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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 ## Digits, Numbers tagged by: Brent@GMATPrepNow ##### This topic has 4 expert replies and 2 member replies ## Digits, Numbers I presume this will be easy to most of the "solving" people here How many 4 digit positive integers do not contain the digit 3 or 6? 1. 2401 2. 3584 3. 4096 4. 5040 5. 7200 _________________ You can, for example never foretell what any one man will do, but you can say with precision what an average number will be up to! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12655 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 vinay1983 wrote: I presume this will be easy to most of the "solving" people here How many 4-digit positive integers do not contain the digit 3 or 6? A. 2401 B. 3584 C. 4096 D. 5040 E. 7200 Take the task of building 4-digit positive integers and break it into stages. Stage 1: Choose a thousands digit This can be 1,2,4,5,7,8,or 9, so we can complete stage 1 in 7 ways Stage 2: Choose a hundreds digit This can be 0,1,2,4,5,7,8,or 9, so we can complete stage 2 in 8 ways Stage 3: Choose a tens digit This can be 0,1,2,4,5,7,8,or 9, so we can complete stage 3 in 8 ways Stage 4: Choose a units digit This can be 0,1,2,4,5,7,8,or 9, so we can complete stage 4 in 8 ways By the Fundamental Counting Principle (FCP) we can complete all 4 stages (and thus build a 4-digit positive integer) in (7)(8)(8)(8) ways IMPORTANT: we don't really need to calculate the product (7)(8)(8)(8) We can just recognize that the units digit will be 4. That is (7)(8)(8)(8) = ---4 Since answer choice B, is the only one with units digit 4, it must be correct. Cheers, Brent Aside: For more information about the FCP, watch our free video: http://www.gmatprepnow.com/module/gmat-counting?id=775 _________________ Brent Hanneson – Creator of GMATPrepNow.com Use our video course along with Sign up for our free Question of the Day emails And check out all of our 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! Master | Next Rank: 500 Posts Joined 02 Mar 2013 Posted: 391 messages Followed by: 4 members Upvotes: 50 vinay1983 wrote: I presume this will be easy to most of the "solving" people here How many 4 digit positive integers do not contain the digit 3 or 6? 1. 2401 2. 3584 3. 4096 4. 5040 5. 7200 We have 4 places to fill to make 4 digit number ---- Now for the thousands digit we have only 7 options( we can't use 0,3 and 6). For hundred tens and units digit we can use 8 digit( because we can't use 3 or 6 but we can use 0). So the total number of 4 digit numbers without 3 or 6 is 7*8*8*8=3584 Answer is B Junior | Next Rank: 30 Posts Joined 16 Jan 2017 Posted: 24 messages What would the answer be if the question said 3 AND 6 instead of 3 or 6? ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1762 messages Followed by: 28 members Upvotes: 470 Zoser wrote: What would the answer be if the question said 3 AND 6 instead of 3 or 6? Do you mean to ask, "How many 4 digit positive integers do not contain the digit 3 AND 6 together (not necessarily in order)?" If yes, then let's follow this. # of 4 digit positive integers do not contain the digit 3 AND 6 together = Total # of 4 digit positive integers - Total # of 4 digit positive integers that contain the digit 3 AND 6 together Total # of 4 digit positive integers = 9*10*10*10 = 9(10^3) = 9000 "Total # of 4 digit positive integers that contain the digit 3 AND 6 together" can be computed the following way. A. For '3' appears before '6': a. Say '3' is in the thousands place and '6' in the hundreds place. 3 6 _ _ : 1*1*10*10 = 100 b. Say '3' is in the thousands place and '6' in the tens place. 3 _ 6 _ : 1*10*1*10 = 100 c. Say '3' is in the thousands place and '6' in the unit place. 3 _ _ 6 : 1*10*10*1 = 100 ----------------------- d. Say '3' is in the hundreds place and '6' in the tens place. _3 6 _ : 9*1*1*10 = 90 e. Say '3' is in the hundreds place and '6' in the unit place. _3 _ 6 : 9*1*10*1 = 90 ------------------------ f. Say '3' is in the tens place and '6' in the unit place. _ _3 6 : 9*10*1*1 = 90 ------------------------- Total # in which '3' appears before '6' = 100 + 100+ 100 + 90 + 90 + 90 = 570; Similarly, total # in which '6' appears before '3' = 570; Total # of 4 digit positive integers that contain the digit 3 AND 6 together = 570 + 570 = 1140 Thus, # of 4 digit positive integers do not contain the digit 3 AND 6 together = 9000 - 1140 = 7860. Hope this is clear. Relevant book: Manhattan Review GMAT Number Properties Guide -Jay _________________ Manhattan Review GMAT Prep Locations: New York | Singapore | London | Dubai | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2009 messages Followed by: 237 members Upvotes: 1443 Zoser wrote: What would the answer be if the question said 3 AND 6 instead of 3 or 6? Jay gave a good explanation, but... you're never actually going to see a question like this on the GMAT. Questions that have vague or confusing wording are open to multiple interpretations, and as a result, they will yield bad data. Some high-scorers will get them wrong while low-scorers get them right, so it won't be a good indicator of ability level. Questions like this would be thrown out after experimentation (remember that a certain percentage of all questions that you'll see will be experimental). Since there's ambiguity about what "and" would mean in this context, it's not a question you'd see on the real test. Broadly speaking, the combinatorics question that you're likely to see on the real GMAT are more straightforward and less tricky than a lot of the ones floating out there on the internet (including on this forum). _________________ 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 Apr 2015 Posted: 2012 messages Followed by: 14 members Upvotes: 43 vinay1983 wrote: I presume this will be easy to most of the "solving" people here How many 4 digit positive integers do not contain the digit 3 or 6? 1. 2401 2. 3584 3. 4096 4. 5040 5. 7200 We need to determine how many 4-digit positive integers do not contain a 3 or a 6. For the first digit (the thousands digit), we have the options of 1, 2, 4, 5, 7, 8, and 9, so there are 7 options. For the next digit (the hundreds digit), we have 8 options, since we can include 0. For the next digit (the tens digit), we have another 8 options. For the last digit (the ones digit), we again have 8 options.Thus, the 4- digit number can be selected in 7 x 8 x 8 x 8 ways. I also agree with Brent: since our answer choices have all different units digits, we simply need to calculate the units digit of the product above. Since 7 x 8 has a units digit of 6, 8 x 8 has a units digit of 4, and 6 x 4 has a units digit of 4, the answer must be 3584. Answer: B _________________ Scott Woodbury-Stewart Founder and CEO • Free Veritas GMAT Class Experience Lesson 1 Live Free 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 • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

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