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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 x and y are positive integers, what is the remainder when tagged by: swerve ##### This topic has 2 expert replies and 1 member reply ### Top Member ## If x and y are positive integers, what is the remainder when ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult If x and y are positive integers, what is the remainder when 10^x+y is divided by y? 1) x=50 2) y=2 The OA is B Source: Official Guide ### GMAT/MBA Expert GMAT Instructor Joined 09 Oct 2010 Posted: 860 messages Followed by: 26 members Upvotes: 59 swerve wrote: If x and y are positive integers, what is the remainder when 10^x+y is divided by y? 1) x=50 2) y=2 Source: Official Guide $$x,y\,\, \ge 1\,\,{\rm{ints}}\,$$ $$?\,\,\,:\,\,\,\left( {{{10}^x} + y} \right)\,\,{\rm{remainder}}\,\,{\rm{when}}\,\,{\rm{divided}}\,\,{\rm{by}}\,\,y$$ $$\left( 1 \right)\,\,x = 50\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,y = 2\,\,\,\, \Rightarrow \,\,\,\,\,{10^{50}} + 2\,\,{\rm{even}}\,\,\,\, \Rightarrow \,\,\,\,\,? = 0\, \hfill \cr \,{\rm{Take}}\,\,y = 3\,\,\,\, \Rightarrow \,\,\,\,\,{10^{50}} + 3\,\,\,{\rm{not}}\,\,{\rm{divisible}}\,\,{\rm{by }}\,{\rm{3}}\,\,\,\,\left( {\sum {\,{\rm{digits}}\,\,\,{\rm{ = }}\,\,{\rm{4}}} } \right)\,\,\,\,\, \Rightarrow \,\,\,\,\,? \ne 0\,\, \hfill \cr} \right.$$ $$\left( 2 \right)\,\,\,y = 2\,\,\,\,\, \Rightarrow \,\,\,\,\,{10^{\,x\, \ge \,1}} + 2\,\,\,{\rm{even}}\,\,\,\, \Rightarrow \,\,\,\,\,? = 0\,$$ This solution follows the notations and rationale taught in the GMATH method. Regards, Fabio. _________________ Fabio Skilnik :: https://GMATH.net (Math for the GMAT) Course release PROMO : finish our test drive till 30/Nov with (at least) 50 correct answers out of 92 (12-questions Mock included) to gain a 50% discount! ### GMAT/MBA Expert GMAT Instructor Joined 08 Dec 2008 Posted: 12329 messages Followed by: 1242 members Upvotes: 5254 GMAT Score: 770 swerve wrote: If x and y are positive integers, what is the remainder when 10^x+y is divided by y? 1) x=50 2) y=2 The OA is B Source: Official Guide Hi Swerve, To avoid ambiguity, you might want to add some spaces or brackets to the original expression. As it stands, 10^x+y could be interpreted as either 10^(x+y) or (10^x) + y Cheers, Brent _________________ 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! ### Top Member Legendary Member Joined 02 Mar 2018 Posted: 664 messages Followed by: 1 members Statement 1 $$when\ x=0;\ 10^0=1;\ sum\ of\ 1=1$$ $$when\ x=1;\ 10^1=10;\ sum\ of\ 1+0=1$$ $$when\ x=2;\ 10^2=100;\ sum\ of\ 1+0+0=1$$ $$when\ x=3;\ 10^3=1000;\ sum\ of\ 1+0+0+0=1$$ $$\since\ the\ sum\ of\ 10^xis\ always=1,$$ $$Then,\ the\ remainder\ of\ \frac{10^x+y}{y}\ is\ only\ dependent\ on\ the\ value\ of\ y.$$ $$if\ y\ =\left(multiple\ of\ \ 3\ +1\right)\ then\ 10^x+y\ will\ yield\ the\ remainder\ 2\$$ $$if\ y\ is\ =\left(miltiple\ of\ 3+2\right);\ then\ \frac{10^x+y}{y}\ will\ remain\ 0$$ $$hence;\ when\ x=50\left(from\ statement\ 1\right)$$ $$\frac{10^{50}+y}{y}\ \ \ remainder\ is\ unknown\ without\ the\ value\ of\ y,$$ Hence, Statement 1 is NOT SUFFICIENT statement 2 $$y=2$$ $$with\ the\ sum\ of\ \ 10^x\ as\ 1$$ $$\frac{1+y}{y}=\frac{1+2}{2}=\frac{3}{2}$$ $$when\ y=2;\ \ 10^x+y\ \ will\ remain\ 1$$ $$Statement\ 2\ is\ \ SUFFICIENT$$ • Award-winning private GMAT tutoring Register now and save up to$200

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