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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 ## What is the remainder when the positive integer n is divided tagged by: AbeNeedsAnswers ##### This topic has 3 expert replies and 0 member replies ### Top Member ## What is the remainder when the positive integer n is divided ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult What is the remainder when the positive integer n is divided by 5 ? (1) When n is divided by 3, the quotient is 4 and the remainder is 1. (2) When n is divided by 4, the remainder is 1. A Source: Official Guide 2020 ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2424 messages Followed by: 349 members Upvotes: 1090 GMAT Score: 780 Statement 1 tells us that n is equal to 13, so of course we can answer any question about n, and Statement 1 is sufficient. The remainder you get when you divide by 4 has no relationship to the remainder you get when you divide by 5, so Statement 2 is useless. For example, n could be 5, and then the remainder is 0 when we divide by 5, or n could be 9, and the remainder is 4 when we divide by 5. So the answer is A. _________________ 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 08 Dec 2008 Posted: 12919 messages Followed by: 1248 members Upvotes: 5254 GMAT Score: 770 AbeNeedsAnswers wrote: What is the remainder when the positive integer n is divided by 5 ? (1) When n is divided by 3, the quotient is 4 and the remainder is 1. (2) When n is divided by 4, the remainder is 1. Target question: What is the remainder when the positive integer n is divided by 5 ? Statement 1: When n is divided by 3, the quotient is 4 and the remainder is 1. There's a nice rule that says, "If N divided by D equals Q with remainder R, then N = DQ + R" For example, since 17 divided by 5 equals 3 with remainder 2, then we can write 17 = (5)(3) + 2 Likewise, since 53 divided by 10 equals 5 with remainder 3, then we can write 53 = (10)(5) + 3 So, from statement 1, we can write: n = (3)(4) + 1 = 13 If n = 13, then we get a remainder of 3 when we divide 13 by 5 Since we can answer the target question with certainty, statement 1 is SUFFICIENT Statement 2: When n is divided by 4, the remainder is 1. 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. Some possible values of n are: 1, 5, 9, 13, 17, . . . etc. Case a: If n = 1, then we get a remainder of 1 when we divide 1 by 5. Case b: If n = 5, then we get a remainder of 0 when we divide 5 by 5. Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT Answer: A 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: 10196 messages Followed by: 494 members Upvotes: 2867 GMAT Score: 800 Hi All, We're told that N is a positive integers. We're asked for the remainder when N is divided by 5. This question can be solved with a mix of Arithmetic and TESTing VALUES. (1) When N is divided by 3, the quotient is 4 and the remainder is 1. Fact 1 gives us remarkably specific information.... N/3 = 4r1 This outcome can only occur when N = 13, since 13/3 = 4r1. No other value of N fits this information, so we have 13/5 = 2r3 and the answer to the question must be 3. Fact 1 is SUFFICIENT (2) When N is divided by 4, the remainder is 1. Fact 2 isn't quite as 'restrictive' as Fact 1 is. There are lots of different values of N that will fit here: IF... N = 1, then 1/4 = 0r1 and the answer to the question is 1/5 = 0r1.... 1 N = 5, then 5/4 = 1r1 and the answer to the question is 5/5 = 1r0.... 0 Fact 2 is INSUFFICIENT Final Answer: A GMAT assassins aren't born, they're made, Rich _________________ Contact Rich at Rich.C@empowergmat.com • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5 Day FREE Trial Study Smarter, Not Harder Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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