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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 options are there for license plate number if each tagged by: BTGmoderatorLU ##### This topic has 2 expert replies and 0 member replies ### Top Member ## How many options are there for license plate number if each ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Source: Economist GMAT How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet) A. $$360\cdot 260^2$$ B. $$36\cdot 260^2$$ C. $$36\cdot 270^2$$ D. $$10^2 \cdot 26^3$$ E. $$10^3 \cdot 26^2$$ The OA is B ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1952 messages Followed by: 30 members Upvotes: 470 BTGmoderatorLU wrote: Source: Economist GMAT How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet) A. $$360\cdot 260^2$$ B. $$36\cdot 260^2$$ C. $$36\cdot 270^2$$ D. $$10^2 \cdot 26^3$$ E. $$10^3 \cdot 26^2$$ The OA is B Number of ways each license plate can include 2 digits and 3 letters (in that order) = 10^2 * 26^3; (there are 10 digits, incl 0; note that digits and alphabets can repeat) Number of ways each license plate can include 3 digits and 2 letters (in that order) = 10^3 * 26^2 Total number of ways = 10^2 * 26^3 + 10^3 * 26^2 = 10^2 * 26^2(26 + 10) = 36 * 10^2 * 26^2 = 36 * 260^2 The correct answer: B Hope this helps! -Jay _________________ Manhattan Review GMAT Prep Locations: GRE Manhattan | ACT Tutoring Houston | SAT Prep Courses Seattle | Charlotte IELTS Tutoring | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 2624 messages Followed by: 18 members Upvotes: 43 BTGmoderatorLU wrote: Source: Economist GMAT How many options are there for license plate numbers if each license plate can include 2 digits and 3 letters (in that order), or 3 digits and 2 letters (in that order)? (Note: there are 26 letters in the alphabet) A. $$360\cdot 260^2$$ B. $$36\cdot 260^2$$ C. $$36\cdot 270^2$$ D. $$10^2 \cdot 26^3$$ E. $$10^3 \cdot 26^2$$ The OA is B The number of ways to create the license plate with 2 digits followed by 3 letters is 10^2 x 26^3. The number of ways to create the license plate with 3 digits followed by 2 letters is 10^3 x 26^2. So we have: 10^2 x 26^3 + 10^3 x 26^2 This expression is not one of the answer choices, so we simplify it by factoring the common (10^2) and (26^2) from each term. Thus, we have: 10^2 x 26^2 x (26 + 10) = (26^2)(10^2)(36) = (260^2)(36) 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 • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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