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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 3-digit positive integer consists of non zero digits. If tagged by: BTGmoderatorLU ##### This topic has 3 expert replies and 0 member replies ### Top Member ## A 3-digit positive integer consists of non zero digits. If ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: GMAT Prep A 3-digit positive integer consists of non zero digits. If each exactly two of the digits are the same, how many such integers are possible? A. 72 B. 144 C. 216 D. 283 E. 300 The OA is C ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2094 messages Followed by: 238 members Upvotes: 1443 There are 3 configurations that would yield a 3-digit integer with 2 of the same digit, one different digit: [same][same][different] [same][different][same] [different][same][same] So, let's calculate the number of combinations for one of these: [same][same][different] There would be 9 non-zero digits as options for the hundreds digit, and then only 1 option for the tens digit, since it has to be the same as the hundreds digit. You might think that there would be 9 options for the units digit, but remember - it has to be different! So there would be only 8 options that are different from whatever we picked for the hundreds & tens digits. 9*1*8 = 72 options It would stand to reason that all 3 configurations mentioned above would have the same number of possibilities: 72. So we add: 72 + 72 + 72 = 216 The answer is C. _________________ Ceilidh Erickson Manhattan Prep GMAT & GRE instructor EdM in Mind, Brain, and Education Harvard Graduate School of Education Manhattan Prep instructors all have 99th+ percentile scores and expert teaching experience. Sign up for a FREE TRIAL, and learn why we have the highest ratings in the GMAT industry! Free Manhattan Prep online events - The first class of every online Manhattan Prep course is free. Classes start every week. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15362 messages Followed by: 1866 members Upvotes: 13060 GMAT Score: 790 BTGmoderatorLU wrote: Source: GMAT Prep A 3-digit positive integer consists of non zero digits. If each exactly two of the digits are the same, how many such integers are possible? A. 72 B. 144 C. 216 D. 283 E. 300 Alternate approach: Integers with exactly 2 digits the same = Total integers - Integers with all 3 digits the same - Integers with all 3 digits different. Total integers: Number of options for the hundreds digit = 9. (Any digit but 0.) Number of options for the tens digit = 9. (Any digit but 0.) Number of options for the units digit = 9. (Any digit but 0.) To combined these options, we multiply: 9*9*9. Integers with all 3 digits the same: 111, 222, 333, 444, 555, 666, 777, 888, 999. Number of options = 9. Integers with all 3 digits different: Number of options for the hundreds digit = 9. (Any digit but 0.) Number of options for the tens digit = 8. (Any digit 1-9 other than the digit already used.) Number of options for the units digit = 7. (Any digit 1-9 other than the two digits already used.) To combine these options, we multiply: 9*8*7. Thus: Integers with exactly 2 digits the same = (9*9*9) - 9 - (9*8*7) = 9(81-1-56) = 9(24) = 216. 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. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2852 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: GMAT Prep A 3-digit positive integer consists of non zero digits. If each exactly two of the digits are the same, how many such integers are possible? A. 72 B. 144 C. 216 D. 283 E. 300 The OA is C The 3 digits are nonzero, and they consist of two distinct digits. The number of ways to choose 2 digits from 9 nonzero digits is 9C2 = (9 x 8)/2 = 36. Now for each pair of digits chosen, for example, 1 and 2, we could have: 112, 121, 211, 221, 212, and 122. Therefore, there are 36 x 6 = 216 such integers. Answer: C _________________ 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. 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