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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 If r, s, and t are all positive integers tagged by: ceilidh.erickson This topic has 2 expert replies and 5 member replies If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst? (1) s is even (2) p = 4t Legendary Member Joined 07 Jul 2008 Posted: 829 messages Followed by: 3 members Upvotes: 84 Target GMAT Score: 700+ ddm wrote: If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst? (1) s is even (2) p = 4t i would got for B for this P= rst statement 1. s is even . thus from this we know rst will so will be even but then assume rst =4 2^4 /10 = 6 as remainder 2^6 /10 = 4 as remainder hence insufficient Statement B p =4t thus we know P is a factor of 4 2^ any factor of 4 divided by 10 will always leave a remainder of 6. hence B is sufficient. thus B. hope that helps.. Legendary Member Joined 12 May 2008 Posted: 1161 messages Followed by: 1 members Upvotes: 23 Test Date: ******** Target GMAT Score: 740 I would go for 'B' too....nice explanation sudhir3127 wrote: ddm wrote: If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst? (1) s is even (2) p = 4t i would got for B for this P= rst statement 1. s is even . thus from this we know rst will so will be even but then assume rst =4 2^4 /10 = 6 as remainder 2^6 /10 = 4 as remainder hence insufficient Statement B p =4t thus we know P is a factor of 4 2^ any factor of 4 divided by 10 will always leave a remainder of 6. hence B is sufficient. thus B. hope that helps.. Junior | Next Rank: 30 Posts Joined 28 Aug 2008 Posted: 14 messages ddm wrote: If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst? (1) s is even (2) p = 4t IMO B. sinct p = 4t (2^4t)/10 = (16^t)10. Since t is positive the last digit for 16 to the power of anything should be 6. Hence the remainder is going to be 6. Junior | Next Rank: 30 Posts Joined 28 Aug 2008 Posted: 14 messages ddm wrote: If r, s, and t are all positive integers, what is the remainder of 2^p/10, if p = rst? (1) s is even (2) p = 4t IMO B. sinct p = 4t (2^4t)/10 = (16^t)10. Since t is positive the last digit for 16 to the power of anything should be 6. Hence the remainder is going to be 6. Newbie | Next Rank: 10 Posts Joined 28 Apr 2012 Posted: 5 messages Why can T not be zero ? Making this 1/10 - and therefore a different remainder ... ? O is a positive integer, is it not ? GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2094 messages Followed by: 238 members Upvotes: 1443 The key to understanding this problem is to think about units digits. Whenever a question asks "what is the remainder when divided by 10?", it's really asking "what is the units digit?" In this problem, we're asking about the units digit of 2 raised to some power. The units digits of powers of 2 form the following pattern: 2^1 = 2 2^2 = 4 2^3 = 8 2^4 = 6 (only looking at the units digit here) 2^5 = 2 2^6 = 4 etc. You can see that the units digit repeats every 4 powers. So, if we know that p is a multiple of 4, we'll know that the units digit is 6. Otherwise, we won't know. Statement (1) tells us that s (and therefore p) is a multiple of 2, but that's not enough. The units digit could be 4 or 6. Statement (2) tells us that p is a multiple of 4, though, so it's sufficient. For more info, check out these posts on patterns of units digits: http://www.beatthegmat.com/if-n-and-m-are-positive-integers-what-is-the-reminder-t151461.html#544266 http://www.beatthegmat.com/what-is-the-units-digit-of-a-36-a-a-2-has-9-as-the-u-t151317.html#544267 _________________ 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 04 Dec 2012 Posted: 2094 messages Followed by: 238 members Upvotes: 1443 indiheats wrote: Why can T not be zero ? Making this 1/10 - and therefore a different remainder ... ? O is a positive integer, is it not ? No, 0 is not a positive integer - it's the only integer that's neither positive nor negative! Without that positive constraint, you're right, the answer here would have been E. But with it, statement (2) is sufficient. _________________ 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. • 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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