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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 ## How many different 3-digit numbers are greater than 299 and tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## How many different 3-digit numbers are greater than 299 and ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Magoosh How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8? A. 222 B. 245 C. 291 D. 315 E. 343 The OA is B ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12991 messages Followed by: 1249 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorLU wrote: Source: Magoosh How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8? A. 222 B. 245 C. 291 D. 315 E. 343 The OA is B Take the task of creating the 3-digit numbers and break it into stages. Stage 1: Select the first digit (hundreds digit) Since the first digit can be 3, 4, 5, 7 or 9, we can complete stage 1 in 5 ways Stage 2: Select the second digit (tens digit) Since the second digit can be 0, 2, 3, 4, 5, 7 or 9, we can complete stage 2 in 7 ways Stage 3: Select the third digit (units digit) Since the third digit can be 0, 2, 3, 4, 5, 7 or 9, we can complete stage 3 in 7 ways By the Fundamental Counting Principle (FCP), we can complete all 3 stages (and thus create a 3-digit number) in (5)(7)(7) ways (= 2445 ways) Answer: B -------------------------- Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting/video/775 You can also watch a demonstration of the FCP in action: https://www.gmatprepnow.com/module/gmat-counting/video/776 Then you can try solving the following questions: EASY - https://www.beatthegmat.com/what-should-be-the-answer-t267256.html - https://www.beatthegmat.com/counting-problem-company-recruitment-t244302.html - https://www.beatthegmat.com/picking-a-5-digit-code-with-an-odd-middle-digit-t273110.html - https://www.beatthegmat.com/permutation-combination-simple-one-t257412.html - https://www.beatthegmat.com/simple-one-t270061.html MEDIUM - https://www.beatthegmat.com/combinatorics-solution-explanation-t273194.html - https://www.beatthegmat.com/arabian-horses-good-one-t150703.html - https://www.beatthegmat.com/sub-sets-probability-t273337.html - https://www.beatthegmat.com/combinatorics-problem-t273180.html - https://www.beatthegmat.com/digits-numbers-t270127.html - https://www.beatthegmat.com/doubt-on-separator-method-t271047.html - https://www.beatthegmat.com/combinatorics-problem-t267079.html DIFFICULT - https://www.beatthegmat.com/wonderful-p-c-ques-t271001.html - https://www.beatthegmat.com/permutation-and-combination-t273915.html - https://www.beatthegmat.com/permutation-t122873.html - https://www.beatthegmat.com/no-two-ladies-sit-together-t275661.html - https://www.beatthegmat.com/combinations-t123249.html 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 GMAT Instructor Joined 25 Apr 2015 Posted: 2811 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: Magoosh How many different 3-digit numbers are greater than 299 and do not contain the digits 1, 6, or 8? A. 222 B. 245 C. 291 D. 315 E. 343 The OA is B The first (or hundreds) digit has 5 choices (digits 3 to 9, excluding 6 and 8). Each of the second (or tens) and the third (or units) digits has 7 choices (digits 0 to 9, excluding 1, 6 and 8). Therefore, the number of 3-digit numbers greater than 299 that do not contain the digits 1, 6, or 8 is 5 x 7 x 7 = 245 Answer: B _________________ 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. Read our reviews • 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 Practice Test & Review How would you score if you took the GMAT 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 • Magoosh Study with Magoosh GMAT prep Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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