.08 we end up with an INTEGER. This means that J has to 'cancel out' the decimal point. Put differently, the units digit of J multiplied by 8 has to create a number that ENDS in a 0. Looking at the 5 answer choices, there's only one answer that would do that... Final Answer: E GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com Newbie | Next Rank: 10 Posts Joined 17 Aug 2018 Posted: 9 messages Hi, Yes, this is a very popular question in GMAT. Using simple logic we can solve this question in few seconds, For example, 5 divided by 2, the remainder is 1 and but 5/2 = 2.5 One thing, we can notice above is we get 2.5 because 2 is the quotient and .5 is the value when the remainder is divided by 2. i.e., 5 = 2*2 + 1 We get decimal value(0.5) because remainder is divided by the divisor. So Similarly here, N/J = 134.08, So here the decimal value 0.08 is because when remainder 14/ J = 0.08 14/ J = 0.08 14/ 0.08 = J J = 1400/8 J = 175 So the answer is E. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15361 messages Followed by: 1865 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorDC wrote: When positive integer N is divided by positive integer J, the remainder is 14. If N/J = 134.08, what is value of J? A. 22 B. 56 C. 78 D. 112 E. 175 N/J = 134.08 = 13408/100 = 3352/25. The resulting ratio indicates that N must be multiple of 3352 and that J must be a multiple of 25. Of the five answer choices, only E is a multiple of 25. The correct answer is E. _________________ 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. 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