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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 successively by 4 and 5 leaves tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 1 member reply ### Top Member ## A number when divided successively by 4 and 5 leaves ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Veritas Prep 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 The OA is E. Junior | Next Rank: 30 Posts Joined 03 Oct 2018 Posted: 10 messages When we divide a positive integer by another positive integer D (divider), we obtain a quotient Q (which is a non-negative integer) and a remainder R(which is an integer such that 0â‰¤R Thus we can write n as n=DQ+r Now according to our problem , x=4Q+1 Now the quotient obtained is divided by 5 yielding a different quotient Q=5q+4 Substituting the second equation in the first x=20q +16 +1 =20q +17 Hence, upon dividing the number x by 20 we would get a remainder of 17. ### 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 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 $$N = {\rm{original}}\,\,{\rm{number}}$$ $$?\,\,\,:\,\,{\rm{remainder}}\,\,{\rm{of}}\,\,N\,\,{\rm{divided}}\,\,{\rm{by}}\,\,20$$ Explaining the question stem: when the "original number" (N) is divided by 4, the remainder is 1. When the quotient of this division (say Q) is divided by 5, the remainder is 4. Hence: $$\left. \matrix{ N = 4Q + 1\,\,\,\left( {Q\,\,{\mathop{\rm int}} } \right) \hfill \cr Q = 5J + 4\,\,\,\left( {J\,\,{\mathop{\rm int}} } \right) \hfill \cr} \right\}\,\,\,\,\,\, \Rightarrow \,\,\,\,\,?\,\,\,:\,\,N = 4\left( {5J + 4} \right) + 1 = 20J + 17$$ $$? = 17$$ 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 Apr 2015 Posted: 2456 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: Veritas Prep 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 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, a remainder of 4 remains. 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 • 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 GMAT Exam Know how you'd score today for$0

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