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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 ## Terminating Decimals ##### This topic has 3 expert replies and 14 member replies Goto page • 1, • 2 Here is a question: Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals. If a, b, c, d and e are non-negative integers and p = 2^a*3^b and q = 2^c*3^d*5^e, is p/q a terminating decimal? (1) a > c (2) b > d Can you please provide an answer to this? ### GMAT/MBA Expert GMAT Instructor Joined 02 Jun 2008 Posted: 2327 messages Followed by: 348 members Upvotes: 1090 GMAT Score: 780 chrisjim5 wrote: Here is a question: Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals. If a, b, c, d and e are non-negative integers and p = 2^a*3^b and q = 2^c*3^d*5^e, is p/q a terminating decimal? (1) a > c (2) b > d Can you please provide an answer to this? You can recognize whether a fraction will produce a terminating decimal by: 1. Reducing your fraction completely 2. Then looking only at the prime factors of the denominator. If the denominator has any prime factor besides 2 or 5, the fraction will give a *repeating* (infinite) decimal. If the only prime factors of the denominator are 2 and/or 5, the fraction will give a terminating decimal. So fractions like 3/16 (only prime factor of denominator is 2), 9/125 (only prime factor of denominator is 5) and 3/40 (only prime factors of denominator are 2 and 5) will all produce terminating decimals. Fractions like 1/13, 9/35, and 11/120 will all produce non-terminating decimals since each is completely reduced, and has a factor different from 2 or 5 in the denominator. The first step above is critical; while a fraction like 7/35 might appear to have a factor of 7 in the denominator, that 7 actually cancels with the 7 in the numerator to give us 1/5, a terminating decimal. So in this question, we have the fraction: (2^a*3^b) / (2^c*3^d*5^e) The only reason this might not terminate is because of the 3's; if our 3^d in the denominator does not cancel out completely, we will get a repeating decimal. If it does cancel, we will get a terminating decimal. Statement 2 tells us that it will cancel completely, so is sufficient. Statement 1 doesn't help. So the answer is B. _________________ If you are looking for online GMAT math tutoring, or if you are interested in buying my advanced Quant books and problem sets, please contact me at ianstewartgmat at gmail.com ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1434 messages Followed by: 32 members Upvotes: 59 The solution provided by Ian is perfect and very informative, but I guess many test takers go to the exam without this knowledge... that´s why I believe the solution I present below is also nice: From the "a, b, c, d and e are non-negative integers" hypothesis, I believe the question should be "seen" as: 2^(a-c) * 3^(b-d) over 5^e is a terminating decimal ? Important: this is just a visually helpful thing, because (for instance) the value of (a-c) may be negative, and that means that 2^(a-c) can be at the denominator, "in reality"... (1) This sttm tells us that 2 is really in numerator, but what about the 3(´s) ? > Take a = 2, c =1 (to be only 2^1) and b = 2 and d = 1 (to let 3 be 3^1, so numerator...) and e = 1 , then we have: (2 * 3) over 5, and if you multiply both numerator and denumerator by 2 , you get (2^2 * 3) over... 10, that is, certainly terminating because it is an integer divided by 10, so you just move decimal point, you do not "alter terminallity"... > Take a =2 , c = 1 (to be only 2^1 again) and b = 1 and d = 2 (to let 3 be 3^(-1), so denumerator) and e =1 , then we have: 2 over (3 times 5) and now we know we are with a non-terminating decimal because of this (for instance): 2/(15) = 2*2 / (15*2) = 4/30 = (1/10) * (4/3) and divide by 10 does not alter the "terminallity of a certain decimal" (as mentioned above) and we know that 4/3 is