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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 ## Integer Properties ##### This topic has 1 expert reply and 2 member replies ## Integer Properties Can someone please advise on how to solve this algebraically? If m>n, then is mn divisible by 3? (1) The remainder when m + n is divided by 6 is 5 (2) The remainder when m - n is divided by 6 is 3 OA is C Or if number picking is the only option, how to pick smart numbers? Thanks! ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15254 messages Followed by: 1861 members Upvotes: 13060 GMAT Score: 790 topspin360 wrote: Can someone please advise on how to solve this algebraically? If m>n, then is mn divisible by 3? (1) The remainder when m + n is divided by 6 is 5 (2) The remainder when m - n is divided by 6 is 3 OA is C Statement 1: In other words, m+n is equal to 5 more than a multiple of 6: m+n = 5, 11, 17, 23, 29... If m+n=5, the following cases are possible: Case 1:m=3 and n=2 In this case, mn=6, which is divisible by 3. Case 2: m=4 and n=1 In this case, mn=4, which is not divisible by 3. INSUFFICIENT. Statement 2: In other words, m-n is equal to 3 more than a multiple of 6: m-n = 3, 9, 15, 21, 27... If m-n=3, the following cases are possible: Case 1: m=6 and n=3 In this case, mn=18, which is divisible by 3. Case 2: m=5 and n=2 In this case, mn=10, which is not divisible by 3. INSUFFICIENT. Statements combined: Case 1: m+n=5 and m-n=3 Adding the equations, we get: 2m=8 m=4, implying that n=1. In this case, mn=4, which is not divisible by 3. Case 2: m+n=23 and m-n=9 Adding the equations, we get: 2m=32 m=16, implying that n=7 In this case, mn=16*7, which is not divisible by 3. In each case, mn is not divisible by 3. Maybe one more case to be safe. Case 3: m+n=29 and m-n=21 Adding the equations, we get: 2m=50 m=25, implying that n=4. In this case, mn=25*4, which is not divisible by 3. The 3 random cases above illustrate that -- when the statements are combined -- mn in every case will not be divisible by 3. SUFFICIENT. The correct answer is C. _________________ 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. Newbie | Next Rank: 10 Posts Joined 10 Dec 2013 Posted: 6 messages Upvotes: 1 For mn to be divisible by 3, we should have either one of two as a multiple of 3 Statement#1 m+n = 6x+5................1 Insufficient by itself Statement#2 m-n = 6y-3.............2 Insufficient by itself Combining statement 1 & 2, Using equation 1&2 and solving for m we get m= 3x+3y+1 where, 3x is multiple of 3, 3y is multiple of 3 but with addition of 1 at the end whole sum is NOT multiple of 3, hence m is not multiple of 3 Again using equation 1 & 2 and solving for n we get, n=3x-3y+4 Using same logic as above, we can deduce that n is not a multiple of 3 And since both M and N are not multiple of 3, MN can not be multiple of 3 Combining 1 & 2 Sufficient Master | Next Rank: 500 Posts Joined 02 Jun 2012 Posted: 103 messages Upvotes: 1 thanks all! • 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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