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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 ## GmaT Practice Exam 6 - Primefactors ##### This topic has 3 expert replies and 4 member replies ## GmaT Practice Exam 6 - Primefactors Hello BTG Got the following question yesterday in the Practice exam 6. It seem to me, that it is asking for all primefactors less than 100. But is there a way to quickly calculate this, as I image listing them up and counting is not the best approach. Thanks in advance Attachments This post contains an attachment. You must be logged in to download/view this file. Please login or register as a user. ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15023 messages Followed by: 1859 members Upvotes: 13060 GMAT Score: 790 Quote: How many positive integers less than 100 are neither multiples of 2 nor multiples of 3? a)30 b)31 c)32 d)33 e)34 WRITE IT OUT and LOOK FOR A PATTERN. 1, 2, 3 4, 5, 6 7, 8, 9 10, 11, 12 As illustrated by the values in red, 1 of every 3 positive integers is neither even nor a multiple of 3. Thus, of the 99 positive integers less than 100, exactly 1/3 will be neither even nor a multiple of 3: (1/3)(99) = 33. The correct answer is D. _________________ 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 08 Dec 2008 Posted: 12540 messages Followed by: 1245 members Upvotes: 5254 GMAT Score: 770 Quote: How many positive integers less than 100 are neither multiples of 2 nor multiples of 3? a)30 b)31 c)32 d)33 e)34 Another approach: Multiples of 2: 2, 4, 6, ..., 96, 98 98/2 = 49, so there are 49 multiples of 2 Multiples of 3: 3, 6, 9, ..., 99 99/3 = 33, so there are 33 multiples of 3 At this point we have counted some multiples TWICE. For example, we counted 6 TWICE, we counted 12 TWICE and so on. In fact, we counted all multiples of 6 TWICE Multiples of 6: 6, 12, 18..., 96 96/6 = 16, so there are 16 multiples of 6 So.....TOTAL multiples of 2 OR 3 = 49 + 33 - 16 = 66 There are 99 positive integers that are less than 100 So, the TOTAL number of those integers that are NEITHER multiples of 2 or 3 = 99 - 66 = 33 Answer: D _________________ Brent Hanneson â€“ 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 GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months! Master | Next Rank: 500 Posts Joined 13 Mar 2015 Posted: 410 messages Followed by: 7 members Upvotes: 120 GMAT Score: 770 lucas211 wrote: Hello BTG Got the following question yesterday in the Practice exam 6. It seem to me, that it is asking for all primefactors less than 100. But is there a way to quickly calculate this, as I image listing them up and counting is not the best approach. How many positive integers less than 100 are neither multiples of 2 nor multiples of 3? a)30 b)31 c)32 d)33 e)34 Thanks in advance I am not sure what you meant by saying "it is asking for all prime factors less than 100" Are you saying that the question is asking about prime factors of 100?? As for the question, the best way would be to write the numbers down and find a pattern. Numbers less than 100 that are neither multiples of 2 or 3. Multiples of 2 = 2, 4, ... 98 - 49 numbers Multiples of 3 = 3, 6, 9, ... 99 = 33 Multiples of 6 - 6, 12, ... 96 - 16numbers Hence total numbers that are either multiples of 2 or 3 = 49 + 33 - 16 = 66 Hence numbers that are not multiples of 2 or 3 = 99 - 66 = 33 Correct Option: D Senior | Next Rank: 100 Posts Joined 04 Aug 2014 Posted: 97 messages Followed by: 1 members Upvotes: 1 OptimusPrep wrote: lucas211 wrote: Hello BTG Got the following question yesterday in the Practice exam 6. It seem to me, that it is asking for all primefactors less than 100. But is there a way to quickly calculate this, as I image listing them up and counting is not the best approach. How many positive integers less than 100 are neither multiples of 2 nor multiples of 3? a)30 b)31 c)32 d)33 e)34 Thanks in advance I am not sure what you meant by saying "it is asking for all prime factors less than 100" Are you saying that the question is asking about prime factors of 100?? As for the question, the best way would be to write the numbers down and find a pattern. Numbers less than 100 that are neither multiples of 2 or 3. Multiples of 2 = 2, 4, ... 98 - 49 numbers Multiples of 3 = 3, 6, 9, ... 99 = 33 Multiples of 6 - 6, 12, ... 96 - 16numbers Hence total numbers that are either multiples of 2 or 3 = 49 + 33 - 16 = 66 Hence numbers that are not multiples of 2 or 3 = 99 - 66 = 33 Correct Option: D Hello Optimusprep Thanks for your reply. I had misunderstood the question, as I thought it was asking for the prime factors less than the number 100. Thanks again Senior | Next Rank: 100 Posts Joined 18 Dec 2018 Posted: 31 messages To find the positive integers less than 100 that are not divisible by 2 or 3, we need to find the number of integers that are divisible by 2, 3 and 6 individually. No of integers divisible by 2 =N2 = 50 No of integers divisible by 3 = N3 = 33 No of integers divisible by 6 = N6 = 16 So, no of integers not divisible by 2 or 3 = 100 - (N2 + N3 - N6) = 100 - (67) = 33. ### Top Member Senior | Next Rank: 100 Posts Joined 12 Jan 2019 Posted: 38 messages To find the positive integers less than 100 that are not divisible by 2 or 3, we need to find the number of integers that are divisible by 2, 3 and 6 individually. No of integers divisible by 2 =N2 = 50 No of integers divisible by 3 = N3 = 33 No of integers divisible by 6 = N6 = 16 So, no of integers not divisible by 2 or 3 = 100 - (N2 + N3 - N6) = 100 - (67) = 33. ### GMAT/MBA Expert GMAT Instructor Joined 25 Apr 2015 Posted: 1808 messages Followed by: 14 members Upvotes: 43 Quote: How many positive integers less than 100 are neither multiples of 2 nor multiples of 3? a)30 b)31 c)32 d)33 e)34 We can use the following equation: Number of integers from 1 to 99, inclusive = (number of integers that are multiples of 2 or 3) + (number of integers that are neither multiples of 2 nor 3) Furthermore: Number of integers that are multiples of 2 or 3 = number of multiples of 2 + number of multiples of 3 - number of multiples of both 2 and 3 Notice that the number of multiples of both 2 and 3 is also the number of multiples of 6. Letâ€™s determine the number of multiples of 2 from 1 to 99 inclusive using the following equation: (largest multiple of 2 in the set - smallest multiple of 2 in the set)/2 + 1 (98 - 2)/2 + 1 = 49 Now we can determine the number of multiples of 3 from 1 to 99 inclusive using the same concept: (99 - 3)/3 + 1 = 33 Finally, letâ€™s determine the number of multiples of 6, since some multiples of 2 are also multiples of 3; we must subtract those out so they are not double-counted. (96 - 6)/6 + 1 = 16 Thus, there are 49 + 33 - 16 = 66 multiples of 2 or 3 from 1 to 99, inclusive. Therefore, there are 99 - 66 = 33 numbers from 1 to 99 inclusive that are not multiples of 2 or 3. 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