not terminating, because it is equal to 1+ 1/3 and (1 is an integer and) 1/3 is non-terminating, for sure (0.333333...) Obs.: this is not stupid calculations, I believe. This is the "insight" that is behind Ian´s statements... (2) Now we know that 3´s are on the numerator, therefore we may have only 2´s , only 5´s or both in the denumerator. From all shown, you should be able to recognize that 2´s and 5´s are no problem, because multiplying by 10´s in enough quantity you turn the fractions into integers, therefore terminating decimals. This one DECIDES affirmatively on the question asked, that is, (2) is sufficient. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br Newbie | Next Rank: 10 Posts Joined 24 Sep 2010 Posted: 6 messages Followed by: 2 members Upvotes: 10 The ans is B when we simplify the question we get 2^(a-c) * 3^(b-d) / 5^e when we have prime factors other than 2 and 5 in the denominator we get non-terminating decimal. 1) a>c is in sufficient. If a>c or a 2) if b>d there is no 3 in the denominator. So, we have terminating number. Hence 2 alone is sufficient to ans the question. Legendary Member Joined 13 Dec 2010 Posted: 1079 messages Followed by: 33 members Upvotes: 118 Test Date: 9th Sept 2011 Target GMAT Score: 730+ GMAT Score: 710 mgmat cat question hmmmmmmmmm already enough on this by the experts, my say in short. remember 2,4,6,8 and 10(because it has 2 and 5) are terminators(the bad guys)(schwarzenegger in terminator 1) any fraction with additional 3,6(because it has 3),7 and 9(because it has 3) as denominators is not a terminator and the good guy(schwarzenegger in terminator 2) hope this helps, u'll remember this now this question can simply be rephrased as is the no of 3's in p greater than no of 3's in q ??? i'e is b>d the answer is right in one of the statements 8) _________________ Cheers !! Quant 47-Striving for 50 Verbal 34-Striving for 40 My gmat journey : https://www.beatthegmat.com/710-bblast-signing-off-thank-you-all-t90735.html My take on the GMAT RC : https://www.beatthegmat.com/ways-to-bblast-the-gmat-rc-t90808.html How to prepare before your MBA: https://www.youtube.com/watch?v=upz46D7l8fA&list=PLUmBNvYMnppJRMpR9fwfcsTWBZF14TKW_ Legendary Member Joined 19 Jun 2011 Posted: 608 messages Followed by: 8 members Upvotes: 37 Target GMAT Score: 700+ Nothing to add here. +1 for B Legendary Member Joined 26 Jul 2011 Posted: 2789 messages Followed by: 43 members Upvotes: 206 Target GMAT Score: 700+ GMAT Score: 640 IMO:B Master | Next Rank: 500 Posts Joined 21 Sep 2011 Posted: 183 messages Followed by: 2 members Upvotes: 6 Target GMAT Score: 700 GMAT Score: 500 Waaaaaaaaaaaaaay to hard Master | Next Rank: 500 Posts Joined 31 Mar 2011 Posted: 382 messages Upvotes: 15 p/q = 2^(a-c)*3^(b-d)/5^e Except bing decimal Statement 1: INSUFFICIENT Statement 2: SUFFICIENT Legendary Member Joined 23 Dec 2011 Posted: 626 messages Followed by: 10 members Upvotes: 31 Test Date: June Target GMAT Score: 750 if the fraction has powers of 2 or 5 only hen the fraction is terminating decimal S1: a>c does not tell about power of 3 S2: b-d>0 hence the fraction is terminating decimal (B) is ans _________________ Follow your passion, Success as perceived by others shall follow you Senior | Next Rank: 100 Posts Joined 11 Apr 2011 Posted: 72 messages Upvotes: 2 Ian Stewart wrote: chrisjim5 wrote: Here is a question: Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals. If a, b, c, d and e are non-negative integers and p = 2^a*3^b and q = 2^c*3^d*5^e, is p/q a terminating decimal? (1) a > c (2) b > d Can you please provide an answer to this? You can recognize whether a fraction will produce a terminating decimal by: 1. Reducing your fraction completely 2. Then looking only at the prime factors of the denominator. If the denominator has any prime factor besides 2 or 5, the fraction will give a *repeating* (infinite) decimal. If the only prime