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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 ## A number when divided by 4 and 5 leaves remainders 1 and 4 tagged by: BTGmoderatorLU ##### This topic has 6 expert replies and 0 member replies ### Top Member ## A number when divided by 4 and 5 leaves remainders 1 and 4 ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Veritas Prep A number when divided by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder the remainder when this number is divided by 20? A. 0 B. 3 C. 4 D. 9 E. 17 The OA is E. ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1975 messages Followed by: 30 members Upvotes: 470 BTGmoderatorLU wrote: Source: Veritas Prep A number when divided by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder the remainder when this number is divided by 20? A. 0 B. 3 C. 4 D. 9 E. 17 The OA is E. Say the number is N, when N is divided by 4, the quotient is p and the remainder is 1, and when N is divided by 5, the quotient is q and the remainder is 4. Thus, N = 4p + 1 and N = 5q + 4 => 4p + 1 = 5q + 4 4p = 5q + 3 p = (5q + 3)/4 = 4q/4 + (q + 3)/4 = q + (q + 3)/4 Since p and q are nonnegative integers, (q + 3) must be divisible by 4. One of the possible values of q = 1. @q = 1, we have N = 5q + 4 = 5*1 + 4 = 9 Thus, the remainder when this number (= 9) is divided by 20 = 9. The correct answer: D Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: Manhattan Review Mehdipatnam | Hyderabad GMAT Prep | Bangalore GMAT Courses | Dilsukhnagar GRE Prep | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorLU wrote: Source: Veritas Prep A number when divided by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder when this number is divided by 20? A. 0 B. 3 C. 4 D. 9 E. 17 \eqalign{ & N = 4Q + 1 \cr & N = 5K + 4 \cr} $$? = R\,\,\,\left( {0 \le R \le 19} \right)\,\,\,,\,\,{\rm{where}}\,\,\,N = 20J + R\,\,\,\left( {J\,\,{\mathop{\rm int}} } \right)\,$$ $$Q,K,J,R\,\,\,{\rm{ints}}$$ All alternative choices are numerical, hence we are allowed to explore a particular viable case! $${\rm{Take}}\,\,N = 9\,\,\,\,\left( {Q = 2,\,\,K = 1} \right)\,\,\,\, \to \,\,\,\,\,J = 0\,\,\,{\rm{and}}\,\,\,\,? = R = 9\,\,$$ 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: 12982 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU wrote: Source: Veritas Prep A number when divided by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder the remainder when this number is divided by 20? A. 0 B. 3 C. 4 D. 9 E. 17 The OA is E. When it comes to remainders, we have a nice rule that says: If N divided by D, leaves remainder R, then the possible values of N are R, R+D, R+2D, R+3D,. . . etc. For example, if k divided by 5 leaves a remainder of 1, then the possible values of k are: 1, 1+5, 1+(2)(5), 1+(3)(5), 1+(4)(5), . . . etc. A number when divided successively by 4 leaves a remainder 1 Possible values of the number are: 1, 5, 9, 13, 17, 21,... A number when divided successively by 5 leaves a remainder 4 Possible values of the number are: 4, 9...STOP! Both lists contain 9, so this could be the number. What will be the remainder when this number is divided by 20? 9 divided by 20 = 0 with remainder 9 Answer: D 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 BTGmoderatorLU wrote: Source: Veritas Prep A number when divided by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder when this number is divided by 20? A. 0 B. 3 C. 4 D. 9 E. 17 Now letÂ´s avoid street fighting and embrace BJJ, a.k.a real MATH ! \eqalign{ & N = 4Q + 1 \cr & N = 5K + 4 \cr} $$? = R\,\,\,\left( {0 \le R \le 19} \right)\,\,\,,\,\,{\rm{where}}\,\,\,N = 20J + R\,\,\,\left( {J\,\,{\mathop{\rm int}} } \right)\,$$ $$Q,K,J,R\,\,\,{\rm{ints}}$$ $$\left\{ \matrix{ N = 4Q + 1\,\,\,\, \Rightarrow \,\,\,\,5N = 20Q + 5 \hfill \cr N = 5K + 4\,\,\, \Rightarrow \,\,\,\,4N = 20K + 16 \hfill \cr} \right.\,\,\,\,\mathop \Rightarrow \limits^{\left( - \right)} \,\,\,\,\,\,\,N = 20\left( {Q - K} \right) - 11\,\,\,\,\,\, \Rightarrow \,\,\,\,N - 9 = 20\left( {Q - K} \right) - 20 = 20\left( {Q - K - 1} \right)\,$$ $$N - 9 = 20J\,\,,\,\,\,J = Q - K - 1\,\,{\mathop{\rm int}} \,\,\,\,\, \Rightarrow \,\,\,\,\,N = 20J + 9\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = 9\,\,$$ 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 25 May 2010 Posted: 15348 messages Followed by: 1864 members Upvotes: 13060 GMAT Score: 790 Please fix the prompt, which has been transcribed incorrectly. It should include the word in red: Quote: A number when divided successively by 4 and 5 leaves remainders 1 and 4, respectively. What will be the remainder when this number is divided by 20? A. 0 B. 3 C. 4 D. 9 E. 17 _________________ 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 25 Apr 2015 Posted: 2791 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: Veritas Prep A number when divided by 4 and 5 leaves remainders 1 and 4 respectively. What will be the remainder the remainder when this number is divided by 20? A. 0 B. 3 C. 4 D. 9 E. 17 The OA is E. We need to find a number that when divided by 4 leaves a remainder of 1 and when the quotient from this division is divided by 5 leaves a remainder of 4. Letâ€™s represent this number by n. Since our number produces a remainder of 1 when divided by 4, it must be true that n = 4p + 1 for some integer p. Since the quotient from the previous division, which is p, produces a remainder of 4 when divided by 5, we have p = 5q + 4. Letâ€™s substitute this expression of p into the previous equation: n = 4p + 1 n = 4(5q + 4) + 1 n = 20q + 16 + 1 n = 20q + 17 Finally, since 20q is divisible by 20, the remainder from the division of n by 20 is 17. Answer: E _________________ Scott Woodbury-Stewart Founder and CEO scott@targettestprep.com See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to200

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