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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 positive 5-digit integer is called "friendly" if tagged by: fskilnik@GMATH ##### This topic has 2 expert replies and 0 member replies ### GMAT/MBA Expert ## A positive 5-digit integer is called "friendly" if ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult GMATH practice exercise (Quant Class 18) A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is: (A) 5 (B) 4 (C) 3 (D) 2 (E) 1 Answer: ____(B)__ _________________ 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 fskilnik@GMATH wrote: [size=17]GMATH practice exercise (Quant Class 18) A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is: (A) 5 (B) 4 (C) 3 (D) 2 (E) 1 Total number of friendly numbers = total number of ways to arrange the 5 digits = 5! = 120. There are 5 options for the first digit: 1, 2, 3, 4, or 5. 120/5 = 24. Thus, the 120 friendly numbers are composed of five 24-number ranges, as follows: The integers beginning with 1 constitute friendly numbers 1-24. The integers beginning with 2 constitute friendly numbers 25-48. The integers beginning with 3 constitute friendly numbers 49-72. The integers beginning with 4 constitute friendly numbers 73-96. The integers beginning with 5 constitute friendly numbers 97-120. The 32nd friendly number is contained within the blue range above. Friendly numbers in the blue range, from least to greatest: 21345 --> 25th friendly number 21354 --> 26th friendly number 21435 --> 27th friendly number 21453 --> 28th friendly number 21534 --> 29th friendly number 21543 --> 30th friendly number 23145 --> 31st friendly number 23154 --> 32nd friendly number The units digit for the 32nd friendly number = 4. The correct answer is B. _________________ 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 09 Oct 2010 Posted: 1449 messages Followed by: 32 members Upvotes: 59 fskilnik@GMATH wrote: GMATH practice exercise (Quant Class 18) A positive 5-digit integer is called "friendly" if each of its digits is 1,2,3,4 or 5 and all of its digits are different. Putting all friendly numbers in increasing order, the units digit of the friendly number that occupies the 32nd place is: (A) 5 (B) 4 (C) 3 (D) 2 (E) 1 FOCUS: the units digit of the 32nd friendly number 1. The first P4 = 4! = 24 friendly numbers "start with 1" (i.e., 1 _ _ _ _ ) , the (few) next ones "start with 2". 2. "Starting with 2" (i.e., 2 _ _ _ _ ), there are P3 = 3! = 6 friendly numbers "beginning with 21" (i.e., 2 1 _ _ _ ), hence: All friendly numbers, from the 25th until the 30th (both included) are of the form 21 _ _ _ . 3. The 31st friendly number is the smallest friendly number that starts with "23", that is, 23145. 4. Finally, the 32nd friendly number is the next one (23154), hence ? = 4. The correct answer is (B). We follow 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 • 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 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 • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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