factors of the denominator are 2 and/or 5, the fraction will give a terminating decimal. So fractions like 3/16 (only prime factor of denominator is 2), 9/125 (only prime factor of denominator is 5) and 3/40 (only prime factors of denominator are 2 and 5) will all produce terminating decimals. Fractions like 1/13, 9/35, and 11/120 will all produce non-terminating decimals since each is completely reduced, and has a factor different from 2 or 5 in the denominator. The first step above is critical; while a fraction like 7/35 might appear to have a factor of 7 in the denominator, that 7 actually cancels with the 7 in the numerator to give us 1/5, a terminating decimal. So in this question, we have the fraction: (2^a*3^b) / (2^c*3^d*5^e) The only reason this might not terminate is because of the 3's; if our 3^d in the denominator does not cancel out completely, we will get a repeating decimal. If it does cancel, we will get a terminating decimal. Statement 2 tells us that it will cancel completely, so is sufficient. Statement 1 doesn't help. So the answer is B. Nice Logic Ian.Thanks!! If the denominator has any prime factor besides 2 or 5, the fraction will give a *repeating* (infinite) decimal. If the only prime factors of the denominator are 2 and/or 5, the fraction will give a terminating decimal. Master | Next Rank: 500 Posts Joined 21 Sep 2011 Posted: 183 messages Followed by: 2 members Upvotes: 6 Target GMAT Score: 700 GMAT Score: 500 Can someone provide and easier to understand explanation please? Master | Next Rank: 500 Posts Joined 06 Apr 2012 Posted: 134 messages Followed by: 5 members Upvotes: 35 Rastis wrote: Can someone provide and easier to understand explanation please? Relatively easier approach for you. Lets put this question as 2^(a-c).3^(b-d)/5^e. Its for sure that this question wishes us to predict nature of 2^(a-c).3^(b-d)/5^e by deducing nature of 2^(a-c), 3^(b-d), & 5^e. => lets put a=c=b=d=0. This will help us find the nature of 5^e. => so 2^(a-c).3^(b-d)/5^e = 2^0.3^0/5^e = 1/5^e. => Now you may try few values of e such as 1, 2, 3... to see if 1/5^e is terminating or non-terminating. We can conclude 1/5^e is terminating.So 5^e has no role to decide if expression is non-terminating. Now lets put b=d=e=0. This will help us find the nature of 2^(a-c). => so 2^(a-c).3^(b-d)/5^e = 2^(a-c).3^0/5^0 = 2^(a-c). => Now you may try few values of (a-c) such as ...., -3, -2, -1 to see if 2^(a-c) is terminating or non-terminating. We can conclude 2^(a-c) is terminating.So 2^(a-c) has no role to decide if expression is non-terminating. Whether a > < c. So stat. 1 is not necessary. Redundant. Now lets put a=c=e=0. This will help us find the nature of 3^(b-d). => so 2^(a-c).3^(b-d)/5^e = 2^0.3^(b-d)/5^0 = 3^(b-d). => Now you may try few values of(b-d) such as ...., -3, -2, -1 to see if 3^(b-d) is terminating or non-terminating. We can conclude 3^(b-d) is non-terminating if (b-d) is negative.So to make it terminating (b-d) should be positive or b>d. So stat. 2 is not necessary & sufficient. Ans B. _________________ Shalabh Jain, e-GMAT Instructor ### GMAT/MBA Expert GMAT Instructor Joined 25 May 2010 Posted: 15203 messages Followed by: 1861 members Upvotes: 13060 GMAT Score: 790 Rastis wrote: Can someone provide and easier to understand explanation please? My explanation is similar to the ones above, but perhaps you will find it helpful: http://www.beatthegmat.com/terminating-decimal-t92476.html _________________ 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. Master | Next Rank: 500 Posts Joined 08 Jan 2013 Posted: 171 messages Upvotes: 1 B in answer. • Get 300+ Practice Questions 25 Video lessons and 6 Webinars for FREE 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 • 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 • FREE GMAT Exam Know how you'd score today for$0

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