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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 ## If the two digit integers M and N are positive and have the tagged by: AAPL ##### This topic has 3 expert replies and 0 member replies ### Top Member ## If the two digit integers M and N are positive and have the ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Official Guide If the two digit integers M and N are positive and have the same digits, but in reverse order, which of the following cannot be the sum of M and N? A. 181 B. 165 C. 121 D. 99 E. 44 OA A ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2531 messages Followed by: 353 members Upvotes: 1090 GMAT Score: 780 If we have a two digit number AB, where A is the tens digit and B the units digit, then the number is equal to 10A + B. So here, if A and B represent digits, our numbers are AB and BA. These are equal to 10A + B and 10B + A, and their sum is equal to 11A + 11B. This sum is clearly divisible by 11. So if an answer choice is not divisible by 11, it cannot be our sum, and A, 181, is correct. _________________ 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 25 Apr 2015 Posted: 2950 messages Followed by: 19 members Upvotes: 43 AAPL wrote: Official Guide If the two digit integers M and N are positive and have the same digits, but in reverse order, which of the following cannot be the sum of M and N? A. 181 B. 165 C. 121 D. 99 E. 44 OA A Since 98 + 89 = 187 and 97 + 79 = 176, we see that there is no way for the sum to be 181. Alternate solution: We can let M = 10t + u where t is the tens digit of M and u is the units digit of M. Thus N = 10u + t and M + N = (10t + u) + (10u + t) = 11t + 11u = 11(t + u). We see that the sum of M and N must be a multiple of 11 and all the given choices are multiples of 11 except choice A. So 181 can’t be the sum of M and N. Answer: A ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 13046 messages Followed by: 1253 members Upvotes: 5254 GMAT Score: 770 AAPL wrote: Official Guide If the two digit integers M and N are positive and have the same digits, but in reverse order, which of the following cannot be the sum of M and N? A. 181 B. 165 C. 121 D. 99 E. 44 OA A This question relies on our ability to determine the VALUE of any 2-digit number. For example, what is the VALUE of 83? For many of us, it has been a very long time since we examined this (we learned this when we were 5 or 6). Most of us just say that 83 has a value of 83, but 83 is really just a "recipe" for determining value. 83 is equal to 8 tens plus 3 ones. Similarly, 76 is equal to 7 tens plus 6 ones. In general, if tu represents a 2-digit number (where the t stands for the digit in the tens position, and the u stands for the digit in the units position), then the value of tu is 10t + u So, if M = tu, then N = ut The VALUE of M is 10t + u, and the VALUE of N us 10u + t So, the VALUE of M+N = (10t + u) + (10u + t) = 11t + 11u = 11(t + u) So, we can see that M+N must be a MULTIPLE OF 11 Answer choices B, C, D and E are all multiples of 11. Since 181 is not a multiple of 11, M+N cannot equal 181 Answer: A Cheers, Brent _________________ Brent Hanneson – 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 GMAT’s FREE 60-Day Study Guide and reach your target score in 2 months! • 1 Hour Free BEAT THE GMAT EXCLUSIVE 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 Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • 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 GMAT Exam Know how you'd score today for$0

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