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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 ## Any decimal that has only a finite number of nonzero digits ##### This topic has 5 expert replies and 1 member reply ### Top Member ## Any decimal that has only a finite number of nonzero digits ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal? (1) 90 < r < 100 (2) s = 4 Source: Official Guide OA B ### Top Member Legendary Member Joined 29 Oct 2017 Posted: 783 messages Followed by: 4 members Top Reply For a fraction to be terminating two conditions must satisfy: 1) numerator is an INTEGER. 2) denominator should be of form 2^x 5^y (x,y => integers which also includes 0). now in this question the denominator is 2^2 5^0 hence it satisfies. Regards! ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 1295 messages Followed by: 29 members Upvotes: 59 Top Reply swerve wrote: For a fraction to be terminating two conditions must satisfy: 1) numerator is an INTEGER. 2) denominator should be of form 2^x 5^y (x,y => integers which also includes 0). Hi swerve! What about 3/30 ? This number/fraction is terminating (=0.1) but it does not satisfy the conditions you have presented... Do not forget that for the conditions above, first you must "simplify your fraction"... in other words: Be sure numerator and denominator are relative prime, then you apply your "laws"! Regards, Fabio. P.S.: curiously, integers x and y MAY be negative... but if so, we are not talking about "denominator", really... therefore I would prefer to add a nonnegative condition on x and y, in your second rule. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br ### GMAT/MBA Expert GMAT Instructor Joined 22 Aug 2016 Posted: 1770 messages Followed by: 28 members Upvotes: 470 BTGmoderatorDC wrote: Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal? (1) 90 < r < 100 (2) s = 4 Source: Official Guide OA B A ratio, here, r/s is a terminating decimal if s has only two prime factors: 2 and 5. Note that there is no role of r, so Statement 1 is insufficient. From Statement 2, we know that s = 4 has a prime factor 2, it's sufficient to collude that r/s is a terminating decimal. The correct answer: B Hope this helps! -Jay _________________ Manhattan Review GRE Prep Locations: GMAT Classes San Diego | GRE Prep Course Boston | GRE Prep Chicago | TOEFL Prep Classes NYC | and many more... Schedule your free consultation with an experienced GMAT Prep Advisor! Click here. ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12663 messages Followed by: 1246 members Upvotes: 5254 GMAT Score: 770 BTGmoderatorDC wrote: Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal? (1) 90 < r < 100 (2) s = 4 Source: Official Guide OA B Target question: Is r/s a terminating decimal? Statement 1: 90 < r < 100 There are several pairs of values that meet this condition. Here are two: Case a: r = 91 and s = 2, in which case r/s = 91/2 = 45.5 = a terminating decimal Case b: r = 91 and s = 3, in which case r/s = 91/3 = 30.33333.... = a non-terminating decimal Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT Statement 2: s = 4 Notice that 1/4 = 0.25, 2/4 = 0.5 and 3/4 = 0.75 So, if the denominator is 4, the resulting decimal will definitely be a terminating decimal. In other words, if s = 4 then r/s must be a terminating decimal. Since we can answer the target question with certainty, statement 2 is SUFFICIENT Aside: There's a nice rule that says something like, If the prime factorization of the denominator contains only 2's and/or 5's, then the decimal version of the fraction will be a terminating decimal. Since the denominator, 4 = (2)(2), the rule tells us that r/s must be a terminating decimal. Answer: B Cheers, Brent _________________ 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! ### GMAT/MBA Expert GMAT Instructor Joined 04 Dec 2012 Posted: 2009 messages Followed by: 237 members Upvotes: 1443 Here is further explanation on the logic of terminating decimals: https://www.beatthegmat.com/ds-decimals-and-ratio-combined-t182983.html#583298 _________________ 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 09 Oct 2010 Posted: 1295 messages Followed by: 29 members Upvotes: 59 BTGmoderatorDC wrote: Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 24, 0.82, and 5.096 are three terminating decimals. If r and s are positive integers and the ratio r/s is expressed as a decimal, is r/s a terminating decimal? (1) 90 < r < 100 (2) s = 4 Source: Official Guide $r,s\,\, \geqslant 1\,\,\,{\text{ints}}$ $\frac{r}{s}\,\,\,\mathop = \limits^? \,\,\,\,{\text{terminating}}$ $\left( 1 \right)\,\,90 < r < 100\,\,\,\,\left\{ \begin{gathered} \,\left( {r,s} \right) = \left( {95,5} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\left( {\frac{{95}}{5} = \operatorname{int} } \right) \hfill \\ \,\left( {r,s} \right) = \left( {91,3} \right)\,\,\,\,\,\, \Rightarrow \,\,\,\,\left\langle {{\text{NO}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\,\left( {\frac{{91}}{3} = 30\frac{1}{3} = 30.333 \ldots } \right) \hfill \\ \end{gathered} \right.$ $\left( 2 \right)\,\,s = 4$ $\left( * \right)\,\,\,\,{\text{r/s}}\,\,\,{\text{division}}\,\,{\text{algorithm}}:\,\,\,\left\{ \begin{gathered} \,r = qs + R\,\,\,\mathop = \limits^{s\,\, = \,\,4} \,\,\,4q + R \hfill \\ \,q\,\,\operatorname{int} \,\,\,,\,\,\,\,0\,\,\, \leqslant \,\,\,R\,\,\operatorname{int} \,\,\, \leqslant \,\,3\,\,\,\,\left( { = s - 1} \right) \hfill \\ \end{gathered} \right.$ $\frac{r}{s}\,\,\,\,\mathop = \limits^{\,\left( * \right)} \,\,\,\,\frac{{4q + R}}{4} = q + \frac{R}{4}\,\, = \,\,\operatorname{int} \,\, + \,\,\frac{R}{4}\,\,\,\,\,\,\,$ $\frac{R}{4} = \,\,\,\left\{ {\begin{array}{*{20}{c}} {\,\,\frac{0}{4}} \\ {\,\,\frac{1}{4}} \\ {\,\,\frac{2}{4}} \\ {\,\,\frac{3}{4}} \end{array}} \right.\begin{array}{*{20}{c}} {\,\,{\text{if}}\,\,\,R = 0\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} } \right)} \\ {\,\,{\text{if}}\,\,\,R = 1\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} \,\, + \,\,0.25} \right)} \\ {\,\,{\text{if}}\,\,\,R = 2\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} \,\, + \,\,0.5} \right)} \\ {\,\,{\text{if}}\,\,\,R = 3\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\left\langle {{\text{YES}}} \right\rangle \,\,\,\,\,\,\,\,\,\,\left( {\frac{r}{4} = \operatorname{int} \,\, + \,\,0.75} \right)} \end{array}$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: GMATH method creator ( Math for the GMAT) English-speakers :: https://www.gmath.net Portuguese-speakers :: https://www.gmath.com.br • Award-winning private GMAT tutoring Register now and save up to$200

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